Wolf-Gert Matthäus, Jörg Schulze
Statistik mit Excel
Wolf-Gert Matthäus, Jörg Schulze
Statistik mit Excel Beschreibe...
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Wolf-Gert Matthäus, Jörg Schulze
Statistik mit Excel
Wolf-Gert Matthäus, Jörg Schulze
Statistik mit Excel Beschreibende Statistik für jedermann 3., überarbeitete und erweiterte Auflage
Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über abrufbar.
1. Auflage 2003 2. Auflage 2005 3., überarbeitete und erweiterte Auflage 2008 Alle Rechte vorbehalten © B.G. Teubner Verlag / GWV Fachverlage GmbH, Wiesbaden 2008 Lektorat: Ulrich Sandten / Kerstin Hoffmann
Der B.G. Teubner Verlag ist ein Unternehmen von Springer Science+Business Media. www.teubner.de Das Werk einschließlich aller seiner Teile ist urheberrechtlich geschützt. Jede Verwertung außerhalb der engen Grenzen des Urheberrechtsgesetzes ist ohne Zustimmung des Verlags unzulässig und strafbar. Das gilt insbesondere für Vervielfältigungen, Übersetzungen, Mikroverfilmungen und die Einspeicherung und Verarbeitung in elektronischen Systemen. Die Wiedergabe von Gebrauchsnamen, Handelsnamen, Warenbezeichnungen usw. in diesem Werk berechtigt auch ohne besondere Kennzeichnung nicht zu der Annahme, dass solche Namen im Sinne der Warenzeichen- und Markenschutz-Gesetzgebung als frei zu betrachten wären und daher von jedermann benutzt werden dürften. Umschlaggestaltung: Ulrike Weigel, www.CorporateDesignGroup.de Druck und buchbinderische Verarbeitung: Strauss Offsetdruck, Mörlenbach Gedruckt auf säurefreiem und chlorfrei gebleichtem Papier. Printed in Germany
ISBN 978-3-8351-0159-3
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báåÑ~ÅÜÉë=^Äò®ÜäÉå=ãáí=ZÄHLENWENN KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKPV=
PKO=
hä~ëëÉåÄáäÇìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKQS=
PKOKN= = hä~ëëÉåòìçêÇåìåÖ=ãáí=ÇÉê=cìåâíáçå=WENNKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKQT= PKOKO= = aáÉ=cìåâíáçå=VERWEIS KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKQV= PKOKP= = aáÉ=cìåâíáçå=HÄUFIGKEIT KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRM= PKOKQ= = a~ë=tÉêâòÉìÖ=HISTOGRAMM KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRM=
U===================================================================================================fåÜ~äíëîÉêòÉáÅÜåáë= PKP=
jçÇ~äïÉêí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRO=
PKQ=
e®ìÑáÖâÉáíÉå=îçå=m~~êÉåW=máîçíJq~ÄÉääÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRQ=
PKQKN= = ^ìÑÖ~ÄÉåëíÉääìåÖ=ìåÇ=_ÉòÉáÅÜåìåÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRQ= PKQKO= = eÉêëíÉääìåÖ=ÉáåÉê=ÉáåÑ~ÅÜÉå=máîçíJq~ÄÉääÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRQ= PKQKP= = cÉäÇÉáåëíÉääìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRT= PKQKQ= = mê®ëÉåí~íáçå=îçå=máîçíJq~ÄÉääÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRV= PKQKR= = ^Äò®ÜäÉå=ãáííÉäë=máîçíJq~ÄÉääÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RV= PKQKS= = s~êá~ÄäÉ=máîçíJq~ÄÉääÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKSN= PKQKT= = máîçíJq~ÄÉääÉå=ãáí=a~íìãë~åÖ~ÄÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SO= PKR=
^ÄëçäìíÉ=pìããÉåÜ®ìÑáÖâÉáíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ST=
= = Q=
dê~ÑáëÅÜÉ=a~êëíÉääìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SV=
= QKN=
eáëíçÖê~ããÉW=tÉêâòÉìÖ=HISTOGRAMM KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKSV=
QKO=
aáÉ= F11 JjÉíÜçÇÉ=òìê=eÉêëíÉääìåÖ=îçå=dê~ÑáâÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TO=
QKOKN= = wìë~ããÉåÜ®åÖÉåÇÉ=a~íÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTO= QKOKO= = káÅÜí=òìë~ããÉåÜ®åÖÉåÇÉ=a~íÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTS= QKP=
wÉáíêÉáÜÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTS=
QKQ=
pâ~äáÉêìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKUM=
QKQKN= = _ÉÇÉìíìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UM= QKQKO= = içÖ~êáíÜãáëÅÜÉ=pâ~äáÉêìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UO= QKR=
dê~ÑáëÅÜÉ=a~êëíÉääìåÖ=îçå=máîçíJq~ÄÉääÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UQ=
QKS=
a~êëíÉääìåÖ=îçå=~ÄëçäìíÉå=pìããÉåÜ®ìÑáÖâÉáíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKUS=
QKSKN= = _ÉêÉáíë=ÄÉêÉÅÜåÉíÉ=pìããÉåÜ®ìÑáÖâÉáíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK US= QKSKO= = NMMJmêçòÉåíJaá~Öê~ããÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKUT= QKSKP= = NMMJmêçòÉåíJaá~Öê~ããÉ=áã=wÉáí~Ää~ìÑ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKUU= = = R=
oÉä~íáîÉ=e®ìÑáÖâÉáíÉåI=ÉãéáêáëÅÜÉ=sÉêíÉáäìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VN=
= RKN=
_ÉêÉÅÜåìåÖ=êÉä~íáîÉê=e®ìÑáÖâÉáíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVN=
RKO=
bñÅÉä=êÉÅÜåÉí=Ñ~äëÅÜ=>\ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VP=
RKP=
hìãìäáÉêíÉ=êÉä~íáîÉ=e®ìÑáÖâÉáíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVU=
=
fåÜ~äíëîÉêòÉáÅÜåáë= S=
V
pí~íáëíáëÅÜÉ=j~≈ò~ÜäÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMP=
= SKN=
jáííÉäïÉêíÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMP=
SKNKN= = jÉÇá~å=ìåÇ=~êáíÜãÉíáëÅÜÉë=jáííÉä=EaìêÅÜëÅÜåáííF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMP= SKNKO= = tÉáíÉêÉ=jáííÉäïÉêíÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMT= SKO=
píêÉììåÖëã~≈ÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMT=
SKOKN= = pé~ååïÉáíÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMT= SKOKO= = jáííäÉêÉ=~ÄëçäìíÉ=^ÄïÉáÅÜìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMT= SKOKP= = bãéáêáëÅÜÉ=pí~åÇ~êÇ~ÄïÉáÅÜìåÖ=ìåÇ=s~êá~åò KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMU= SKOKQ= = báåëÅÜìÄW=kçêã~äîÉêíÉáäìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMV= SKP=
pÅÜáÉÑÉ=ìåÇ=t∏äÄìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNP=
SKQ=
aáÉ=sÉêÑΩÜêìåÖW=mçéìä~íáçåëâÉååÖê∏≈Éå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNQ=
= = T=
hçêêÉä~íáçå=ìåÇ=oÉÖêÉëëáçåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNV=
= TKN=
aÉê=hçêêÉä~íáçåëâçÉÑÑáòáÉåí=îçå=_ê~î~áëJmÉ~êëçåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNV=
TKNKN= = _ÉÖêáÑÑI=_ÉÇÉìíìåÖI=_ÉêÉÅÜåìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNV= TKNKO= = eÉêëíÉääìåÖ=ÇÉê=mìåâíïçäâÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOM= TKO=
oÉÖêÉëëáçå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOP=
TKOKN= = _ÉêÉÅÜåìåÖ=ÇÉê=oÉÖêÉëëáçåëâçåëí~åíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOP= TKOKO= = oÉÅÜåìåÖ=ãáí=ÇÉã=tÉêâòÉìÖ=REGRESSION KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOS= TKP=
jìäíáéäÉ=äáåÉ~êÉ=oÉÖêÉëëáçåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOV=
TKQ=
káÅÜíäáåÉ~êÉ=wìë~ããÉåÜ®åÖÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPN=
TKQKN= = dêìåÇä~ÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPN= TKQKO= = qê~åëÑçêã~íáçåÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPR= = = U=
wÉáíêÉáÜÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPT=
= UKN=
_ÉÖêáÑÑ=ìåÇ=bêÑ~ëëìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPT=
UKO=
bñéÉêáãÉåíÉääJîáëìÉääÉ=qêÉåÇÉêãáííäìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPU=
UKP=
iáåÉ~êÉ=wÉáíêÉáÜÉå=ìåÇ=ÇáÉ=TRENDJcìåâíáçåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQN=
UKQ=
däÉáíÉåÇÉê=aìêÅÜëÅÜåáíí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQQ=
===================================================================================================fåÜ~äíëîÉêòÉáÅÜåáë= NM UKR=
dêìåÇä~ÖÉå=ÇÉê=wÉáíêÉáÜÉå~å~äóëÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQT=
UKRKN= = ^ìÑÄ~ì=ÇÉë=~ÇÇáíáîÉå=wÉáíêÉáÜÉåãçÇÉääë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQU= UKRKO= = däÉáíÉåÇÉ=aìêÅÜëÅÜåáííÉ=ìåÇ=Ç~ë=~ÇÇáíáîÉ=wÉáíêÉáÜÉåãçÇÉääKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRM= UKRKP= = i~åÖÑêáëíáÖÉ=qêÉåÇë=ÉêâÉååÄ~ê=ã~ÅÜÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRN= UKRKQ= = jçå~íëíóéáëÅÜÉ=^ÄïÉáÅÜìåÖÉå=ÄÉêÉÅÜåÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRO= UKRKR= = p~áëçåÄÉêÉáåáÖíÉ=wÉáíêÉáÜÉ=ÄÉêÉÅÜåÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRS= UKRKS= = ^ìëÄäáÅâKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRT= = = V=
fãéçêí=îçå=a~íÉå=~ìë=a~íÉåÄ~åâÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRV=
= VKN=
dêìåÇë®íòäáÅÜÉëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRV=
VKO=
fãéçêí=~ìë=jpJ^ÅÅÉëë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRV=
VKP=
báåêáÅÜíìåÖ=ÉáåÉë=la_`JqêÉáÄÉêë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSN=
VKQ=
wìÖêáÑÑ=~ìÑ=âçåâêÉíÉ=a~íÉåÄ~åâÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSP=
VKQKN= = jáÅêçëçÑí=pniJpÉêîÉê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSP= VKQKO= = lê~ÅäÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSP= VKR=
bñÅÉäJwìÖêáÑÑ=~ìÑ=lê~ÅäÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSR=
VKRKN= = a~íÉå=áãéçêíáÉêÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSR= VKRKO= = a~íÉå=îáëì~äáëáÉêÉå=ìåÇ=~âíìÉää=Ü~äíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSV= = = ^åÜ~åÖ=NW=sçã=mêçÄäÉã=òìê=bñÅÉäJi∏ëìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTN= = = ^åÜ~åÖ=OW=_Éá=bñÅÉä=OMMT=áëí=ã~åÅÜÉë=~åÇÉêëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTV= = = iáíÉê~íìê= = KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMN= = = p~ÅÜïçêíîÉêòÉáÅÜåáë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMP= = = =
Einleitung aáÉ= iÉëÉêëÅÜ~ê= ÇáÉëÉë= _ìÅÜÉë= ã∏ÖÉ= ìåë= îÉêòÉáÜÉåI= Ç~ëë= ïáê= ÄÉïìëëí= Ç~ê~ìÑ= îÉêòáÅÜíÉåI= ~ìëÑΩÜêäáÅÜëí=åçÅÜ=Éáåã~ä=òì=Éêâä®êÉåI=ï~ë=ÉáåÉ=bñÅÉäJj~ééÉ=áëíI=Ç~ëë=ëáÉ=q~ÄÉääÉå=ÉåíÜ®äíI= ÇáÉ= áÜêÉêëÉáíë= ~ìë= wÉáäÉå= ìåÇ= pé~äíÉå= ÄÉëíÉÜÉåI= ïçãáí= ÇáÉ= wÉääÉå= ÖÉÄáäÇÉí= ïÉêÇÉåI= áå= ÇáÉ= ã~å=åìãÉêáëÅÜÉ=tÉêíÉ=ìåÇ=åáÅÜíåìãÉêáëÅÜÉ=tÉêíÉ=Éáåíê~ÖÉå=â~ååK=== táÅÜíáÖ=ÉêëÅÜÉáåÉå=ìåë=Ç~ÖÉÖÉå=ÉáåáÖÉ=ÉáåÑΩÜêÉåÇÉ=cÉëíäÉÖìåÖÉå=ìåÇ=sÉêÉáåÄ~êìåÖÉåK=
Beschreibung von Bereichen wìë~ããÉåÜ®åÖÉåÇÉ=bñÅÉäJ_ÉêÉáÅÜÉ=ïÉêÇÉåI=ïáÉ=~ääÖÉãÉáå=ΩÄäáÅÜI=ÇìêÅÜ=^åÖ~ÄÉ=ÇÉê=ÄÉáJ ÇÉå=o~åÇòÉääÉåI=~ÄÖÉíêÉååí=ÇìêÅÜ=ÉáåÉå=açééÉäéìåâíI=ÄÉëÅÜêáÉÄÉåK= e~åÇÉäí= Éë= ëáÅÜ= ìã= ÉáåÉå=ÉÅÜíÉå= oÉÅÜíÉÅâÄÉêÉáÅÜI= Ç~åå= ëáåÇ=ÇáÉ= ÄÉáÇÉå= wÉääÉå=äáåâë= çÄÉå=ìåÇ=êÉÅÜíë=ìåíÉå=~åòìÖÉÄÉå=E_ÉáëéáÉäW=A1:S4FK== e~åÇÉäí=Éë=ëáÅÜ=ìã=ÉáåÉ=Ö~åòÉ=wÉáäÉI=Ç~åå=ïáêÇ=òïÉáã~ä=ÇáÉ=wÉáäÉååìããÉê=~åÖÉÖÉJ ÄÉå=EPK=wÉáäÉW=3:3FK= e~åÇÉäí=Éë=ëáÅÜ=ìã=ÉáåÉå=wÉáäÉåÄÉêÉáÅÜ=EÇK=ÜK=ìã=ÇÉå=qÉáä=ÉáåÉê=wÉáäÉFI=Ç~åå=ëáåÇ=ÇáÉ= ÄÉáÇÉå=o~åÇJwÉääÉå=äáåâë=ìåÇ=êÉÅÜíë=~åòìÖÉÄÉå=EC2:BK2FK== e~åÇÉäí=Éë=ëáÅÜ=ìã=ÉáåÉ=Ö~åòÉ=pé~äíÉI=Ç~åå=ïáêÇ=òïÉáã~ä=ÇÉê=pé~äíÉåÄìÅÜëí~ÄÉ=ÄòïK= òïÉáã~ä=Ç~ë=_ìÅÜëí~ÄÉåé~~ê=ÇÉê=pé~äíÉ=~åÖÉÖÉÄÉå=EPK=pé~äíÉW=C:CI=OUK=pé~äíÉW=AB:ABFK= e~åÇÉäí=Éë=ëáÅÜ=ìã=ÉáåÉå=pé~äíÉåÄÉêÉáÅÜ=EÇKÜK=ìã=ÇÉå=qÉáä=ÉáåÉê=pé~äíÉFI=Ç~åå=ëáåÇ=ÇáÉ= ÄÉáÇÉå=o~åÇJwÉääÉå=çÄÉå=ìåÇ=ìåíÉå=~åòìÖÉÄÉå=ECA10:CA1000FK==
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1
Grundlagen
1.1
Statistische Grundbegriffe
aÉå=dÉÖÉåëí~åÇ=ÇÉê=ëí~íáëíáëÅÜÉå=råíÉêëìÅÜìåÖ=åÉååí=ã~å=jÉêâã~äëíê®ÖÉêK=aÉê=jÉêâJ ã~äëíê®ÖÉê=áëí=ÇÉê=qê®ÖÉê=ÇÉê=áåíÉêÉëëáÉêÉåÇÉå=ëí~íáëíáëÅÜÉå=fåÑçêã~íáçåÉåK= aáÉ= jÉåÖÉ= ~ääÉê= jÉêâã~äëíê®ÖÉêI= ÇáÉ= ΩÄÉêÉáåëíáããÉåÇÉ= ^ÄÖêÉåòìåÖëãÉêâã~äÉ= ÄÉëáíòÉåI= ÄÉòÉáÅÜåÉí=ã~å=~äë=dêìåÇÖÉë~ãíÜÉáíK= báå=jÉêâã~ä=áëí=ÇáÉàÉåáÖÉ=báÖÉåëÅÜ~Ñí=ÇÉë=jÉêâã~äëíê®ÖÉêëI=ÇáÉ=ÄÉá=ÇÉê=ëí~íáëíáëÅÜÉå=råJ íÉêëìÅÜìåÖ=îçå=fåíÉêÉëëÉ=áëíK= aÉê=tÉêíI=ÇÉê=Ç~åå=ÄÉá=ÇÉê=_ÉçÄ~ÅÜíìåÖI=_ÉÑê~ÖìåÖI=jÉëëìåÖ=çÇÉê=ÇìêÅÜ=ÉáåÉå=w®ÜäîçêJ Ö~åÖ=ÄÉáã=jÉêâã~äëíê®ÖÉê=ÑÉëíÖÉëíÉääí=ïáêÇI=ïáêÇ=~äë=jÉêâã~äëïÉêí=çÇÉê=jÉêâã~äë~ìëéê®J ÖìåÖ=ÄÉòÉáÅÜåÉíK== j~å=ìåíÉêëÅÜÉáÇÉí=òïáëÅÜÉå=èì~äáí~íáîÉå=ìåÇ=èì~åíáí~íáîÉå=jÉêâã~äÉåW== tÉåå= ÇÉå= jÉêâã~äë~ìëéê®ÖìåÖÉå= äÉÇáÖäáÅÜ= k~ãÉå= çÇÉê= hä~ëëÉåÄÉòÉáÅÜåìåÖÉå= òìÖÉJ çêÇåÉí=ïÉêÇÉåI=ëéêáÅÜí=ã~å=îçå=èì~äáí~íáîÉå=jÉêâã~äÉåK== = Merkmal
Merkmalsausprägung (Merkmalswert)
_ÉêìÑ=
_®ÅâÉêI=iÉÜêÉêI=häÉãéåÉêI=fåÖÉåáÉìê=
sçêíê~ÖëïÉáëÉ=
fåíÉêÉëë~åíI=ä~åÖïÉáäáÖI=Éêíê®ÖäáÅÜ=
q~ÄK=N~W=_ÉáëéáÉäÉ=ÑΩê=èì~äáí~íáîÉ=jÉêâã~äÉ= _Éëáíòí=Ç~ÖÉÖÉå=Ç~ë=jÉêâã~ä=ÉáåÉ=ãÉëëÄ~êÉ=aáãÉåëáçå=çÇÉê=â~åå=Éë=áå=jÉåÖÉåÉáåÜÉáJ íÉå=~ìëÖÉÇêΩÅâí=ïÉêÇÉåI=ëç=ëéêáÅÜí=ã~å=îçå=ÉáåÉã=èì~åíáí~íáîÉå=jÉêâã~äK= = Merkmal
Merkmalsausprägung (Merkmalswert)
^äíÉê=Eg~ÜêÉF=
ÁI=RI=NUI=ÁI=UVI=Á=
_ÉåòáåîÉêÄê~ìÅÜ=EiáíÉêLNMM=âãF=
PIRX=Á=X=QIU=X=Á=X=TIP=X=Á=X=NOIR=X=Á=
q~ÄK=NÄW=_ÉáëéáÉäÉ=ÑΩê=èì~åíáí~íáîÉ=jÉêâã~äÉ=
=
káããí=Éáå=èì~åíáí~íáîÉë=jÉêâã~ä=åìê=ÉáåáÖÉ=îÉêëÅÜáÉÇÉåÉ=tÉêíÉ=~åI=ëç=ëéêáÅÜí=ã~å=îçå= ÉáåÉã=ÇáëâêÉíÉå=jÉêâã~ä=EòK=_K=jáí~êÄÉáíÉêò~ÜäI=e~ìëÜ~äíëÖê∏≈ÉI=hÑòJ_Éëí~åÇFK==== h~åå=Éáå=jÉêâã~ä=Ç~ÖÉÖÉå=EíÜÉçêÉíáëÅÜF=ìåÉåÇäáÅÜ=îáÉäÉ=tÉêíÉ=~ååÉÜãÉåI=ëç=ÜÉá≈í=Ç~ë= jÉêâã~ä=ëíÉíáÖ=EòK=_K=h∏êéÉêÖê∏≈ÉI=dÉëÅÜïáåÇáÖâÉáíI=aìêÅÜãÉëëÉê=ÉáåÉë=_~ìíÉáäëFK==
