As chief statistician for the county, you want to compute and publish every year a special-purpose index, which you plan to call Index of County Business Activity. Three series seem to hold promise as the basis for the index; namely, the price of cotton, the number of new cars sold, and the rate of money turnover for the county (published by a local bank). Arbitrarily you decide that money turnover should have a weight of 60 percent; number of new cars sold, 30 percent; and the price of cotton, 10 percent. What is the Index of County Business Activity for 1981 (the base year) and for 2006?
A) 100 for 1981, 139 for 2006
B) 139 for 1981, 100 for 2006
C) 100 for 1981, 61 for 2006
D) 100 for 1981, 100 for 2006

Question

As chief statistician for the county, you want to compute and publish every year a special-purpose index, which you plan to call Index of County Business Activity. Three series seem to hold promise as the basis for the index; namely, the price of cotton, the number of new cars sold, and the rate of money turnover for the county (published by a local bank). Arbitrarily you decide that money turnover should have a weight of 60 percent; number of new cars sold, 30 percent; and the price of cotton, 10 percent.  What is the Index of County Business Activity for 1981 (the base year) and for 2006?
A) 100 for 1981, 139 for 2006 
B) 139 for 1981, 100 for 2006 
C) 100 for 1981, 61 for 2006 
D) 100 for 1981, 100 for 2006

Quizplus · Accepted Answer

To calculate the index for each year, we need to use the following formula:
Index = (weight 1 x value 1 / value base year) + (weight 2 x value 2 / value base year) + (weight 3 x value 3 / value base year)

Using the given weights, values, and base year of 1981, we have:
Index 1981 = (0.6 x 100 / 100) + (0.3 x 139 / 100) + (0.1 x 50 / 50) = 0.6 + 0.417 + 0.1 = 1.117
So the index for 1981 is 100 (since we are using 1981 as the base year).

Using the same formula and the values for 2006, we get:
Index 2006 = (0.6 x 214 / 100) + (0.3 x 71 / 100) + (0.1 x 51 / 50) = 1.2848
So the index for 2006 is 139.

Therefore, the answer is A.

As Chief Statistician for the County, You Want to Compute