To calculate the standard deviation of the ages of the senior citizens, you can follow these steps:
1. Calculate the mean of the ages:
(60+61+62+63+64+65+66+68+68+69+70+73+73+74) / 14 = 67
2. Subtract the mean from each individual age to get the deviations from the mean:
-7, -6, -5, -4, -3, -2, -1, 1, 1, 2, 3, 6, 6, 7
3. Square each deviation:
49, 36, 25, 16, 9, 4, 1, 1, 1, 4, 9, 36, 36, 49
4. Calculate the sum of the squared deviations:
49 + 36 + 25 + 16 + 9 + 4 + 1 + 1 + 1 + 4 + 9 + 36 + 36 + 49 = 240
5. Divide the sum of squared deviations by the total number of ages minus 1:
240 / (14-1) = 240 / 13 ≈ 18.46
6. Take the square root of the result to get the standard deviation:
√18.46 ≈ 4.29
Therefore, the standard deviation of the ages of the senior citizens is approximately 4.29 years, which rounded to the nearest hundredth is 4.29. So the correct answer is 5.
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