The number of Americans on Medicare is increasing as expected with the aging bab

Question

The number of Americans on Medicare is increasing as expected with the aging baby boomer population. The following table shows the number of Americans on Medicare in 2005 and 2009 for eight U.S. states. Note: the numbers listed are in thousands.

a. Calculate the mean number of Americans on Medicare in these eight states for both 2005 and 2009. How would you characterize the difference in the number of Americans on Medicare between 2005 and 2009? Does the mean adequately represent the central tendency of the distribution of Americans on Medicare in each year for these eight states? Why or why not?

b. Recalculate the mean for each year after removing Florida, Illinois, and New York form the table. Is the mean now a better representation of central tendency for the remaining five states? Explain.

State 2005 2009 Alabama 740 828 Delaware 125 145 Florida 3,008 3,289 Illinois 1,674 1,806 Minnesota 691 767 New Hampshire 185 217 New York 2,758 2,937 Washington 807 938

Explanation / Answer

Formula for mean:

Mean = (Sum of observations) / (Number of observations)

a) Number of observations = 8

For 2005,

Sum of observations = 740 + 125 + 3008 + 1674 + 691 + 185 + 2758 + 807 = 9988

For 2009,

Sum of observations = 828 + 145 + 3289 + 1806 + 767 + 217 + 2937 + 938 = 10927

Hence,

Mean number of people in medicare in 2005 = 9988 / 8 = 1248.5

Mean number of people in medicare in 2009 = 10927 / 8 = 1365.875

We can see that the number of Americans in medicare has increased in 2009 as compared to 2005.

the mean doesn't adequately represent the central tendency of the distribution of Americans on Medicare in each year for these eight states because only 3 of the obervations in both the years are greater than mean. This happened due to the presence of outliers (Florida, Illinois and New York) in the data. Due to outliers, mean is very high and therefore, median should be the appropriate measure of number of Americans in Medicare in 8 states.

b) After removing Florida, Illinois and New York,

Number of observations = 5

For 2005,

Sum of observations = 740 + 125 + 691 + 185 + 807 = 2548

And for 2009,

Sum of observations = 828 + 145 + 767 + 217 + 938 = 2895

Hence,

Mean number of people in medicare in 2005 = 2548 / 5 = 509.6

Mean number of people in medicare in 2009 = 2895 / 5 = 579

Yes, now since we have removed the outliers, the mean is a better representative of central tendency for the given data.

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