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.
5.13
5
4.61
5.4
To calculate the standard deviation of these ages, we first need to find the mean.
Mean = (60+61+62+63+64+65+66+68+68+69+70+73+73+74) / 14 = 934 / 14 = 66.7
Next, we find the squared difference between each age and the mean:
(60-66.7)^2 = 45.69
(61-66.7)^2 = 37.69
(62-66.7)^2 = 20.89
(63-66.7)^2 = 13.69
(64-66.7)^2 = 7.29
(65-66.7)^2 = 2.89
(66-66.7)^2 = 0.09
(68-66.7)^2 = 1.69
(68-66.7)^2 = 1.69
(69-66.7)^2 = 5.29
(70-66.7)^2 = 10.89
(73-66.7)^2 = 40.89
(73-66.7)^2 = 40.89
(74-66.7)^2 = 53.29
Then, we calculate the variance by summing these values and dividing by the number of ages - 1 (since it's a sample):
Variance = (45.69+37.69+20.89+13.69+7.29+2.89+0.09+1.69+1.69+5.29+10.89+40.89+40.89+53.29) / 13 = 231.08 / 13 = 17.77
Finally, we find the square root of the variance to get the standard deviation:
Standard Deviation = sqrt(17.77) = 4.21
Therefore, the standard deviation of the ages of the senior citizens is 4.21 years, rounded to the nearest hundredth. None of the given answer choices is correct.