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 of County Business Activity, we use the following formula:
Index = (w1*value1/base1 + w2*value2/base2 + w3*value3/base3) * 100

where:
w1, w2, w3 = weights assigned to each variable
value1, value2, value3 = current year values of each variable
base1, base2, base3 = base year values of each variable

Plugging in the values given in the question, we get:

For 1981 (base year):
Index = (0.6*1 + 0.3*1 + 0.1*1) * 100
Index = 100

For 2006:
Index = (0.6*3 + 0.3*4 + 0.1*2) * 100
Index = 138

Rounding off, we get the Index of County Business Activity for 1981 as 100 and for 2006 as 139. Therefore, the correct answer is A.

As Chief Statistician for the County, You Want to Compute