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

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.