Compute Simple Average of Price Relatives Using A.M. and Median | Query Point Official

 

Compute Simple Average of Relatives’ Price Indices Using A.M. and Median

Problem Statement

Using 1990 as the base year, the table below gives prices of three commodities A, B, and C. Compute:

• Simple average of price relatives using Arithmetic Mean (A.M.)
• Price relatives using Median

Price Data (Using 1990 as Base)

Year	A	B	C
1990	30.00	12.00	20.00
1991	35.50	13.50	23.50
1992	32.50	14.50	25.00
1993	32.50	14.00	25.00

Step 1: Compute Price Relatives

Price relative for a given year = (Price in that year ÷ Price in base year) × 100

• 1990: A = 100, B = 100, C = 100
• 1991: A = 101.6, B = 112.5, C = 117.5
• 1992: A = 108.3, B = 120.8, C = 125
• 1993: A = 108.3, B = 116.6, C = 125

Step 2: Compute Simple Average (A.M.) and Median

Year	Price Relatives	A.M.	Median
1990	100, 100, 100	100	100
1991	101.6, 112.5, 117.5	110.53	112.5
1992	108.3, 120.8, 125	118.03	120.8
1993	108.3, 116.6, 125	116.63	116.6

Explanation

To find the simple average using A.M., we add the price relatives and divide by the number of commodities (3). Median is the middle value when the relatives are arranged in order. This helps us understand general price movement over time compared to the base year. Price indices are key in inflation and cost of living studies.

FAQ

What is a price relative?

A price relative is the ratio of a commodity’s price in a given year to its price in the base year, expressed as a percentage.

Why use Median as well as A.M.?

Median helps reduce the effect of extreme values and shows the central tendency of price changes when data are skewed.

Where is this method used?

This method appears in cost of living studies, economic indices, and STA304 statistics assignments.

Related Topics

See Statistics Index & MCQs for more problems related to price indices and averages.