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 standard deviation of the ages of the senior citizens correct to the nearest hundredth of a year.
The first step in calculating the standard deviation is 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, calculate the squared difference of each age from the mean:
(60 - 67.57)^2 = 57.1
(61 - 67.57)^2 = 43.9
(62 - 67.57)^2 = 31.8
(63 - 67.57)^2 = 21.5
(64 - 67.57)^2 = 13.0
(65 - 67.57)^2 = 6.6
(66 - 67.57)^2 = 2.5
(68 - 67.57)^2 = 0.2
(68 - 67.57)^2 = 0.2
(69 - 67.57)^2 = 1.7
(70 - 67.57)^2 = 5.9
(73 - 67.57)^2 = 29.2
(73 - 67.57)^2 = 29.2
(74 - 67.57)^2 = 41.0
Now, sum up all the squared differences:
57.1 + 43.9 + 31.8 + 21.5 + 13.0 + 6.6 + 2.5 + 0.2 + 0.2 + 1.7 + 5.9 + 29.2 + 29.2 + 41.0 = 282.6
Divide this sum by the number of ages (14) minus 1, then take the square root of the result:
√(282.6 / (14-1)) = √(282.6 / 13) = √21.7 = 4.66
Therefore, the standard deviation of the ages of the senior citizens is approximately 4.66.