Question

The Consumer Price Index is reported monthly by the U.S. Bureau of Labor Statistics. It reports the change in prices for a market basket of goods from one period to another. The index for 2002 was 200.2. By 2013, it increased to 241.600. What was the geometric mean annual increase for the period? (Round your answer to 2 decimal places.) Geometric mean % k ces ?

Answer 1

The geometric mean annual increase in the Consumer Price Index (CPI) from 2002 to 2013 is approximately 1.9% per year.

Step-by-step explanation:

To calculate the geometric mean annual increase in the Consumer Price Index (CPI) from 2002 to 2013, we use the formula for geometric mean, which is appropriate since we are interested in the constant rate of change per year over the 11-year period. Given that the CPI for 2002 was 200.2 and for 2013 was 241.600, first we find the total increase factor by dividing the final CPI by the initial CPI:

increase factor = CPI2013 / CPI2002 = 241.600 / 200.2

We then take the nth root (where n is the number of years in the period, which is 11) of the increase factor to find the geometric mean annual increase:

geometric mean annual increase = (increase factor)1/n

Substituting the values, we get:

geometric mean annual increase = (241.600 / 200.2)1/11 ≈ 1.019 or 1.9% after rounding to two decimal places.

This means that, on average, the cost of the basket of goods increased by approximately 1.9% per year over the period from 2002 to 2013.