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Zusammenfassung Deskriptive Statistik
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Deskriptive Statistik, Indexzahlen
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9. Statistik IndexzahlenÜberblick:
• Preisindizes
• Mengenindizes
Definition: Indexzahl nach Bourier:
Eine Indexzahl beschreibt die durchschnittliche relative Veränderung mehrerer Merkmale.
Betrachten wir einen Warenkorb: n Waren zu einem Zeitpunkt t
Mengen qt1, ..., qtn Preise pt1, ..., ptn
Wert des Warenkorbes in Periode t:
Wertindex: Vergleich Wert eines Warenkorbes zur Berichtsperiode t mit dem zur Basisperiode 0
Bsp. Durchschnittlicher Verbrauch an Fleisch aller privaten Haushalte in einer Gemeinde.
Basismonat 1, Berichtsmonat 12.
• (Mengen in g, Preise in €/kg)
Wertindex: Preisindex nach Paasche:
Fleisch P0i q0i P12i q12i p0iq0i p12iq12i P01q12i p12iq01
F1 5,75 1450 6,2 1410 8337,5 8742 8107,5 8990
F2 12,25 1260 13,55 1200 15435 16260 14700 17073
F3 24,1 50 24,8 50 1205 1240 1205 1240
F4 17,8 210 18,1 215 3738 3891,5 3827 3801
F5 4,55 2450 4,6 2470 11147,5 11362 11238,5 11270
F6 10,25 1310 10,4 1230 13427,5 12792 12607,5 13624
F7 8,9 980 9,1 930 8722 8463 8277 8918
gesam 7710 7505 62012,5 62750,5 59962,5 64916
t
Wertindex aus Beispiel:
• 100 · W012 = 100 · 1,0119 = 101,19%
• D.h. der tatsächliche Aufwand für Fleisch für die privaten Haushalte ist vom Basismonat bis zum Berichtsmonat um
1,19% gestiegen. • Es ist hier nicht berücksichtigt, dass der durchschnittliche Verbrauch im Berichtsmonat um 205g
geringer ist.
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