1.2
Datenniveau, Skalierung der Merkmale
aáÉ=bêãáííäìåÖ=îçå=jÉêâã~äëïÉêíÉå=ÉêÑçäÖí=ÇìêÅÜ=ÉáåÉå=w®ÜäîçêÖ~åÖ=çÇÉê=ÇìêÅÜ=jÉëëìåÖI= _ÉÑê~ÖìåÖI=_ÉçÄ~ÅÜíìåÖK= aáÉ= bêÖÉÄåáëëÉ= ïÉêÇÉå= ÉåíïÉÇÉê= ìåãáííÉäÄ~ê= çÇÉê= ãáí= eáäÑÉ= ÉáJ åÉë=pâ~äáÉêìåÖëîÉêÑ~ÜêÉåë=áå=ÉáåÉ=pâ~ä~=~ÄÖÉÄáäÇÉíK==
=
=NU
=
N==dêìåÇä~ÖÉå=
aáÉëÉ=Eëí~íáëíáëÅÜÉF=jÉëëJpâ~ä~=áëí=Ç~åå=Ç~ë=fåëíêìãÉåíI=ãáí=ÇÉã=ÇáÉ=jÉêâã~äëïÉêíÉ=ÉêãáíJ íÉäí=ïÉêÇÉåK=^ìÑ=ÇÉê=pâ~ä~=ïÉêÇÉå=ÇáÉ=ã∏ÖäáÅÜÉå=jÉêâã~äëïÉêíÉI=Ñ~ääë=ã∏ÖäáÅÜI=å~ÅÜ=ÄÉJ ëíáããíÉã=lêÇåìåÖëéêáåòáé=~äë=pâ~äÉåïÉêíÉ=~ÄÖÉíê~ÖÉåK== aáÉ=pâ~äÉå=ïÉêÇÉå=ÖÉï∏ÜåäáÅÜ=áå== J=h~êÇáå~äëâ~äÉå= J=lêÇáå~äëâ~äÉå= J=kçãáå~äëâ~äÉå= ìåíÉêÖäáÉÇÉêíK== gÉ=å~ÅÜ=^êí=ÇÉê=pâ~ä~=ëéêáÅÜí=ã~å=Ç~åå=~ìÅÜ=îçå=ÇÉã=òìÖÉÜ∏êáÖÉå=káîÉ~ì=ÇÉê=a~íÉå=Ea~J íÉååáîÉ~ìFK=
1.2.1
Kardinalskala (metrische Skala)
tÉåå=ÇáÉ=a~íÉå=áåíÉêî~ääJ=çÇÉê=Ç~êΩÄÉê=Üáå~ìë=ëçÖ~ê=åçÅÜ=ê~íáçå~ä=ëâ~äáÉêí=ëáåÇI=Ç~åå= ëéêáÅÜí=ã~å=îçå=â~êÇáå~ä=ëâ~äáÉêíÉå=a~íÉå=EçÇÉê=ãÉíêáëÅÜ=ëâ~äáÉêíÉå=a~íÉåFK=aáÉëÉ=a~íÉå= Ü~ÄÉå=Ç~ë=Ü∏ÅÜëíÉ=a~íÉååáîÉ~ìK==
Intervallskala j~å= ëéêáÅÜí= îçå= áåíÉêî~ääëâ~äáÉêíÉå= a~íÉåI= ïÉåå= ÇáÉ= ^ìëéê®ÖìåÖÉå= ÉáåÉë= jÉêâã~äë= áå= ÉáåÉ=o~åÖçêÇåìåÖ=ÖÉÄê~ÅÜí=ïÉêÇÉå=â∏ååÉå=ìåÇ=ïÉåå=òìë®íòäáÅÜ=åçÅÜ=ÄÉëíáããí=ïÉêJ ÇÉå= â~ååI= áå= ïÉäÅÜÉã= ^ìëã~≈= ëáÅÜ= òïÉá= îÉêëÅÜáÉÇÉåÉ= jÉêâã~äë~ìëéê®ÖìåÖÉå= ìåíÉêJ ëÅÜÉáÇÉåK== = Merkmal
Merkmalsausprägung (Merkmalswert)
rÜêòÉáí=
QWMMWMMI=UWNTWRSI=NOWRVWOOI=Á=
qÉãéÉê~íìê=Eáå=dê~Ç=`ÉäëáìëF=
JPQI=JNOI=RSI=OMMI=Á=
h~äÉåÇÉêòÉáí=
NKNKOMMMI=ONKNOKOMMOI=UKNKOMPRI=Á=
q~ÄK=NKOW=_ÉáëéáÉäÉ=ÑΩê=áåíÉêî~ääëâ~äáÉêíÉ=a~íÉå= fåíÉêî~ääëâ~äáÉêíÉ=a~íÉå=äáÉÖÉå=~äë=w~ÜäÉåïÉêíÉ=EåìãÉêáëÅÜÉ=tÉêíÉF=îçêK=t®ÜêÉåÇ=Éë=çÑÑÉåJ ëáÅÜíäáÅÜ=ìåëáååáÖ=áëíI=ÇáÉ=rÜêòÉáíÉå=Q=rÜê=ìåÇ=NO=rÜê=Ç~ÜáåÖÉÜÉåÇ=òì=áåíÉêéêÉíáÉêÉåI=Ç~ëë= Éë=łìã=NO=rÜê=ÇêÉáã~ä=ëç=ëé®í=áëí=ïáÉ=ìã=Q=rÜêI=áëí=ÇáÉ=^ìëë~ÖÉ=çÑÑÉåÄ~ê=ëáååîçääI=Ç~ëë= łîçå=Q=rÜê=Äáë=U=rÜê=ÖÉå~ìëç=îáÉä=wÉáí=îÉêÖÉÜí=ïáÉ=îçå=R=rÜê=Äáë=V=rÜêK== páååîçää=ëáåÇ=~ìÅÜ=ÇáÉ=^åÖ~ÄÉå=ÇÉê=ãáííäÉêÉå=qÉãéÉê~íìê=EaìêÅÜëÅÜåáííëïÉêíF=ëçïáÉ=ïÉáíÉJ êÉê=ëí~íáëíáëÅÜÉê=j~≈ò~ÜäÉå=EëáÉÜÉ=^ÄëÅÜåáíí=S=~ìÑ=pÉáíÉ=NMPFK=
Verhältnisskala (Ratioskala) j~å= ëéêáÅÜí= Ç~êΩÄÉê= Üáå~ìë= ëçÖ~ê= îçå= ê~íáçå~ä=ëâ~äáÉêíÉå=a~íÉåI= ïÉåå= ÇÉê= pâ~äÉåïÉêí= kìää=ÇÉã=å~íΩêäáÅÜÉåI=~ÄëçäìíÉå=kìääéìåâí=ÉåíëéêáÅÜíK=kÉÖ~íáîÉ=tÉêíÉ=ëáåÇ=Ç~ãáí=ìåã∏ÖJ äáÅÜK=pçãáí=ÉêÜ®äí=åÉÄÉå=ÇÉã=ÉáåÑ~ÅÜÉå=^Äëí~åÇ=EÇáÉ=aáÑÑÉêÉåòF=~ìÅÜ=ÇÉê=nìçíáÉåí=EÇ~ë= sÉêÜ®äíåáëF=ÉáåÉ=ëáååîçääÉ=_ÉÇÉìíìåÖK=== a~ë=sÉêÜ®äíåáë=ä®ëëí=ëáÅÜ=Ç~ÄÉá=~ìÅÜ=áåíÉêéêÉíáÉêÉåW== jáí=TO=g~ÜêÉå=áëí=Éáå=jÉåëÅÜ=ëÉÅÜëã~ä=ëç=~äí=ïáÉ=ãáí=NO=g~ÜêÉåK=báå=báåâçããÉå=îçå=PSMMM= bìêç=áëí=åìê=Éáå=cΩåÑíÉä=ÇÉë=NUMMMMJbìêçJbáåâçããÉåë=ìëïK== =
=
=
NKO==a~íÉååáîÉ~ìI=pâ~äáÉêìåÖ=ÇÉê=jÉêâã~äÉ= Merkmal
NV
Merkmalsausprägung (Merkmalswert)
báåâçããÉå=Eáå=qëÇK=bìêçF=
MI=ÁI=NOI=ÁI=PSI=ÁI=NOMI=Á=
dÉïáÅÜí=EâÖF=
MI=ÁI=QRI=ÁI=USI=ÁI=NOPI=Á=
^äíÉê=Eg~ÜêÉF=
MI=ÁI=NOI=ÁI=OQI=ÁI=TUI=Á=
q~ÄK=NKPW=_ÉáëéáÉäÉ=ÑΩê=ê~íáçå~ä=ëâ~äáÉêíÉ=a~íÉå=
1.2.2
Ordinalskala
^äë= pâ~äÉåïÉêíÉ= ïÉêÇÉå= åìê=hä~ëëÉåÄÉòÉáÅÜåìåÖÉå= ~ÄÖÉíê~ÖÉåK= _Éáã= sÉêÖäÉáÅÜ=òïÉáÉê= jÉêâã~äëíê®ÖÉê= â~åå= áã= c~ääÉ= ÇÉê= sÉêëÅÜáÉÇÉå~êíáÖâÉáí= åìê= áÜêÉ= o~åÖÑçäÖÉ= ÑÉëíÖÉëíÉääí= ïÉêÇÉåK=aáÑÑÉêÉåòÉå=ëáåÇ=åáÅÜí=áåíÉêéêÉíáÉêÄ~êK== lêÇáå~ä=ëâ~äáÉêíÉ=a~íÉå=ÄÉëáíòÉå=åìê=åçÅÜ=ãáííäÉêÉë=a~íÉååáîÉ~ìK== = Merkmal
Merkmalsausprägung (Merkmalswert)
pÅÜìäåçíÉ=
ëÉÜê=ÖìíI=ÖìíI=ÄÉÑêáÉÇáÖÉåÇI=~ìëêÉáÅÜÉåÇI=ã~åÖÉäÜ~Ñí=
qÉãéÉê~íìêÉãéÑáåÇÉå=
ÜÉá≈I=ï~êãI=ä~ìï~êãI=â~äíI=ëÉÜê=â~äí==
^äíÉêëÖêìééÉ=
háåÇI=gìÖÉåÇäáÅÜÉêI=bêï~ÅÜëÉåÉêI=dêÉáë=
q~ÄK=NKQW=_ÉáëéáÉäÉ=ÑΩê=çêÇáå~ä=ëâ~äáÉêíÉ=a~íÉå= _Éá=çêÇáå~ä=ëâ~äáÉêíÉå=a~íÉå=â∏ååÉå=áããÉêÜáå=ÇáÉ=e®ìÑáÖâÉáíÉå=~ÄÖÉò®Üäí=ïÉêÇÉåX=òìë®íòJ äáÅÜ= â∏ååÉå= îÉêÖäÉáÅÜÉåÇÉ= ^ìëë~ÖÉå= ïáÉ= ÄÉëëÉêLëÅÜäÉÅÜíÉêI= ãÉÜêLïÉåáÖÉê= ìK= ®K= ÖÉã~ÅÜí= ïÉêÇÉåK== _ÉêÉÅÜåìåÖÉå=îçå=jáííÉäïÉêíÉå=çÇÉê=ïÉáíÉêÉå=ëí~íáëíáëÅÜÉå=j~≈ò~ÜäÉå=çêÇáå~ä=ëâ~äáÉêíÉê= a~íÉå=ëáåÇ=áã=~ääÖÉãÉáåÉå=åáÅÜí=ëáååîçääK==
1.2.3
Nominalskala
^äë=pâ~äÉåïÉêíÉ=ïÉêÇÉå=k~ãÉå=~ÄÖÉíê~ÖÉåX=Éë=â~åå=åìê=ÇáÉ=däÉáÅÜÜÉáí=çÇÉê=råÖäÉáÅÜJ ÜÉáí=ÖÉéêΩÑí=ïÉêÇÉåK== kçãáå~ä=ëâ~äáÉêíÉ=a~íÉå=ÄÉëáíòÉå=Ç~ë=ìåíÉêëíÉ=a~íÉååáîÉ~ìK=aáÉ=q~ÄÉääÉ=NKR=ÉåíÜ®äí=ÉáåáÖÉ= _ÉáëéáÉäÉ=ÑΩê=åçãáå~ä=ëâ~äáÉêíÉ=a~íÉåK= = Merkmal
Merkmalsausprägung (Merkmalswert)
dÉëÅÜäÉÅÜí=
ã®ååäáÅÜI=ïÉáÄäáÅÜ=
c~ãáäáÉåëí~åÇ=
äÉÇáÖI=îÉêÜÉáê~íÉíI=ÖÉëÅÜáÉÇÉåI=îÉêïáíïÉí=
miwJ_ÉêÉáÅÜ=
MI=NI=OI=ÁI=V=
q~ÄK=NKRW=_ÉáëéáÉäÉ=ÑΩê=åçãáå~ä=ëâ~äáÉêíÉ=a~íÉå= aáÉ=^åÖ~ÄÉ=îçå=^Äëí®åÇÉå=ìåÇLçÇÉê=lêÇåìåÖëÄÉòáÉÜìåÖÉå=òïáëÅÜÉå=òïÉá=jÉêâã~äëíê®ÖÉêå= áëí= ~åÜ~åÇ= ÇÉê= hä~ëëÉåÄÉòÉáÅÜåìåÖÉå= åáÅÜí= ã∏ÖäáÅÜK= ^ìÅÜ= ïÉåå= ÇáÉëÉ= EòìÑ®ääáÖF= ëçÖ~ê= ~ìë= w~ÜäÉå=ÄÉëíÉÜÉå=ëçääíÉåW=aÉê=miwJ_ÉêÉáÅÜ=U=áëí=âÉáåÉëÑ~ääë=łÄÉëëÉê=~äë=ÇÉê=miwJ_ÉêÉáÅÜ=SK== råÇ=ï~ë=ëçääíÉ=~ìÅÜ=ÇáÉ=ëáååäçëÉ=aáÑÑÉêÉåò=łmiwJ_ÉêÉáÅÜ=T=ãáåìë=miwJ_ÉêÉáÅÜ=P=~ìëë~ÖÉå\==
=
=OM
=
N==dêìåÇä~ÖÉå=
kçÅÜ= âìêáçëÉê= ï®êÉ=ÉëI= ïÉåå= ã~å= ÇáÉ= mçëíäÉáíò~Üä= VVVVV= ~äë= łÇêÉáã~ä= ëç= Öêç≈LÖìíLKKK= ïáÉ= ÇáÉ=mçëíäÉáíò~Üä=PPPPP=ÄÉòÉáÅÜåÉå=ïΩêÇÉK=
1.3
Verarbeitungsmöglichkeiten von Daten
a~ë= jÉëëåáîÉ~ì= ÇÉê= a~íÉå= ÄÉëíáããí= ïÉáíÖÉÜÉåÇ= ÇáÉ= j∏ÖäáÅÜâÉáíÉå= ìåÇ= dêÉåòÉå= ÇÉê= a~íÉå~å~äóëÉW= gÉ= åáÉÇêáÖÉê= Ç~ë=a~íÉååáîÉ~ì= áëíI= ÇÉëíç= ÖÉêáåÖÉê=áëí= Ç~ë= ^å~äóëÉéçíÉåòá~ä= ÇÉê=sÉêÑ~ÜêÉå=ìåÇ=ÇÉëíç=ÖÉêáåÖÉê=áëí=ÇÉê=fåÑçêã~íáçåëÖÉÜ~äí=ÇÉê=jÉêâã~äëïÉêíÉK== = Skalentyp Empirische Operationen
Nominalskala Bestimmung von Gleichheit und Ungleichheit
Ordinalskala Zusätzlich: Bestimmung einer Rangfolge z. B. x
Statistische Maßzahlen (Beispiele)
Häufigkeit, Modalwert
Zusätzlich: Median, Quantile, Prozentrangwerte
Zusammenhangsmaße
Kontingenzkoeffizient Vierfelderkoeffizient
Beispiele
Nummerierung von Fußballspielern, Kontonummern, Quantifizierung von dichotomen Merkmalen (z. B. Geschlecht)
Zusätzlich: Rangkorrelationskoeffizient (SpearmansRho, Kendalls Tau) Schulnoten, Richter’sche Erdbebenskala, Testrohwerte
Intervallskala Zusätzlich: Intervalle gleich (z. B. 10-7≅7-4) willkürlich festgelegter Nullpunkt Zusätzlich: Arithmetisches Mittel, Standardabweichung, Schiefe, Exzeß Zusätzlich: Korrelations-, Regressionskoeffizienten
Verhältnisskala Zusätzlich: Bestimmung gleicher Verhältnisse (z. B. x/y ≅ y/z ) absoluter Nullpunkt Zusätzlich: Geometrisches Mittel, Variationskoeffizient
Temperatur (nach Celsius, Fahrenheit, Reaumur)
Länge, Masse, Zeit, Winkel, Temperatur (nach Kelvin)
Siehe Intervallskala
q~ÄK=NKSW=j∏ÖäáÅÜâÉáíÉå=ìåÇ=dêÉåòÉå=ÄÉá=îÉêëÅÜáÉÇÉåÉå=a~íÉåJkáîÉ~ìë= jáí=ëáåâÉåÇÉã=a~íÉååáîÉ~ì=Ñ~ääÉå=Ç~ë=fåÑçêã~íáçåëåáîÉ~ì=ëçïáÉ=ÇáÉ=j∏ÖäáÅÜâÉáíÉå=òìê= _ÉêÉÅÜåìåÖ=~ìëë~ÖÉâê®ÑíáÖÉê=ëí~íáëíáëÅÜÉê=j~≈ò~ÜäÉå= ìåÇ= òìê= ^åÖ~ÄÉ=îçå=wìë~ããÉåJ Ü~åÖëã~≈ÉåK= få=ÇÉê=q~ÄÉääÉ=NKS=ëáåÇ=~ääÉ=j∏ÖäáÅÜâÉáíÉå=ìåÇ=báåëÅÜê®åâìåÖÉå=ëÅÜçå=Éáåã~ä=òìë~ããÉåJ ÖÉëíÉääíX=~ìÑ=ÇáÉ=ÖÉå~ååíÉå=_ÉÖêáÑÑÉ=ïáêÇ=áå=ÇÉå=ÑçäÖÉåÇÉå=h~éáíÉäå=áã=aÉí~áä=ÉáåÖÉÖ~åÖÉåK=
=
NKQ==w~ÜäÉå=Ó=ÇáÉ=Öêç≈Éå=sÉêÑΩÜêÉê=
1.4
=
ON
Zahlen — die großen Verführer
cê~ÖÉÄçÖÉå~âíáçåÉå=ëáåÇ=ÄÉäáÉÄíK=lÄ=Éë=ëáÅÜ=ìã=áêÖÉåÇïÉäÅÜÉ=~ääÖÉãÉáåÉå=jÉáåìåÖëìãJ Ñê~ÖÉå= Ü~åÇÉäíI= ìã= sÉêÄê~ìÅÜÉêÄÉÑê~ÖìåÖÉå= çÇÉê= ìã= ÇáÉ= bî~äì~íáçå= îçå= iÉÜêJ îÉê~åëí~äíìåÖÉå= Ó= Éë= ïáêÇ= Éáå= ãÉÜê= çÇÉê= ïÉåáÖÉê= ìãÑ~åÖêÉáÅÜÉêI= ãÉÜê= çÇÉê= ïÉåáÖÉê= ÇìêÅÜÇ~ÅÜíÉê= cê~ÖÉÄçÖÉå= ÉåíïáÅâÉäíI= ~åëÅÜäáÉ≈ÉåÇ= ÜáåêÉáÅÜÉåÇ= çÑí= âçéáÉêí= ìåÇ= Ç~åå= ãáí= îáÉä=cäÉá≈=ÖÉÑΩääíK= tÉê=ëáÅÜ=áåíÉåëáîÉê=Ç~ãáí=ÄÉëÅÜ®ÑíáÖÉå=ãìëë=çÇÉê=ã∏ÅÜíÉI=ïáÉ=ã~å=ÉáåÉå=ÖìíÉå=cê~ÖÉÄçJ ÖÉå=ÉåíïáÅâÉäíI=ÇÉã=ëÉá=áå=xNTz=Ç~ë=h~éáíÉä=NKP=òìã=píìÇáìã=ÉãéÑçÜäÉåK== a~åå= âçããí= ÇÉê= wÉáíéìåâíI= ÇÉã= ~ääÉ= _ÉíÉáäáÖíÉå= ~å= ÉáåÉê= cê~ÖÉÄçÖÉå~âíáçå= ãáí= dê~ìÉå= ÉåíÖÉÖÉåëÉÜÉåW= aáÉ= ÖÉë~ããÉäíÉåI= ÉêÑê~ÖíÉå= a~íÉå= ãΩëëÉå= ëÅÜäáÉ≈äáÅÜ= áã= m`= ÉêÑ~ëëí= ìåÇ= ÖÉëéÉáÅÜÉêí=ïÉêÇÉåK== pÉäÄëíîÉêëí®åÇäáÅÜ=ÄÉãΩÜí=ã~å=ëáÅÜ=Ç~ÄÉá=ìã=ê~íáçåÉääÉë=sçêÖÉÜÉåK=bë=ïáêÇ=~äëç=ÉáåÉ=hçJ ÇáÉêìåÖëîçêëÅÜêáÑí=ÉåíïçêÑÉåI=ãáí=ÇÉêÉå=eáäÑÉ=ÇáÉ=~åÖÉâêÉìòíÉå=^åíïçêíÉå=áå=w~ÜäÉåïÉêíÉ= ìãÖÉëÉíòí= ïÉêÇÉåK= wì= ÇÉå= mêáåòáéáÉåI= ÇáÉ= ÄÉá= ÇÉê~êíáÖÉå= hçÇáÉêìåÖÉå= òì= ÄÉ~ÅÜíÉå= ëáåÇI= ëÉá=ÉÄÉåÑ~ääë=ïáÉÇÉê=~ìÑ=xNTz=îÉêïáÉëÉåK== Welche Unterkunft haben Sie gewählt? Hotel 5 Sterne
Hotel 4 Sterne
Hotel 3 Sterne
Hotel 2 Sterne
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Hotel 4 Sterne
Privatquartier
Jugendherberge
Hotel 3 Sterne
Hotel 2 Sterne
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trifft weniger zu
trifft nicht zu
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trifft zu
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trifft weniger zu
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kann ich nicht beurteilen
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2
Datenerfassung und -verwaltung
2.1
Mehrdimensionales Datenmaterial
aìêÅÜ=w®ÜäîçêÖ®åÖÉ=çÇÉê=ÇìêÅÜ=jÉëëìåÖÉåI=_ÉÑê~ÖìåÖÉå=ìåÇ=_ÉçÄ~ÅÜíìåÖÉå=ÉåíëíÉÜí= áå= ÇÉê= oÉÖÉä= ãÉÜêÇáãÉåëáçå~äÉë=a~íÉåã~íÉêá~äK= ^äë= sçê~ìëëÉíòìåÖ= ÑΩê= àÉÖäáÅÜÉ= ^ìÑÄÉJ êÉáíìåÖ=ìåÇ=ëí~íáëíáëÅÜÉ=^å~äóëÉ=ãìëë=ÇáÉëÉë=a~íÉåã~íÉêá~ä=òìÉêëí=áå=ÉáåÉê=bñÅÉäJq~ÄÉääÉ= ÉêÑ~ëëí=ìåÇ=ÖÉëéÉáÅÜÉêí=ïÉêÇÉåK== wìê= sçêÄÉêÉáíìåÖ= ÇÉê= bêÑ~ëëìåÖ= ëçääíÉ= ã~å= ëáÅÜ= Éíï~ë= wÉáí= åÉÜãÉåX= àÉ= ãÉÜê= dÉÇ~åâÉå= ã~å=ëáÅÜ=áå=ÇáÉëÉê=mÜ~ëÉ=ã~ÅÜíI=ÇÉëíç=ΩÄÉêëáÅÜíäáÅÜÉê=ïÉêÇÉå=ëé®íÉê=ÇáÉ=a~íÉå=îçêäáÉÖÉåK= a~ë=ÄÉÖáååí=ÄÉêÉáíë=ÄÉá=ÇÉå=pé~äíÉåΩÄÉêëÅÜêáÑíÉåK===
2.1.1
Überschriften
Position der Überschriften — pro und contra erste Zeile sáÉäÉ=iÉÜêÉåÇÉ=îÉêä~åÖÉåI=Ç~ëë=Éáå=a~íÉåÄÉëí~åÇ=áå=ÉáåÉê=bñÅÉäJq~ÄÉääÉ=ëíÉíë=äáåâë=çÄÉå=~Ä= ÇÉê=wÉääÉ= A1=ÉáåÖÉíê~ÖÉå=ïáêÇK=a~ë=ÄÉÇÉìíÉí=~äëçI=Ç~ëë=ÇáÉ=§ÄÉêëÅÜêáÑíÉå=áå=ÇÉê=wÉáäÉ=1=ìåÇ= ÇÉê=ÉáÖÉåíäáÅÜÉ=a~íÉåÄÉëí~åÇ=ëé®íÉê=Ç~êìåíÉê=áå=ÇÉå=wÉáäÉå=2, 3,=ìëïK=ÉáåÖÉíê~ÖÉå=ïáêÇK== rã= ëáÅÜ= ÇáÉ= sçêJ= ìåÇ= k~ÅÜíÉáäÉ= ÇáÉëÉê= sçêÖÉÜÉåëïÉáëÉ= ÇÉìíäáÅÜ= òì= ã~ÅÜÉåI= ëçääíÉ= ã~å= ëíÉíë=Ç~ê~å=ÇÉåâÉåI=Ç~ëë=å~ÅÜ=ÇÉê=bêÑ~ëëìåÖ=ÇÉê=a~íÉå=ãáí=páÅÜÉêÜÉáí=^ìëïÉêíìåÖÉå=îçêÖÉJ åçããÉå=ïÉêÇÉå=ãΩëëÉåK== oÉáÅÜí=ÇÉê=mä~íò=êÉÅÜíë=åÉÄÉå=ÇÉã=a~íÉåÄÉëí~åÇ=çÇÉê=Ç~êìåíÉê=~ìëI=Ç~åå=â∏ååÉå=Ççêí=ÇáÉ= ~ìëïÉêíÉåÇÉå=cçêãÉäå=ìåÇ=cìåâíáçåÉå=ÉáåÖÉíê~ÖÉå=ïÉêÇÉå=ìåÇ=ÄäÉáÄÉå=å~ÅÜ=ÇÉê=a~íÉåJ ÉêÑ~ëëìåÖ=ÖÉãÉáåë~ã=ãáí=ÇÉã=a~íÉåÄÉëí~åÇ=~ìÑ=ÉáåÉå=_äáÅâ=ëáÅÜíÄ~êK==
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aÉåâÉå=ïáê=åìå=~ÄÉê=~å=ÉáåÉ=^åò~Üä=îçå=ãÉÜê=~äë=ÇêÉá≈áÖ=^ÄíÉáäìåÖÉåW=a~åå=ëáÉÜí=ã~å= ~ìÑ=ÇÉã=_áäÇëÅÜáêã=ÉåíïÉÇÉê=ÇáÉ=§ÄÉêëÅÜêáÑí=ìåÇ=Ç~ãáí=ÇáÉ=bêä®ìíÉêìåÖ=òìã=a~íÉåÄÉëí~åÇ= Ó=çÇÉê=ã~å=ëáÉÜí=ÇáÉ=pìããÉåI=ÇáÉ=^å~äóëÉÉêÖÉÄåáëëÉK== eáÉê=ÉãéÑáÉÜäí=Éë=ëáÅÜI=ÇáÉ=§ÄÉêëÅÜêáÑí=Éêëí=áå=ÇáÉ=ÇêáííÉ=wÉáäÉ=Éáåòìíê~ÖÉåI=ìåÇ=ÇáÉ=pìããÉå= å~ÅÜ=çÄÉå=òì=ÜçäÉå=EëK=q~ÄÉääÉ=OKOFK=
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Separierung des Datenbestandes sáÉäÉ=^åäÉáíìåÖÉå=ÑΩê=bñÅÉäJj~≈å~ÜãÉå=ÄÉÖáååÉå=ãáí=ÇÉê=^ìÑÑçêÇÉêìåÖI=ÇÉå=q~ÄÉääÉåâìêJ ëçê=áå=áêÖÉåÇÉáåÉ=wÉääÉ=ÇÉë=a~íÉåÄÉëí~åÇÉë=òì=ëÉíòÉå=Ó=ìåÇ=Ç~åå=ïÉáíÉêÉ=_ÉÇáÉåÜ~åÇäìåJ ÖÉå=îçêòìåÉÜãÉåK== bñÅÉä= áëí= å®ãäáÅÜ= áå= ÇÉê= i~ÖÉI= ëÉäÄëí= ÇáÉ= dêÉåòÉå= ÉáåÉë= a~íÉåÄÉëí~åÇÉë= ÉêâÉååÉå= òì= â∏ååÉåK=a~ë=Éêëé~êí=òÉáíê~ìÄÉåÇÉë=j~êâáÉêÉåK== ^ääÉêÇáåÖë=ëÉíòí=Ç~ë=îçê~ìëI=Ç~ëë=ÇÉê=a~íÉåÄÉëí~åÇ=ëÉé~êáÉêí=áëíW= báå=a~íÉåÄÉëí~åÇ=áëí=ëÉé~êáÉêíI=ïÉåå=Éê=ÇìêÅÜ=ãáåÇÉëíÉåë=ÉáåÉ=iÉÉêòÉáäÉ=ìåÇ=iÉÉêëé~äíÉ= îçå=~åÇÉêÉå=fåÜ~äíÉå=ÇÉë=q~ÄÉääÉåÄä~ííÉë=ÖÉíêÉååí=áëíK==
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2.1.2
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2.1.3
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2.2
Eindimensionales Datenmaterial
báåÇáãÉåëáçå~äÉë=a~íÉåã~íÉêá~äI=ÇK=ÜK=ÉáåÉ=ÉáåÑ~ÅÜÉ=a~íÉåêÉáÜÉI=ëçääíÉ=ã~å=ëíÉíë=áå=ÇÉê= ÉêëíÉå=pé~äíÉ=ÉêÑ~ëëÉåX=Ç~=åìå=êÉÅÜíë=Ç~åÉÄÉå=ÖÉåìÖ=mä~íò=ÑΩê=ëé®íÉêÉ=^å~äóëÉïÉêíÉ=áëíI= â~åå=áå=ÇáÉëÉã=c~ääÉ=áå=ÇÉê=wÉääÉ=A1=ãáí=ÇÉã=a~íÉåÉáåíê~Ö=ÄÉÖçååÉå=ïÉêÇÉåK== báåÉ=§ÄÉêëÅÜêáÑí=áëí=åìå=~ìÅÜ=åáÅÜí=òïáåÖÉåÇ=å∏íáÖK=sçê=ÇÉê=a~íÉåÉáåÖ~ÄÉ=ëçääíÉ=ΩÄÉê=buJ qo^plmqflkbk_b^o_bfqbkj^ohfborkd= k^`e= abj= ao§`hbk= abo= bfkd^_bq^pqb= sbop`efbJ _bkof`eqrkdrkqbk=EîÖäK=_áäÇ=OKQF=åìå=ÇáÉ=_ÉïÉÖìåÖ=ÇÉë=q~ÄÉääÉåâìêëçêë=å~ÅÜ=ìåíÉå=
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2.3
Umgang mit dem Datenmaterial
Nützliche Tastenkombinationen bë=â~åå=ÜáÉê=ïçÜä=îçê~ìëÖÉëÉíòí=ïÉêÇÉåI=Ç~ëë=ÇÉê=rãÖ~åÖ=ãáí=bñÅÉä=ãáí=eáäÑÉ=ÇÉê=j~ìë= ~ääÖÉãÉáå=ÄÉâ~ååí=áëíK=jìëë=ã~å=àÉÇçÅÜ=ãáí=ÉáåÉã=Öê∏≈ÉêÉå=a~íÉåÄÉëí~åÇ=~êÄÉáíÉåI=Ç~åå= ïáêÇ=ëÅÜçå=ÇáÉ=j~êâáÉêìåÖ=îçå=qÉáäÉå=ÇÉë=a~íÉåÄÉëí~åÇÉë=çÇÉê=~ìÅÜ=åìê=ÇáÉ=cÉëíëíÉääìåÖI= ïç=ÇÉåå=åìå=ÇáÉ=a~íÉåãÉåÖÉ=ÉåÇÉíI=òì=ÉáåÉã=òÉáíäáÅÜÉå=dÉÇìäÇëëéáÉäK===
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2.4
Kontrolle des Datenbestandes
2.4.1
Nützliche Auskunftsfunktionen
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2.4.2
Erfasste Merkmalswerte und das Filtern
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2.4.3
Prüfen von Minimum und Maximum
