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.
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
1 answer