Weighted Index Numbers Contains Questions With Solutions & Points To Remember

HARD

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 1

Construct Paasche’s index for the following data by considering $2014$ as the base year

Items	year $2014$		year $2015$
Items	Price	Quantity	Price	Quantity
A	$6$	$50$	$10$	$56$
B	$2$	$100$	$2$	$120$
C	$4$	$60$	$6$	$60$
D	$10$	$30$	$12$	$24$
E	$8$	$40$	$12$	$36$

HARD

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 2

Construct Marshall–Edgeworth price index number for the following data taking $2016$ as base year

Commodity	Year $2016$		Year $2017$
Commodity	Price	Quantity	Price	Quantity
A	$4$	$58500$	$6$	$62000$
B	$3.5$	$15630$	$5.5$	$13050$
C	$3$	$26230$	$5$	$25000$
D	$2.5$	$11360$	$4$	$10000$
E	$2$	$30000$	$3$	$31500$

HARD

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 3

From the data given, Obtain Laspeyre’s quantity index for 2018 using 2015 as the base year

commodity	Base year		current year
commodity	Prices	Quantity	Price	Quantity
A	$10$	$12$	$12$	$15$
B	$7$	$15$	$5$	$20$
C	$5$	$24$	$9$	$20$
D	$16$	$5$	$14$	$5$

HARD

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 4

For the given data, Obtain the Compute Index number using Fisher’s formula and show it satisfies time reversal test and factor reversal test

commodity	Base year		current year
commodity	Prices	Quantity	Price	Quantity
A	$10$	$12$	$12$	$15$
B	$7$	$15$	$5$	$20$
C	$5$	$24$	$9$	$20$
D	$16$	$5$	$14$	$5$

EASY

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 5

Express tests for Index Numbers.

EASY

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 6

Construct Marshall-Edgeworth index for the following data taking 2014 as base year

Items	year $2014$		year $2015$
Items	Price	Quantity	Price	Quantity
A	$16$	$59$	$22$	$87$
B	$21$	$32$	$21$	$38$
C	$42$	$47$	$16$	$47$
D	$22$	$62$	$18$	$57$
E	$82$	$52$	$18$	$64$

EASY

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 7

Construct Paasche’s index for the following data taking 2014 as base year

Items	year $2014$		year $2015$
Items	Price	Quantity	Price	Quantity
A	$32$	$49$	$33$	$57$
B	$42$	$73$	$42$	$92$
C	$86$	$66$	$32$	$66$
D	$33$	$13$	$35$	$94$
E	$84$	$70$	$35$	$75$

EASY

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 8

Construct Laspeyre’s index for the following data taking 2014 as base year

Items	year $2014$		year $2015$
Items	Price	Quantity	Price	Quantity
A	$25$	$57$	$11$	$68$
B	$39$	$13$	$39$	$20$
C	$43$	$15$	$25$	$15$
D	$11$	$62$	$23$	$42$
E	$52$	$31$	$23$	$70$

EASY

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 9

Construct the price indices from the following data by applying Fisher ideal number by taking 2010 as the base year

Commodity	$2010$		$2011$
Commodity	Price in Rs	Quantity	Price in Rs	Quantity
A	$21$	$21$	$25$	$32$
B	$29$	$7$	$23$	$8$
C	$8$	$19$	$6$	$7$

MEDIUM

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 10

Compute price index for the following data by applying weighted average of price relative method using arithmetic mean

Item	Price Rs in $2006$	Price Rs in $2007$	quantity
A	$5$	$3.2$	$30$
B	$10$	$4.2$	$15$
C	$13$	$6$	$25$

MEDIUM

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 11

Compute price index for the following data by applying weighted average of price relative method using geometric mean.

Item	Price Rs in $2006$	Price Rs in $2007$	quantity
A	$2$	$2.5$	$40$
B	$3$	$3.25$	$20$
C	$1.5$	$1.75$	10

MEDIUM

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 12

Compute price index for the following data by applying weighted average of price relative method using geometric mean.

Item	Price Rs in $2006$	Price Rs in $2007$	quantity
A	$13$	$12$	$35$
B	$15$	$24$	$28$
C	$32$	$42$	$36$

MEDIUM

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 13

Compute price index for the following data by applying weighted average of price relative method using arithmetic mean

Item	Price Rs in $2006$	Price Rs in $2007$	quantity
A	$20$	$25$	$28$
B	$31$	$21$	$41$
C	$12$	$18$	$23$

MEDIUM

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 14

Construct the index of 2014 from the following data for the year 2012 taking 2011 as base year as base using geometric mean

Item	Price Rs in $2014$	Price Rs in $2015$
A	$31$	$15$
B	$11$	$27$
C	$14$	$42$
D	$22$	$18$
E	$21$	$32$

MEDIUM

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 15

Construct the index from the following data for the year $2015$ taking $2014$ as base year using arithmetic mean

Item	Price Rs in $2014$	Price Rs in $2015$
A	$16$	$26$
B	$21$	$32$
C	$24$	$17$
D	$32$	$36$
E	$18$	$23$

MEDIUM

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 16

From the data given, in problem. Obtain the following Compute Index number using Fisher’s formula and show it satisfies time reversal test and factor reversal test

commodity	Base year		current year
commodity	Prices	Quantity	Price	Quantity
A	$20$	$6$	$11$	$50$
B	$17$	$10$	$4$	$24$
C	$3$	$21$	$2$	$27$
D	$15$	$9$	$12$	$22$

EASY

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 17

From the data given, in problem. Obtain the following Paasche’s quantity index for 2018 using 2015 as the base

commodity	Base year		current year
commodity	Prices	Quantity	Price	Quantity
A	$20$	$11$	$14$	$18$
B	$3$	$19$	$17$	$29$
C	$10$	$23$	$16$	$32$
D	$26$	$6$	$27$	$10$

EASY

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 18

From the data given, in problem. Obtain the following (a) Laspeyre’s quantity index for 2018 using 2015 as the base year

commodity	Base year		current year
commodity	Prices	Quantity	Price	Quantity
A	$13$	$16$	$44$	$28$
B	$10$	$28$	$12$	$36$
C	$4$	$30$	$9$	$30$
D	$11$	$4$	$28$	$24$

EASY

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 19

A popular consumer co-operative store located in a labour colony reported the average monthly data on prices and quantities sold of a group of selected items of mass consumption as follows

Compute the following indices Paasche’s price index for 2018 using 2015 as base year.

Items	Jan $2015$		Jan $2018$
Items	Prices Rs Per kg	Quantity sold kg	Price Rs Per kg	Quantity sold kg
Veg oil	$21$	$52$	$27$	$56$
Sugar	$25$	$83$	$44$	$94$
Rice	$11$	$105$	$19$	$70$
Wheat	$13$	$98$	$29$	$14$

EASY

IMPORTANT

mathematics>Index Numbers>Weighted Index Numbers> Q 20

A popular consumer co-operative store located in a labour colony reported the average monthly data on prices and quantities sold of a group of selected items of mass consumption as follows.

Compute Laspeyre’s price index for 2018 using 2015 us base year.

Items	Jan $2015$		Jan $2018$
Items	Prices Rs Per kg	Quantity sold kg	Price Rs Per kg	Quantity sold kg
Veg oil	$22$	$36$	$15$	$54$
Sugar	$24$	$87$	$19$	$93$
Rice	$11$	$90$	$21$	$17$
Wheat	$18$	$81$	$32$	$118$

Weighted Index Numbers

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Important Questions on Weighted Index Numbers

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