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.
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
1 answer
1 answer