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
First, calculate the mean age:
Mean = (60 + 61 + 62 + 63 + 64 + 65 + 66 + 68 + 68 + 69 + 70 + 73 + 73 + 74) / 14
Mean = 929 / 14
Mean = 66.36
Next, calculate the squared differences between each age and the mean:
(60 - 66.36)^2 = 39.48
(61 - 66.36)^2 = 28.01
(62 - 66.36)^2 = 20.09
(63 - 66.36)^2 = 11.55
(64 - 66.36)^2 = 5.69
(65 - 66.36)^2 = 1.85
(66 - 66.36)^2 = 0.13
(68 - 66.36)^2 = 2.68
(68 - 66.36)^2 = 2.68
(69 - 66.36)^2 = 6.99
(70 - 66.36)^2 = 12.48
(73 - 66.36)^2 = 44.57
(73 - 66.36)^2 = 44.57
(74 - 66.36)^2 = 58.10
Now, calculate the variance:
Variance = (39.48 + 28.01 + 20.09 + 11.55 + 5.69 + 1.85 + 0.13 + 2.68 + 2.68 + 6.99 + 12.48 + 44.57 + 44.57 + 58.10) / 14
Variance = 278.87 / 14
Variance = 19.91
Therefore, the variance of the ages of the senior citizens is 19.91 years squared, which rounded to the nearest hundredth is 19.91.