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.
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
1 answer