To calculate the standard deviation of the ages of the senior citizens, we first need to find the mean of the ages.
Mean = (60 + 61 + 62 + 63 + 64 + 65 + 66 + 68 + 68 + 69 + 70 + 73 + 73 + 74) / 14
Mean = 962 / 14
Mean = 68.71
Next, we need to find the squared difference between each age and the mean:
(60-68.71)^2 = 71.76
(61-68.71)^2 = 59.17
(62-68.71)^2 = 45.80
(63-68.71)^2 = 31.98
(64-68.71)^2 = 22.14
(65-68.71)^2 = 11.96
(66-68.71)^2 = 8.25
(68-68.71)^2 = 0.51
(68-68.71)^2 = 0.51
(69-68.71)^2 = 0.07
(70-68.71)^2 = 1.67
(73-68.71)^2 = 18.19
(73-68.71)^2 = 18.19
(74-68.71)^2 = 29.50
Now, sum up all of these squared differences:
71.76 + 59.17 + 45.80 + 31.98 + 22.14 + 11.96 + 8.25 + 0.51 + 0.51 + 0.07 + 1.67 + 18.19 + 18.19 + 29.50 = 318.20
Next, divide this sum by the number of ages (14), and then take the square root to find the standard deviation:
Standard Deviation = √(318.20 / 14)
Standard Deviation = √22.73
Standard Deviation ≈ 4.77
Therefore, the standard deviation of the ages of the senior citizens is 4.77 years, which rounded to the nearest hundredth would be 4.77.
ealth 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