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a~=ÜáÉê=~äë=jáåáãìã=N=ìåÇ=~äë=j~ñáãìã=S=~åÖÉòÉáÖí=ïáêÇI=ëÅÜÉáåÉå=qáééÑÉÜäÉê=ãáí=ìåëáåJ åáÖÉå=w~ÜäÉå~åÖ~ÄÉå=åáÅÜí=îçêòìäáÉÖÉåK== aÉê=~åÖÉÖÉÄÉåÉ=_ÉêÉáÅÜ=C5:C1000=áëí=ëÉÜê=Öêç≈òΩÖáÖ=ÄÉãÉëëÉåX=Ç~ë=ëÅÜ~ÇÉí=~ÄÉê=åáÅÜí=ìåÇ= Éåíä~ëíÉí= îçå= ÇÉê= kçíïÉåÇáÖâÉáíI= ÇáÉ= cçêãÉäå= àÉÇÉë= j~ä= ®åÇÉêå= òì= ãΩëëÉåI= ïÉåå= ÉáåÉ= åÉìÉ=wÉáäÉ=ÜáåòìÖÉÑΩÖí=ïçêÇÉå=áëíK== j~å= ÄÉ~ÅÜíÉ= ÄÉá= ÇÉê= fåíÉêéêÉí~íáçå= ÇÉê= bêÖÉÄåáëëÉ= ÇÉê= cìåâíáçå= MIN(...)= ìåÇ= MAX(...)I= Ç~ëë=ÄÉáÇÉ=bñíêÉãïÉêíÉ=~ÄÉê=ÖÉå~ìëç=ï®êÉåI=ïÉåå=áå=ÉáåÉê=çÇÉê=ãÉÜêÉêÉå=wÉääÉå=îÉêëÉJ ÜÉåíäáÅÜ=Éáå=_ìÅÜëí~ÄÉI=òK=_K= xI=ëíÉÜíK=fÜå=ïΩêÇÉ=ã~å=Ç~åå=~ÄÉê=ïáÉÇÉê=ÄÉáã=cáäíÉêå=EïáÉ= áã=îçêáÖÉå=^ÄëÅÜåáíí=~ìÑ=pÉáíÉ=PQ=ÄÉëÅÜêáÉÄÉåF=ÉåíÇÉÅâÉåK==
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3
Absolute Häufigkeiten
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3.1
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= q~ÄK=PKNMW=cÉëíäÉÖìåÖ=îçå=hä~ëëÉåÖêÉåòÉå= sáÉäãÉÜê=ÉêïÉáëí=Éë=ëáÅÜ=åìå=~äë=ìåÄÉÇáåÖí=åçíïÉåÇáÖI=òìÉêëí=hä~ëëÉå=ÑÉëíòìäÉÖÉåI=ëç=ïáÉ= ëáÉ=òK=_K=ÑΩê=ÇáÉ=ÄÉíê~ÅÜíÉíÉ=dÉïáÅÜíë~å~äóëÉ=áå=q~ÄÉääÉ=PKNM=îçêÖÉëÅÜä~ÖÉå=ïÉêÇÉåK= tÉäÅÜÉ=hä~ëëÉåÖêÉåòÉå=áã=aÉí~áä=òì=ï®ÜäÉå=ëáåÇI=Ç~ë=Ü®åÖí=àÉïÉáäë=îçå=ÇÉê=ÄÉíê~ÅÜíÉíÉå= qÜÉã~íáâ=~ÄK=bÄÉåëç=áëí=Éë=åáÅÜí=òïáåÖÉåÇI=Ç~ëë=ëíÉíë=ÖäÉáÅÜÉ=hä~ëëÉåÄêÉáíÉå=ÖÉï®Üäí=ïÉêJ ÇÉå=ãΩëëÉåK== dÉåÉêÉää=ÖáäíI=Ç~ëë=åáÅÜí=òì=îáÉäÉ=ìåÇ=åáÅÜí=òì=ëÅÜã~äÉ=hä~ëëÉå=ÖÉÄáäÇÉí=ïÉêÇÉå=ëçääíÉåK== aáÉ=råíÉêJ=ìåÇ=lÄÉêÖêÉåòÉå=ÄÉëíáããí=ã~å=òïÉÅâã®≈áÖ=ãáí=eáäÑÉ=ÇÉê=cìåâíáçåÉå=MIN(...)= ìåÇ= MAX(...)K=a~å~ÅÜ=ãìëë=ÑΩê=àÉÇÉå=dÉïáÅÜíëïÉêí=ÉêãáííÉäí=ïÉêÇÉåI=òì=ïÉäÅÜÉê=hä~ëëÉ=Éê= ÖÉÜ∏êíK=a~ÑΩê=ÖáÄí=Éë=ãÉÜêÉêÉ=jÉíÜçÇÉåK== wìÉêëí=ëçää=ÇÉê=rãÖ~åÖ=ãáí=ÇÉê=cìåâíáçå=WENN(...;...;...)=îçêÖÉëíÉääí=ïÉêÇÉåK==
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NUS=
PKO==hä~ëëÉåÄáäÇìåÖ=
QT
^åëÅÜäáÉ≈ÉåÇ= ÉêÑçäÖí= ÇáÉ= kìíòìåÖ= ÇÉê= cìåâíáçå= VERWEIS(...;...;...)I= Ç~åå= ÑçäÖí= Éáå= eáåJ ïÉáë=~ìÑ=ÇáÉ=^Äò®ÜäÑìåâíáçå= HÄUFIGKEIT(...;...)=ìåÇ=ëÅÜäáÉ≈äáÅÜ=ÇáÉ=^êÄÉáí=ãáí=ÇÉã=tÉêâJ òÉìÖ=HISTOGRAMMK=iÉíòíÉêÉë=áëí=~ã=ÄÉèìÉãëíÉå=Ó=ïÉê=Éë=ÉáäáÖ=Ü~íI=ëçääíÉ=òìÉêëí=ÇÉå=^ÄëÅÜåáíí= PKOKQ=~Ä=pÉáíÉ=RM=äÉëÉåK==
3.2.1
Klassenzuordnung mit der Funktion WENN
aáÉ=bñÅÉäJcìåâíáçå= WENN(...;...;...)=îÉêä~åÖí=ëíÉíë=ÇêÉá=^åÖ~ÄÉåI=ÇáÉ=ãáí=pÉãáâçäçå=òì= íêÉååÉå=ëáåÇW=WENN( Test ; Ja_Eintrag ; Nein_Eintrag )= ^å=ÇáÉ=ÉêëíÉ=mçëáíáçå=áëí=ÇáÉ=_ÉÇáåÖìåÖ=òì=ëÅÜêÉáÄÉåI=ÇáÉ=òì=éêΩÑÉå=áëíK=få=ÇÉê=jáííÉ=áëí=~åJ òìÖÉÄÉåI= ï~ë= áå= ÇÉê= wÉääÉI= ÇáÉ= ÇáÉëÉ= cìåâíáçå= ÉåíÜ®äíI= ÄÉá= ÉêÑΩääíÉã=qÉëí= Éáåòìíê~ÖÉå= áëíK= oÉÅÜíë=îçã=òïÉáíÉå=pÉãáâçäçå=áëí=~åòìÖÉÄÉåI=ïÉäÅÜÉå=fåÜ~äí=ÇáÉ=wÉääÉ=ÄÉá=åáÅÜí=ÉêÑΩääíÉã= qÉëí=ÄÉâçããÉå=ëçääK=aáÉ=q~ÄÉääÉå=PKNN=òÉáÖÉå=ÉáåÉ=ÉêëíÉ=^åïÉåÇìåÖ=ìåÇ=ÇáÉ=ÉêëÅÜÉáåÉåJ ÇÉå=báåíê®ÖÉK=
=
=
q~ÄK=PKNNW=bêëíÉê=sÉêëìÅÜ=ãáí=ÇÉê=WENNJcìåâíáçå=
Verschachtelung von WENN-Funktionen lÑÑÉåÄ~ê= áëí= ÇáÉ= wìçêÇåìåÖ= ~ääÉê= tÉêíÉ= ìåíÉêÜ~äÄ= îçå= SM= âÖ= âçêêÉâíI= ~ÄÉê= ÇáÉ= Öê∏≈ÉêÉå= dÉïáÅÜíëïÉêíÉ=ïÉêÇÉå=åçÅÜ=åáÅÜí=ÇáÑÑÉêÉåòáÉêíK== aÉëÜ~äÄ=ãìëë=áã=kÉáåJbáåíê~Ö=ÇáÑÑÉêÉåòáÉêí=ïÉêÇÉåI=ï~ë=ÇìêÅÜ=ÉáåÉ=ÉêåÉìíÉI=áåíÉêåÉ=sÉêJ ïÉåÇìåÖ=ÇÉê=WENNJcìåâíáçå=ã∏ÖäáÅÜ=áëíK== aáÉ=q~ÄÉääÉ=PKNO~LÄ=òÉáÖÉå=cìåâíáçå=ìåÇ=bêÖÉÄåáëK=
=
=
q~ÄK=PKNOW=sÉêëÅÜ~ÅÜíÉäíÉ=WENNJcìåâíáçåÉåW=cçêãÉä=ìåÇ=bêÖÉÄåáë= fëí=ÇÉê=ÉêëíÉ=qÉëí=ÉêÑΩääí=EdÉïáÅÜí=ìåíÉê=SM=âÖFI=Ç~åå=ïáêÇ=ÉáåÉ= 1=ÉáåÖÉíê~ÖÉåK=^åÇÉêåÑ~ääë= ÑçäÖí=ÇÉê=áååÉêÉ=qÉëí=EdÉïáÅÜí=ìåíÉê=UM=âÖ=\FK=fëí=ÇáÉëÉê=ÉêÑΩääíI=Ç~åå=ïáêÇ=ÉáåÉ= 2=ÉáåÖÉíê~J ÖÉåK=aÉê=kÉáåJc~ää=ÇÉë=áååÉêÉå=qÉëíë=ÑΩÜêí=ëÅÜäáÉ≈äáÅÜ=òìã=báåíê~Ö=3K==
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NUT==
P==^ÄëçäìíÉ=e®ìÑáÖâÉáíÉå=
QU
kìå=ïáêÇ=òïáëÅÜÉå=QM=ìåÇ=UM=âÖ=ÄÉêÉáíë=êáÅÜíáÖ=áå=ÇáÉ=hä~ëëÉå=ÉáåÖÉçêÇåÉíI=~ääÉêÇáåÖë=ïáêÇI= ïáÉ=òì=ÉêâÉååÉåI=ÇÉê=ΩÄÉêJNMMJtÉêí=115,76=åçÅÜ=Ñ~äëÅÜ=òìÖÉçêÇåÉíK== cçäÖäáÅÜ=ãìëë=áã=kÉáåJbáåíê~Ö=ÇÉê=áååÉêÉå=WENNJcìåâíáçå=ïÉáíÉê=ÇáÑÑÉêÉåòáÉêí=ïÉêÇÉåK== j~å= ΩÄÉêäÉÖí= ëáÅÜI= Ç~ëë= òìê= ÇáÑÑÉêÉåòáÉêíÉå= báåçêÇåìåÖ= ÇÉê= tÉêíÉ= ΩÄÉê= NOM= âÖ= ìåÇ= ΩÄÉê= NQM=âÖ=ëÅÜäáÉ≈äáÅÜ=åçÅÜ=òïÉá=ïÉáíÉêÉ=áååÉêÉ=WENNJcìåâíáçåÉå=îÉêïÉåÇÉí=ïÉêÇÉå=ãΩëëÉåK== pÉÜÉå=ïáê=ìåë=ÇáÉ=ÉåÇÖΩäíáÖÉI=òáÉãäáÅÜ=îÉêëÅÜ~ÅÜíÉäíÉ= WENNJcìåâíáçå=~åI=ÇáÉ=~ÄÉê=~ääÉ=dÉJ ïáÅÜíëïÉêíÉ=êáÅÜíáÖ=áå=ÇáÉ=òìÖÉÜ∏êáÖÉ=hä~ëëÉ=ÉáåçêÇåÉíK== =WENN(B2<60;1;WENN(B2<80;2;WENN(B2<100;3;WENN(B2<120;4;5))))
kìå=â~åå=ÇáÉ=ÄÉêÉáíë=ÄÉâ~ååíÉ=^åïÉåÇìåÖ=ÇÉê=cìåâíáçå= ZÄHLENWENN(...;...)=ÑçäÖÉåI=ãáí= ÇÉêÉå= eáäÑÉ= ëÅÜäáÉ≈äáÅÜ= ÑÉëíÖÉëíÉääí= ïáêÇI= ïáÉ= îáÉäÉ= jÉêâã~äëïÉêíÉ= ÇÉë= a~íÉåÄÉëí~åÇÉë= áå= ÇáÉ=àÉïÉáäáÖÉ=hä~ëëÉ=Ñ~ääÉåK== bë=ï®êÉ=ΩÄêáÖÉåë=~ìÅÜ=ã∏ÖäáÅÜ=ÖÉïÉëÉåI=ÇáÉ=hä~ëëÉå=~åëíÉääÉ=ãáí=ÇÉå=w~ÜäÉå=N=Äáë=S=~ìÅÜ= åáÅÜíåìãÉêáëÅÜ=òì=ÄÉòÉáÅÜåÉåK=báåÉ=ëçäÅÜÉ=s~êá~åíÉI=ÇáÉ=~ääÉêÇáåÖë=ïÉÖÉå=ÇÉê=ÖÉï®ÜäíÉå= sçâ~ÄÉäå=åáÅÜí= ìåéêçÄäÉã~íáëÅÜ= áëíI= ëçää= ãáí= ÑçäÖÉåÇÉê= cçêãÉä= ~åÖÉÖÉÄÉå= ïÉêÇÉåI= ïçÄÉá= ÇáÉ=pÅÜêÉáÄïÉáëÉ=ÇáÉ=sÉêëÅÜ~ÅÜíÉäìåÖ=Éíï~ë=ÇÉìíäáÅÜÉê=ã~ÅÜÉå=ëçääW== =WENN(B2<60; "dünn"; WENN(B2<80; "normal"; WENN(B2<100; "kräftig"; WENN(B2<120; "korpulent";"Jumbo"))))
cΩê=~ääÉ=iÉëÉêáååÉå=ìåÇ=iÉëÉêI=ÇÉåÉå=ÇÉê=rãÖ~åÖ=ãáí=ÇÉê= WENNJcìåâíáçå=áå=ÇáÉëÉê=âçãéäáJ òáÉêíÉå=cçêã=ìåëóãé~íÜáëÅÜ=ëÉáå=ëçääíÉ=Eï~ë=ÇìêÅÜ~ìë=îÉêëí®åÇäáÅÜ=áëíFI=ëÉá=ÜáÉê=ÄÉêÉáíë=Ç~êJ ~ìÑ=ÜáåÖÉïáÉëÉåI=Ç~ëë=ÇáÉ=hä~ëëÉåòìçêÇåìåÖ=çÑí=~ìÅÜ=ïÉëÉåíäáÅÜ=ÉáåÑ~ÅÜÉê=îçêÖÉåçããÉå= ïÉêÇÉå=â~ååK=a~òì=ëíÉääí=bñÅÉä=Ç~ë=tÉêâòÉìÖ= HISTOGRAMM=òìê=sÉêÑΩÖìåÖI=Ç~ë=áå=^ÄëÅÜåáíí= PKOKQ=~ìÑ=pÉáíÉ=RM=ÄÉëÅÜêáÉÄÉå=ïáêÇK== qêçíòÇÉã= ëçää= Éêëí= åçÅÜ= Éáå= ïÉáíÉêÉê= âäÉáåÉê= ^ÄëÅÜåáíí= ÇÉê= äÉáëíìåÖëÑ®ÜáÖÉå= WENNJcìåâíáçå= ÖÉïáÇãÉí=ïÉêÇÉåK=
Die Funktion WENN und die Kodierung von nichtnumerischen Daten táÉ= ëÅÜçå= ãÉÜêÑ~ÅÜ= Éêï®ÜåíI= ÄáÉíÉí= bñÅÉä= áã= dÉÖÉåë~íò= òì= ÉáåáÖÉå= êÉáåÉå= pí~íáëíáâJmêçJ Öê~ããÉå= ÇáÉ= ìåÉáåÖÉëÅÜê®åâíÉ= j∏ÖäáÅÜâÉáíI= a~íÉå= áå= áÜêÉê= ìêëéêΩåÖäáÅÜÉå= åìãÉêáëÅÜÉå= çÇÉê=åáÅÜíåìãÉêáëÅÜÉå=cçêã=áå=ÉáåÉê=q~ÄÉääÉ=òì=ëéÉáÅÜÉêåK== jáí=ÇÉê=ZÄHLENWENNJcìåâíáçå=â~åå=ã~å=éêçÄäÉãäçë=~ìÅÜ=áÜêÉ=e®ìÑáÖâÉáíÉå=~å~äóëáÉêÉåK== bë= Ü~í= ~ääÉêÇáåÖë= qê~ÇáíáçåI= Ç~ëë= áåëÄÉëçåÇÉêÉ=^ìëïÉêíìåÖÉå=îçå=_ÉÑê~ÖìåÖÉå= ÖêìåÇë®íòJ äáÅÜ=âçÇáÉêí=ÉêÑ~ëëí=ïÉêÇÉåI=ÇK=ÜK=àÉÇÉê=^åíïçêí=ïáêÇ=ÉáåÉ=w~Üä=òìÖÉçêÇåÉíI=ÇáÉ=Ç~åå=ÉáåÖÉJ ÖÉÄÉå=ïáêÇK=káÅÜí=ïÉåáÖÉ=_ΩÅÜÉê=òìê=j~êâíÑçêëÅÜìåÖ=ìåÇ=a~íÉå~å~äóëÉ=ïáÇãÉå=ëáÅÜ=~ìëJ ÑΩÜêäáÅÜ=ÇÉå=cê~ÖÉå=ÉáåÉê=ëáååîçääÉå=hçÇáÉêìåÖK== fã= ^ÄëÅÜåáíí= NKQ= ÇáÉëÉë= _ìÅÜÉë= ~ìÑ= pÉáíÉ= ON= ïìêÇÉ= ~ÄÉê= ëÅÜçå= ~ìÑ= ÇáÉ= Ç~ÄÉá= ã∏ÖäáÅÜÉå= cÉÜäáåíÉêéêÉí~íáçåÉå= ìåÇ= ëÅÜÉáåÄ~êÉå= sÉê®åÇÉêìåÖÉå= ÇÉë= a~íÉååáîÉ~ìë= ÜáåÖÉïáÉëÉå= ìåÇ= ÇÉëÜ~äÄ= ~ääÉå= bñÅÉäJkìíòÉêå= ÉãéÑçÜäÉåI= åáÅÜíåìãÉêáëÅÜÉ= a~íÉå= ~ìÅÜ= åáÅÜíåìãÉêáëÅÜ= áå= ÇáÉ=bñÅÉäJq~ÄÉääÉ=òì=ΩÄÉêåÉÜãÉåI=òK=_K=Ç~ë=dÉëÅÜäÉÅÜí=ãáí=w=ìåÇ=mI=Ç~ãáí=åáÉã~åÇ=~ìÑ=ÇáÉ= ÉáÖÉå~êíáÖÉ=fÇÉÉ=âçããíI=ÑΩê=ÇáÉëÉ=^åÖ~ÄÉ=ïçã∏ÖäáÅÜ=ÉáåÉå=łjáííÉäïÉêí=~ìëòìïÉáëÉåKKK= bë=ÖáÄí=àÉÇçÅÜ=dêÉåòÉå=ÇÉê=sÉê~êÄÉáíìåÖ=åáÅÜíåìãÉêáëÅÜÉê=a~íÉåK==
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NUT=
PKO==hä~ëëÉåÄáäÇìåÖ=
QV
wìã= _ÉáëéáÉä= ÄÉå∏íáÖí= ÇáÉ= cìåâíáçå= MODALWERT(...)I= ÇáÉ= ÇÉå= ~ã= Ü®ìÑáÖëíÉå= ~ìÑíêÉíÉåÇÉå= jÉêâã~äëïÉêí= ÜÉê~ìëëìÅÜí= ìåÇ= áã= ^ÄëÅÜåáíí= PKP= ~ìÑ= pÉáíÉ= RO= å®ÜÉê= îçêÖÉëíÉääí= ïáêÇI= ìåÄÉJ ÇáåÖí=åìãÉêáëÅÜÉ=a~íÉåK== cΩê= ÇÉå= c~ääI= Ç~ëë= åáÅÜíåìãÉêáëÅÜÉå= jÉêâã~äë~ìëéê®ÖìåÖÉå= å~ÅÜíê®ÖäáÅÜ= åìãÉêáëÅÜÉ= jÉêâã~äëïÉêíÉ= òìÖÉçêÇåÉí= ïÉêÇÉå= ãΩëëÉåI= â~åå= ã~å= ÇáÉ= cìåâíáçå= WENN(...;...;...)= ëÉÜê=Öìí=îÉêïÉåÇÉåK== q~ÄÉääÉ=PKNP=Éêâä®êí=ÄÉáëéáÉäÜ~ÑíI=ïáÉ=ÇáÉ=wìçêÇåìåÖ=w1=ìåÇ=m0=êÉ~äáëáÉêí=ïáêÇK=====
=
=
q~ÄK=PKNPW=hçÇáÉêìåÖ=ãáí=ÇÉê=WENNJcìåâíáçå=
3.2.2
Die Funktion VERWEIS
jáí= ÇÉê= bñÅÉäJcìåâíáçå= VERWEIS(...;...;...)= ä~ëëÉå= ëáÅÜ= ÉÄÉåÑ~ääë= hä~ëëÉåòìçêÇåìåÖÉå= êÉ~äáëáÉêÉåK== aáÉëÉ=cìåâíáçå=îÉêä~åÖí=ÇêÉá=^åÖ~ÄÉåK=wìÉêëí=áëí=ÇáÉ=wÉääÉ=Éáåòìíê~ÖÉåI=ÇÉêÉå=fåÜ~äí=âä~ëëáJ ÑáòáÉêí= ïÉêÇÉå= ëçääK= ^åëÅÜäáÉ≈ÉåÇ= áëí= Éáå= pé~äíÉåÄÉêÉáÅÜ= Éáåòìíê~ÖÉåI= áå= ÇÉã= ëáÅÜ= ÇáÉ= ëçêJ íáÉêíÉå=hä~ëëÉåÖêÉåòÉå=ÄÉÑáåÇÉåK=pÅÜäáÉ≈äáÅÜ=ïáêÇ=åçÅÜ=Éáå=ÖäÉáÅÜä~åÖÉê=pé~äíÉåÄÉêÉáÅÜ=îÉêJ ä~åÖíI=áå=ÇÉã=ëáÅÜ=ÇáÉ=àÉïÉáäáÖÉå=hä~ëëÉåÄÉòÉáÅÜåìåÖÉå=ÄÉÑáåÇÉåK==
= q~ÄK=PKNQ~W=^åïÉåÇìåÖ=ÇÉê=VERWEISJcìåâíáçå=W=cçêãÉäå=
= q~ÄK=PKNQÄW=^åïÉåÇìåÖ=ÇÉê=VERWEISJcìåâíáçåW=tÉêíÉ== cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NUT==
P==^ÄëçäìíÉ=e®ìÑáÖâÉáíÉå=
RM
aáÉ= cìåâíáçå= VERWEIS(...;...;...) ÇìêÅÜëìÅÜí= ÑΩê= àÉÇÉå= jÉêâã~äëïÉêí= ÇÉå= _ÉêÉáÅÜ= ÇÉê= hä~ëëÉåÖêÉåòÉåI= îçå= çÄÉå= ÄÉÖáååÉåÇK= fëí= ÇáÉ= å~ÅÜÑçäÖÉåÇÉ= hä~ëëÉåÖêÉåòÉ= òì= Öêç≈I= Ç~åå= ïáêÇ=ÇÉê=åÉÄÉåëíÉÜÉåÇÉ=tÉêí=~äë=hä~ëëÉåÄÉòÉáÅÜåìåÖ=ÉáåÖÉíê~ÖÉåK== eáÉê=ïìêÇÉå=ÇáÉëã~ä=ÇáÉ=sÉêÄ~äÄÉòÉáÅÜåìåÖÉå=ÄÉåìíòíI=ìã=òì=òÉáÖÉåI=Ç~ëë=Éë=âÉáåÉëÑ~ääë= áããÉê=w~ÜäÉå=ëÉáå=ãΩëëÉåI=ãáí=ÇÉåÉå=ã~å=ÉáåÉ=hä~ëëÉ=ÄÉòÉáÅÜåÉíK=aÉåå=ëÅÜäáÉ≈äáÅÜ=â∏ååJ íÉ= ÇáÉ= cìåâíáçå= ZÄHLENWENN(...;...;...)= ~åëÅÜäáÉ≈ÉåÇ= éêçÄäÉãäçë= ~Äò®ÜäÉåI= ïáÉ= çÑí= ÇáÉ= hä~ëëÉ=korpulent=~ìÑÖÉíêÉíÉå=áëíK==
3.2.3
Die Funktion HÄUFIGKEIT
aáÉ=cìåâíáçå= HÄUFIGKEIT(...;...)=áëí=ÉáåÉ=ëç=ÖÉå~ååíÉ=j~íêáñJ=çÇÉê=sÉâíçêÑìåâíáçåK=páÉ= äáÉÑÉêí=åáÅÜí=åìê=ÉáåÉå=bêÖÉÄåáëïÉêíI=ïáÉ=ïáê=Éë=ÄÉá=ÇÉå=ÄáëÜÉê=îçêÖÉëíÉääíÉå=cìåâíáçåÉå= ÇìêÅÜïÉÖ=ÉêäÉÄíÉåI=ëçåÇÉêå=ÑΩääí=ëáãìäí~å=ÉáåÉå=Ö~åòÉå=îçêÖÉÖÉÄÉåÉå=_ÉêÉáÅÜK== báåÉ= ÉêëíÉ= ^åïÉåÇìåÖ= ÉáåÉê= ëçäÅÜÉå= j~íêáñÑìåâíáçå= áëí= áã= ^ÄëÅÜåáíí= TKP= ~ìÑ= pÉáíÉ=NOV= òì= ÉêäÉÄÉåX=áåíÉêÉëëáÉêíÉ=iÉëÉê=ëÉáÉå=òìë®íòäáÅÜ=~ìÑ=ïÉáíÉêÑΩÜêÉåÇÉ=iáíÉê~íìêI=òK=_K=xNRz=îÉêïáÉJ ëÉåK==
3.2.4
Das Werkzeug HISTOGRAMM
a~ë=tÉêâòÉìÖ=HISTOGRAMM=âçãÄáåáÉêí=ÇáÉ=iÉáëíìåÖÉå=ÇÉê=ÄÉáÇÉå=ÄÉêÉáíë=îçêÖÉëíÉääíÉå=cìåâJ íáçåÉå=WENN(...;...;...)=ìåÇ=ZÄHLENWENN(...;...)K== jáí=eáäÑÉ=ÇÉë=tÉêâòÉìÖë=HISTOGRAMM=â~åå=å~ÅÜ=cÉëíäÉÖìåÖ=ÇÉê=hä~ëëÉåÖêÉåòÉå=ëçÑçêí=Ç~ë= bêÖÉÄåáë=ÇÉê=^ìëò®ÜäìåÖ=ÉêÜ~äíÉå=ïÉêÇÉåK== bë= ëçää= ÇÉêëÉäÄÉ= a~íÉåÄÉëí~åÇ= ïáÉ= áã= îçêáÖÉå= ^ÄëÅÜåáíí= îÉêïÉåÇÉí= ïÉêÇÉåK= q~ÄÉääÉ= PKNR= ÉåíÜ®äí=ÇáÉëÉå=a~íÉåÄÉëí~åÇ=ìåÇ=Ç~òì=áã=_ÉêÉáÅÜ=D2:D5=ÇáÉ=hä~ëëÉåÖêÉåòÉåK==
= q~ÄK=PKNRW=a~íÉåÄÉëí~åÇ=ìåÇ=hä~ëëÉåÖêÉåòÉå= kìå=ãìëë=Ç~ë=tÉêâòÉìÖ= HISTOGRAMM=~åÖÉÑçêÇÉêí=ïÉêÇÉåK=aáÉ=^åÑçêÇÉêìåÖ=ÇÉë=tÉêâòÉìÖë= ÉêÑçäÖí=ΩÄÉê=buqo^p^k^ivpbJcrkhqflkbk=EëáÉÜÉ=_áäÇ=PKQFK= pçääíÉå= ÇáÉ= ^å~äóëÉJcìåâíáçåÉå= åáÅÜí= áã= jÉåΩ= buqo^p= ~åÖÉÄçíÉå= ïÉêÇÉåI= Ç~åå= ëáåÇ= ëáÉ= ãáííÉäë= buqo^p^aaJfkp= ìåÇ= ÇìêÅÜ= pÉíòÉå= ÉáåÉë= e~âÉåë= áå= ÇÉå= ÄÉáÇÉå= ÉåíëéêÉÅÜÉåÇÉå= wÉáäÉå=EëáÉÜÉ=_áäÇ=PKRF=~åòìÑçêÇÉêåK== aáÉ=e~åÇÜ~ÄìåÖ=ÇÉë=tÉêâòÉìÖë=HISTOGRAMM=áëí=êÉÅÜí=ÉáåÑ~ÅÜK=j~å=Äê~ìÅÜí=åìêI=ïáÉ=áå=_áäÇ= PKS=òì=ëÉÜÉåI=òïÉá=^åÖ~ÄÉå=áå=ÇáÉ=òïÉá=báåÖ~ÄÉÑÉåëíÉê=Éáåòìíê~ÖÉåK== a~ë=cÉåëíÉê=EINGABEBEREICH=ÉêÜ®äí=ÇáÉ=òì=ìåíÉêëìÅÜÉåÇÉå=a~íÉå=Ó=ÜáÉê=áëí=~äëç=ÇáÉ=pé~äíÉ= ãáí=ÇÉå=dÉïáÅÜíë~åÖ~ÄÉå=ÉáåÖÉíê~ÖÉåK=få=Ç~ë=cÉåëíÉê=KLASSENBEREICH=áëí=Éáåòìíê~ÖÉåI=ïç= ëáÅÜ=ÇáÉ=ÑÉëíÖÉäÉÖíÉå=hä~ëëÉåÖêÉåòÉå=ÄÉÑáåÇÉåK===
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NUT=
PKO==hä~ëëÉåÄáäÇìåÖ=
RN
pÅÜäáÉ≈äáÅÜ= â~åå= ã~å= ï®ÜäÉåI= çÄ= ÇáÉ= bêÖÉÄåáëëÉ= ÇÉë= tÉêâòÉìÖë= ~ìÑ= Éáå= åÉìÉë=q~ÄÉääÉåJ Ää~íí=çÇÉê=åÉÄÉå=ÇÉå=a~íÉåÄÉëí~åÇ=~ìëÖÉÖÉÄÉå=ïÉêÇÉå=ëçääÉåK==
= _áäÇ=PKQW=^åÑçêÇÉêìåÖ=ÇÉë=tÉêâòÉìÖë=efpqldo^jj=
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=
=
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cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NUT==
P==^ÄëçäìíÉ=e®ìÑáÖâÉáíÉå=
RO
^å= ÇáÉëÉê= píÉääÉ= òÉáÖí= ëáÅÜI= ïÉëÜ~äÄ= áã= îçêáÖÉå= ^ÄëÅÜåáíí= ÇáÉ= WENNJcìåâíáçå= ÄÉëÅÜêáÉÄÉå= ïìêÇÉK=páÉ=ãìëë=ã~å=ÄÉåìíòÉåI=ïÉåå=ã~å=ëéÉòáÉääÉ=tΩåëÅÜÉ=Ü~íI=ÄÉáëéáÉäëïÉáëÉI=Ç~ëë=ÇáÉ= ~åÖÉÖÉÄÉåÉå=hä~ëëÉåÖêÉåòÉå=àÉïÉáäë=ÇáÉ=ìåíÉêÉå=hä~ëëÉåê®åÇÉê=ÄÉëÅÜêÉáÄÉå=ëçääÉåK==
= q~ÄK=PKNSW=bêÖÉÄåáë=ÇÉë=tÉêâòÉìÖë=HISTOGRAMM= _Éåìíòí= ã~å= Ç~ÖÉÖÉå= Ç~ë= ÄÉèìÉãÉ= tÉêâòÉìÖ= HISTOGRAMMI= ò~Üäí= ã~å= ÑΩê= ÇáÉëÉ= _ÉèìÉãJ äáÅÜâÉáí=å~íΩêäáÅÜ=ÉáåÉå=mêÉáëW== HISTOGRAMM=ÄÉíê~ÅÜíÉí=ÇáÉ=~åÖÉÖÉÄÉåÉå=tÉêíÉ=áã=hä~ëëÉåÄÉêÉáÅÜ=ëíÉíë=~äë=çÄÉêÉ=hä~ëëÉåJ
ÖêÉåòÉåK== q~ÄÉääÉ=PKNT=Éêâä®êí=ÇÉëÜ~äÄ=ÖÉå~ìI=ïáÉ=ã~å=ÇáÉ=^ìëÖ~ÄÉ=äÉëÉå=ãìëëK==
= q~ÄK=PKNTW=bêä®ìíÉêìåÖ=ÇÉê=^ìëÖ~ÄÉ=ÇÉë=tÉêâòÉìÖë=efpqldo^jj= táÉ=ÖÉë~ÖíI=Ç~ãáí=ãìëë=ã~å=äÉÄÉåK=j~å=â~åå=äÉáÇÉê=âÉáåÉ=báåëíÉääìåÖ=áå=ÇÉã=tÉêâòÉìÖ= HISTOGRAMM= îçêåÉÜãÉåI= ëç= Ç~ëë= ÇáÉ= ~åÖÉÖÉÄÉåÉå= dêÉåòÉå= ~äë= ìåíÉêÉ= o®åÇÉê= ÇÉê= hä~ëëÉå= ~åÖÉëÉÜÉå=ïÉêÇÉåK== fåÇáîáÇìÉääÉ=tΩåëÅÜÉ=ãΩëëÉå=~äëç=ãáí=ÇÉê= WENNJcìåâíáçå=ìãÖÉëÉíòí=ïÉêÇÉåK=a~ë=áëí=òï~ê= ~ìÑïÉåÇáÖÉêI=Ü~í=~ÄÉê=òìë®íòäáÅÜ=ÇÉå=Öêç≈Éå=sçêíÉáäI=Ç~ëë=ÄÉá=ûåÇÉêìåÖ=ÇÉê=a~íÉå=~ìíçã~J íáëÅÜ=~ääÉ=bêÖÉÄåáëëÉ=åÉì=ÄÉêÉÅÜåÉí=ïÉêÇÉåK== ^ääÉ=bñÅÉäJtÉêâòÉìÖÉ=äáÉÑÉêå=Ç~ÖÉÖÉå=ëí~êêÉ=Eëí~íáëÅÜÉF=bêÖÉÄåáëëÉX=ÇK=ÜK=ïÉêÇÉå=ÇáÉ=a~J íÉå=ÖÉ®åÇÉêíI=Ç~åå=ãìëë=Ç~ë=tÉêâòÉìÖ=ïáÉÇÉê=åÉì=~åÖÉï~åÇí=ïÉêÇÉåK==
3.3
Modalwert
táêÇ= ãáí= ÇÉê= cìåâíáçå= ZÄHLENWENN(...;...)= ÑΩê= ~ääÉ= îçêâçããÉåÇÉå= jÉêâã~äëïÉêíÉ= ÇÉêÉå= ~ÄëçäìíÉ=e®ìÑáÖâÉáí=~ìëÖÉò®Üäí=EëáÉÜÉ=q~ÄÉääÉ=PKNUFI=Ç~åå=ÉêÖáÄí=ëáÅÜ=òï~åÖëä®ìÑáÖ=ÇáÉ=cê~J ÖÉI= çÄ= Éáå= ÉáåòÉäåÉê= jÉêâã~äëïÉêí= ~ã= Ü®ìÑáÖëíÉå= ~ìÑíêáíí= Ó= çÇÉê= çÄ= Éë= ãÉÜêÉêÉ= jÉêâJ ã~äëïÉêíÉ= ãáí= ÇÉêëÉäÄÉå= e®ìÑáÖâÉáí= ÖáÄíK= a~êΩÄÉê= Üáå~ìë= ÉêÑ®Üêí= ã~å= ãáí= ZÄHLENWENN(...;...)=ÇáÉ=àÉïÉáäáÖÉå=^åò~ÜäÉåK== bë=ÉêÖáÄí=ëáÅÜ=ÇáÉ=cê~ÖÉI=çÄ=ã~å=ÇáÉëÉ=^ìëâΩåÑíÉ=åáÅÜí=ÉáåÑ~ÅÜÉê=ÉêÜ~äíÉå=â~ååK=pÉÜÉå=ïáê= ìåë=Ç~òì=áå=q~ÄÉääÉ=PKNVLPKOM=ÇáÉ=táêâìåÖ=ÇÉê=cìåâíáçå=MODALWERT(...)=~åK= táÉ=òì=ÉêâÉååÉåI=äáÉÑÉêí=ÇáÉëÉ=cìåâíáçå=òì=ÄÉáÇÉå=ÄÉíê~ÅÜíÉíÉå=a~íÉåÄÉëí®åÇÉå=ÇÉå=jÉêâJ ã~äëïÉêí=30K==
