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# 100 p0 140 150 125 150 565 p 1 100 p simple average of

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Unformatted text preview: by the sum of the prices of those commodities by 100. Symbolically, ∑ p1 Simple aggregate price index = P01 = × 100 ∑ p0 243 Where , p1 = t otal prices for the current year p0 = Total prices for the base year Example 1: Calculate index numbers from the following data by simple aggregate method taking prices of 2000 as base. Commodity A B C D Solution: Commodity A B C D Total Price per unit (in Rupees) 2000 2004 80 95 50 60 90 100 30 45 Price per unit (in Rupees) 2000 2004 (P0) (P1) 80 95 50 60 90 100 30 45 250 300 ∑ p1 × 100 ∑ p0 300 = × 100 = 120 250 10.5.2 Simple Average Price Relative index: In this method, first calculate the price relative for the various commodities and then average of these relative is obtained by using arithmetic mean and geometric mean. When arithmetic mean is used for average of price relative, the formula for computing the index is Simple aggregate Price index = P01 = 244 Simple average of price relative by arithmetic mean P01 = ∑ × 100 p0 n p1 P1 = Prices of current year P0 = Prices of base year n = Number of items or commodities when geometric mean is used for average of price relative, the formula for obtaining the index is Simple average of price relative by geometric Mean p1 Σ log( p × 100) 0 P01 = Antilog n Example 2: From the following data, construct an index for 1998 taking 1997 as base by the average of price relative using (a) arithmetic mean and (b) Geometric mean Commodity Price in 1997 Price in 1998 A 50 70 B 40 60 C 80 100 D 20 30 Solution: (a) Price relative index number using arithmetic mean Commodity Price in 1997 (P0) A B C D 50 40 80 20 Price in 1998 (P1) 70 60 100 30 Total 245 p1 × 100 p0 140 150 125 150 565 p Σ 1 × 100 p Simple average of price relative index = (P01) = 0 4 565 = = 141.25 4 (b) Price relative index number using Geometric Mean Commodity Price in Price in p1 p × 100 log( 1 ×100) 1998 1997 p0 p0 (P1) (P0) A 50 70 140 2.1461 B 40 60 150 2.1761 C 80 100 125 2.0969 D 20 30 150 2.1761 Total 8.5952 Simple average of price Relative index p Σ log 1 x100 po (P01) = Antilog...
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