Question

suppose mortgage interest tax deductions average $8268 for people with incomes between 50000 and 200000 and 36
5 for those with income of 40000 to 50000. suppose also the standard deviation of the housing benefits in these two categories were equal to 2750 and 120, respectively
a. examine the two standard deviations. what do these indicate about the range of benefits enjoyed by the two groups?
b. repeat part a using the coefficient of variation as the measure of relative variation.

Answer 1

a) Observe that the first group has a bigger standard deviation, hence as the sample data depends on the standard deviation proportionally, the first group would enjoy more range of benefits.

b) Now the coefficient of variation for both groups is (2750/8268) = 0.3326 and (120/365) = 0.3288 respectively. In this case as well first group has larger relative variance than the other group. Hence, the first group would enjoy more range of benefits relative to their mean as well.