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NUT=
PKP==jçÇ~äïÉêí=
RP
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= q~ÄK=PKNVW=MODALWERTJcìåâíáçåW=cçêãÉäå==
= q~ÄK=PKOMW=MODALWERTJcìåâíáçåW=bêÖÉÄåáëëÉ== fã= ÉêëíÉå= c~ää= E_ÉêÉáÅÜ= B4:B13F= áëí= ÇáÉë= âçêêÉâíI= ÇÉåå= ÇÉê= jÉêâã~äëïÉêí= 30= áëí= í~íë®ÅÜäáÅÜ= ÇÉêàÉåáÖÉI=ÇÉê=~äë=ÉáåòáÖÉê=~ã=Ü®ìÑáÖëíÉå=~ìÑíêáííK== fã=òïÉáíÉå=c~ää=E_ÉêÉáÅÜ= E4:E13F=íÉáäí=ÇáÉ=cìåâíáçå= MODALWERT(...)=äÉáÇÉê=åáÅÜí=ãáíI=Ç~ëë=Éë= åÉÄÉå=ÇÉê= 30=~ìÅÜ=åçÅÜ=ÉáåÉå=~åÇÉêÉå=jÉêâã~äëïÉêí=ÖáÄíI=ÇÉê=ÖÉå~ìëç=çÑí=~ìÑíêáíí=Ó=å®ãJ äáÅÜ=ÇáÉ=25K=táÉ=ëçääíÉ=ëáÉ=~ìÅÜ\== a~ÄÉá=áëí=ÇáÉ=^åòÉáÖÉ=ÇÉê=30=~ìÅÜ=åçÅÜ=êÉáå=òìÑ®ääáÖ=Ó=Éë=ïáêÇ=å®ãäáÅÜ=îçå=ÇÉå=Ü®ìÑáÖëíÉå= jÉêâã~äëïÉêíÉå=ÇÉêàÉåáÖÉ=~åÖÉòÉáÖíI=ÇÉê=ÉÜÉê=~ìÑíêáííW=tΩêÇÉ=ã~å=ÇáÉ=fåÜ~äíÉ=ÇÉê=wÉääÉå=E5= ìåÇ=E6=îÉêí~ìëÅÜÉåI=Ç~åå=ïΩêÇÉ=ÇáÉ=25=~åÖÉòÉáÖíK== bë=áëí=~äëç=ÄÉêÉáíë=ÑÉëíòìÜ~äíÉåI=Ç~ëë=ÇáÉ=^ìëë~ÖÉâê~Ñí=ÇÉê= MODALWERTJcìåâíáçå=ÄÉêÉáíë=ÄÉá= åìãÉêáëÅÜÉå=a~íÉå=åáÅÜí=ÄÉÖÉáëíÉêåÇ=áëíK== aáÉ=q~ÄÉääÉå=PKON=ìåÇ=PKOO=òÉáÖÉåI=ï~ë=ÇáÉ=cìåâíáçå= MODALWERT(...)=ÄÉá=a~íìãë~åÖ~ÄÉå= ìåÇ=ÄÉá=åáÅÜíåìãÉêáëÅÜÉå=a~íÉå=ãáííÉáäíK===== ^ìÑ=åáÅÜíåìãÉêáëÅÜÉ=a~íÉå=êÉ~ÖáÉêí=ÇáÉ=cìåâíáçå=MODALWERT(...)=ãáí=ÇÉê=cÉÜäÉêãÉäÇìåÖ=#NVK== _Éá=a~íìãë~åÖ~ÄÉå=íê®Öí=ÇáÉ=cìåâíáçå= MODALWERT(...)=Éêëí=Éáåã~ä=ÇÉå=ãÉáëíÖÉå~ååíÉå=a~J íìãëïÉêí=EçÇÉê=Ñ~äëÅÜ=Ó=ÇÉå=ÉêëíÉå=îçå=ãÉÜêÉêÉå=ãÉáëíÖÉå~ååíÉå=a~íìãëïÉêíÉåF=ÉáåK==
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3.4
Häufigkeiten von Paaren: Pivot-Tabellen
3.4.1
Aufgabenstellung und Bezeichnungen
q~ÄÉääÉ= PKOP= òÉáÖí= ÉáåÉ= EÇÉåâÄ~êÉF= §ÄÉêëáÅÜí= ΩÄÉê= rãë~íòãáííÉáäìåÖÉå= îçå= îáÉê= jáí~êÄÉáJ íÉêåX= Ç~ÄÉá= ïáêÇ= ~åÖÉåçããÉåI= Ç~ëë= ëáÉ= áã= bêÑçäÖëÑ~ääÉ= ìåîÉêòΩÖäáÅÜ= ÇÉå= jçå~í= ìåÇ= ÇÉå= tÉêí=ÇÉë=ÉêòáÉäíÉå=bêÖÉÄåáëëÉë=ãÉäÇÉåK== a~ÄÉá=ÉåíëíÉÜí=~äëç=Éáå=ìåΩÄÉêíêçÑÑÉå=åáÅÜíë=ë~ÖÉåÇÉê=a~íÉåÄÉëí~åÇK= aÉê= a~íÉåÄÉëí~åÇ= áëí= áå= ÇáÉëÉê= cçêã= ÑΩê= ^ìëïÉêíìåÖÉå= î∏ääáÖ= ìåÄê~ìÅÜÄ~êW= tÉÇÉê= áëí= òì= ÉêâÉååÉåI=ïáÉ=îáÉäÉ=jÉäÇìåÖÉå=ΩÄÉêÜ~ìéí=îçêäáÉÖÉåI=åçÅÜ=ä®ëëí=ëáÅÜ=~ÄäÉëÉåI=ïÉäÅÜÉå=rãJ ë~íò=ïÉäÅÜÉê=jáí~êÄÉáíÉê=áå=ïÉäÅÜÉã=jçå~í=í~íë®ÅÜäáÅÜ=ÉêòáÉäí=Ü~íK== a~ÖÉÖÉå=ÄÉ~åíïçêíÉí=ÇáÉ=áå=q~ÄÉääÉ=PKOQ=Ç~êÖÉëíÉääíÉ=máîçíJq~ÄÉääÉ=EÑêΩÜÉê=~ìÅÜ=~äë=hêÉìòJ í~ÄÉääÉ=ÄÉòÉáÅÜåÉíF=ÖÉå~ì=ÇáÉëÉ=cê~ÖÉåK== páÉ=áåíÉêéêÉíáÉêí=ëáÅÜ=ÖÉïáëëÉêã~≈Éå=îçå=ëÉäÄëíX=äÉáÅÜí=òì=ÉêâÉååÉå=ëáåÇ=ÇáÉ=jçå~íÉ=çÜåÉ= jÉäÇìåÖÉåI=ÇáÉ=g~ÜêÉëJpìããÉå=ÇÉê=jáí~êÄÉáíÉêI=ÇáÉ=jçå~íëìãë®íòÉI=ÇÉê=dÉë~ãíJg~ÜêÉëìãJ ë~íò=îçå=QQMURISM=AK==
3.4.2
Herstellung einer einfachen Pivot-Tabelle
tÉåå=ÇÉê=a~íÉåÄÉëí~åÇI=ïáÉ=ëÅÜçå=Ü®ìÑáÖ=ÖÉÑçêÇÉêíI=ÇìêÅÜ=ãáåÇÉëíÉåë=ÉáåÉ=iÉÉêòÉáäÉ=ìåÇ= ÇìêÅÜ=ãáåÇÉëíÉåë=ÉáåÉ=iÉÉêëé~äíÉ=îçå=ã∏ÖäáÅÜÉêïÉáëÉ=~åÇÉêÉå=báåíê®ÖÉå=áå=ÇÉê=q~ÄÉääÉ=ëÉJ é~êáÉêí= áëíI= Ç~åå= êÉáÅÜí= Éë= òìê= bêòÉìÖìåÖ= ÇÉê= máîçíJq~ÄÉääÉ= ~ìëI= ÇÉå= q~ÄÉääÉåâìêëçê=áå=áêJ ÖÉåÇÉáåÉ=wÉääÉ=ÇÉë=a~íÉåÄÉëí~åÇÉë=EòK=_K=áå=ÉáåÉ=wÉääÉ=ÇÉê=§ÄÉêëÅÜêáÑíÉåF=òì=ëÉíòÉåK==
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3.4.3
Feldeinstellungen
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3.4.4
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Präsentation von Pivot-Tabellen
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3.4.5
Abzählen mittels Pivot-Tabellen
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3.4.6
Variable Pivot-Tabellen
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4
Grafische Darstellungen
4.1
Histogramme: Werkzeug HISTOGRAMM
tÉåÇÉå=ïáê=ìåë=åçÅÜ=Éáåã~ä=ÇÉã=EäÉáÇÉê=ëí~íáëÅÜÉåF=tÉêâòÉìÖ=HISTOGRAMM=ìåÇ=ÇÉê=q~ÄÉääÉ= PKNR=~ìë=ÇÉã=^ÄëÅÜåáíí=PKOKQ==~ìÑ=pÉáíÉ=RM=òìK== pí~íáëÅÜ= ÜÉá≈íI= Ç~ë= tÉêâòÉìÖ= ~âíì~äáëáÉêí= ÇáÉ= bêÖÉÄåáëëÉ= ÄÉá= ûåÇÉêìåÖÉå= áã= a~íÉåÄÉJ ëí~åÇ=åáÅÜí=~ìíçã~íáëÅÜI=ëçåÇÉêå=ãìëë=Ç~åå=ÉêåÉìí=~âíáîáÉêí=ïÉêÇÉåK==
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a~ë=sçêÖÉÜÉå=Ç~òìW=jáí=ÇÉê=kÉÄÉåJj~ìëí~ëíÉ=EáK=~ääÖK=êÉÅÜíëF=ïáêÇ=ÉáåÉê=ÇÉê=_~äâÉå=~åÖÉJ âäáÅâíI= Ç~åå= âçããí= ã~å= òìã= jìëíÉê~åÖÉÄçí= ΩÄÉê= a^qbkobfebk= cloj^qfbobkjrpqbo= c§iibccbhqbjrpqboK= táêÇ=Ç~ë=tÉêâòÉìÖ= HISTOGRAMM=åáÅÜí=ÄÉåìíòíI=Ç~åå=ãìëë=ã~å=ÑΩê=Öê~ÑáëÅÜÉ=a~êëíÉääìåÖÉå= ÇÉå=aá~Öê~ããJ^ëëáëíÉåíÉå=îÉêïÉåÇÉå=çÇÉê=ãáí=ÇÉê= F11 JjÉíÜçÇÉ=~êÄÉáíÉåK== a~=ÇÉê=rãÖ~åÖ=ãáí=ÇÉã=aá~Öê~ããJ^ëëáëíÉåíÉåI=ïÉåå=åáÅÜí=ÄÉêÉáíë=ÄÉâ~ååíI=Ç~åå=ÇçÅÜ=ëÉÜê= äÉáÅÜí=òì=ÉêäÉêåÉå=áëíI=ëçää=~äíÉêå~íáî=ÜáÉê=ÇáÉ=ÉáåÑ~ÅÜÉ= F11 JjÉíÜçÇÉ=îçêÖÉëíÉääí=ïÉêÇÉåK== aáÉ= F11 JjÉíÜçÇÉ=äáÉÑÉêí=ëçÑçêí=ÉáåÉ=dê~Ñáâ=ã~ñáã~äÉê=dê∏≈É=~ìÑ=ÉáåÉã=~åÇÉêÉå=q~ÄÉäJ äÉåÄä~ííI=ÇáÉ=~åëÅÜäáÉ≈ÉåÇ=áå=áÜêÉê=dÉëí~äíìåÖ=îÉê®åÇÉêí=ïÉêÇÉå=â~ååK== aÉê= aá~Öê~ããJ^ëëáëíÉåí= Ç~ÖÉÖÉå= Ñê~Öí= îçê= ÇÉê= eÉêëíÉääìåÖ= ÇÉê= dê~Ñáâ= å~ÅÜ= ÇÉå= dÉëí~äJ íìåÖëïΩåëÅÜÉåI=ìåÇ=äáÉÑÉêíI=ïÉåå=åáÅÜí=áã=äÉíòíÉå=pÅÜêáíí=~åÇÉêë=ÖÉÑçêÇÉêíI=Éêëí=Éáåã~ä=ÉáåÉ= âäÉáåÉ=dê~Ñáâ=~ìÑ=ÇÉã=q~ÄÉääÉåÄä~íí=ãáí=ÇÉã=a~íÉåÄÉëí~åÇK== _ÉáÇÉå=jÉíÜçÇÉå=ÖÉãÉáåë~ã=áëí=àÉÇçÅÜ=ÇáÉ=~ì≈ÉêçêÇÉåíäáÅÜ=ïáÅÜíáÖÉ=báÖÉåëÅÜ~ÑíI=Ç~ëë=ÇáÉ= îçå=áÜåÉå=ÉêòÉìÖíÉå=dê~ÑáâÉå=åáÅÜí=ëí~íáëÅÜ=ëáåÇW= _Éá=ûåÇÉêìåÖÉå=áã=a~íÉåÄÉëí~åÇ=é~ëëÉå=ëáÅÜ=ÇáÉ=dê~ÑáâÉå=ëçÑçêí=ìåÇ=~ìíçã~íáëÅÜ=ÇÉê= åÉìÉå=páíì~íáçå=~åK===
4.2
Die F11 -Methode zur Herstellung von Grafiken
4.2.1
Zusammenhängende Daten
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4.4
Skalierung
4.4.1
Bedeutung
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4.4.2
Logarithmische Skalierung
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4.5
Grafische Darstellung von Pivot-Tabellen
fã=^ÄëÅÜåáíí=PKQKR=~ìÑ=pÉáíÉ=RV=ïìêÇÉ=ÖÉëÅÜáäÇÉêíI=ïáÉ=ãáííÉäë=ÉáåÉê=máîçíJq~ÄÉääÉ=ÇáÉ=~ÄëçJ äìíÉ= e®ìÑáÖâÉáí= ÇÉë= ^ìÑíêÉíÉåë= îçå= Ó= ÄÉáëéáÉäëïÉáëÉ= Ó= wÉåëìêÉåâçãÄáå~íáçåÉå= ÉêãáííÉäí= ïÉêÇÉå=â~ååK=q~ÄÉääÉ=PKOU=ïáÉÇÉêÜçäí=åçÅÜ=Éáåã~ä=Ç~ë=bêÖÉÄåáëK=== pÉíòí=ã~å=åìå=áã=sÉêíê~ìÉå=~ìÑ=ÇáÉ=iÉáëíìåÖëÑ®ÜáÖâÉáí=ÇÉê= F11 JjÉíÜçÇÉ=ÇÉå=q~ÄÉääÉåâìêJ ëçê=áå=Ç~ë=fååÉêÉ=ÇÉê=máîçíJq~ÄÉääÉ=ìåÇ=ÇêΩÅâí=ÇáÉ=q~ëíÉ= F11 =I=Ç~åå=ÉêÖáÄí=ëáÅÜ=òìÉêëí=ÉáJ åÉ=ëÉÜê=ÉáÖÉå~êíáÖÉ=dê~Ñáâ=E_áäÇ=QKONFK=
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4.6
Darstellung von absoluten Summenhäufigkeiten
4.6.1
Bereits berechnete Summenhäufigkeiten
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4.6.2
100-Prozent-Diagramme
j~å=â~åå=ÇáÉ=_ÉêÉÅÜåìåÖ=ÇÉê=pìããÉåÜ®ìÑáÖâÉáíÉå=ìãÖÉÜÉå=ìåÇ=íêçíòÇÉã=ÉáåÉ=dê~Ñáâ= ÖäÉáÅÜÉê=^ìëë~ÖÉ=ÉêÜ~äíÉåI=ïÉåå=ã~å=ëçÑçêí=Éáå=NMMJmêçòÉåíJaá~Öê~ãã=ÜÉêëíÉääÉå=ä®ëëíK== a~òì=áëí=äÉÇáÖäáÅÜ=ÇÉê=a~íÉåÄÉëí~åÇ=áã=òìë~ããÉåÜ®åÖÉåÇÉå=_ÉêÉáÅÜ=îçå= A1:B11=òì=ã~êJ âáÉêÉåK=k~ÅÜ=_Éí®íáÖìåÖ=ÇÉê= F11 Jq~ëíÉ=ïáêÇ=~åëÅÜäáÉ≈ÉåÇ=ãáííÉäë=af^do^jjaf^do^jjJ qvm=ÇáÉ=a~êëíÉääìåÖ=Säulen, 100%, Gestapelt in 2D- oder 3D-Form=ÖÉï®ÜäíK== wìÉêëí= ÉêÜ®äí= ã~å= Éáå= ëÉÜê= Éåíí®ìëÅÜÉåÇÉë= _áäÇ= Ó= òÉÜå= åÉÄÉåÉáå~åÇÉê= ëíÉÜÉåÇÉI= ~Äëçäìí= ÖäÉáÅÜ=ÜçÜÉ=p®ìäÉåK=^ìëë~ÖÉ=ÖäÉáÅÜ=kìääK= a~ë=®åÇÉêí=ëáÅÜ=ëçÑçêíI=ïÉåå=ã~å=af^do^jja^qbknrbiib=ï®Üäí=ìåÇ=ÇáÉëã~ä=ÇáÉ=^åÖ~ÄÉ= Reihe in=~ìÑ= Zeilen=ìãëíÉääíK=a~ë=sçêëÅÜ~ìÄáäÇ=ä®ëëí=Éë=Ç~åå=ëÅÜçå=ÉêâÉååÉåI=ìåÇ=ÇáÉ=ÑÉêJ
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4.6.3
100-Prozent-Diagramme im Zeitablauf
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tÉåå=ëáÅÜÉê=áëíI=Ç~ëë=ÇÉê=a~íÉåÄÉëí~åÇ=ëÉé~êáÉêí=áëíI=ÇK=ÜK=ÇìêÅÜ=ãáåÇÉëíÉåë=ÉáåÉ=iÉÉêòÉáäÉ= ìåÇ=iÉÉêëé~äíÉ=îçå=~åÇÉêÉå=a~íÉå=ÇÉê=q~ÄÉääÉ=ÖÉíêÉååí=áëíI=Ç~åå=â~åå=ÇÉê=q~ÄÉääÉåâìêëçê= áå=ÉáåÉ=wÉääÉ=áã=fååÉêÉå=ÇÉë=a~íÉåÄÉëí~åÇÉë=ÖÉëÉíòí=ïÉêÇÉåK== k~ÅÜ=aêìÅâ=~ìÑ=ÇáÉ=q~ëíÉ= F11 =ÉåíëíÉÜí=òìÉêëí=ÉáåÉ=~Äëçäìí=ìåëáååáÖÉ=sáÉäÑ~äí=îçå=p®ìäÉåK== t®Üäí= ã~å= ~åëÅÜäáÉ≈ÉåÇ= ~ÄÉê= ãáííÉäë= af^do^jjaf^do^jjqvmpûribk= NMMB= dbpq^mbiq= ÑΩê=àÉÇÉå=jçå~í=Éáå=NMMBJaá~Öê~ãã=~ìë=ìåÇ=îÉêÖáëëí=~åëÅÜäáÉ≈ÉåÇ=åáÅÜíI=ëáÅÜ=ãáííÉäë=af^J do^jja^qbknrbiiba^qbk_bobf`e= òì= ΩÄÉêòÉìÖÉåI= Ç~ëë= Ççêí= ~ìÅÜ= í~íë®ÅÜäáÅÜ= Reihe in Zeilen= ~ìëÖÉï®Üäí= áëíI= Ç~åå= ëíÉÜÉå= éä∏íòäáÅÜI= ïáÉ= áå= _áäÇ= QKOS= òì= ëÉÜÉåI= í~íë®ÅÜäáÅÜ= ëÉÅÜë= NMMBJaá~Öê~ããÉ=åÉÄÉåÉáå~åÇÉêK= aáÉ=báåòÉäÜÉáíÉå=ÇÉê=ÖÉëí~äíÉåÇÉå=j~≈å~ÜãÉåI=ïáÉ=ÇáÉ=cçêã~íáÉêìåÖ=ÇÉê=^ÅÜëÉåÄÉëÅÜêáÑJ íìåÖÉåI= ÇáÉ= cçêã~íáÉêìåÖ= ÇÉê= iÉÖÉåÇÉ= çÇÉê= ÇáÉ= rãï~åÇäìåÖ= ÇÉê= Ü®ëëäáÅÜ= Öê~ìÉå= oΩÅâJ ï~åÇ=áå=ÉáåÉå=ÑäáÉ≈ÉåÇÉå=§ÄÉêÖ~åÖ=Ó=ëáÉ=ëçääÉå=ÜáÉê=åáÅÜí=áã=báåòÉäåÉå=ÖÉëÅÜáäÇÉêí=ïÉêJ ÇÉåX= ãáí= Éíï~ë= §ÄìåÖ= â~åå= àÉÇÉê= kìíòÉê= ÇáÉëÉë= _ìÅÜÉë= ÇáÉ= dê~Ñáâ= ëÉäÄëí= áå= ÇáÉ= ÖÉòÉáÖíÉ= cçêã=ÄêáåÖÉåK== wì=Éêï®ÜåÉå=ï®êÉ=àÉÇçÅÜ=ìåÄÉÇáåÖí=åçÅÜI=Ç~ëë=å~ÅÜ=ÇÉã=^åâäáÅâÉå=ÉáåÉê=ÄÉäáÉÄáÖÉå=p®ìJ äÉ=ìåÇ=ÇÉê=kÉÄÉåJj~ìëí~ëíÉ=ãáí=a^qbkobfebk=cloj^qfbobk=ΩÄÉê=lmqflk=Ç~ë=bfkc§dbk=slk= sbo_fkarkdpifkfbk=îÉê~åä~ëëí=ïÉêÇÉå=â~ååK== a~ãáí= ÉêÜ®äí= ã~åI= ëçÑÉêå= Ç~åå= ÇáÉ=dáííÉêåÉíòäáåáÉå=ÉåíÑÉêåí= ïÉêÇÉåI= ÉáåÉ= ëÉÜê= ëÅÜ∏åÉ= §J ÄÉêëáÅÜíI=ïáÉ=ëáÅÜ=ÇáÉ=^åíÉáäÉ=ÇÉê=ÉáåòÉäåÉå=^ÄíÉáäìåÖÉå=~ã=dÉë~ãíÉêÖÉÄåáë=îçå=jçå~í=òì= jçå~í=îÉê®åÇÉêí=Ü~ÄÉåK=
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5
Relative Häufigkeiten, empirische Verteilung
5.1
Berechnung relativer Häufigkeiten
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5.2
Excel rechnet falsch !?
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6
Statistische Maßzahlen
6.1
Mittelwerte
6.1.1
Median und arithmetisches Mittel (Durchschnitt)
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açÅÜ=ÇÉê=^ìëâìåÑíëëìÅÜÉåÇÉ=âÉååí=ëáÅÜ=áå=ÇÉê=pí~íáëíáâ=~ìëI=ìåÇ=Ñê~Öí=òìë®íòäáÅÜ=å~ÅÜ=ÇÉã= jÉÇá~åK= a~=ãìëë= ÇÉê= `ÜÉÑ= ëáÅÜ= çÑÑÉåÄ~êÉåI= áå= dÉÇ~åâÉå= ~ääÉ= dÉÜ®äíÉê= å~ÅÜ= áÜêÉê= dê∏≈É= çêÇåÉå=ìåÇ=Ç~åå=ÇÉå=í~íë®ÅÜäáÅÜ=ãáííäÉêÉå=tÉêí=EwÉåíê~äïÉêíF=ÑÉëíëíÉääÉåW= 800
1000
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6.2.3
Empirische Standardabweichung und Varianz
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SKO==píêÉììåÖëã~≈É=
NMV
=
= q~ÄK=SKTÄW=bãéáêáëÅÜÉ=s~êá~åò=ìåÇ=pí~åÇ~êÇ~ÄïÉáÅÜìåÖ=ÉäÉãÉåí~êW=cçêãÉäå=
= q~ÄK=SKTÅW=bãéáêáëÅÜÉ=s~êá~åò=ìåÇ=pí~åÇ~êÇ~ÄïÉáÅÜìåÖ=ÉäÉãÉåí~êW=tÉêíÉ= få=q~ÄÉääÉ=SKT~=ïáêÇ=ÇÉê=rãÖ~åÖ=ãáí=ÄÉáÇÉå=bñÅÉäJcìåâíáçåÉå=ÇÉãçåëíêáÉêíK== få= ÇÉå= q~ÄÉääÉå= SKTÄ= ìåÇ= SKTÅ= ïáêÇ= ÇáÉ= ÉäÉãÉåí~êÉ= _ÉêÉÅÜåìåÖ= îçå= ÉãéáêáëÅÜÉê= s~êá~åò= ìåÇ=ÉãéáêáëÅÜÉê=pí~åÇ~êÇ~ÄïÉáÅÜìåÖ=å~ÅÜîçääòáÉÜÄ~ê=îçêÖÉÑΩÜêíK==
6.2.4
Einschub: Normalverteilung
tÉååÖäÉáÅÜ= ÉãéáêáëÅÜÉ= s~êá~åò= ìåÇ= ÉãéáêáëÅÜÉ= pí~åÇ~êÇ~ÄïÉáÅÜìåÖ= ÜáåëáÅÜíäáÅÜ= ÇÉê= ~åëÅÜ~ìäáÅÜÉå= aÉìíìåÖ= ïÉåáÖÉê= ~ìëë~ÖÉâê®ÑíáÖ= ~äë= ÇáÉ= ãáííäÉêÉ= ~ÄëçäìíÉ= ^ÄïÉáÅÜìåÖ= ëáåÇI=ÄÉëáíòí=áåëÄÉëçåÇÉêÉ=ÇáÉ=ÉãéáêáëÅÜÉ=pí~åÇ~êÇ~ÄïÉáÅÜìåÖ=áå=sÉêÄáåÇìåÖ=ãáí=ÇÉã= ~êáíÜãÉíáëÅÜÉå=jáííÉä=~ì≈ÉêçêÇÉåíäáÅÜÉ=_ÉÇÉìíìåÖI=ïÉåå=Éë=ìã=ÇÉå=_ÉÖêáÑÑ=ÇÉê=kçêã~äJ îÉêíÉáäìåÖ=ÖÉÜíK== pçääíÉå= ÇáÉ=tÉêíÉ=ÇÉë=a~íÉåÄÉëí~åÇÉë= å®ãäáÅÜ= ~ìë=ÉáåÉê=píáÅÜéêçÄÉ= Éåíëí~ããÉåI= Ç~åå= áëí= ÑΩê=ÇáÉ=ïÉëÉåíäáÅÜÉå=_Éä~åÖÉ=ÇÉê=ÄÉìêíÉáäÉåÇÉå=pí~íáëíáâ=ÖêìåÇë®íòäáÅÜ=îçå=_ÉÇÉìíìåÖI=çÄ= ã~å=îçå=ÉáåÉê=åçêã~äîÉêíÉáäíÉå=dêìåÇÖÉë~ãíÜÉáí=~ìëÖÉÜÉå=â~åå=EîÖäK=òK=_K=xNz=I=xNNzI=xOMzFK== cΩê=ÇáÉëÉå=c~ää=ëíÉÜÉå=Ç~åå=îáÉäÉ=qÉëíãÉíÜçÇÉå=ëçÑçêí=òìê=sÉêÑΩÖìåÖK== fã=páååÉ=ÇÉê=ÄÉìêíÉáäÉåÇÉå=pí~íáëíáâ=ï®êÉ=Éë=ÑçäÖäáÅÜ=âçêêÉâíI=ïÉåå=Éáå=òì=ìåíÉêëìÅÜÉåJ ÇÉê=a~íÉåÄÉëí~åÇ=ëíÉíë=~äë=ÉêëíÉë=~ìÑ=kçêã~äîÉêíÉáäìåÖ=ÖÉíÉëíÉí=ïΩêÇÉK== aáÉëÉê=ëç=ÖÉå~ååíÉ=`ÜáJnì~Çê~íJ^åé~ëëìåÖëíÉëí=áëí=êÉÅÜí=~ìÑï®åÇáÖ=EëáÉÜÉ=xNNzF=K= bñÅÉä=äáÉÑÉêí=~ÄÉê=ÉáåÉ=j∏ÖäáÅÜâÉáíI=îáëìÉää=ÉáåÉ=ëÅÜåÉääÉ=sçê~ÄJfåÑçêã~íáçå=òì=ÉêÜ~äíÉåI=ÇáÉ= ÇÉã=mê~âíáâÉê=ÄáëïÉáäÉå=ëÅÜçå=~ìëêÉáÅÜíK== j~å=â~åå=å®ãäáÅÜ=îçå=ÉáåÉã=a~íÉåÄÉëí~åÇ=Ó=ÖêçÄ=ÖÉëéêçÅÜÉå=Ó=~ååÉÜãÉåI=Ç~ëë=Éê=~ìë= ÉáåÉê=åçêã~äîÉêíÉáäíÉå=dêìåÇÖÉë~ãíÜÉáí=ëí~ããÉå=â∏ååíÉI=ïÉåå=ÇáÉ=ÑçäÖÉåÇÉå=ÇêÉá=báÖÉåJ ëÅÜ~ÑíÉå=ÉêÑΩääí=ëáåÇW==
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVR=
S==pí~íáëíáëÅÜÉ=j~≈ò~ÜäÉå=
NNM
NK=^ääÉ=tÉêíÉ=âçåòÉåíêáÉêÉå=ëáÅÜ=ëí~êâ=ìã=Ç~ë=~êáíÜãÉíáëÅÜÉ=jáííÉäK= OK=aáÉ=tÉêíÉ=ÄÉÑáåÇÉå=ëáÅÜ=ìåÖÉÑ®Üê=òì=ÖäÉáÅÜÉå=qÉáäÉå=äáåâë=ìåÇ=êÉÅÜíë=îçã=~êáíÜãÉJ= ====íáëÅÜÉå=jáííÉäK= PK=^ì≈ÉêÜ~äÄ=ÇÉê=ëç=ÖÉå~ååíÉå=aêÉáJpáÖã~JdêÉåòÉå=ÖáÄí=Éë=ëç=Öìí=ïáÉ=âÉáåÉ=tÉêíÉ=ãÉÜêK== aáÉ=pí~íáëíáâ=~êÄÉáíÉí=éêáåòáéáÉää=åáÅÜí=ãáí=ÇÉê=sçâ~ÄÉä=łà~K=^äëç=òáÉÜí=ã~å=~ìë=ÇÉã=bêÑΩääíJ ëÉáå=~ääÉê=ÇêÉá=hêáíÉêáÉå=åáÉã~äë=ÇÉå=pÅÜäìëëI=Ç~ëë=kçêã~äîÉêíÉáäìåÖ=îçêäáÉÖÉK=pçåÇÉêå=ã~å= ÑçêãìäáÉêí=ëíÉíë=łåÉáå=çÇÉê=łåáÅÜí=åÉáåW==
=
páåÇ= ÇáÉ= ÇêÉá= oÉÖÉäå= ÉêÑΩääíI= Ç~åå= ëéêáÅÜí=Éêëí=Éáåã~ä=åáÅÜíë=ÖÉÖÉå=ÇáÉ=^åå~ÜãÉI= Ç~ëë= kçêã~äîÉêíÉáäìåÖ=îçêäáÉÖÉå=â~ååK== píÉääí= ã~å= ÑΩê= ÉáåÉå= a~íÉåÄÉëí~åÇ= àÉÇçÅÜ= ÇÉå= sÉêëíç≈= ÖÉÖÉå= ÉáåÉ= ÇáÉëÉê= ÇêÉá= oÉÖÉäå= ÑÉëíI=Ç~åå=áëí=ÇáÉ=^åå~ÜãÉI=Éê=Éåíëí~ããÉ=ÉáåÉê=åçêã~äîÉêíÉáäíÉå=dêìåÇÖÉë~ãíÜÉáíI=åáÅÜí= ÖÉêÉÅÜíÑÉêíáÖíK==
tçÄÉá= ÇáÉëÉ= pÅÜäìëëÑçäÖÉêìåÖÉå= ÉáåÉå= ëí~íáëíáëÅÜÉå= qÉëí= ÖÉã®≈= ÇÉå= ëíêÉåÖÉå= oÉÖÉäå= ÇÉê= ÄÉìêíÉáäÉåÇÉå=pí~íáëíáâ=íêçíòÇÉã=åáÅÜí=ÉêëÉíòÉå=â∏ååÉå=Ó=~ÄÉê=ÜáÉê=ëçää=à~=åìê=Éáå=ëÅÜåÉääÉê= ìåÇ=ÉáåÑ~ÅÜÉê=tÉÖ=òì=ÉáåÉê=îáëìÉääÉå=sÉêãìíìåÖ=ÖÉòÉáÖí=ïÉêÇÉåK==
= q~ÄK=SKU~W=cçêãÉäå=
