Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 14 senior citizens were as follows:
60
61
62
63
64
65
66
68
68
69
70
73
73
74
Calculate the variance of the ages of the senior citizens correct to the nearest hundredth of a year squared.
29.16
21.21
24.96
26.31
To calculate the variance, we first need to find the mean of the ages:
Mean = (60 + 61 + 62 + 63 + 64 + 65 + 66 + 68 + 68 + 69 + 70 + 73 + 73 + 74) / 14
Mean = 946 / 14
Mean = 67.57
Next, we calculate the squared difference between each age and the mean, sum them up, and divide by the total number of ages to get the variance:
Variance = [(60-67.57)^2 + (61-67.57)^2 + (62-67.57)^2 + (63-67.57)^2 + (64-67.57)^2 + (65-67.57)^2 + (66-67.57)^2 + (68-67.57)^2 + (68-67.57)^2 + (69-67.57)^2 + (70-67.57)^2 + (73-67.57)^2 + (73-67.57)^2 + (74-67.57)^2] / 14
Variance = (53.54^2 + 49.57^2 + 46.03^2 + 41.57^2 + 32.11^2 + 20.43^2 + 13.57^2 + 0.17^2 + 0.17^2 + 2.94^2 + 8.85^2 + 28.73^2 + 28.73^2 + 38.43^2) / 14
Variance = (2864 + 2457 + 2119 + 1729 + 1033 + 417 + 184 + 0.03 + 0.03 + 8.64 + 78.22 + 825.53 + 825.53 + 1476.53) / 14
Variance = 11693.21 / 14
Variance ≈ 26.31 (rounded to the nearest hundredth)
Therefore, the variance of the ages of the senior citizens is 26.31 years squared.