Calculate weighted index number for 2010 by weighted aggregative method and weighted average of relative method for the following data:

$\begin{matrix} Items & Weights & Prices in 2011 & Prices in 2012 A & 10 & 100 & 161 B & 7 & 200 & 210 C & 15 & 50 & 60 D & 9 & 20 & 30 E & 10 & 10 & 14 \end{matrix}$

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Solution

$\begin{matrix} Items & W & P_{0} & P_{1} & P_{0} W & P_{1} W & R = \frac{P_{1}}{P_{0}} \times 100 & RW A & 10 & 100 & 161 & 1000 & 1610 & 161 & 1610 B & 7 & 200 & 210 & 1400 & 1470 & 105 & 735 C & 15 & 50 & 60 & 750 & 900 & 120 & 1800 D & 9 & 20 & 30 & 180 & 270 & 150 & 1350 E & 10 & 10 & 14 & 100 & 140 & 140 & 1400 \sum W = 51 & \sum P_{0} W & \sum P_{1} W & \sum R W = 6895 = 3430 & 4390 \end{matrix}$

Weighted Aggregate Method :

$P_{01} = \frac{\sum P_{1} W}{\sum P_{0} W} \times 100 = \frac{4390}{3430} \times 100 = 127.98$

Weighted Average of Price Relative Method :

$P_{01} = \frac{\sum R W}{\sum W} = \frac{6895}{51} = 135.19$

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Calculate weighted average of price relative index from the following data:

$\begin{matrix} Itmes & Weight in % & Base year price (Rs) & Current Year Price (Rs) A & 40 & 2 & 4 B & 30 & 5 & 6 C & 20 & 4 & 5 D & 10 & 2 & 3 \end{matrix}$

Q. Calculate price index number for 2016 of following data by weighted aggregative method using (a) Laspeyre's method, (b) Paasche's method, (c) Fisher's method.

Commodity	Price (2012)	Quantity (2012)	Price (2016)	Quantity (2016)
A	4	20	6	10
B	3	15	5	23
C	2	25	3	15
D	5	10	4	15

Q. Calculate the index number for the year

2014

, with

2010

as the base year by the weighted aggregate method from the following data :

Commodity	Price in rupees $(2010)$	Price in rupees $(2014)$	Weight
$A$	$2$	$4$	$8$
$B$	$5$	$6$	$10$
$C$	$4$	$5$	$14$
$D$	$2$	$2$	$19$

The weighted aggregative index number for the following table is given as 166.31 considering Paasche’s method. Find the approx.value of m.

$\begin{matrix} Commodity & Base Period & Current Period Price (P0) (In dollars) & Quantity (Q0) & Price (P1) (In dollars) & Quantity (Q1) H & 1 & 7 & 3 & 25 I & 10.5 & 10 & 7 & 11 J & m & 8 & 4 & 12 K & 7 & 25 & 14 & 30 L & 15 & 13 & 22 & 18 \end{matrix}$

An index number which accounts for the relative importance of the items is known as

(i) weighted index

(ii) simple aggregative index

(iii) simple average of relatives

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Calculate weighted index number for 2010 by weighted aggregative method and weighted average of relative method for the following data: ItemsWeightsPrices in 2011Prices in 2012A10100161B7200210C155060D92030E101014