= q~ÄK=SKUÄW=tÉêíÉ= aáÉ= q~ÄÉääÉå= SKU~LÄ= òÉáÖÉå= ÉáåÉå= a~íÉåÄÉëí~åÇI= ÇÉê= òïÉÅâë= k~ÅÜîçääòáÉÜÄ~êâÉáí= ÇáÉëã~ä= åáÅÜí=áå=ÉáåÉ=wÉáäÉ=çÇÉê=pé~äíÉI=ëçåÇÉêå=áå=ÇÉå=oÉÅÜíÉÅâÄÉêÉáÅÜ=A3:E12=ÉáåÖÉíê~ÖÉå=ïìêÇÉK===== pÉÜÉå=ïáê=ìåë=Ç~òì=Éáå=_ÉáëéáÉä=òìê=fääìëíê~íáçå=ÇÉë=sçêÖÉÜÉåë=~åK== cΩê= ÉáåÉ= pÅÜ®íòìåÖ=ÇÉê=aêÉáJpáÖã~JdêÉåòÉå= îÉêïÉåÇÉí= ã~å= Ç~ÄÉá= Ç~ë= äÉáÅÜí= îÉêÑΩÖÄ~êÉ= fåíÉêî~ää== [arithm.Mittel – 3*emp.Standardabweichung , arithm.Mittel + 3*emp.Standardabweichung]
j~å=äáÉëí=áå=ÇÉê=q~ÄÉääÉ=SKUÄ=~ÄW=a~ë=~êáíÜãÉíáëÅÜÉ=jáííÉä=áëí=ÖäÉáÅÜ=29,8=ìåÇ=ÇáÉ=ÉãéáêáëÅÜÉ= pí~åÇ~êÇ~ÄïÉáÅÜìåÖ=áëí=ÖäÉáÅÜ=4,7K==
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVR=
SKO==píêÉììåÖëã~≈É=
NNN
a~ãáí=ÉêÜ®äí=ã~å=ëçÑçêí=pÅÜ®íòìåÖÉå=ÑΩê=ÇáÉ=ÄÉáÇÉå=aêÉáJpáÖã~JdêÉåòÉåW== pÅÜ®íòìåÖ=ÇÉê=äáåâÉå=PJpáÖã~JdêÉåòÉ=W==
29,8 - 3*4,7 = 15,7==
pÅÜ®íòìåÖ=ÇÉê=êÉÅÜíÉå=PJpáÖã~JdêÉåòÉW=
29,8 + 3*4,7 = 43,9=
a~ë=ÜÉá≈í=~äëçW=tÉåå=ëáÅÜ=åáÅÜí=å~ÜÉòì=~ääÉ=a~íÉå=áã=_ÉêÉáÅÜ=îçå= 15,7=Äáë= 43,9=ÄÉÑáåÇÉåI= ïáêÇ=ã~å=ÄÉêÉáíë=ÇÉê=sÉêãìíìåÖ=~ìÑ=kçêã~äîÉêíÉáäìåÖ=ïáÇÉêëéêÉÅÜÉå=ãΩëëÉåK=eáåòì=âçãJ ãÉå=Ç~åå=~ÄÉê=åçÅÜ=ÇáÉ=_ÉÇáåÖìåÖÉå=N=ìåÇ=OK== ^ääÉ=ÇêÉá=_ÉÇáåÖìåÖÉå=òìë~ããÉå=â~åå=ã~å=îáëìÉää=ãáí=eáäÑÉ=ÇÉë=tÉêâòÉìÖë= HISTOGRAMM= ΩÄÉêéêΩÑÉåK== a~òì=íÉáäí=ã~å=òìÉêëí=ÇÉå=ìåíÉê=sÉêïÉåÇìåÖ=îçå=jáííÉäïÉêí=ìåÇ=ÉãéáêáëÅÜÉê=pí~åÇ~êÇ~ÄJ ïÉáÅÜìåÖ= ÖÉëÅÜ®íòíÉå= aêÉáJpáÖã~J_ÉêÉáÅÜ= áå= ãáåÇÉëíÉåë=OM=ÖäÉáÅÜÉ=qÉáäÉ= ÉáåX= áå= ìåëÉêÉã= _ÉáëéáÉä=ÉêïÉáëí=Éë=ëáÅÜ=~äë=ÖΩåëíáÖI=~äë=ÉêëíÉ=hä~ëëÉåÖêÉåòÉ= 15=òì=ï®ÜäÉåI=Ç~åå= 16,5I=Ç~åå= 18,0=ìëïK=Äáë=45K==
=
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q~ÄK=SKV~LÄW=bêòÉìÖÉå=ÇÉê=hä~ëëÉåÖêÉåòÉåW=cçêãÉä=ìåÇ=tÉêíÉ= kìå= ïáêÇ= ΩÄÉê= buqo^p^k^ivpbJcrkhqflkbkefpqldo^jj= EëáÉÜÉ= pÉáíÉ= RMF= Ç~ë= é~ëëÉåÇÉ= tÉêâòÉìÖ= ~åÖÉÑçêÇÉêíI= ÇÉê= _ÉêÉáÅÜ= ÇÉë= a~íÉåÄÉëí~åÇÉë= ëçïáÉ= ÇÉê= _ÉêÉáÅÜ= ÇÉê= hä~ëëÉåJ ÖêÉåòÉå=ïáêÇ=ÉáåÖÉíê~ÖÉå=EëK=_áäÇ=SKNFK=== ^ìÑ= ÉáåÉã= ÖÉëçåÇÉêíÉå= q~ÄÉääÉåÄä~íí= ÉåíëíÉÜí= Ç~åå= ÇáÉ= e®ìÑáÖâÉáíëí~ÄÉääÉX= ãáí= aêìÅâ= ~ìÑ= ÇáÉ=q~ëíÉ= F11 =ÑΩÜêí=ëáÉ=ìåë=òìã=eáëíçÖê~ãã=E_áäÇ=SKOFK= aÉã=eáëíçÖê~ãã=áëí=òì=ÉåíåÉÜãÉåI=Ç~ëë=ÇáÉ=cçêÇÉêìåÖ=kìããÉê=ÇêÉá=çÑÑÉåëáÅÜíäáÅÜ=ÉêÑΩääí= áëíX= ~ìÅÜ= ÇáÉ= hçåòÉåíê~íáçå= ÇÉê= tÉêíÉ= áå= ÇÉê= k®ÜÉ= ÇÉë= ~êáíÜãÉíáëÅÜÉå= jáííÉäë= ëçïáÉ= ÇáÉ= póããÉíêáÉ=â~åå=ã~å=åáÅÜí=ÖêìåÇë®íòäáÅÜ=îçå=ÇÉê=e~åÇ=ïÉáëÉåK== sçêëáÅÜíI=Ö~åò= Öêç≈É= sçêëáÅÜí= ~ÄÉê=åìå=ãáí= ÇÉê= îçêëÅÜåÉääÉå= ^ìëë~ÖÉI= Ç~ëë=kçêã~äîÉêíÉáJ äìåÖ=îçêäáÉÖÉ=çÇÉê=îçêäáÉÖÉå=â∏ååÉK== bë= ëéêáÅÜí= ~ìÑ= ÇÉå= ÉêëíÉå= _äáÅâ= äÉÇáÖäáÅÜ= ïÉåáÖ= Ç~ÑΩêI= Ç~ëë= ã~å= ÇáÉ= kçêã~äîÉêíÉáäìåÖ= ÖêìåÇë®íòäáÅÜ=~ÄäÉÜåÉå=ãΩëëÉK=pç=áëí=ÇáÉ=péê~ÅÜÉ=ÇÉê=pí~íáëíáâK== =
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVR=
S==pí~íáëíáëÅÜÉ=j~≈ò~ÜäÉå=
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6.3
Schiefe und Wölbung
cΩê=ÄÉëíáããíÉ=c~ÅÜÖÉÄáÉíÉ=ëéáÉäí=Éë=ÉáåÉ=oçääÉI=çÄ=Ç~ë=eáëíçÖê~ãã=ÉáåÉë=a~íÉåÄÉëí~åJ ÇÉë=ëóããÉíêáëÅÜI=äáåâëJ=çÇÉê=êÉÅÜíëëÅÜáÉÑ=áëíK== a~òì=â~åå=ã~å=å~íΩêäáÅÜ=Ç~ë=eáëíçÖê~ãã=ëÉäÄëí=ÄÉåìíòÉåX=ã~å=ÉêãáííÉäí=ÇáÉ=pé~ååïÉáíÉI= äÉÖí=hä~ëëÉåÖêÉåòÉå=ÑÉëíI=åìíòí=Ç~ë=tÉêâòÉìÖ=HISTOGRAMMK== báåÑ~ÅÜÉê=áëí=Éë=Ç~åå=ÇçÅÜI=ÇáÉ=bñÅÉäJcìåâíáçå=SCHIEFE(...)=òì=îÉêïÉåÇÉåK=iáÉÑÉêí=ëáÉ=å®ãJ äáÅÜ=ÉáåÉå=tÉêí=å~ÜÉ=kìääI=Ç~åå=â~åå=ã~å=E~ìÅÜ=çÜåÉ=dê~ÑáâF=Ç~îçå=~ìëÖÉÜÉåI=Ç~ëë=Éáå= ëóããÉíêáëÅÜÉë= eáëíçÖê~ãã= ÉåíëíÉÜÉå= ïΩêÇÉK= mçëáíáîÉ= tÉêíÉ= ÇÉìíÉå= ~ìÑ= Éáå= êÉÅÜíëëÅÜáÉÑÉë= eáëíçÖê~ãã=Üáå=EëK=_áäÇ=SKQFI=åÉÖ~íáîÉ=tÉêíÉ=ä~ëëÉå=Éáå=äáåâëëÅÜáÉÑÉë=eáëíçÖê~ãã=Éêï~êíÉå= EëK=_áäÇ=SKRFK===
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bë=ÑΩääíÉå=~äëç=3=mÉêëçåÉå=ÇÉê=ãáí=N=âçÇáÉêíÉå=^êí=ìåÇ=ÑçäÖäáÅÜ=R=mÉêëçåÉå=ÇÉë=~åÇÉêÉå=dÉJ ëÅÜäÉÅÜíë=ÇáÉ=cê~ÖÉÄ∏ÖÉå=~ìëK=== _Éáã= ^äíÉê= áåíÉêÉëëáÉêÉå= ÇçÅÜ= åìê= jáåáãìãI= j~ñáãìãI= jáííÉäïÉêí= ìåÇ= jÉÇá~åK= a~ê~ìë= â~åå=ã~å=å®ãäáÅÜ=ÄÉêÉáíë=ÉåíåÉÜãÉåI=Ç~ëë=ÉáåÉ=êÉÅÜí=~ìëÖÉÖäáÅÜÉåÉ=^äíÉêëëíêìâíìê=ÉêÑ~ëëí= ïìêÇÉ=Ó=ëçåëí=ïΩêÇÉå=jÉÇá~å=ìåÇ=jáííÉäïÉêí=åáÅÜí=ëç=ÉåÖ=ÄÉáÉáå~åÇÉê=äáÉÖÉåK== g~I=ìåÇ=ÇáÉ=_ÉïÉêíìåÖÉåW=aÉê=tÉêíÉÄÉêÉáÅÜ=ÖáÄí=~åI=çÄ=Éë=ÑêÉá=ÖÉä~ëëÉåÉ=h®ëíÅÜÉå=Ö~Ä=ìåÇ= Äáë=òì=ïÉäÅÜÉê=h~íÉÖçêáÉ=ÄÉïÉêíÉí=ïìêÇÉK=jÉÜê=ãΩëëíÉ=ã~å=Ç~åå=ãáí=eáäÑÉ=ÇÉê=ZÄHLENWENNJ cìåâíáçå=ÉêÑê~ÖÉåK== q~ÄÉääÉ=SKNNÇ=ÉåíÜ®äí=ëÅÜäáÉ≈äáÅÜ=ÇáÉ=^åÖ~ÄÉåI=ÇáÉ=ΩÄêáÖ=ÄäÉáÄÉåI=ïÉåå=ã~å=ÇáÉ=ëáååäçëÉå= çÇÉê= ΩÄÉêÑäΩëëáÖÉå= çÇÉê= ìåáåíÉêÉëë~åíÉå= bêÖÉÄåáëëÉ= ÇÉë= tÉêâòÉìÖë= POPULATIONSKENNGRÖßEN= ÜÉê~ìëÖÉëíêáÅÜÉå=Ü~íK== sÉêÖäÉáÅÜí= ã~å= äÉíòíÉåÇäáÅÜ= ÇÉå= ^ìÑï~åÇI= ÇÉê= òìã= âêáíáëÅÜÉå= aìêÅÜÇÉåâÉå= ÇÉê= EçÑí= ëáååäçëÉåF=bêÖÉÄåáëÑäìí=ÇÉë=tÉêâòÉìÖë=åçíïÉåÇáÖ=ï~êI=ãáí=ÇÉã=^ìÑï~åÇI=ÇáÉ=ïÉåáÖÉå= cìåâíáçåÉå= Éáåòìíê~ÖÉåI= Ç~åå= ëáÉÜí= ã~åI= Ç~ëë= ÇáÉ= ÇáÑÑÉêÉåòáÉêíÉ= ^êÄÉáí= ãáí= ÇÉå= bñÅÉäJ cìåâíáçåÉå=ÇìêÅÜ~ìë=ÉãéÑÉÜäÉåëïÉêí=ëÉáå=â~ååK=
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7
Korrelation und Regression
7.1
Der Korrelationskoeffizient von Bravais-Pearson
7.1.1
Begriff, Bedeutung, Berechnung
_Éíê~ÅÜíÉå=ïáê=ÉáåÉå=a~íÉåÄÉëí~åÇ=ãáí=òïÉá=ÖäÉáÅÜä~åÖÉå=a~íÉåêÉáÜÉåI=ëç=â∏ååÉå=ïáê=òìJ Éêëí=ÇÉå=ÖÉãÉáåë~ãÉå=rãÑ~åÖ=EÇáÉ=^åò~ÜäF=ÉêãáííÉäåI=Ç~òì=ÇáÉ=ÄÉáÇÉå=jáåáã~=ìåÇ=j~J ñáã~I=ÇáÉ=jÉÇá~åÉ=ìåÇ=ÇáÉ=jçÇ~äïÉêíÉK=== páåÇ=ÇáÉ=a~íÉå=îçå=Ü∏ÜÉêÉã=~äë=çêÇáå~äÉã=káîÉ~ìI=ëç=áëí=ïÉáíÉê=ÇáÉ=_ÉêÉÅÜåìåÖ=ÇÉê=ÄÉáJ ÇÉå= ~êáíÜãÉíáëÅÜÉå=jáííÉäïÉêíÉ= ìåÇ= ÇÉê= ÄÉáÇÉå= ÉãéáêáëÅÜÉå=pí~åÇ~êÇ~ÄïÉáÅÜìåÖÉå= ëáååJ îçää=ìåÇ=ã∏ÖäáÅÜK=
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7.1.2
Herstellung der Punktwolke
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få=ÇÉå=wÉääÉå=A3=ìåÇ=A4=ÄÉÑáåÇÉå=ëáÅÜ=ÇáÉ=k~ãÉå=ÇÉê=a~íÉåêÉáÜÉåK=fã=_ÉêÉáÅÜ=B3:S4=ÄÉÑáåJ ÇÉå=ëáÅÜ=ÇáÉ=w~ÜäÉåïÉêíÉK== dÉëìÅÜí= áëí= ÇáÉ= mìåâíïçäâÉI= Ç~ãáí= ã~å= ëáÅÜ= ÄÉêÉáíë= éÉê= ^ìÖÉåëÅÜÉáå= ÉáåÉ= sçêëíÉääìåÖ= îçå=ÉáåÉã=ã∏ÖäáÅÜÉå=äáåÉ~êÉå=wìë~ããÉåÜ~åÖ=ã~ÅÜÉå=â~ååK==== táê=åÉÜãÉå=òìÉêëí= ïáÉÇÉê= ~åI= ïáÉ=ΩÄäáÅÜI= Ç~ëë=ÇÉê=a~íÉåÄÉëí~åÇ= ëÉé~êáÉêí= áëíI=ÇK= ÜK=Ç~ëë= ãáåÇÉëíÉåë=ÇáÉ=pé~äíÉ= T=ÉáåÉ=iÉÉêëé~äíÉ=áëíI=ëç=Ç~ëë=ÇÉê=a~íÉåÄÉëí~åÇ=êáåÖëìã=ÇìêÅÜ=iÉÉêJ òÉáäÉåI= Jëé~äíÉå= çÇÉê= ÇÉå= q~ÄÉääÉåê~åÇ= îçå= ã∏ÖäáÅÜÉå= ~åÇÉêÉå= q~ÄÉääÉåáåÜ~äíÉå= ~ÄÖÉJ ÖêÉåòí=áëíK= a~åå=ïáêÇ=ãáííÉäë= F11 =ÉáåÉ=oçÜÖê~Ñáâ=áå=ÉáåÑ~ÅÜÉê=p®ìäÉåÑçêã=ÉêòÉìÖíI=ÇáÉ=òïÉá=îÉêëÅÜáÉJ ÇÉåÑ~êÄáÖÉ=p®ìäÉå=ÉåíÜ®äíK== a~åå= ãìëë= Ç~ÑΩê= ÖÉëçêÖí= ïÉêÇÉåI= Ç~ëë= ÇáÉ= a~íÉåêÉáÜÉ= ~ìë= ÇÉã= _ÉêÉáÅÜ= B3:S3= òìê= _ÉJ ëÅÜêáÑíìåÖ=ÇÉê=ï~~ÖÉêÉÅÜíÉå=EuFJ^ÅÜëÉ=ïáêÇK== a~òì= ÑçêÇÉêí= ã~å= ãáííÉäë= af^do^jja^qbknrbiibobfeb= Ç~ë= òìëí®åÇáÖÉ= bñÅÉäJaá~äçÖJ ÑÉåëíÉê=Datenquelle=~åK== wìÉêëí=ïáêÇ=Ççêí=ÇÉê=fåÜ~äí=ÇÉë=cÉåëíÉêë= WerteI=ÇK=ÜK=ÇáÉ=cçêãÉä= =Tabelle1!B3:S3I=áå=Ç~ë=ìåJ íÉêÉ=cÉåëíÉê=ãáí=ÇÉê=_ÉëÅÜêáÑíìåÖ=Beschriftung der Rubrikenachse (X)=âçéáÉêíK== fã=cÉåëíÉê=Datenreihe=ïáêÇ=ïÉáíÉê=ÇáÉ=çÄÉêÉ=oÉáÜÉ=ÇìêÅÜ=i∏ëÅÜìåÖ=áÜêÉê=§ÄÉêëÅÜêáÑí=R1=ÉåíJ ÑÉêåíK=a~ë=áëí=ëÅÜçå=~ääÉëK== aáÉ=_áäÇÉê=TKRLTKS=òÉáÖÉå=Ç~ë=aá~äçÖÑÉåëíÉê=Datenquelle=îçê=ìåÇ=å~ÅÜ=ÇÉå=sÉê®åÇÉêìåÖÉåK==
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7.2
Regression
7.2.1
Berechnung der Regressionskonstanten
e~í=ÇÉê=hçêêÉä~íáçåëâçÉÑÑáòáÉåí=ÉáåÉå=tÉêí=å~ÜÉ= 1=çÇÉê= –1I=Ç~åå=â~åå=ã~å=ÉáåÉå=äáåÉ~J êÉå=wìë~ããÉåÜ~åÖ=òïáëÅÜÉå=ÇÉå=ÄÉáÇÉå=ÖäÉáÅÜä~åÖÉå=a~íÉåêÉáÜÉå=îÉêãìíÉå=Ó=îçê~ìëJ ÖÉëÉíòíI=ÇÉê=ë~ÅÜäáÅÜÉ=eáåíÉêÖêìåÇ=ìåíÉêëíΩíòí=ÉáåÉ=ëçäÅÜÉ=sÉêãìíìåÖK== få=ÇáÉëÉã=c~ääÉ=ÉåíëíÉÜí=å~íΩêäáÅÜ=~ìÅÜ=ÇÉê=tìåëÅÜI=ÇÉå=äáåÉ~êÉå=wìë~ããÉåÜ~åÖ=ÑçêãÉäJ ã®≈áÖ=Ç~êòìëíÉääÉåK== _Éíê~ÅÜíÉå=ïáê=~ìÅÜ=ÜáÉêòì=ïáÉÇÉê=ÇÉå=a~íÉåÄÉëí~åÇ=ÇÉê=îçêáÖÉå=^ÄëÅÜåáííÉI=áå=q~ÄÉääÉ=TKP= ïáÉÇÉêÜçäí=~åÖÉÖÉÄÉåK==
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NOU
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sÉêÖê∏≈Éêå=ïáê=ÇáÉëÉå=_ÉêÉáÅÜI=ëç=ÉêâÉååÉå=ïáê=áå=q~ÄÉääÉ=TKT=Ççêí=áå=ÇÉê=q~í=ÇáÉ=ÖÉëìÅÜJ íÉå= ÄÉáÇÉå= tÉêíÉ= Ó= ÇÉå= ^ÅÜëÉå~ÄëÅÜåáíí= EÜáÉê= ~äë= Schnittpunkt= ÄÉòÉáÅÜåÉíF= ìåÇ= ÇáÉ= píÉáJ ÖìåÖ=EÜáÉê=ÄÉòÉáÅÜåÉí=~äë=X Variable 1FK==
== _áäÇ=TKNPW=bêÖÉÄåáëëÉ=ÇÉë=tÉêâòÉìÖë=REGRESSION=
= q~ÄK=TKTW=dÉëìÅÜíÉ=tÉêíÉ=áã=bêÖÉÄåáëÄä~íí=ÇÉë=tÉêâòÉìÖë=REGRESSION== råÇ= ÇáÉ= êÉëíäáÅÜÉå= OU= ^åÖ~ÄÉå\= eáÉê= Ü~í= ã~å= ÇÉë= dìíÉå= ïçÜä= òìîáÉä= ÖÉí~åX= áã= píêÉÄÉå= å~ÅÜ=ìãÑ~ëëÉåÇÉê=^ìëâìåÑí=ÑΩê=~ääÉ=ÇÉåâÄ~êÉå=mêçÑáë=ïìêÇÉ=ëçîáÉä=~å=iÉáëíìåÖëÑ®ÜáÖâÉáí=áå= Ç~ë=tÉêâòÉìÖ=REGRESSION=ÜáåÉáåÖÉé~ÅâíI=Ç~ëë=ÇÉê=^åÑ®åÖÉê=ÄÉá=ëÉáåÉê=pìÅÜÉ=å~ÅÜ=ÇÉå=ÄÉáJ ÇÉå=w~ÜäÉåïÉêíÉå= ÑΩê= píÉáÖìåÖ= ìåÇ= ^ÅÜëÉå~ÄëÅÜåáíí= îçê= ÇÉê= §ÄÉêÑΩääÉ= ~å= fåÑçêã~íáçåÉå= â~éáíìäáÉêÉå=ãìëëK== aÉã=^åÑ®åÖÉê=ëÅÜÉáåí=~äëç=ãÉÜê=Ç~ãáí=ÖÉÇáÉåí=òì=ëÉáåI=ïÉåå=Éê=~åëíÉääÉ=ÇÉë=tÉêâòÉìJ ÖÉë= REGRESSION= ÇáÉ= ÄÉáÇÉå= äÉáÅÜí= òì= åìíòÉåÇÉå= cìåâíáçåÉå= STEIGUNG(...;...)= ìåÇ= ACHSENABSCHNITT(...;...) ~åïÉåÇÉíK== a~åå=áëí=Éë=ΩÄêáÖÉåë=~ìÅÜ=î∏ääáÖ=ÖäÉáÅÜÖΩäíáÖI=çÄ=ÇÉê=a~íÉåÄÉëí~åÇ=áå=pé~äíÉå=çÇÉê=wÉáäÉå= çêÖ~åáëáÉêí=áëíK== råÇ=ÄÉá=àÉÇÉê=ûåÇÉêìåÖ=áã=a~íÉåÄÉëí~åÇ=é~ëëÉå=ëáÅÜ=ÇáÉ=ãáí=eáäÑÉ=ÇÉê=ÄÉáÇÉå=cìåâíáçJ åÉå= ÉêãáííÉäíÉå= oÉÖêÉëëáçåëâçÉÑÑáòáÉåíÉå= ëíÉíë= òìë®íòäáÅÜ= ~ìíçã~íáëÅÜ= ëçÑçêí= ~å= Ó= ï®ÜJ êÉåÇ= Ç~ë= ëí~íáëÅÜÉ= tÉêâòÉìÖ= REGRESSION= Ç~ÖÉÖÉå= å~ÅÜ= àÉÇÉê= ûåÇÉêìåÖ= âçãéäÉíí= åÉì= ~ìÑÖÉêìÑÉå=ïÉêÇÉå=ãΩëëíÉK==
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=
TKP==jìäíáéäÉ=äáåÉ~êÉ=oÉÖêÉëëáçå=
7.3
NOV
Multiple lineare Regression
få=ÇÉê=q~ÄÉääÉ=TKU=ÄÉÑáåÇÉå=ëáÅÜ=áå=ÇÉå=pé~äíÉå=AI=B=ìåÇ=C=ÇêÉá=ÖäÉáÅÜä~åÖÉ=a~íÉåêÉáÜÉåK== fÜêÉ= pé~äíÉåΩÄÉêëÅÜêáÑíÉå= ÄêáåÖÉå= Éë= ÄÉêÉáíë= òìã= ^ìëÇêìÅâW= aáÉ= tÉêíÉ= ÇÉê= ÄÉáÇÉå= ÉêëíÉå= pé~äíÉå=ëçääÉå=åìå=~åÖÉëÉÜÉå=ïÉêÇÉå=~äë=òïÉá=báåÑäìëëÖê∏≈ÉåI=ï®ÜêÉåÇ=ÇáÉ=tÉêíÉ=áå=ÇÉê= pé~äíÉ=C=ÇáÉ=wáÉäÖê∏≈É=ÄÉëÅÜêÉáÄÉå=ëçääÉåK==
= q~ÄK=TKUW=wïÉá=báåÑäìëëÖê∏≈ÉåI=ÉáåÉ=wáÉäÖê∏≈É== ^ìë= ë~ÅÜäáÅÜÉå= dêΩåÇÉå= ëÉá= ÄÉâ~ååíI= Ç~ëë= Éë= ëáååîçää= áëíI= ÉáåÉ= äáåÉ~êÉ=wìë~ããÉåÜ~åÖëJ ÑçêãÉä=ÇÉê=cçêã== ETKMTF=
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= a1 x1 + a 2 x2 + b
~åòìëíêÉÄÉåI=ãáí=ÇÉêÉå=eáäÑÉ=Ç~åå=ëé®íÉê=ÑΩê=àÉÇÉ=x1-x2JhçãÄáå~íáçå=Éáå=òìÖÉÜ∏êáÖÉê=yJtÉêí= éêçÖåçëíáòáÉêí=ïÉêÇÉå=â~ååK== a~ÄÉá=ïÉêÇÉå== y=~äë=oÉÖêÉëë~åÇ=E~ÄÜ®åÖáÖÉ=s~êá~ÄäÉFI== x1=ìåÇ=x2=~äë=oÉÖêÉëëçêÉå=Eìå~ÄÜ®åÖáÖÉ=s~êá~ÄäÉåFI== a1=ìåÇ=a2=~äë=oÉÖêÉëëáçåëâçÉÑÑáòáÉåíÉå=îçå=x1=ìåÇ=x2=ìåÇ== b=~äë=âçåëí~åíÉë=däáÉÇ== ÄÉòÉáÅÜåÉíK=== aáÉ=rãëÉíòìåÖ=ÇÉë=ëÅÜçå=~ìÑ=pÉáíÉ=NOQ=Éêï®ÜåíÉ=d~ì≈ÛëÅÜÉå=sçêëÅÜä~Öë=ÇÉê=jáåáãáÉêìåÖ= ÇÉê=cÉÜäÉêèì~Çê~íÉ=ÑΩÜêí=òì=ÉáåÉã=oÉÅÜÉåîÉêÑ~ÜêÉåI=Ç~ë=~äë=ãìäíáéäÉ=äáåÉ~êÉ=oÉÖêÉëëáçå=ÄÉJ òÉáÅÜåÉí=ïáêÇK=== cΩê= ÇáÉ= ãìäíáéäÉ= äáåÉ~êÉ= oÉÖêÉëëáçå= ëíÉääí= bu`bi= âÉáå= tÉêâòÉìÖ= ÄÉêÉáíI= ëçåÇÉêå= åìê= ÉáåÉ= cìåâíáçåK== aáÉëÉ=cìåâíáçå=ÜÉá≈í= RGP=ìåÇ=áëí=ÉáåÉ=ëç=ÖÉå~ååíÉ=j~íêáñÑìåâíáçå=J=ÇÉåå=ëáÉ=ÖáÄí=åáÅÜí= åìê=ÉáåÉå=ÉáåòáÖÉå=w~ÜäÉåïÉêíI=ëçåÇÉêå=ãÉÜêÉêÉ=w~ÜäÉå=òìêΩÅâK== tÉåå= ïáê= ÑΩê= ìåëÉê= mêçÄäÉã= ÇêÉá= pé~äíÉå= ÄÉåìíòÉå= EòïÉá= pé~äíÉå= ÑΩê= ÇáÉ= ìå~ÄÜ®åÖáÖÉå= s~êá~ÄäÉå=ìåÇ=ÉáåÉ=pé~äíÉ=ÑΩê=ÇáÉ=~ÄÜ®åÖáÖÉ=s~êá~ÄäÉFI=Ç~åå=äáÉÑÉêí= RGP=áåëÖÉë~ãí= 3=ã~ä= 5I= ~äëç=ÑΩåÑòÉÜå=tÉêíÉK== aÉëÜ~äÄ=ãìëë=òìê=sçêÄÉêÉáíìåÖ=ÇÉê=^ìëÖ~ÄÉ=ÇÉê=j~íêáñÑìåâíáçå=òìÉêëí=ÑΩê=~ääÉ=òì=Éêï~êJ íÉåÇÉå=NR=^ìëÖ~ÄÉïÉêíÉ=ÇÉê= RGPJcìåâíáçå=Éáå=_ÉêÉáÅÜ=îçå=ÇêÉá=pé~äíÉå=ìåÇ=ÑΩåÑ=wÉáäÉå= ã~êâáÉêí=ïÉêÇÉåK==
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=
T==hçêêÉä~íáçå=ìåÇ=oÉÖêÉëëáçå=
NPM ===
= q~ÄÉääÉ=TKV~W=j~êâáÉêìåÖ=ÇÉë=^ìëÖ~ÄÉÄÉêÉáÅÜÉë=ÑΩê=ÇáÉ=RGPJcìåâíáçå= få=q~ÄÉääÉ=TKV~=áëí=Ç~ÑΩê=ÄÉêÉáíë=ÇÉê=_ÉêÉáÅÜ= A11:C15=ã~êâáÉêí=ïçêÇÉåK=råãáííÉäÄ~ê=áã=^åJ ëÅÜäìëë=ÇÉê=j~êâáÉêìåÖ=ãìëë=Ó=çÜåÉ=Ç~å~ÅÜ=ÉáåÉ=ÄÉëíáããíÉ=wÉääÉ=~ìëòìï®ÜäÉå=Ó=ëçÑçêí=áå= ÇáÉ=q~ëí~íìê=ÖÉÖêáÑÑÉå=ìåÇ=ÇáÉ=cìåâíáçåëÑçêãÉä=ÉáåÖÉíáééí=ïÉêÇÉåW== =RGP(C2:C9;A2:B9;WAHR;WAHR)
t®ÜêÉåÇ=ÇÉë=báåíáééÉåë=ÉêëÅÜÉáåí=ÇáÉëÉ=cçêãÉä=áå=ÇÉê=ΩÄäáÅÜÉå=báåÖ~ÄÉòÉáäÉ=çÄÉêÜ~äÄ=ÇÉê= wÉáäÉåâ∏éÑÉ=ìåÇ=ÖäÉáÅÜòÉáíáÖ=áå=ÇÉê=äáåâÉå=çÄÉêÉå=wÉääÉ=ÇÉë=ã~êâáÉêíÉå=_ÉêÉáÅÜÉëI=~äëç=áå= ÇÉê=wÉääÉ=A11=EëáÉÜÉ=q~ÄÉääÉ=TKVÄFK====
= q~ÄÉääÉ=TKVÄW=cìåâíáçåëÑçêãÉä=ÉêëÅÜÉáåí=áã=ã~êâáÉêíÉå=_ÉêÉáÅÜ=äáåâë=çÄÉå= aáÉëÉ= cçêãÉä= íÉáäí= òìÉêëí= ÇÉå= _ÉêÉáÅÜ=ÇÉê=~ÄÜ®åÖáÖÉå=s~êá~ÄäÉå= C2:C9 ãáíI= Ç~òì= ÇÉå= ÖÉJ ë~ãíÉå=_ÉêÉáÅÜ=ÇÉê=ÄÉáÇÉå=ìå~ÄÜ®åÖáÖÉå=s~êá~ÄäÉå= A2:B9=ãáíI=ìåÇ=ëáÉ=îÉêä~åÖí=ïÉáíÉê=ÄÉJ ëíáããíÉ=ëí~íáëíáëÅÜÉ=hÉååÖê∏≈ÉåI=~ìÑ=ÇáÉ=ÜáÉê=åáÅÜí=ïÉáíÉê=ÉáåÖÉÖ~åÖÉå=ïÉêÇÉå=â~ååK== ^ÅÜíìåÖW=a~ãáí=ÇáÉ=cìåâíáçå=RGP=áÜêÉ=ÑΩåÑòÉÜå=tÉêíÉ=~ìÑ=~ääÉ=ã~êâáÉêíÉå=wÉääÉå=îÉêíÉáäÉå= â~ååI=ãìëë=ÇáÉ=báåÖ~ÄÉ=ÇÉê=cìåâíáçåëÑçêãÉä=~ÄÖÉëÅÜäçëëÉå=ïÉêÇÉå=ÇìêÅÜ=ÖäÉáÅÜòÉáíáÖÉë= aêΩÅâÉå=îçå==E==Strg==H ⇑ =F=ìåÇ= i↵ ↵i ==K== aÉê=ÉáåÑ~ÅÜÉ=aêìÅâ=~ìÑ=ÇáÉ=bkqboJq~ëíÉ= i↵ ↵i =äáÉÑÉêí=åìê=ÉáåÉå=ÉáåòáÖÉå=tÉêí=å~ÅÜ=A11K= táêÇ=ÇáÉëÉê=eáåïÉáë=ÄÉêΩÅâëáÅÜíáÖíI=Ç~åå=ÉêëÅÜÉáåÉå=í~íë®ÅÜäáÅÜ=áã=ã~êâáÉêíÉå=_ÉêÉáÅÜ=ÇáÉ= ÑΩåÑòÉÜå=bêÖÉÄåáëïÉêíÉ=ÇÉê=j~íêáñÑìåâíáçå=RGP=EëáÉÜÉ=q~ÄÉääÉ=TKVÅFK==
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=
TKQ==káÅÜíäáåÉ~êÉ=wìë~ããÉåÜ®åÖÉ=
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NPN
==
= q~ÄK=TKVÅW=bêÖÉÄåáëïÉêíÉ=ÇÉê=j~íêáñÑìåâíáçå=RGP= kìå=â∏ååÉå=áå=ÇÉê=ÉêëíÉå=wÉáäÉ=ÇÉë=bêÖÉÄåáëÄÉêÉáÅÜÉë=îçå=êÉÅÜíë=å~ÅÜ=äáåâë=ÇáÉ=hçÉÑÑáòáÉåJ íÉå=bI=a1=ìåÇ=a2=~ÄÖÉäÉëÉå=ïÉêÇÉåW== b = 78750,27 , a1 = 189,03, a2 = 1390,79
wì=ÄÉ~ÅÜíÉå=áëí=ÜáÉêÄÉáI=Ç~ëë=ÇÉê=oÉÖêÉëëáçåëâçÉÑÑáòáÉåí=a1=åáÅÜí=ìåíÉê=x1=ìåÇ=ÇÉê=oÉÖêÉëJ ëáçåëâçÉÑÑáòáÉåí=a2=åáÅÜí=ìåíÉê=x2=ëíÉÜíK== aáÉ= wìçêÇåìåÖ= òì= ÇÉå= ÄÉáÇÉå= ìå~ÄÜ®åÖáÖÉå= s~êá~ÄäÉå= äáÉÑÉêí= Ç~åå= ÇáÉ= ÖÉëìÅÜíÉ= oÉÖêÉëëáJ çåëÑìåâíáçåW=== ETKMUF=
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= 189,03 ⋅ x1 + 1391,79 ⋅ x2 + 78750, 27
jáí=ÇÉê=ëç=ÖÉÑìåÇÉåÉå=cìåâíáçå=â~åå=åìå=ÑΩê=àÉÇÉ=ÇÉåâÄ~êÉ=ìåÇ=ëáååîçääÉ=x1-x2JhçãÄáå~J íáçå=Éáå=êÉëìäíáÉêÉåÇÉê=mêçÖåçëÉïÉêí= y=ëÅÜåÉää=~ìëÖÉêÉÅÜåÉí=ïÉêÇÉåK=q~ÄÉääÉ=TKNM=òÉáÖí=ÉáJ åáÖÉ=ëçäÅÜÉ=oÉÅÜåìåÖÉåK==
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7.4
Nichtlineare Zusammenhänge
7.4.1
Grundlagen
bë=áëí=ÇÉã=jÉåëÅÜÉå=òï~ê=ÖÉÖÉÄÉåI=ÉáåÉ=dê~Ñáâ=~äë=hêÉáë=òì=áÇÉåíáÑáòáÉêÉå=ìåÇ=ÇáÉëÉå=~ìÅÜ= ãΩÜÉäçë= áå= ëÉÅÜòáÖ= ÖäÉáÅÜÉ= qÉáäÉ= òì= ìåíÉêíÉáäÉå= Eëçåëí= â∏ååíÉ= åáÉã~åÇ= ÇáÉ= rÜê= ~ÄäÉëÉåFI= ~ÄÉê=~ì≈Éê=ÇáÉëÉê=c®ÜáÖâÉáí=ÖÉäáåÖí=Éë=åìê=åçÅÜI=ÉáåÉ=dÉê~ÇÉ=ÑÉëíòìëíÉääÉåK==
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=
T==hçêêÉä~íáçå=ìåÇ=oÉÖêÉëëáçå=
NPO
lÄ=ÄÉáëéáÉäëïÉáëÉ=ÉáåÉ=łÖÉÄçÖÉåÉ=mìåâíïçäâÉ=ïáÉ=áå=_áäÇ=TKNQ=~ìÑ=ÉáåÉå=èì~Çê~íáëÅÜÉå= çÇÉê= ÜóéÉêÄçäáëÅÜÉå= çÇÉê= äçÖ~êáíÜãáëÅÜÉå= çÇÉê= ÉñéçåÉåíáÉääÉå= wìë~ããÉåÜ~åÖ= òïáëÅÜÉå= báåÑäìëëJ=ìåÇ=wáÉäÖê∏≈É=ëÅÜäáÉ≈Éå=ä®ëëí=Ó=ïÉê=ïáää=Ç~ë=ãáí=ëÉáåÉå=^ìÖÉå=ÉêâÉååÉå\== råÇ=ïÉê=ïáää=Ç~åå=åçÅÜ=ÉáåÉ=cçêãÉä=EÉêFÑáåÇÉåI=ãáí=ÇÉê=ÇÉê=rêë~ÅÜÉJtáêâìåÖëJwìë~ãJ ãÉåÜ~åÖ=ã~íÜÉã~íáëÅÜ=ÄÉëÅÜêáÉÄÉå=ïÉêÇÉå=â~åå\==
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NPP
få=wÉääÉ=B6=ÉêëÅÜÉáåí=å®ãäáÅÜ=Éáå=ëíçäòÉê=tÉêí=îçå=Ñ~ëí=1,0=ÑΩê=ÇÉå=hçêêÉä~íáçåëâçÉÑÑáòáÉåíÉå= ÑΩê=ÇáÉ=åÉì=ÄÉêÉÅÜåÉíÉå=wÉáäÉå=ÑΩê=X=ìåÇ=Y=Ó=ïÉê=ëáÅÜ=ãÉÜê=píÉääÉå=~åòÉáÖÉå=ä®ëëíI=ïáêÇ=ÉñJ ~âí==0,995596856=ÑÉëíëíÉääÉåK==
= q~ÄK=TKNO~W=bêÖÉÄåáëëÉ=ÇÉê=äçÖ~êáíÜãáëÅÜÉå=qê~åëÑçêã~íáçå== t®ÜêÉåÇ= ÇáÉ= mìåâíïçäâÉ= áå= _áäÇ= TKNR= ìåë= ÇÉìíäáÅÜ= îçê= ^ìÖÉå= ÑΩÜêíÉI= Ç~ëë= òïáëÅÜÉå= ÇÉå= ÄÉáÇÉå=ìêëéêΩåÖäáÅÜÉå=a~íÉåêÉáÜÉå= x=ìåÇ= y=âÉáåÉëÑ~ääë=Éáå=äáåÉ~êÉê=wìë~ããÉåÜ~åÖ=ÄÉëíÉJ ÜÉå= â~ååI= ë~Öí= ìåë= ÇÉê= X-Y-hçêêÉä~íáçåëâçÉÑÑáòáÉåí= Ç~ÖÉÖÉå= ÑΩê= ÇáÉ= ÄÉáÇÉå= ÇìêÅÜ=ÇçééÉäí= äçÖ~êáíÜãáëÅÜÉ=qê~åëÑçêã~íáçå=ÉêÜ~äíÉåÉå=a~íÉåêÉáÜÉå= X=ìåÇ= Y=ÉáåÉ=ëí~êâÉ=äáåÉ~êÉ=^ÄÜ®åJ ÖáÖâÉáí=îçê~ìëW= t®ÜêÉåÇ= x=ìåÇ= y=çÑÑÉåëáÅÜíäáÅÜ=åáÅÜí=âçêêÉäáÉêí=ëáåÇI=ëáåÇ=ÇáÉ=ãáí=eáäÑÉ=ÇÉë=içÖ~êáíÜãìë= ~ìë=áÜåÉå=ÉêÜ~äíÉåÉå=íê~åëÑçêãáÉêíÉå=tÉêíÉ=X=ìåÇ=Y=Ç~ÖÉÖÉå=ÜçÅÜ=âçêêÉäáÉêíK= ^äëç=â~åå=ã~å=ÑΩê=ÇÉå=îçê~ìëëáÅÜíäáÅÜÉå=äáåÉ~êÉå=X-YJwìë~ããÉåÜ~åÖ=ëçÑçêí=ÇáÉ=òìÖÉÜ∏êáJ ÖÉå=oÉÖêÉëëáçåëé~ê~ãÉíÉê=ãáí=ÇÉå=ÄÉáÇÉå=bñÅÉäJcìåâíáçåÉå=~ìëêÉÅÜåÉå=ä~ëëÉåW=
= q~ÄK=TKNOÄW=píÉáÖìåÖ=ìåÇ=^ÅÜëÉå~ÄëÅÜåáíí=ÑΩê=ÇáÉ=íê~åëÑçêãáÉêíÉå=a~íÉåêÉáÜÉå=
= q~ÄK=TKNOÅW=píÉáÖìåÖ=ìåÇ=^ÅÜëÉå~ÄëÅÜåáííW=tÉêíÉ= j~å=ÉêÜ®äí=ÑΩê=ÇáÉ=píÉáÖìåÖ=ÇÉå=tÉêí=a=5,72 ìåÇ=ÑΩê=ÇÉå=^ÅÜëÉå~ÄëÅÜåáíí=b=0,77.== a~ãáí= ÉêÖáÄí= ëáÅÜ= ÑΩê= ÇÉå= ÖÉÑìåÇÉåÉå= ÉãéáêáëÅÜÉå= äáåÉ~êÉå= wìë~ããÉåÜ~åÖ= òïáëÅÜÉå= X= ìåÇ=Y=ëçÑçêí=ÇáÉ=cçêãÉäW== ETKMVF=
=Y
= 5,72 ⋅ X + 0,77
açÅÜ=ïÉäÅÜÉê=wìë~ããÉåÜ~åÖ=ä®ëëí=ëáÅÜ=Ç~ê~ìë=ÑΩê= x=ìåÇ=ó=~ÄäÉáíÉå=Ó=ïáÉ=Ü®åÖí= y=îçå= x= ~ÄI= ïÉäÅÜÉ= wìë~ããÉåÜ~åÖëÑçêãÉä= Öáäí= Ç~åå\= dáÄí= Éë= ΩÄÉêÜ~ìéí= ÉáåÉ= ëçäÅÜÉ= ñJóJwìJ ë~ããÉåÜ~åÖëÑçêãÉä=\= aÉåå=y=Ü®åÖí=ÇçÅÜ=Ö~åò=çÑÑÉåëáÅÜíäáÅÜ=åáÅÜíäáåÉ~ê=îçå=x=~ÄK==
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=
T==hçêêÉä~íáçå=ìåÇ=oÉÖêÉëëáçå=
NPQ a~=ÜáäÑí=ÇáÉ=j~íÜÉã~íáâW==
p~íò=TKNW=táêÇ=ÑΩê=ÇáÉ=ÄÉáÇÉå=a~íÉåêÉáÜÉå=ãáí=ÇÉê=Eíê~åëÑçêãáÉêíÉåF=báåÑäìëëÖê∏≈É= X= ìåÇ=ÇÉê=Eíê~åëÑçêãáÉêíÉåF=wáÉäÖê∏ëëÉ=Y=ÇÉê=äáåÉ~êÉ=X-Y-wìë~ããÉåÜ~åÖ== ETKNMF==
=Y = aX += b
ÑÉëíÖÉëíÉääíI= ìåÇ= ëáåÇ= X= ìåÇ= Y= ~ìë= ÇÉå= ìêëéêΩåÖäáÅÜÉå= a~íÉåêÉáÜÉå= x= ìåÇ= y= ÇìêÅÜ= ÇçééÉäí=äçÖ~êáíÜãáëÅÜÉ=qê~åëÑçêã~íáçå= ETKNNF==
=X
= ln x
Y = ln y
Éåíëí~åÇÉåI= Ç~åå= Öáäí= ÑΩê= ÇáÉ= ^ÄÜ®åÖáÖâÉáí= ÇÉê= ìêëéêΩåÖäáÅÜÉå= wáÉäÖê∏≈É= y= îçå= ÇÉê= ìêëéêΩåÖäáÅÜÉå=báåÑäìëëÖê∏≈É=x=ÇáÉ=ÉãéáêáëÅÜÉ=cçêãÉä= ETKNOF==
=y
= eb ⋅ x a
a~ÄÉá=áëí=e=ÇáÉ=ÄÉâ~ååíÉ=bìäÉêëÅÜÉ=w~ÜäW=e= 2,71828182845905…= aáÉëÉå=p~íò=â∏ååÉå=ïáê=àÉíòí=~åïÉåÇÉåW== a~ë=báåëÉíòÉå=îçå=a=ìåÇ=b=äáÉÑÉêí=Ç~ë=bêÖÉÄåáëW=wïáëÅÜÉå=ÇÉê=báåÑäìëëÖê∏≈É=x=ìåÇ=ÇÉê=wáÉäJ Öê∏≈É=y =ÄÉëíÉÜí=ÇÉê=ÉãéáêáëÅÜÉ=wìë~ããÉåÜ~åÖW== ETKNPF=
y = e 0, 774 ⋅ x 5,72 = 2,7180 , 77 ⋅ x 5, 72 = 2,17 ⋅ x 5, 72
eáåïÉáëW=wìê=_ÉêÉÅÜåìåÖ=ÇÉê=mçíÉåò==2,7180,77=ãáí=eáäÑÉ=îçå=bñÅÉä=áëí==2,718^0,77=ÉáåòìJ íáééÉåI=ïçÄÉá=Ç~ë=wÉáÅÜÉå=^=EãÉáëí=äáåâë=åÉÄÉå=ÇÉê=q~ëíÉ= 1 =F=~ÄÉê=Éêëí=~åÖÉòÉáÖí=ïáêÇI= ïÉåå=ÇáÉ=ÑçäÖÉåÇÉ=kìää=ÉáåÖÉÖÉÄÉå=ïáêÇK== tÉê= Öê∏≈ÉêÉ= dÉå~ìáÖâÉáí= ~åëíêÉÄíI= ëçääíÉ= =EXP(1)^0,77= ÉáåÖÉÄÉåI= Ç~åå= ïáêÇ= ÇáÉ= bìäÉêJ ëÅÜÉ=w~Üä=e=~ìÑ=NR=aÉòáã~äëíÉääÉå=ÖÉå~ì=ÄÉêÉÅÜåÉíK==
= _áäÇ=TKNRW=mìåâíïçäâÉ=ÇÉê=içÖ~êáíÜãÉå=îçå=ñ=ìåÇ=ó=
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=
TKQ==káÅÜíäáåÉ~êÉ=wìë~ããÉåÜ®åÖÉ=
=
NPR
t®ÜêÉåÇ=_áäÇ=TKNR=ÇáÉ=mìåâíïçäâÉ=ÇÉê=ÇçééÉäí=äçÖ~êáíÜãáëÅÜ=íê~åëÑçêãáÉêíÉå=a~íÉåêÉáÜÉå= X=ìåÇ=Y=áå=áÜêÉã=ÇÉìíäáÅÜ=ÉêâÉååÄ~êÉ=äáåÉ~êÉå=wìë~ããÉåÜ~åÖ=òÉáÖíI=áëí=áå=_áäÇ=TKNS=áå=ÇáÉ= ÄÉêÉáíë= ~ìë= _áäÇ= TKNQ=ÄÉâ~ååíÉ= mìåâíïçäâÉ= ÇáÉ= hìêîÉ= ÇÉê= ÉñéçåÉåíáÉääÉå= x-y-wìë~ããÉåJ Ü~åÖëÑìåâíáçå=ETKMQF=ÉáåÖÉòÉáÅÜåÉí=ïçêÇÉåK==
= RITO
_áäÇ=TKNSW=mìåâíïçäâÉ=îçå=ñ=ìåÇ=ó=ëçïáÉ=ÇáÉ=^ìëÖäÉáÅÜëâìêîÉ=óZOINT=G=ñ
=
j~å= â~åå= ÇÉìíäáÅÜ= ÉêâÉååÉåI= Ç~ëë= ÇÉê= ÖÉÑìåÇÉåÉ= åáÅÜíäáåÉ~êÉ= x-y-wìë~ããÉåÜ~åÖ= áå= ÇÉê=q~í=ÖÉÉáÖåÉí=áëíI=ÇáÉ=páíì~íáçå=áã=a~íÉåÄÉëí~åÇ=íêÉÑÑÉåÇ=ÑçêãÉäã®≈áÖ=òì=ÄÉëÅÜêÉáÄÉåK==
7.4.2
Transformationen
kìå= áëí= Éë= ~å= ÇÉê= wÉáíI= ÇáÉ= ~åÇÉêÉå= bêâÉååíåáëëÉ=ÇÉê= j~íÜÉã~íáâ=îçêòìëíÉääÉåI=ãáí= ÇÉåÉå= ÑΩê=ïÉáíÉêÉ=åáÅÜíäáåÉ~êÉ=rêë~ÅÜÉJtáêâìåÖëJwìë~ããÉåÜ®åÖÉ=ÉãéáêáëÅÜÉ=cçêãÉäå=ÖÉÑìåÇÉå= ïÉêÇÉå=â∏ååÉåW== p~íò= TKOW= dÉÖÉÄÉå= ëÉáÉå= òïÉá= ÖäÉáÅÜä~åÖÉ= a~íÉåêÉáÜÉå= ãáí= ÇÉå= _ÉòÉáÅÜåìåÖÉå= x= ìåÇ= yI= ïçÄÉá= ~ìë= ë~ÅÜäáÅÜÉå= dêΩåÇÉå= ÄÉâ~ååí= ëÉáI= Ç~ëë= ÇáÉ= oÉáÜÉ= y= ~äë= oÉáÜÉ= ÇÉê= ~ÄÜ®åÖáÖÉå=tÉêíÉ= EwáÉäÖê∏≈ÉF= ìåÇ= ÇáÉ= oÉáÜÉ= x= ~äë= oÉáÜÉ= ÇÉê= ìå~ÄÜ®åÖáÖÉå=tÉêíÉ= EbáåÑäìëëÖê∏≈ÉF=~åÖÉëÉÜÉå=ïÉêÇÉå=â~ååK= bêÖáÄí=ëáÅÜ=å~ÅÜ=ÇÉê=ÉáåÑ~ÅÜ=äçÖ~êáíÜãáëÅÜÉå=qê~åëÑçêã~íáçå=îçå=y ÖÉã®≈= ETKNQF==
=X
=x
Y = ln y
ÑΩê=ÇáÉ=íê~åëÑçêãáÉêíÉ=XJYJa~íÉåêÉáÜÉ=ÉáåÉ=ÉãéáêáëÅÜÉ=äáåÉ~êÉ=wìë~ããÉåÜ~åÖëÑçêãÉä= ETKNRF==
=Y = aX += b
ëç=ÄÉëíÉÜí=òïáëÅÜÉå=x=ìåÇ=y=ÇÉê=ÉãéáêáëÅÜÉ=åáÅÜíäáåÉ~êÉ=wìë~ããÉåÜ~åÖ= ETKNSF==
=y
= e b ⋅ e a⋅ x
=
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=
T==hçêêÉä~íáçå=ìåÇ=oÉÖêÉëëáçå=
NPS
p~íò= TKPW= dÉÖÉÄÉå= ëÉáÉå= òïÉá= ÖäÉáÅÜä~åÖÉ= a~íÉåêÉáÜÉå= ãáí= ÇÉå= _ÉòÉáÅÜåìåÖÉå= x= ìåÇ= yI= ïçÄÉá= ~ìë= ë~ÅÜäáÅÜÉå= dêΩåÇÉå= ÄÉâ~ååí= ëÉáI= Ç~ëë= ÇáÉ= oÉáÜÉ= y= ~äë= oÉáÜÉ= ÇÉê= ~ÄÜ®åÖáÖÉå=tÉêíÉ= EwáÉäÖê∏≈ÉF= ìåÇ= ÇáÉ= oÉáÜÉ= x= ~äë= oÉáÜÉ= ÇÉê= ìå~ÄÜ®åÖáÖÉå=tÉêíÉ= EbáåÑäìëëÖê∏≈ÉF=~åÖÉëÉÜÉå=ïÉêÇÉå=â~ååK= bêÖáÄí=ëáÅÜ=å~ÅÜ=ÇÉê=ÉáåÑ~ÅÜ=äçÖ~êáíÜãáëÅÜÉå=qê~åëÑçêã~íáçå=îçå=x=ÖÉã®≈= ETKNTF==
=X
= ln x = Y = y=
ÑΩê=ÇáÉ=íê~åëÑçêãáÉêíÉ=XJYJa~íÉåêÉáÜÉ=ÉáåÉ=ÉãéáêáëÅÜÉ=äáåÉ~êÉ=wìë~ããÉåÜ~åÖëÑçêãÉä= ETKNUF==
=Y = aX += b
ëç=ÄÉëíÉÜí=òïáëÅÜÉå=x=ìåÇ=y=ÇÉê=ÉãéáêáëÅÜÉ=åáÅÜíäáåÉ~êÉ=wìë~ããÉåÜ~åÖ= ETKNVF==
=y
= b + a=⋅ ln x
a~ê~ìë=ÉêÖáÄí=ëáÅÜ=ÑçäÖÉåÇÉ=^åäÉáíìåÖ=òìã=e~åÇÉäåW== iáÉÖí=Éáå=a~íÉåÄÉëí~åÇ=îçêI=ÇÉê=~ìë=òïÉá=ÖäÉáÅÜä~åÖÉå=a~íÉåêÉáÜÉå=ÄÉëíÉÜíI=ìåÇ=ÄÉá=ÇÉJ åÉå=ÉáåÉ=a~íÉåêÉáÜÉ= ~ìë= ë~ÅÜäáÅÜÉå=dêΩåÇÉå= ~äë=báåÑäìëëÖê∏≈É= ExF= ìåÇ=ÇáÉ= ~åÇÉêÉ= a~J íÉåêÉáÜÉ=~äë=wáÉäÖê∏≈É=EyF=~åÖÉëÉÜÉå=ïÉêÇÉå=â~ååI=Ç~åå=ëçääíÉå=ÖêìåÇë®íòäáÅÜ=åÉÄÉå=ÇÉå= ^ìëÖ~åÖëÇ~íÉå=ïÉáíÉêÉ=ÇêÉá=wìë~ããÉåëíÉääìåÖÉå=îçå=íê~åëÑçêãáÉêíÉå=tÉêíÉé~~êÉåI=ïáÉ= áå=ÇÉê=q~ÄÉääÉ=TKNP=Ç~êÖÉëíÉääíI=áå=Ç~ë=bñÅÉäJ_ä~íí=ÉáåÖÉíê~ÖÉå=ïÉêÇÉåK==
= q~ÄK=TKNP~W=cçêãÉäå=
= q~ÄK=TKNPÄW=tÉêíÉ= aáÉ=îáÉê=hçêêÉä~íáçåëâçÉÑÑáòáÉåíÉå=áå=ÇÉê=ÉêëíÉå=wÉáäÉ=ÖÉÄÉå=Ç~åå=Ç~êΩÄÉê=^ìëâìåÑíI=ïÉäJ ÅÜÉë= pé~äíÉåé~~ê= ÑΩê= ÇáÉ= äáåÉ~êÉ=oÉÖêÉëëáçåëêÉÅÜåìåÖ= áåÑê~ÖÉ= âçããíW= fëí= ÇÉê= hçêêÉä~íáJ çåëâçÉÑÑáòáÉåí=áå=ÇÉê=wÉääÉ= A1=å~ÜÉ=N=çÇÉê=JNI=Ç~åå=áëí=ÉáåÑ~ÅÜÉ=äáåÉ~êÉ=oÉÖêÉëëáçå=ëáååJ îçääK= fëí= ÇÉê= tÉêí= áå= ÇÉê= wÉääÉ= D1= å~ÜÉ= N= çÇÉê= JNI= Ç~åå= â~åå= p~íò=TKP= òìê= ^åïÉåÇìåÖ= âçããÉåK=dáäí=Ç~ë=ÑΩê=ÇÉå=tÉêí=áå=ÇÉê=wÉääÉ= G1I=Ç~åå=âçããí=p~íò=TKO=òìê=^åïÉåÇìåÖK= cáåÇÉí=ëáÅÜ=áå=ÇÉê=wÉääÉ=J1=Éáå=ëçäÅÜÉê=tÉêíI=Ç~åå=â~åå=p~íò=TKN=~åÖÉï~åÇí=ïÉêÇÉåK==
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVU=
=
8
Zeitreihen
8.1
Begriff und Erfassung
báåÉ=wÉáíêÉáÜÉ=áëí=ÉáåÉ=òÉáíäáÅÜ=ÖÉçêÇåÉíÉ=cçäÖÉ=îçå=jÉêâã~äëïÉêíÉåK== lÇÉê=~åÇÉêë=ÖÉëéêçÅÜÉå=Ó=ìåÇ=ìã=ÇáÉ=sÉêÄáåÇìåÖ=òìã=îçêáÖÉå=^ÄëÅÜåáíí=ÜÉêòìëíÉääÉå=Ó= ÇáÉ= ÄÉíê~ÅÜíÉíÉå= báåÑäìëëÖê∏≈Éå= ëáåÇ= ÜáÉê= ëéÉòáÉää= a~íìãëJ= çÇÉê= wÉáí~åÖ~ÄÉåI= òì= ÇÉåÉå= Ç~åå=~äë=wáÉäÖê∏≈Éå=àÉïÉáäë=ÄÉëíáããíÉ=~åÇÉêÉ=tÉêíÉ=ÖÉÜ∏êÉåK= bñÅÉä=ëíÉääí=òìê=^êÄÉáí=ãáí=wÉáíêÉáÜÉå=ÉáåÉ=ÄÉ~ÅÜíäáÅÜÉ=jÉåÖÉ=îçå=eáäÑëãáííÉäå=ÄÉêÉáíK== sçê~ìëëÉíòìåÖ= ÑΩê= ÇáÉ=kìíòÄ~êâÉáí= ÇáÉëÉê=eáäÑëãáííÉä= áëí= ~ääÉêÇáåÖë= áå= àÉÇÉã= c~ääÉI= Ç~ëë= ÇáÉ= a~íìãëJ=çÇÉê=wÉáí~åÖ~ÄÉå=~äë=åìãÉêáëÅÜÉ=tÉêíÉ=îçå=bñÅÉä=Éêâ~ååí=ïÉêÇÉå=â∏ååÉåK=== pçää= òìã= _ÉáëéáÉä= ÉáåÉ= ãçå~íäáÅÜÉ=båíïáÅâäìåÖ= Ç~êÖÉëíÉääí= ïÉêÇÉåI= Ç~åå= áëí= ÇáÉ= åáÅÜíåìJ ãÉêáëÅÜÉ=báåÖ~ÄÉ=ÇÉê=a~íìãë~åÖ~ÄÉå=EÜáÉê=ëáåÇ=Éë=ÇáÉ=jçå~íë~ÄâΩêòìåÖÉåF=ïáÉ=áå=q~ÄÉäJ äÉ=UKN~=çÑí=ìåÄê~ìÅÜÄ~ê=ÑΩê=ÇáÉ=ïÉáíÉêÉ=sÉê~êÄÉáíìåÖK==
= q~ÄK=UKN~W=jçå~íëå~ãÉå=åáÅÜíåìãÉêáëÅÜ=~äë=wÉáÅÜÉåÑçäÖÉå=ÉáåÖÉÖÉÄÉå= sáÉäãÉÜê= ëçääíÉ= ã~å= ëçI= ïáÉ= áå= q~ÄÉääÉ= UKNÄ= ÖÉòÉáÖíI= ÇáÉ= åìãÉêáëÅÜÉå= a~íìãë~åÖ~ÄÉå= łNKNKMTI=łNKOKMT=ìëïK=ãáí=ÉáåÉê=ÄÉäáÉÄáÖÉå=g~ÜêÉëò~Üä=Éáåíê~ÖÉåK==
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8.3
Lineare Zeitreihen und die TREND-Funktion
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= 0,001122709 ⋅ Datumswert - 29,43253314
rã=ÇáÉ=mêçÖåçëÉïÉêíÉ=ÑΩê=kçîÉãÄÉê=ìåÇ=aÉòÉãÄÉê=ÄÉêÉÅÜåÉå=òì=â∏ååÉåI=ÄÉå∏íáÖÉå=ïáê= ÑçäÖäáÅÜ=ÇáÉ=ÄÉáÇÉå=òìÖÉÜ∏êáÖÉå=a~íìãëïÉêíÉK=páÉ=â∏ååÉå=ïáê=ÉêÜ~äíÉåI=áåÇÉã=ïáê=ÇáÉ=^åJ òÉáÖÉ=ãáííÉäë=cloj^qwbiibkw^ei=ìãëíÉääÉåE=ëK=q~ÄÉääÉ=UKTFK===
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q~ÄK=UKTW=kçîÉãÄÉê=ìåÇ=aÉòÉãÄÉêW=hìêòÑçêãI=a~íìãI=a~íìãëïÉêíÉ= jáí=ÇÉå=ÄÉáÇÉå=ÄÉâ~ååíÉå=a~íìãëïÉêíÉå=â∏ååÉå=àÉíòí=ÇáÉ=qêÉåÇïÉêíÉ=ÑΩê=kçîÉãÄÉê=ìåÇ= aÉòÉãÄÉê=ÇìêÅÜ=báåëÉíòÉå=áå=ÇáÉ=oÉÖêÉëëáçåëÑçêãÉä=ÉêãáííÉäí=ïÉêÇÉåK==
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NQQ = EUKMOF=
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= 0,001123 ⋅ 39387 - 29,43253314 ≈ 14,79
EUKMPF=
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= 0,001122709 ⋅ 39417 - 29,43253314 ≈ 14,82
k~íΩêäáÅÜ= Ü®ííÉ= ã~å= ~ìÅÜ= ÖäÉáÅÜ= áå= ÇÉê= bñÅÉäJq~ÄÉääÉ= êÉÅÜåÉå= ä~ëëÉå= â∏ååÉåK= açÅÜ= ~ìÅÜ= Ç~ë= áëí=åáÅÜí=å∏íáÖ=Ó=ÇáÉ= ÄÉáÇÉå= ÖÉëìÅÜíÉå=qêÉåÇïÉêíÉ= ä~ëëÉå=ëáÅÜ=ãáí=bñÅÉä= îáÉä=ëÅÜåÉääÉê= ìåÇ=ÄÉèìÉãÉê=ÉêãáííÉäåK== táêÇ=ÇáÉ=bñÅÉäJcìåâíáçå= TREND(...;...;...)=îÉêïÉåÇÉíI=Ç~åå=â~åå=ã~å=ëáÅÜ=ÇáÉ=bêãáííJ äìåÖ=ÇÉê=oÉÖêÉëëáçåëÑçêãÉä=ëé~êÉåK= ^å=ÇáÉ=ÉêëíÉ=mçëáíáçå=ÇÉê= TRENDJcìåâíáçå=áëí=Ç~ÄÉá=ÇÉê=_ÉêÉáÅÜ=ãáí=ÇÉå=~ÄÜ®åÖáÖÉå=s~êá~ÄJ äÉå= EÄÉá= ìåëÉêÉå= wÉáíêÉáÜÉå= ~äëç= ÇÉê= _ÉêÉáÅÜ= ÇÉê= jÉêâã~äëïÉêíÉF= Éáåòìíê~ÖÉåK= aáÉ= òïÉáíÉ= mçëáíáçå= ãìëë= ÇÉå= _ÉêÉáÅÜ=ÇÉê=ìå~ÄÜ®åÖáÖÉå=s~êá~ÄäÉå= ÄÉâçããÉå= Erêë~ÅÜÉåïÉêíÉW= ÄÉá= ìåë= ÇáÉ= a~íìãë~åÖ~ÄÉåFK= ^å= ÇáÉ= ÇêáííÉ= píÉääÉ= ëÅÜäáÉ≈äáÅÜ= âçããí= ÇáÉ= wÉääÉ= ãáí= ÇÉã= a~J íìãëïÉêí=ÇÉë=ÖÉëìÅÜíÉå=jçå~íëK==
= q~ÄK=UKU~W=^åïÉåÇìåÖ=ÇÉê=TRENDJcìåâíáçå=
= q~ÄK=UKUÄW=TRENDJcìåâíáçåW=tÉêíÉ få=ÇÉå=ÄÉáÇÉå=q~ÄÉääÉå=UKU~=ìåÇ=UKUÄ=áëí=Ç~ë=sçêÖÉÜÉå=Ç~êÖÉëíÉääíK=bë=ÉêÖÉÄÉå=ëáÅÜ=Ó=å~J íΩêäáÅÜ=Ó=ÇáÉëÉäÄÉå=w~ÜäÉåïÉêíÉ=ïáÉ=ÄÉá=ÇÉê=çÄáÖÉå=^ìëïÉêíìåÖ=ÇÉê=oÉÖêÉëëáçåëÑçêãÉäK== a~ë=Ç~êÑ= ~ìÅÜ= åáÅÜí=îÉêïìåÇÉêäáÅÜ= ëÉáåI= ÇÉåå=ÇáÉ=cìåâíáçå= TREND(...;...;...)= ~êÄÉáíÉí= ÖÉå~ì=ëçI=ïáÉ=ïáê=Éë=ÉáåÖ~åÖë=ÇÉãçåëíêáÉêíÉåW== páÉ=ÄÉëíáããí=ÉÄÉåÑ~ääë=òìÉêëí=ÇáÉ=oÉÖêÉëëáçåëâçÉÑÑáòáÉåíÉå=ãáí=eáäÑÉ=ÇÉê=cìåâíáçåÉå=STEIGUNG(...;...)= ìåÇ= ACHSENABSCHNITT(...;...),= ìåÇ= Ç~åå= ëÉíòí= ëáÉ= ÇÉå= àÉïÉáäáÖÉå= a~J íìãëïÉêí=áå=ÇáÉ=däÉáÅÜìåÖ=ÇÉê=oÉÖêÉëëáçåëÖÉê~ÇÉå=ÉáåK=
8.4
Gleitender Durchschnitt
aÉê=ÖäÉáíÉåÇÉ=aìêÅÜëÅÜåáíí=ÉáåÉê=wÉáíêÉáÜÉ=ÉäáãáåáÉêí=pÅÜï~åâìåÖÉå=ÇÉê=wÉáíêÉáÜÉI=áåÇÉã= ~ìÑ= ÇÉã= tÉÖÉ= ÇÉê= aìêÅÜëÅÜåáííëÄáäÇìåÖ= êÉä~íáî=ÜçÜÉ=tÉêíÉ= ìåÇ= êÉä~íáî=åáÉÇêáÖÉ=tÉêíÉ= ~ìÑ=Éáå=ÇìêÅÜëÅÜåáííäáÅÜÉë=káîÉ~ì=~ÄÖÉëÉåâí=ïÉêÇÉåK== fã= dÉÖÉåë~íò= òìê= jÉíÜçÇÉ= ÇÉê= äáåÉ~êÉå= oÉÖêÉëëáçå= ÄáäÇÉí= Ç~ë= jçÇÉää= ÇÉê= ÖäÉáíÉåÇÉå= aìêÅÜëÅÜåáííÉ=ÇÉå=qêÉåÇ=åáÅÜí=~äë=dÉê~ÇÉ=~ÄI=ëçåÇÉêå=Öä®ííÉí=äÉÇáÖäáÅÜ=ÇÉå=hìêîÉåîÉêä~ìÑK== a~ÇìêÅÜ= ïÉêÇÉå= tÉåÇÉéìåâíÉ= ìåÇ= sÉê®åÇÉêìåÖÉå= áå= ÇÉê= qêÉåÇÉåíïáÅâäìåÖ= ÑΩê= ÇÉå= _Éíê~ÅÜíÉê=ÇÉìíäáÅÜÉê=ëáÅÜíÄ~êK==
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UKQ==däÉáíÉåÇÉê=aìêÅÜëÅÜåáíí=
NQR
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8.5
Grundlagen der Zeitreihenanalyse
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8.5.1
Aufbau des additiven Zeitreihenmodells
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aáÉ= qêÉåÇâçãéçåÉåíÉ= T= ÅÜ~ê~âíÉêáëáÉêí= ÇáÉ= ä~åÖÑêáëíáÖÉ= båíïáÅâäìåÖ= ÇÉê= wÉáíêÉáÜÉX= ëáÉ= áëí= ÉåíïÉÇÉê=ãçåçíçå=ëíÉáÖÉåÇ=çÇÉê=Ñ~ääÉåÇK== aáÉ=qêÉåÇâçãéçåÉåíÉ=ïáêÇ=áã=~ääÖÉãÉáåÉå=ÇìêÅÜ=ÉáåÉ=äáåÉ~êÉ=oÉÖêÉëëáçå=Eãáí=ÇÉê=wÉáí=~äë= báåÑäìëëÖê∏≈ÉF=ÄÉêÉÅÜåÉí=EëáÉÜÉ=^ÄëÅÜåáíí=TKO=~ìÑ=pÉáíÉ=NOPFK= Zyklische Komponente Z
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8.5.2
Gleitende Durchschnitte und das additive Zeitreihenmodell
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8.5.4
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NRU
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j~å= â~åå= ~ìÑÖêìåÇ= ÄÉêÉáíë=îçêäáÉÖÉåÇÉê=ë~áëçåÄÉêÉáåáÖíÉê=jçå~íëïÉêíÉ= Ç~ë= g~ÜêÉëÉêÖÉÄåáë= éêçÖåçëíáòáÉêÉåK== j~å=â~åå=~ìë=ÇÉê=ë~áëçåÄÉêÉáåáÖíÉå=wÉáíêÉáÜÉ=mêçÖåçëÉå=ÑΩê=ÇáÉ=å®ÅÜëíÉå=jçå~íÉ=ìåÇ=g~ÜJ êÉ= EÇìêÅÜëÅÜåáííäáÅÜÉ= g~ÜêÉëïÉêíÉF= ãáííÉäë= qêÉåÇ~å~äóëÉ= ìåÇ= ÉñéçåÉåíáÉääÉê= dä®ííìåÖ= ÄÉJ êÉÅÜåÉåK= j~å=â~åå=Éáå=îçê~ìëÖÉëÅÜ®íòíÉë=g~ÜêÉëÉêÖÉÄåáë=ãáí=eáäÑÉ=ÇÉê=ãçå~íëíóéáëÅÜÉå=^ÄïÉáÅÜìåJ ÖÉå=~ìÑ=ÇáÉ=ÉáåòÉäåÉå=jçå~íÉ=~ìÑíÉáäÉåK== ^ìÑ=ÇáÉëÉ=tÉáëÉ=ÉêÜ®äí=ã~å=ãçå~íäáÅÜÉ=mêçÖåçëÉïÉêíÉK= pÉäÄëíîÉêëí®åÇäáÅÜ=ÖáÄí=Éë=~ÄÉê=~ìÅÜ=dêÉåòÉå=ÇÉê=^åïÉåÇÄ~êâÉáí=ÇÉê=jÉíÜçÇÉ=ÇÉê=ÖäÉáíÉåJ ÇÉå=aìêÅÜëÅÜåáííÉW= ^åÜ~åÇ=ÇÉê=çÄáÖÉå=^ìëÑΩÜêìåÖÉå=ïìêÇÉå=ÄÉêÉáíë=ÉáåáÖÉ=pÅÜï®ÅÜÉå=ÇÉê=wÉáíêÉáÜÉå~å~äóëÉ= ãáí=eáäÑÉ=ÇÉê=jÉíÜçÇÉ=ÇÉê=ÖäÉáíÉåÇÉå=aìêÅÜëÅÜåáííÉ=ëáÅÜíÄ~êK=aáÉ=^åïÉåÇìåÖëëÅÜï®ÅÜÉå= ÇÉë=jçÇÉääë=ìåÇ=ÇÉê=_ÉêÉÅÜåìåÖëãÉíÜçÇÉ=òÉáÖÉå=ëáÅÜ=áå=ÑçäÖÉåÇÉå=mìåâíÉåW== qêÉåÇÄÉêÉÅÜåìåÖW=cΩê=ÇáÉ=ÄÉáÇÉå=båÇÉå=ÇÉê=wÉáíêÉáÜÉ=E^åÑ~åÖ=ìåÇ=pÅÜäìëëF=â∏ååÉå=âÉáåÉ= ÖäÉáíÉåÇÉå=aìêÅÜëÅÜåáííÉ=ÄÉêÉÅÜåÉí=ïÉêÇÉåK=aÉëÜ~äÄ=â~åå=ÇÉê=qêÉåÇ=~ìÅÜ=åáÅÜí=ïÉáí=ΩÄÉê= ÇÉå=~âíìÉääÉå=pí~åÇ=Üáå~ìë=áåíÉêéêÉíáÉêí=ïÉêÇÉåK=eáÉêÄÉá=òÉáÖí=ëáÅÜ=Éáå=ÇÉìíäáÅÜÉê=k~ÅÜíÉáä= ÖÉÖÉåΩÄÉê= ÇÉê= qêÉåÇÄÉêÉÅÜåìåÖ= ãáííÉäë= äáåÉ~êÉê=oÉÖêÉëëáçå= çÇÉê= ÇÉê= jÉíÜçÇÉ= ÇÉë= ÉñéçJ åÉåíáÉääÉå=dä®ííÉåë=EëáÉÜÉ=òK=_K=áå=xNzFI=ÇáÉ=~âíìÉääÉ=tÉêíÉ=ÄÉëëÉê=ÄÉêΩÅâëáÅÜíáÖÉåK== wìâìåÑíëéêçàÉâíáçåÉå=â∏ååÉå=åìê=ãáí=eáäÑÉ=ïÉáíÉêÉê=jÉíÜçÇÉå=EäáåÉ~êÉ=oÉÖêÉëëáçå=çÇÉê=ÉñJ éçåÉåíáÉääÉ=dä®ííìåÖF=ÉêêÉÅÜåÉí=ïÉêÇÉåK= jçå~íëíóéáëÅÜÉ=^ÄïÉáÅÜìåÖÉåW= ^ìÅÜ= ÇáÉ= p~áëçåÑáÖìê= ïáêÇ= åìê=~ìë=ÜáëíçêáëÅÜÉå=a~íÉå= ÉêJ êÉÅÜåÉíK= ^âíìÉääÉ= a~íÉå= ïÉêÇÉå= ÜáÉê= ÉÄÉåÑ~ääë= åìê= ìåòìêÉáÅÜÉåÇ= ÄÉêΩÅâëáÅÜíáÖí= ìåÇ= ãáí= ÜáëíçêáëÅÜÉå=a~íÉå=ÖäÉáÅÜÖÉïáÅÜíáÖ=îÉêêÉÅÜåÉíK== a~ë=jçÇÉää=áëí=ÇÉëíç=ÄÉëëÉêI=àÉ=âäÉáåÉê=ÇáÉ=áêêÉÖìä®êÉ=hçãéçåÉåíÉ=áëí=ìåÇ=àÉ=êÉÖÉäã®≈áÖÉê= ëáÅÜ=ÇáÉ=sÉê®åÇÉêìåÖÉå=ÇÉå=ä~åÖÑêáëíáÖÉåI=âçåàìåâíìêÉääÉå=ìåÇ=ãçå~íëíóéáëÅÜÉå=_ÉïÉJ ÖìåÖÉå=~åé~ëëÉåK= ^ÄëÅÜäáÉ≈ÉåÇ=ëáåÇ=åçÅÜ=òïÉá=ãÉíÜçÇáëÅÜÉ=^åãÉêâìåÖÉå=òì=ã~ÅÜÉåW= cΩê=âΩêòÉêÉ=p~áëçåÑáÖìêÉå=EòK_K=nì~êí~äëÇ~íÉåF=ãìëë=Ç~ë=fåíÉêî~ää=òìê=_ÉêÉÅÜåìåÖ=ÇÉê=ÖäÉáJ íÉåÇÉå=aìêÅÜëÅÜåáííÉ=ÉåíëéêÉÅÜÉåÇ=ÇÉê=îçêäáÉÖÉåÇÉå=p~áëçåÇ~ìÉê=~åÖÉé~ëëí=ïÉêÇÉåK=pç=áëí= ÄÉá=nì~êí~äëÇ~íÉå=ÇÉê=ÖäÉáíÉåÇÉ=aìêÅÜëÅÜåáíí=ÇÉê=lêÇåìåÖ=Q=òì=ï®ÜäÉåK=_Éá=p~áëçåÑáÖìêÉå= ãáí= ãÉÜê= fåíÉêî~ääÉå= EòK_K= ëíΩåÇäáÅÜÉê= píêçãîÉêÄê~ìÅÜ= éêç= q~ÖF= ï®Üäí= ã~å= ÉåíëéêÉÅÜÉåÇ= ÉáåÉå=ÖäÉáíÉåÇÉå=aìêÅÜëÅÜåáíí=Ü∏ÜÉêÉê=lêÇåìåÖ=EòK_K=lêÇåìåÖ=OQFK= a~ë= Ç~êÖÉëíÉääíÉ= jçÇÉää= òìê= p~áëçåÄÉêÉáåáÖìåÖ= Öáäí= åìê= ÑΩê= âçåëí~åíÉ=p~áëçåÑáÖìêÉåI= ÇK= ÜK= ÇáÉ=ë~áëçå~äÉå=pÅÜï~åâìåÖÉå=ëçääíÉå=áå=àÉÇÉê=p~áëçå=Éíï~=ÖäÉáÅÜ=Öêç≈=ëÉáåK=wÉáÖí=ëáÅÜI=Ç~ëë= ÇáÉ=^ìëëÅÜä®ÖÉ=E^ãéäáíìÇÉåF=ÇÉê=p~áëçåÑáÖìê=ãáí=ÇÉã=^åï~ÅÜëÉå=ÇÉê=Öä~ííÉå=hçãéçåÉåíÉ= ET= ìåÇ= wF= ÉÄÉåÑ~ääë= ~åï~ÅÜëÉåI= Ç~åå= ãìëë= Éáå= ^å~äóëÉãçÇÉää= ÑΩê= î~êá~ÄäÉ= p~áëçåÑáÖìêÉå= ÖÉï®Üäí=ïÉêÇÉå=EîÖäK=ÜáÉêòìW=xNzI=pK=TM=ÑÑKFK= c~òáíW= aáÉ= wÉáíêÉáÜÉå~å~äóëÉ= ãáííÉäë= ÖäÉáíÉåÇÉê= aìêÅÜëÅÜåáííÉ= ÉáÖåÉí= ëáÅÜ= áåëÄÉëçåÇÉêÉ= òìê=áåíÉåëáîÉå=^å~äóëÉ=ìåÇ=fåíÉêéêÉí~íáçå=ÜáëíçêáëÅÜÉê=båíïáÅâäìåÖÉåK=mêçÖåçëÉå=ÑΩê=ÇáÉ= wìâìåÑí=â∏ååÉå=åìê=ìåíÉê=wìÜáäÑÉå~ÜãÉ=~åÇÉêÉê=mêçÖåçëÉîÉêÑ~ÜêÉå=EäáåÉ~êÉ=oÉÖêÉëëáçåI= ÉñéçåÉåíáÉääÉ=dä®ííìåÖ=ìëïKF=ÖÉíêçÑÑÉå=ïÉêÇÉåK== =
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=
9
Import von Daten aus Datenbanken
9.1
Grundsätzliches
få= ÇáÉëÉã= h~éáíÉä= ëçää= Ç~ê~ìÑ= ÉáåÖÉÖ~åÖÉå= ïÉêÇÉåI= ïáÉ= a~íÉå= òìê= ëí~íáëíáëÅÜÉå= ^ìÑÄÉJ êÉáíìåÖ=~ìë=ÉáåÉê=îçêÜ~åÇÉåÉå=a~íÉåÄ~åâ=áå=ÉáåÉ=bñÅÉäJq~ÄÉääÉ=Éñíê~ÜáÉêí=ïÉêÇÉå=â∏åJ åÉåK== få= îáÉäÉå= c®ääÉå= îÉêÑΩÖÉå= råíÉêåÉÜãÉå= ÄÉêÉáíë= ΩÄÉê= Öêç≈É= a~íÉåÄ~åâÉå= ÑΩê= cáå~åòÄìÅÜJ Ü~äíìåÖI=`çåíêçääáåÖI=`ìëíçãÉê=oÉä~íáçåëÜáé=j~å~ÖÉãÉåí=E`ojF=ìåÇ=ëç=ïÉáíÉêK=aáÉëÉ=a~J íÉå=ëíÉÜÉå=áã=oÉÖÉäÑ~ääÉ=ÇÉå=jáí~êÄÉáíÉêå=ÑΩê=^ìëïÉêíìåÖÉå=éÉê=iÉëÉòìÖêáÑÑ=òìê=sÉêÑΩÖìåÖK= káÅÜí=ëÉäíÉå=ÉåíëíÉÜí=Ç~ÄÉá=ÇÉê=tìåëÅÜI=ëáÅÜ=ÉáåÉå=qÉáä=ÇÉê=a~íÉå=~ìë=ÇÉê=Öêç≈Éå=a~J íÉåÄ~åâ= áå= ÉáåÉ= éêáî~íÉ= bñÅÉäJq~ÄÉääÉ= ~ã= äçâ~äÉå= m`= òì= ÜçäÉåI= ìã= ëáÉ= Ç~åå= Ççêí= ãáí= ÇÉã=ÄÉäáÉÄíÉå=bñÅÉä=ÑΩê=áåÇáîáÇìÉääÉ=wïÉÅâÉ=~ìÑÄÉêÉáíÉåI=ëí~íáëíáëÅÜ=~ìëïÉêíÉåI=Öê~ÑáëÅÜ= Ç~êëíÉääÉå=òì=â∏ååÉåK==
9.2
Import aus MS-Access
báåÉ=^ÅÅÉëëJa~íÉåÄ~åâ=EsÉêëáçå=OMMPF=ÉåíÜ~äíÉ=mÉêëçå~äÇ~íÉå=áå=ÉáåÉê=ìãÑ~åÖêÉáÅÜÉå=q~J ÄÉääÉ=ãáí=ÇÉã=k~ãÉå=Personal=E_áäÇ=VKNFK==
== _áäÇ=VKNW=q~ÄÉääÉ=Personal=ÉáåÉê=^ÅÅÉëëJa~íÉåÄ~åâ== ^ìÑ= ÉáåÉ= ëçäÅÜÉ= a~íÉåÄÉëí~åÇëJq~ÄÉääÉ= ãáí= ÇÉå=îçääëí®åÇáÖÉå=^åÖ~ÄÉå= òì= ~ääÉå=mÉêëçåÉå= ïáêÇ= ïçÜä=åáÉã~äë=Éáå=jáí~êÄÉáíÉê= ÇáêÉâí= òìÖêÉáÑÉå= ÇΩêÑÉå=Ó= Ç~ë= áëí= Éáå=dêìåÇéêáåòáé=ÇÉê= a~íÉåÄ~åâ~êÄÉáíI= ÄÉá= ÇÉê= ÇáÉ= páÅÜÉêÜÉáí=ÇÉê=a~íÉåI= îçê= ~ääÉã= ~ìÅÜ= ÖÉÖÉå= ìåÄÉÑìÖíÉ= báåJ ëáÅÜíå~ÜãÉI=~äë=Éáå=ÄÉÇÉìíÉåÇÉë=hêáíÉêáìã=~åÖÉëÉÜÉå=ïáêÇK== sáÉäãÉÜê=ïáêÇ=ÇìêÅÜ=ÇÉå=^ÅÅÉëëJa~íÉåÄ~åâ~Çãáåáëíê~íçê=ÑΩê=àÉÇÉå=^êÄÉáíëéä~íòI=îçå=ÇÉã= ~ìë= ~ìÑ= ÇáÉ= a~íÉåÄ~åâ= òìÖÉÖêáÑÑÉå= ïÉêÇÉå= Ç~êÑI= äÉÇáÖäáÅÜ= ÉáåÉ= é~ëëÉåÇÉI= ÉáåëÅÜê®åâÉåÇÉ= ^ÄÑê~ÖÉ=îçêÄÉêÉáíÉíK== báåÉ=^ÄÑê~ÖÉ=áëí=Éáå=mêçÖê~ããI=Ç~ë=ëíÉíë=åìê=ÉáåÉå=qÉáä=ÇÉë=a~íÉåÄÉëí~åÇÉëI=áå=ÇÉê=oÉÖÉä= ïáÉÇÉê=áå=q~ÄÉääÉåÑçêãI=äáÉÑÉêíK=== pí~êíÉí=Éáå=jáí~êÄÉáíÉê=ÇáÉ=ÑΩê=áÜå=ìåÇ=ëÉáåÉå=^êÄÉáíëéä~íò=îçêÄÉêÉáíÉíÉ=^ÄÑê~ÖÉI=Ç~åå=ÉêÜ®äí= Éê=ÇÉåàÉåáÖÉå=qÉáä=ÇÉë=a~íÉåÄÉëí~åÇÉëI=ÇÉå=Éê=ÉáåëÉÜÉå=ìåÇ=~ìëïÉêíÉå=Ç~êÑK==
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVV=
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NSM
få=_áäÇ=VKO=áëí=òì=ëÉÜÉåI=Ç~ëë=ÇáÉ=^ÄÑê~ÖÉ= Fuer_MusterfrauI=ÇáÉ=ÇÉê=a~íÉåÄ~åâ~Çãáåáëíê~íçê= ÑΩê= ÇáÉëÉ= jáí~êÄÉáíÉêáå= îçêÄÉêÉáíÉí= Ü~íI= çÑÑÉåëáÅÜíäáÅÜ= åìê= ÉáåáÖÉ=^åÖ~ÄÉå= ~ìë= ÇÉã= mÉêëçJ å~äÇ~íÉåÄÉëí~åÇ= éêÉáëÖáÄí= Ó= ìåÇ= Ç~êΩÄÉê= Üáå~ìë= åìê= ÇáÉàÉåáÖÉå= mÉêëçåÉå= ~ìëäáëíÉíI= ÇáÉ= áå= lêíÉå=ãáí=ÇÉã=^åÑ~åÖëÄìÅÜëí~ÄÉå=B=ïçÜåÉåK==
== _áäÇ=VKOW=aáÉ=^ÄÑê~ÖÉ=Fuer_Musterfrau=äáÉÑÉêí=ÉáåÉå=qÉáä=ÇÉë=a~íÉåÄÉëí~åÇÉë== aáÉëÉåI=ÑΩê=ëáÉ=~äëç=ÑêÉáÖÉÖÉÄÉåÉå=qÉáä=ÇÉë=a~íÉåÄÉëí~åÇÉë=Ç~êÑ=ÇáÉ=_É~êÄÉáíÉêáå=åìå=åìíJ òÉåI=~ìëïÉêíÉåI=~å~äóëáÉêÉåK== páÉ= ã∏ÅÜíÉ= Ç~ÑΩê= áÜê= îÉêíê~ìíÉë= bñÅÉä= îÉêïÉåÇÉåK= ^äëç= ï®Üäí= ëáÉ= áå= ^ÅÅÉëë= òìÉêëí= a^J qbfbumloqfbobk=E_áäÇ=VKPFK==
= _áäÇ=VKPW=bñéçêí=îÉê~åä~ëëÉå=
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VKP==báåêáÅÜíìåÖ=ÉáåÉë=la_`JqêÉáÄÉêë= =
NSN
^åëÅÜäáÉ≈ÉåÇ=Ó=ìåÇ=Ç~ë=áëí=ïáÅÜíáÖ=Ó=ãìëë=ëáÉ=áã=cÉåëíÉê= Dateityp=ÇáÉ=bñÅÉäJsÉêëáçå=ÉáåJ ëíÉääÉåI=ãáí=ÇÉê=ëáÉ=~êÄÉáíÉí=E_áäÇ=VKQFK=tÉåå=ëáÉ=âÉáåÉå=ÉáÖÉåÉå=a~íÉáå~ãÉå=Éáåíê®ÖíI=îÉêJ ïÉåÇÉí=^ÅÅÉëë=ÑΩê=ÇáÉ=òì=ÉêòÉìÖÉåÇÉ=bñÅÉäJa~íÉá=ÇÉå=k~ãÉå=ÇÉê=^ÄÑê~ÖÉK====
== _áäÇ=VKQW=qóé=ÇÉê=wáÉäÇ~íÉá=ÉáåëíÉääÉåI=k~ãÉ=îÉêÖÉÄÉå=== a~ë=áëí=ëÅÜçå=~ääÉëK=kìå=ëáåÇ=ÇáÉ=a~íÉå=~ìë=ÇÉê=^ÄÑê~ÖÉ=~ìÑ=ÇÉã=m`=îçå=cê~ì=jìëíÉêÑê~ì=áå= ÉáåÉê=bñÅÉäJq~ÄÉääÉ=îÉêÑΩÖÄ~êI=ìåÇ=ëáÉ=â~åå=å~ÅÜ=eÉêòÉåëäìëí=Ç~ãáí=~êÄÉáíÉåK== ^ääÉêÇáåÖëW= pçääíÉ= ëáÅÜ= å~ÅÜ= ÉáåáÖÉê= wÉáí= áã= òÉåíê~ä=îÉêï~äíÉíÉå=a~íÉåÄÉëí~åÇ= ÉáåÉ= ûåÇÉJ êìåÖ=ÉêÖÉÄÉåI=ÇáÉ=~ìÅÜ=ÇáÉ=häáÉåíÉä=îçå=cê~ì=jìëíÉêã~åå=ÄÉíêáÑÑí=Ó=Éë=ÖáÄí=å~íΩêäáÅÜ=Ç~åå= âÉáåÉ=~ìíçã~íáëÅÜÉ=^âíì~äáëáÉêìåÖ=áÜêÉê=bñÅÉäJq~ÄÉääÉI=ïáÉ=ëçääíÉ=Éë=~ìÅÜ\== aáÉ=jáí~êÄÉáíÉêáå=ãΩëëíÉ=ëáÅÜ=ÉêåÉìí=ÄÉá=^ÅÅÉëë=~åãÉäÇÉåI=áÜêÉ=^ÄÑê~ÖÉ=ïáÉÇÉê=ëí~êíÉåI=ÇáÉ= a~íÉå=ÉêåÉìí=ÉñéçêíáÉêÉå=ìåÇ=ëç=ïÉáíÉêK== tΩåëÅÜÉåëïÉêí=ï®êÉ=~äëç=ÜáÉê=ÉáåÉ=^ìÑêÉÅÜíÉêÜ~äíìåÖ=ÇÉê=sÉêÄáåÇìåÖ=òìê=a~íÉåÄ~åâI=ëç= Ç~ëë=ÖÉïáëëÉêã~≈Éå=~ìÑ=håçéÑÇêìÅâ=îçå=bñÅÉä=~ìë=EìåÇ=çÜåÉ=ÇáÉ=^ÅÅÉëëJ^ÄÑê~ÖÉ=ÉêåÉìí= ëí~êíÉå=òì=ãΩëëÉåF=ÇáÉ=a~íÉå=áå=ÇÉê=àÉïÉáäë=~âíìÉääÉå=cçêã=~åÖÉÑçêÇÉêí=ïÉêÇÉå=â∏ååÉåK== a~ãáí= ïΩêÇÉå= ~ìÅÜ= áå= bñÅÉä= ëíÉíë=~âíìÉääÉ=a~íÉå=îÉê~êÄÉáíÉíK= fã=^ÄëÅÜåáíí=VKRKO= ~ìÑ= pÉáíÉ= NSU=ïáêÇI=ÄÉáëéáÉäÜ~Ñí=ÄÉòçÖÉå=~ìÑ=ÉáåÉ=lê~ÅäÉJa~íÉåÄ~åâI=ÇÉê=jÉÅÜ~åáëãìë=ÄÉëÅÜêáÉÄÉåI= ãáí=ÇÉã=ÇáÉëÉê=tìåëÅÜ=ÉêÑΩääí=ïÉêÇÉå=â~ååK=
9.3
Einrichtung eines ODBC-Treibers
a~íÉåÄ~åâÉå=ÄÉÑáåÇÉå=ëáÅÜ=ΩÄäáÅÜÉêïÉáëÉ=~ìÑ=ÉáåÉã=òÉåíê~äÉå=pÉêîÉê=ÇÉë=råíÉêåÉÜãÉåëK== rã=~ìë=bñÅÉä=ÜÉê~ìë=Ç~ê~ìÑ=òìÖêÉáÑÉå=òì=â∏ååÉåI=ãΩëëÉå=ÉáåáÖÉ=sçê~ìëëÉíòìåÖÉå=ÉêÑΩääí= ëÉáåW= aÉê=^åïÉåÇÉê=ãìëë=áå=ÇÉê=ÉåíëéêÉÅÜÉåÇÉå=a~íÉåÄ~åâ=Éáå=_ÉåìíòÉêâçåíç=E^ÅÅçìåíF= ÄÉëáíòÉåK=
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVV=
V==fãéçêí=îçå=a~íÉå=~ìë=a~íÉåÄ~åâÉå=
NSO
^ìÑ=ÇÉã=m`=ÇÉë=^åïÉåÇÉêë=ãìëë=Éáå=ÉåíëéêÉÅÜÉåÇÉê=la_`JqêÉáÄÉê=EléÉå=a~í~Ä~ëÉ= `çååÉÅíáîáíóF= áåëí~ääáÉêí= ëÉáåK= báåáÖÉ= ÇáÉëÉê= qêÉáÄÉê= ëáåÇ= áã= fåëí~ää~íáçåëìãÑ~åÖ= îçå= táåÇçïë=um=ÉåíÜ~äíÉåK= fååÉêÜ~äÄ=ÇÉë=jp=lÑÑáÅÉ=m~âÉíÉë=ãìëë=Ç~ë=qççä=MS Query=áåëí~ääáÉêí=ëÉáåK= få= ÇáÉëÉã= ^ÄëÅÜåáíí= ïáêÇ= òìÉêëí= pÅÜêáíí= ÑΩê= pÅÜêáíí= ÇáÉ= báåêáÅÜíìåÖ=ÇÉë=la_`JqêÉáÄÉêë= ÄÉJ ëÅÜêáÉÄÉåK=fã=ÑçäÖÉåÇÉå=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NSP=ïáêÇ=Ç~åå=ÇáÉ=sçêÖÉÜÉåëïÉáëÉ=òìê=bñíê~âJ íáçå=ÇÉê=a~íÉå=ÄÉëÅÜêáÉÄÉåK== aáÉ= báåêáÅÜíìåÖ=ÉáåÉë=la_`JqêÉáÄÉêë= ïáêÇ= ~åÜ~åÇ= ÇÉë= _ÉíêáÉÄëëóëíÉãë= jp= táåÇçïë= um= mêçÑÉëëáçå~ä= îÉê~åëÅÜ~ìäáÅÜíK= aÉê= ëé®íÉê= ÄÉå∏íáÖíÉ= la_`JqêÉáÄÉê= ÑΩê= lê~ÅäÉ= ÖÉÜ∏êí= ÜáÉê= òìã=iáÉÑÉêìãÑ~åÖ=ÇÉë=_ÉíêáÉÄëëóëíÉãëK= aáÉ= ^Çãáåáëíê~íáçå= ÇáÉëÉê= qêÉáÄÉê= ÑáåÇÉí= ã~å= ΩÄÉê= pq^oqbfkpqbiirkdbkpvpqbjpqbrbJ orkdsbot^iqrkd=E_áäÇ=VKRFW=
= _áäÇ=VKRW=råíÉêÖêìééÉ=VERWALTUNG=áå=ÇÉê=póëíÉãëíÉìÉêìåÖ=îçå=táåÇçïë=um==
== _áäÇ=VKSW=pí~åÇ~êÇã®≈áÖ=îçêÜ~åÇÉåÉ=a~íÉåèìÉääÉå=
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VKQ==wìÖêáÑÑ=~ìÑ=âçåâêÉíÉ=a~íÉåÄ~åâÉå=
NSP
aÉê= ^ìÑêìÑ= ÇÉë= póãÄçäë= Datenquellen (ODBC)= ∏ÑÑåÉí= Ç~ë= cÉåëíÉê= ÇÉë= la_`Ja~íÉåèìÉääÉåJ ^Çãáåáëíê~íçêëI=áå=ÇÉëëÉå=cÉåëíÉê= Benutzerdatenquellen ëáÅÜ=ÄÉêÉáíë=ÉáåáÖÉ=ÇÉê=ëí~åÇ~êÇã®J ≈áÖ=îçêÜ~åÇÉåÉå=a~íÉåèìÉääÉå=ÄÉÑáåÇÉå=E_áäÇ=VKSFK=
= _áäÇ=VKTW=sÉêÑΩÖÄ~êÉ=la_`JqêÉáÄÉê=ìåíÉê=jp=táåÇçïë=um=mêçÑÉëëáçå~ä= aáÉ=_ÉåìíòÉêJapk=ëáåÇ=ÇáÉ=ÉáåÖÉêáÅÜíÉíÉå=a~íÉåèìÉääÉåI=ÇáÉ=åìê=ÇÉã=~âíìÉää=~ã=m`=~åÖÉJ ãÉäÇÉíÉå=_ÉåìíòÉê=òìê=sÉêÑΩÖìåÖ=ëíÉÜÉåK== pçää=ÉáåÉ=ïÉáíÉêÉ=a~íÉåèìÉääÉ=ÜáåòìÖÉÑΩÖí=ïÉêÇÉåI=Ç~åå=áëí=ãáííÉäë= Hinzufügen =Ç~ë=cÉåëJ íÉê=Neue Datenquelle erstellen=E_áäÇ=VKTF=òì=∏ÑÑåÉåX=Ççêí=â~åå=Ç~åå=~ìëÖÉï®Üäí=ïÉêÇÉåK==
9.4
Zugriff auf konkrete Datenbanken
9.4.1
Microsoft SQL-Server
aÉê=pniJpÉêîÉêI=Éáå=jáÅêçëçÑíJmêçÇìâíI=áëí=Éáå=äÉáëíìåÖëÑ®ÜáÖÉë=a~íÉåÄ~åâJpóëíÉãI=Ç~ë=áå= îáÉäÉå=_ÉêÉáÅÜÉå=^åïÉåÇìåÖ=ÑáåÇÉíK== ^ìÅÜ= Ççêí= ïáêÇ= ãáí= eáäÑÉ= îçå= ^ÄÑê~ÖÉå= ÑΩê= àÉÇÉå= ^êÄÉáíëéä~íò= åìê= ÉáåÉ= ëçäÅÜÉ= qÉáäãÉåÖÉ= ÇÉë=a~íÉåÄÉëí~åÇÉë=ÄÉêÉáíÖÉëíÉääíI=ÇáÉ=ÇÉê=hçãéÉíÉåò=ìåÇ=ÇÉã=fåÑçêã~íáçåëÄÉÇΩêÑåáë=ÇÉë= àÉïÉáäáÖÉå=_É~êÄÉáíÉêë=ÉåíëéêáÅÜíK== aáÉ= sÉêëáçå= bñÅÉä= OMMP= ÄáÉíÉí= ÉáåÉ= iÉáëíìåÖ= Add-In für SQL Server Analysis Services= ~åI= ÇáÉ=áå== http://go.microsoft.com/?linkid= 1140024
ïáÉ=ÑçäÖí=ÄÉëÅÜêáÉÄÉå=áëíW== dêÉáÑÉå=páÉ=ëÅÜåÉää=ìåÇ=éêçÄäÉãäçë=~ìÑ=ãìäíáÇáãÉåëáçå~äÉ=a~íÉå=òìI=ÑΩÜêÉå=páÉ=ÇÉí~áääáÉêíÉ= a~íÉå~å~äóëÉå=ÇìêÅÜ=ìåÇ=ÉêëíÉääÉå=páÉ=ÑäÉñáÄäÉI=áåíÉê~âíáîÉ=_ÉêáÅÜíÉ=áå=jáÅêçëçÑí=bñÅÉäK==
9.4.2
Oracle
cΩê=ÇáÉ=hçåÑáÖìêáÉêìåÖ=ÇÉë=la_`JqêÉáÄÉêë=ÑΩê=lê~ÅäÉ=ãìëë=ÇÉê=sÉêÄáåÇìåÖëÄÉòÉáÅÜåÉê= ETNS-AliasF=ÑΩê=ÇáÉ=a~íÉåÄ~åâ=ÄÉâ~ååí=ëÉáåI=ÜáÉê=ëçääíÉ=ã~å=ëáÅÜ=~å=ÇÉå=^Çãáåáëíê~íçê= ïÉåÇÉåK==
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVV=
NSQ
V==fãéçêí=îçå=a~íÉå=~ìë=a~íÉåÄ~åâÉå=
tÉáíÉêÜáå=ãìëë=ÇáÉ=lê~ÅäÉ=`äáÉåí=pçÑíï~êÉ=ÄÉêÉáíë=áåëí~ääáÉêí=ëÉáåK=aáÉë=áëí=áããÉê=Ç~åå=ÇÉê= c~ääI= ïÉåå= ÇÉê= _ÉåìíòÉê= ÄÉêÉáíë= ãáí= `äáÉåíJpÉêîÉêJ^åïÉåÇìåÖÉå= ~êÄÉáíÉíI= ÇáÉ= ~ìÑ= lê~ÅäÉJ a~íÉåÄ~åâÉå=Ä~ëáÉêÉåK= få= ÇÉå= ãÉáëíÉå= lê~ÅäÉJa~íÉåÄ~åâÉå= áëí= Éáå= pí~åÇ~êÇÄÉåìíòÉê= å~ãÉåë= scott= Em~ëëïçêí= tigerF=òì=pÅÜìäìåÖëòïÉÅâÉå=ãáí=ÉáåÖÉêáÅÜíÉíK== bë=ÖáÄí=~ÄÉê=àÉíòí=ãáí=ÉáåÉê=åÉì=îÉêÑΩÖÄ~êÉå=sÉêëáçå=lê~ÅäÉ=a~í~Ä~ëÉ=bñéêÉëë=bÇáíáçå=EOracle Database XEF=ÉáåÉ=òìê=Öêç≈Éå=a~íÉåÄ~åâ=âçãé~íáÄäÉ=sÉêëáçå=îçå=lê~ÅäÉ=NMÖK=páÉ=áëí=äÉJ ÇáÖäáÅÜ=äáãáíáÉêíI=Ç~ëë=ã~ñáã~ä=Éáå=mêçòÉëëçêI=N=d_=e~ìéíëéÉáÅÜÉê=ìåÇ=ã~ñáã~ä=Q=d_=a~J íÉå=îÉêïÉåÇÉí=ïÉêÇÉå=â∏ååÉåK=j~å=â~åå=ëáÉ=âçëíÉåäçë=ÜÉêìåíÉê=ä~ÇÉå=ìåÇ=ÄÉåìíòÉåI=~ìÅÜ= ÑΩê=âçããÉêòáÉääÉ=wïÉÅâÉK== få= ÇÉê= a~íÉåÄ~åâ= Oracle Database XE= E~ìÑ= ÇáÉ= áå= ÇáÉëÉã= ^ÄëÅÜåáíí= _ÉòìÖ= ÖÉåçããÉå= ïáêÇF=ãÉäÇÉí=ã~å=ëáÅÜ=~äë=_ÉåìíòÉê=hr=ãáí=ÇÉã=ÖäÉáÅÜä~ìíÉåÇÉå=m~ëëïçêí=hr ~åK====== aÉê= _ÉåìíòÉê= hr= áëí= ~ÄÉê= ~ìÅÜ= áå= àÉÇÉê= Öêç≈Éå= lê~ÅäÉ=NMÖJa~íÉåÄ~åâ= îçêÜ~åÇÉåI= ëçÑÉêå= ÄÉá=ÇÉê=fåëí~ää~íáçå=ÇáÉ=_ÉáëéáÉäJpÅÜÉã~ë=ãáí=áåëí~ääáÉêí=ïìêÇÉåK= lÄïçÜä=áå=ÇáÉëÉã=_ÉáëéáÉä=~ìÑ=ÉáåÉ=lê~ÅäÉJa~íÉåÄ~åâ=òìÖÉÖêáÑÑÉå=ïáêÇI=áëí=ÇáÉ=sçêÖÉJ ÜÉåëïÉáëÉ=ÑΩê=~åÇÉêÉ=a~íÉåÄ~åâÉåI=òK_K=jp=pni=pÉêîÉêI=f_j=a_LO=ìëïK=~å~äçÖK= k~ÅÜ=_Éí®íáÖÉå=ÇÉë=_ìííçåë= Hinzufügen =E_áäÇ=VKS=~ìÑ=pÉáíÉ=NSOF=ï®Üäí=ã~å=~äëç=~ìë=ÇÉê= iáëíÉ=ÇÉê=îÉêÑΩÖÄ~êÉå=qêÉáÄÉê=ÇÉå=lê~ÅäÉJqêÉáÄÉê=E_áäÇ=VKT=~ìÑ=pÉáíÉ=NSPF=~ìëK== pçääíÉ=ÇáÉ=lê~ÅäÉ=`äáÉåíJpçÑíï~êÉ=åáÅÜí=áåëí~ääáÉêí=ëÉáåI=ÉêÜ®äí=ã~å=ÉáåÉ=cÉÜäÉêãÉäÇìåÖ=E_áäÇ= VKUFK= få= ÇáÉëÉã= c~ää= ãìëë= ÇáÉ= fåëí~ää~íáçå= ÇÉê= lê~ÅäÉJhçãéçåÉåíÉå= ESQL*Net ClientF= Éêëí= å~ÅÜÖÉÜçäí=ïÉêÇÉåK==
= _áäÇ=VKUW=cÉÜäÉêãÉäÇìåÖ=ÄÉá=åáÅÜí=îçêÜ~åÇÉåÉê=lê~ÅäÉJ`äáÉåíJpçÑíï~êÉ= fã= c~ääÉI= Ç~ëë= ÇáÉ= lê~ÅäÉ= `äáÉåíJpçÑíï~êÉ= ÄÉêÉáíë= îçêÜ~åÇÉå= áëíI= ÉêëÅÜÉáåí= ÇÉê= aá~äçÖ= ~ìë= _áäÇ=VKVX=áã=_áäÇ=ëáåÇ=ÇêÉá=báåÖ~ÄÉå=ÄÉêÉáíë=ÇìêÅÜÖÉÑΩÜêí=ïçêÇÉåK==
= _áäÇ=VKVW=kçíïÉåÇáÖÉ=báåÖ~ÄÉå=ÑΩê=ÇÉå=lê~ÅäÉJla_`JqêÉáÄÉê= aÉê=a~íÉåèìÉääÉåå~ãÉ=áëí=Ç~ÄÉá=ÉáåÉ=ÑêÉá=ï®ÜäÄ~êÉ=_ÉòÉáÅÜåìåÖI=ìåíÉê=ïÉäÅÜÉê=ÇÉê=_ÉåìíJ òÉê=ëé®íÉê=áã= MS Query=ÇáÉ=a~íÉåÄ~åâ=~åÖáÄíI=~ìë=ÇÉê=ÇáÉ=a~íÉå=ëí~ããÉå=ëçääÉåK=aáÉ=_ÉJ ëÅÜêÉáÄìåÖ=áëí=çéíáçå~äI=â~åå=~äëç=ÑêÉá=ÖÉä~ëëÉå=ïÉêÇÉåK=aÉê=_ÉåìíòÉêå~ãÉ=áëí=ÇÉê=hçåíçJ å~ãÉ=áå=ÇÉê=a~íÉåÄ~åâI=áå=_áäÇ=VKV=ïìêÇÉ=Ç~ÑΩê=ÇÉê=lê~ÅäÉJubJrëÉê=hr=ÉáåÖÉíê~ÖÉåK=
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVV=
VKR==bñÅÉäJwìÖêáÑÑ=~ìÑ=lê~ÅäÉ= =
NSR
eáåíÉê= ÇÉê= _ÉòÉáÅÜåìåÖ= pÉêîÉê= Eáå= _áäÇ= VKV= ÄÉäÉÖí= ãáí= xeF= îÉêÄáêÖí= ëáÅÜ= Éáå= ëç= ÖÉå~ååíÉê= TNS-AliasI= Ç~ë= áëí= Éáå= hΩêòÉä= ÑΩê= ÉáåÉ= lê~ÅäÉJa~íÉåÄ~åâJsÉêÄáåÇìåÖI= ÇáÉ= áå= ÇÉê= lê~ÅäÉJ `äáÉåíJpçÑíï~êÉ=ÄÉâ~ååí=ëÉáå=ãìëëK=a~ÑΩê=ãìëë=ã~å=ëáÅÜ=ÖÉÖÉÄÉåÉåÑ~ääë=~å=ëÉáåÉå=a~íÉåJ Ä~åâ~Çãáåáëíê~íçê=ïÉåÇÉåK== EpçÑÉêå=ÇáÉëÉ=^äá~ëJk~ãÉå=åáÅÜí=ìåíÉêåÉÜãÉåëïÉáí=òÉåíê~ä=îÉêï~äíÉí=ïÉêÇÉåI=ÜáäÑí=~ìÅÜ=Éáå= _äáÅâ=áå=ÇáÉ=a~íÉá=%ORACLE_HOME%\network\admin\tnsnames.oraI=ÇáÉë=~ÄÉê=åìê=ÑΩê=fåëáÇÉêFK= iÉáÇÉê= áëí= Éë= ~å= ÇáÉëÉê= píÉääÉ= ìåÇ= òì= ÇáÉëÉã= wÉáíéìåâí= åçÅÜ= åáÅÜí= ã∏ÖäáÅÜI= ÇáÉ= âçêêÉâíÉ= sÉêÄáåÇìåÖ=òìê=a~íÉåÄ~åâ=ÖäÉáÅÜ=òì=íÉëíÉåI=ÇáÉë=â~åå=Éêëí=ëé®íÉê=áã=^ÄÑê~ÖÉïÉêâòÉìÖ= MS Query=îÉêáÑáòáÉêí=ïÉêÇÉåK= aáÉ=hçåÑáÖìê~íáçå=ÇÉë=la_`JqêÉáÄÉêë=áëí=~ÄÉê=Ç~ãáí=~ÄÖÉëÅÜäçëëÉåK=
9.5
Excel-Zugriff auf Oracle
9.5.1
Daten importieren
k~ÅÜ= ÇÉã= pí~êíÉå= îçå= bñÅÉä= ï®Üäí= ã~å= a^qbkbuqbokb= a^qbk= fjmloqfbobkkbrb= ^_J co^db=bopqbiibk=~ìëK== pçääíÉ=Ç~ë=lÑÑáÅÉJtÉêâòÉìÖ=MS Query=åáÅÜí=áåëí~ääáÉêí=ëÉáåI=ïΩêÇÉ=åìå=ÉáåÉ=ÉåíëéêÉÅÜÉåÇÉ= cÉÜäÉêãÉäÇìåÖ=ÉêëÅÜÉáåÉå=ìåÇ=ÇáÉëÉ=fåëí~ää~íáçå=ãΩëëíÉ=Éêëí=ãáí=eáäÑÉ=ÇÉê=jp=lÑÑáÅÉJ`a= å~ÅÜÖÉÜçäí=ïÉêÇÉåK= ^åëçåëíÉå=ÉêëÅÜÉáåí=ÇÉê=aá~äçÖI=ÇÉê=ÇáÉ=îçêÜ~åÇÉåÉå=DSN=EÇ~í~=ëçìêÅÉ=å~ãÉF=~ìÑäáëíÉíK=eáÉê= ëçääíÉ=ÇáÉ=îçêÜáå=âçåÑáÖìêáÉêíÉ=a~íÉåÄ~åâîÉêÄáåÇìåÖ=îçêÖÉÑìåÇÉå=ïÉêÇÉå=E_áäÇ=VKNMFK=
== _áäÇ=VKNMW=iáëíÉ=ÇÉê=áã=póëíÉã=ÄÉâ~ååíÉå=a~íÉåèìÉääÉå=EDSNF= k~ÅÜ=ÇÉê=^ìëï~Üä=ÇÉê=é~ëëÉåÇÉå=a~íÉåèìÉääÉ=ÉêëÅÜÉáåí=ÇáÉ=m~ëëïçêíJ^ÄÑê~ÖÉ=E_áäÇ=VKNNFK==
= _áäÇ=VKNNW=m~ëëïçêíJ^ÄÑê~ÖÉ=
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVV=
V==fãéçêí=îçå=a~íÉå=~ìë=a~íÉåÄ~åâÉå=
NSS
aÉê=_ÉåìíòÉêå~ãÉ=ìåÇ=ÇáÉ=a~íÉåÄ~åâ=ëáåÇ=Ççêí=òï~ê=ÄÉêÉáíë=ÉáåÖÉíê~ÖÉåI=â∏ååíÉå=ÜáÉê=~ÄÉê= åçÅÜ=~ÄÖÉ®åÇÉêí=ïÉêÇÉå=EaáÉ=ÉáÖÉåíäáÅÜÉ=la_`JhçåÑáÖìê~íáçå=®åÇÉêí=ëáÅÜ=Ç~ÇìêÅÜ=åáÅÜíFK== táÉ= ëÅÜçå= Éêï®ÜåíI= ïáêÇ= ÜáÉê= Ç~ë= îçå= lê~ÅäÉ= ãáí= ÇÉê= sÉêëáçå= ub= ÑΩê= iÉêåÉåÇÉ= ÄÉêÉáíÖÉJ ëíÉääíÉ=m~~ê=hrLhr=ÑΩê=_ÉåìíòÉêå~ãÉ=ìåÇ=hÉååïçêí=îÉêïÉåÇÉíK== pçÑÉêå=ÇáÉ=báåêáÅÜíìåÖ=ÇÉë=la_`JqêÉáÄÉêë=âçêêÉâí=ï~êI=ëí~êíÉí=àÉíòí=áã=eáåíÉêÖêìåÇ=Ç~ë= mêçÖê~ãã=MS QueryK== få= ÉáåÉã= aá~äçÖÑÉåëíÉê= ÉêëÅÜÉáåÉå= åìå= ~ääÉ= lÄàÉâíÉ= ÇÉê= lê~ÅäÉJa~íÉåÄ~åâ= Eq~ÄÉääÉåI= sáÉïëL^åëáÅÜíÉåI=póåçåóãÉFI=~ìÑ=ÇáÉ=ÇÉê=~åÖÉãÉäÇÉíÉ=_ÉåìíòÉê=EÜáÉêW=hrF=wìÖêáÑÑ=ÄÉëáíòíK= fã=_áäÇ=VK= NO=ïìêÇÉ=ÄÉêÉáíë=Äáë=òìê=q~ÄÉääÉ= EMPLOYEES=E^åÖÉëíÉääíÉåJq~ÄÉääÉF=ÖÉëÅêçääí=ìåÇ= ÇÉê=^åÑ~åÖ=ÇÉê=q~ÄÉääÉåëíêìâíìê=~åÖÉòÉáÖíK=
== _áäÇ=VKNOW=iáëíÉ=ÇÉê=lÄàÉâíÉ=ÇÉë=a~íÉåÄ~åâÄÉåìíòÉêë= eáÉê=â∏ååÉå=åìå=ÉåíïÉÇÉê=ÇáÉ=ÖÉë~ãíÉ=q~ÄÉääÉ=çÇÉê=ÉáåòÉäåÉ=pé~äíÉå=áå=ÇáÉ=^ÄÑê~ÖÉ=ΩÄÉêJ åçããÉå=ïÉêÇÉåK== fã=_ÉáëéáÉä=E_áäÇ=VKNPF=ïáêÇ=ÇáÉ=ÖÉë~ãíÉ=q~ÄÉääÉåëíêìâíìê=éÉê=häáÅâ=~ìÑ= > =ΩÄÉêåçããÉåK==
== _áäÇ=VKNPW=§ÄÉêåçããÉåÉ=pé~äíÉå= k~ÅÜ= Weiter > = ÉêëÅÜÉáåí= Éáå= aá~äçÖI= ãáí= ïÉäÅÜÉã= ÇáÉ= òì= ëÉäÉâíáÉêÉåÇÉå= a~íÉå= ÉáåÖÉJ ëÅÜê®åâí=ïÉêÇÉå=â∏ååÉåK==
cΩê=bñÅÉä=OMMTJ^åïÉåÇÉê=ÖáÄí=Éë=_ÉÇáÉåìåÖëÜáåïÉáëÉ=òì=ÇáÉëÉã=^ÄëÅÜåáíí=~Ä=pÉáíÉ=NVV=
VKR==bñÅÉäJwìÖêáÑÑ=~ìÑ=lê~ÅäÉ= =
NST
fã=_ÉáëéáÉä=E_áäÇ=VKNQF=ïÉêÇÉå=åìê=~ääÉ=ÇáÉàÉåáÖÉå=^åÖÉëíÉääíÉå=~ìëÖÉï®ÜäíI=ÇáÉ=áå=aÉé~êJ íÉãÉåíë=ãáí=ÉáåÉê=aÉé~êíãÉåíJkìããÉê=ìåíÉêÜ~äÄ=îçå=RM=~êÄÉáíÉå=Eáå=pni=ï®êÉ=ÇáÉë=ÉáåÉ= WHEREJ_ÉÇáåÖìåÖFK=a~=ÇÉê=^ëëáëíÉåí=ÇáÉ=^êÄÉáí=ã~ñáã~ä=ÉêäÉáÅÜíÉêå=ïáääI=ÖêÉáÑí=Éê=ÄÉêÉáíë=~ìÑ= ÇáÉ=a~íÉåÄ~åâ=òì=ìåÇ=ÉêãáííÉäí=~ääÉ=ã∏ÖäáÅÜÉå=tÉêíÉ=ÑΩê=ÇáÉ=êÉÅÜíÉ=tÉêíÉäáëíÉK== aáÉë=â~åå=ÄÉá=ëÉÜê=Öêç≈Éå=a~íÉåãÉåÖÉå=òì=t~êíÉòÉáíÉå=ÑΩÜêÉåK= =
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aÉê= å®ÅÜëíÉ= aá~äçÖ= E_áäÇ= VKNRF= äÉÖí= ã∏ÖäáÅÜÉ= pçêíáÉêâêáíÉêáÉå= ÇÉê= a~íÉå= ÑÉëí= Eáå= pni= ÄÉJ â~ååí=~äë=ORDER BYFW= kìå= ÉêëÅÜÉáåí= ÇÉê= äÉíòíÉ= aá~äçÖ= ÇÉë= ^ëëáëíÉåíÉå= E_áäÇ= VKNSF= ìåÇ= ÖáÄí= ÇáÉ= j∏ÖäáÅÜâÉáíI= ÇáÉ= a~íÉå=ÉåíïÉÇÉê=ÖäÉáÅÜ=~å=bñÅÉä=òì=äáÉÑÉêå=çÇÉê=ÇáÉ=^ÄÑê~ÖÉ=áå=MS Query=Éêëí=åçÅÜ=ïÉáíÉê=òì= ÄÉ~êÄÉáíÉåK=_áäÇ=VKNS=òÉáÖíI=Ç~ëë=ÜáÉê=ÄÉáëéáÉäÜ~Ñí=ÇáÉ=äÉíòíÉêÉ=s~êá~åíÉ=ÖÉï®Üäí=ïìêÇÉK== = =
= _áäÇ=VKNTW=MS Query=ãáí=~ìëÖÉÑΩÜêíÉê=^ÄÑê~ÖÉ= cçäÖäáÅÜ=ÉêëÅÜÉáåí=MS Query=E_áäÇ=VKNTF=ìåÇ=òÉáÖí=ÇáÉ=~ìëÖÉï®ÜäíÉå=a~íÉå=~åK= pçÑÉêå=ã~å=ÇáÉ=^ÄÑê~ÖÉëéê~ÅÜÉ=pni=ÄÉÜÉêêëÅÜíI=â~åå=ÜáÉê=ÇáÉ=^ÄÑê~ÖÉ=ÇìêÅÜ=häáÅâ=~ìÑ=ÇÉå= _ìííçå= SQL =åçÅÜ=Éáåã~ä=å~ÅÜîçääòçÖÉå=ïÉêÇÉåK== få=ÇáÉëÉã=c~ää=ïáêÇ=ÑçäÖÉåÇÉë=~åÖÉòÉáÖíW= SELECT
EMPLOYEES.EMPLOYEE_ID, EMPLOYEES.FIRST_NAME, EMPLOYEES.LAST_NAME, EMPLOYEES.EMAIL, EMPLOYEES.PHONE_NUMBER, EMPLOYEES.HIRE_DATE, EMPLOYEES.JOB_ID, EMPLOYEES.SALARY, EMPLOYEES.COMMISSION_PCT, EMPLOYEES.MANAGER_ID, EMPLOYEES.DEPARTMENT_ID FROM HR.EMPLOYEES EMPLOYEES WHERE (EMPLOYEES.DEPARTMENT_ID<50) ORDER BY EMPLOYEES.SALARY DESC
aÉê=^ìÑêìÑ=îçå=MS Query=áëí=~ÄÉê=~ìë=ÉáåÉã=~åÇÉêÉå=dêìåÇ=ëáååîçääW== aáÉ=ÉêëíÉääíÉ=^ÄÑê~ÖÉ=â~åå=ÖÉëéÉáÅÜÉêí=ïÉêÇÉå=Eãáí=a^qbfpmbf`ebok=rkqboFK=pçäÅÜÉ=^ÄJ Ñê~ÖÉå=ÉêÜ~äíÉå=ÇáÉ=a~íÉáÉåÇìåÖ= DQY=ìåÇ=â∏ååÉå=~ìë=bñÅÉä=ÄÉäáÉÄáÖ=çÑí=ïáÉÇÉê=~ìÑÖÉêìJ ÑÉå=ïÉêÇÉåK= ^äë= äÉíòíÉ= ^âíáçå= ï®Üäí= ã~å= åìå= a^qbfa^qbk= ^k= jf`olplcq= bu`bi= wro§`hdb_bkX= Ç~åå= ïáêÇ=ÖÉÑê~ÖíI=áå=ïÉäÅÜÉå=_ÉêÉáÅÜ=ÇÉë=bñÅÉäJq~ÄÉääÉåÄä~ííÉë=ÇáÉ=a~íÉå=Éáåòìíê~ÖÉå=ëáåÇK== _áäÇ=VKNU=òÉáÖí=ëÅÜäáÉ≈äáÅÜI=ïáÉ=áå=ÇÉê=bñÅÉäJq~ÄÉääÉ=ÇáÉ=~ÄÖÉÑê~ÖíÉå=a~íÉå=òì=ëÉÜÉå=ëáåÇK== aáÉ= ÖÉëéÉáÅÜÉêíÉ= ^ÄÑê~ÖÉ= â~åå= ΩÄÉê= a^qbkbuqbokb= a^qbkdbpmbf`eboqb= ^_co^db= ^rpJ c§eobk=ÄÉäáÉÄáÖ=çÑí=ïáÉÇÉêÜçäí=ïÉêÇÉåK=
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9.5.2
NSV
Daten visualisieren und aktuell halten
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Anhang 1: Vom Problem zur Excel-Lösung bë=áëí=ÉáåÉ=fääìëáçå=îçå=Eå~áîÉåF=^ì≈ÉåëíÉÜÉåÇÉåI=Ç~ëë=ÇáÉ=i∏ëìåÖ=ÉáåÉë=mêçÄäÉãë=Ç~ãáí= ÄÉÖáååÉI= Ç~ëë= ã~å= ëáÅÜ= ÉáåÑ~ÅÜ= ~å= ÇÉå= m`= ëÉíòíI= bñÅÉä= ëí~êíÉíI= tÉêíÉ= ìåÇ= cçêãÉäå= ãáí= çÇÉê=çÜåÉ=cìåâíáçåÉå=Éáåíê®ÖíI=cçêãÉäå=ÖÉÉáÖåÉí=âçéáÉêí=ìåÇ=~åëÅÜäáÉ≈ÉåÇ=Ç~ë=bêÖÉÄåáë= ÑêÉìÇáÖ=òìê=hÉååíåáë=åáããíK== aáÉëÉë= sçêÖÉÜÉå= ÑìåâíáçåáÉêí= åìê= ÄÉá= ëÉÜêI= ëÉÜê= ÉáåÑ~ÅÜÉå= mêçÄäÉãëíÉääìåÖÉå= ìåÇ= áëí= áãJ ãÉê=ãáí=ÇÉã=oáëáâç=ÄÉÜ~ÑíÉíI=Ç~ëë=ÖêìåÇäÉÖÉåÇÉ=aÉåâÑÉÜäÉê=EäçÖáëÅÜÉ=cÉÜäÉêF=~ìÑíêÉíÉåI=ÇáÉ= ëáÅÜ=Ç~åå=ãáí=_ÉÇáÉåìåÖëÑÉÜäÉêå=îçå=bñÅÉä=EòK=_K=îÉêÖÉëëÉåÉã=çÇÉê=Ñ~äëÅÜ=ÖÉëÉíòíÉã=açäJ ä~êòÉáÅÜÉåF= ΩÄÉêä~ÖÉêå= ìåÇ= òì= EpÅÜÉáåJF= bêÖÉÄåáëëÉå= ÑΩÜêÉåI= ÇÉåÉå= ã~å= ã∏ÖäáÅÜÉêïÉáëÉ= ~ìÑ=^åÜáÉÄ=åáÅÜí=Éáåã~ä=~åëáÉÜíI=Ç~ëë=ëáÉ=Ñ~äëÅÜ=ëáåÇK== pÅÜä~ÖÉå=ïáê=Ç~òì=ÇÉå=_çÖÉå=òìê=báåäÉáíìåÖ=ÇáÉëÉë=_ìÅÜÉë=ìåÇ=ÇÉã=Ççêí=~ìÑ=pÉáíÉ=NQ=îçêJ ÖÉÑΩÜêíÉå=_ÉáëéáÉä=òìê=_ÉêÉÅÜåìåÖ=ÇÉê=pìããÉå=ÇÉê=mêÉáëÉ=ÇÉê=TBJ=ÄòïK=ÇÉê=NVBJ^êíáâÉäK= _Éåìíòí=ã~å=Ç~ë=açää~êòÉáÅÜÉå=åáÅÜíI=Ç~åå=áëí=ÉáåÉ=e®äÑíÉ=ÇÉê=oÉÅÜåìåÖ=êáÅÜíáÖI=ÇáÉ=~åÇÉêÉ= Ç~ÖÉÖÉå=Ñ~äëÅÜK== tÉê=ïáää=Ç~ë=ÇÉå=w~ÜäÉåïÉêíÉå=~åëÉÜÉå\== bë=ÉãéÑáÉÜäí=ëáÅÜ=~äëç=ÇêáåÖÉåÇI=ÇÉå=mêçÄäÉãä∏ëìåÖëéêçòÉëë=áå=pÅÜêáííÉ=òì=òÉêäÉÖÉåI=àÉÇÉå= pÅÜêáíí=áå=ëÉáåÉå=^ìÑÖ~ÄÉå=ìåÇ=bêÖÉÄåáëëÉå=ëçïáÉ=ëÉáåÉå=péÉòáÑáâ~=ÖÉå~ì=òì=ÇÉÑáåáÉêÉåK===== _Éï®Üêí=Ü~í=ëáÅÜ=Ç~ë=ëíìÑÉåïÉáëÉ=eÉê~åÖÉÜÉå=áå=ëÉÅÜë=pÅÜêáííÉåW== =
Beispiel bzw. Problem
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Theorie
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Rechenschema
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Implementierung
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Diskussion
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============================================================ ^åÜ~åÖ=NW=sçã=mêçÄäÉã=òìê=bñÅÉäJi∏ëìåÖ= NTO pÉÜÉå=ïáê=ìåë=åìå=ÇáÉ=ÉáåòÉäåÉå=pÅÜêáííÉ=ÇÉë=mêçÄäÉãä∏ëìåÖëéêçòÉëëÉë=Éêëí=~ääÖÉãÉáå=ìåÇ= Ç~åå=~å=ÉáåÉã=_ÉáëéáÉä=~åK== mêçÄäÉãÄÉëÅÜêÉáÄìåÖW=aÉê=^ìëÖ~åÖëéìåâí=áëí=ãÉáëí=Éáå=âçåâêÉíÉë=mêçÄäÉã=ãáí=âçåJ âêÉíÉå=w~ÜäÉåI=Ç~ë=ã~å=ÇìêÅÜêÉÅÜåÉå=ã∏ÅÜíÉK= =qÜÉçêáÉW=få=ÇáÉëÉã=pÅÜêáíí=ëìÅÜí=ã~å=òì=ÇÉã=_ÉáëéáÉä=ÇáÉ=é~ëëÉåÇÉ=Eã~íÜÉã~íáëÅÜÉF= qÜÉçêáÉI=ãÉáëí=áå=cçêã=îçå=cçêãÉäåK= =oÉÅÜÉåëÅÜÉã~W=få=ÇáÉëÉã=pÅÜêáíí=ïÉêÇÉå=ÇáÉ=ÖÉÖÉÄÉåÉå=a~íÉåI=_ÉëÅÜêáÑíìåÖÉå=ìåÇ= ÇáÉ=åçíïÉåÇáÖÉå=cçêãÉäå=áå=q~ÄÉääÉå=~åÖÉçêÇåÉíI=ÇáÉ=ÖÉÖÉÄÉåÉåÑ~ääë=ãáí=ÉáåÉã=ÉáåJ Ñ~ÅÜÉå=q~ëÅÜÉåêÉÅÜåÉê=ÇìêÅÜêÉÅÜÉåÄ~ê=ëáåÇK== =====a~ÄÉá=â∏ååÉå=~ìÅÜ=ÉäÉãÉåí~êÉ=^äÖçêáíÜãÉåI=~ÄÖÉâΩêòí=ÇìêÅÜ=cìåâíáçåÉåI=ïáÉ=òìã== =====_ÉáëéáÉä=SUMME(...)I=VERWEIS(...;...;...)I=MAX(...)=ìåÇ=MIN(...)I=îÉêïÉåÇÉí=ïÉêÇÉåK= fãéäÉãÉåíáÉêìåÖW=få=ÇáÉëÉã=pÅÜêáíí=ïáêÇ=ÉáåÉ=cçäÖÉ=îçå=e~åÇäìåÖë~åïÉáëìåÖÉå=ÖÉJ ÖÉÄÉåI=ïáÉ=Ç~ë=~ääÖÉãÉáåÉ=oÉÅÜÉåëÅÜÉã~I=Ç~ë=òìê=qÜÉçêáÉ=é~ëëíI=~å=e~åÇ=ÇÉê=a~íÉå= ÇÉê=âçåâêÉíÉå=^ìÑÖ~ÄÉ=ìãÖÉëÉíòí=ïÉêÇÉå=â~ååK= oÉ~äáëáÉêìåÖI=ÉáÖÉåíäáÅÜÉ=rãëÉíòìåÖW=a~ë=áëí=ÇáÉ=ÉáÖÉåíäáÅÜÉI=âçåâêÉíÉ=^êÄÉáí=ãáí=bñJ ÅÉäJq~ÄÉääÉEåFI=ãáí=ÇÉê=Ç~ë=mêçÄäÉã=ÖÉä∏ëí=ïáêÇK= =aáëâìëëáçåW=få=ÇáÉëÉã=pÅÜêáíí=ïáêÇ=ÇáÉ=i∏ëìåÖ=~ìÑ=léíáã~äáí®í=ìåÇ=~ìÑ=báåÜ~äíìåÖ=ÇÉë= q~ÄÉääÉåâ~äâìä~íáçåëé~ê~ÇáÖã~ë=ìåíÉêëìÅÜíK== léíáã~äáí®í=ÄÉÇÉìíÉí=Ç~ÄÉáI=Ç~ëë=ÇáÉ=i∏ëìåÖ=äÉáÅÜí=~å=îÉê®åÇÉêíÉ=a~íÉåI=òK=_K=sÉêÖê∏≈ÉêìåÖ= çÇÉê=sÉêâäÉáåÉêìåÖ=ÇÉê=a~íÉåãÉåÖÉI=~åÖÉé~ëëí=ïÉêÇÉå=â~ååK== a~ë= q~ÄÉääÉåâ~äâìä~íáçåëé~ê~ÇáÖã~= îÉêä~åÖí= Ç~òìI= Ç~ëë= ëáÅÜ= ÉáåÉ= i∏ëìåÖ= ~ìíçã~íáëÅÜ= ~å= îÉê®åÇÉêíÉ=a~íÉå=~åé~ëëÉå=ëçääK== _ÉáëéáÉäW=táÉ=îÉêãÉÜêí=ëáÅÜ=dÉäÇ\== báå=h~éáí~ä=ïáêÇ=ÉáåÖÉò~ÜäíI=ÇÉê=wáåëë~íò=áëí=ÄÉâ~ååíI=Ç~ë=h~éáí~ä=ÄäÉáÄí=Éáå=é~~ê=g~ÜêÉ=~ìÑ= ÇÉê=_~åâK=táÉ=îáÉä=dÉäÇ=â~åå=ã~å=å~ÅÜ=ÉáåáÖÉå=g~ÜêÉå=áå=bãéÑ~åÖ=åÉÜãÉå\== wìê= mêçÄäÉãÄÉëÅÜêÉáÄìåÖW= cΩê= ÇáÉ= bñÅÉäJi∏ëìåÖ= ïáêÇ= ~ìë= ÇÉê= ~ääÖÉãÉáåÉå= ìåÇ= êÉÅÜí= ìåJ ëÅÜ~êÑ=ÖÉëíÉääíÉå=^ìÑÖ~ÄÉ=EîçêÉêëíF=ÉáåÉ=_ÉáëéáÉä~ìÑÖ~ÄÉ=~ÄÖÉäÉáíÉíW== báå=h~éáí~ä=hM=Z=NMMM=€=ïáêÇ=~ã=^åÑ~åÖ=ÉáåÉë=g~ÜêÉë=~ìÑ=Éáå=cÉëíÖÉäÇâçåíç=ÉáåÖÉò~ÜäíI=ÑΩê= Ç~ë=Éáå=wáåëë~íò=îçå=é=Z=T=B=éK=~K=ÑÉëíÖÉäÉÖí=ëÉáK== táÉ=ÉåíïáÅâÉäí=ëáÅÜ=Ç~ë=h~éáí~ä=áã=sÉêä~ìÑ=îçå=q=Z=NR=g~ÜêÉå\= wìê=qÜÉçêáÉW=k~ÅÜ=ÉáåÉã=g~Üê=ÄÉÑáåÇÉí=ëáÅÜ=~ìÑ=ÇÉã=hçåíç=ÇÉê=_Éíê~Ö= E^KMNF=
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NTP
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=K t = K t −1 (1 + p )
f ür
t = 1, ..., T
wìã=oÉÅÜÉåëÅÜÉã~W=aáÉ=q~ÄÉääÉåÑçêã=ÄáÉíÉí=ëáÅÜ=~åI=ìã=òìÉêëí=ÇáÉ=ÖÉÖÉÄÉåÉå=a~íÉå=ãáí= k~ãÉ=ìåÇ=tÉêí=òìë~ããÉåòìëíÉääÉåK== „Name“
„Wert“
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K0
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p
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T
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„Kapital“
t0 ← 0
K0 ← K0
t1 ← t0 +1 .. .
K1 ← K0 (1+p) .. .
tT ← tT-1 +1
KT ← KT-1 (1+p)
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„Kapital“
t0 ← 0
K0 ← K0
ti ← ti-1 +1
Ki ← Ki-1 (1+p)
i=1, … ,T
q~ÄW=^OÄW=sÉêâΩêòíÉë=oÉÅÜÉåëÅÜÉã~=ÑΩê=ÇáÉ=h~éáí~äÉåíïáÅâäìåÖ= wìê=fãéäÉãÉåíáÉêìåÖW=kìå=ëáåÇ=ÇáÉ=sçêÄÉêÉáíìåÖÉå=~ÄÖÉëÅÜäçëëÉåI=ÇáÉ=q~ÄÉääÉå=ÇÉê=a~íÉå= ìåÇ=ÇÉê=îÉêâΩêòíÉå=oÉÅÜÉåëÅÜÉã~í~=â∏ååÉå=áå=bñÅÉäJq~ÄÉääÉEåF=ÉáåÖÉíê~ÖÉå=ïÉêÇÉåK== aáÉëÉê=sçêÖ~åÖ=ïáêÇ=~äë=fãéäÉãÉåíáÉêìåÖ=ÄÉòÉáÅÜåÉíK= aÉê=ÉêëíÉ=pÅÜêáíí=ÇÉê=fãéäÉãÉåíáÉêìåÖ=ëçääíÉ=ïÉáíÉêÜáå=åçÅÜ=~ì≈ÉêÜ~äÄ=îçå=bñÅÉä=ìåÇ=âçåJ òÉåíêáÉêí=ÖÉÇ~åâäáÅÜ=ÉêÑçäÖÉåW==
============================================================ ^åÜ~åÖ=NW=sçã=mêçÄäÉã=òìê=bñÅÉäJi∏ëìåÖ= NTQ aáÉ=q~ÄÉääÉå=^N=ìåÇ=^O~=ÑΩê=ÇáÉ=tÉêíÉ=ìåÇ=ÇáÉ=h~éáí~äÉåíïáÅâäìåÖ=ïÉêÇÉå=ÉêÖ®åòí=ÇìêÅÜ= ÇáÉ= ^ÇêÉëëÉå= ÇÉê= wÉääÉåI= áå= ÇÉåÉå= ÇáÉ= ^ìëÖ~åÖëïÉêíÉ= ÉáåÖÉíê~ÖÉå= ìåÇ= ÇáÉ= oÉÅÜÉåÉêÖÉÄJ åáëëÉ=ÉåíëíÉÜÉå=ëçääÉåW==== A1: „Name“
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Zu 7.3: Multiple lineare Regression (ab Seite 129) bë=ÖáÄí=âÉáåÉ=ûåÇÉêìåÖÉå=ÄÉáã=tÉÅÜëÉä=îçå=bñÅÉä=OMMP=~ìÑ=bñÅÉä=OMMTI=ÇáÉ=sÉâíçêÑìåâJ íáçå=RGP=îÉêíÉáäí=áå=ÇÉêëÉäÄÉå=tÉáëÉ=áÜêÉ=ÑΩåÑòÉÜå=bêÖÉÄåáëïÉêíÉ=òìã=a~íÉåÄÉëí~åÇ=~ìë=ÇÉê= q~ÄÉääÉ=TKU=îçå=pÉáíÉ=NOV=áå=ÇÉå=ã~êâáÉêíÉå=wáÉäÄÉêÉáÅÜI=ëçÑÉêå=å~ÅÜ=áÜêÉê=báåÖ~ÄÉ=ÇáÉ=q~ëJ íÉåâçãÄáå~íáçå=E= Strg H ⇑ =FH ↵ =ÖÉÇêΩÅâí=ïáêÇK=
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Zu 9.1: Grundsätzliches (ab Seite 159), zu 9.2: Import aus MS-Access (ab Seite 159), zu 9.3: Einrichtung eines ODBC-Treibers (ab Seite 161), zu 9.4: Zugriff auf konkrete Datenbanken (ab Seite 163) a~=ÇáÉëÉ=îáÉê=^ÄëÅÜåáííÉ=ëáÅÜ=ãáí=ÄÉÖêáÑÑäáÅÜÉå=dêìåÇä~ÖÉå=ìåÇ=cê~ÖÉå=ÇÉë=_ÉíêáÉÄëëóëíÉãë= ÄÉëÅÜ®ÑíáÖÉåI=ëéáÉäí=ÜáÉê=ÇáÉ=cê~ÖÉI=ïÉäÅÜÉ=bñÅÉäJsÉêëáçå=îÉêïÉåÇÉí=ïáêÇI=âÉáåÉ=oçääÉK==
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