The standard deviation of the ages of five people in the region is approximately 9.96.
The standard deviation is the square root of the average of the squared differences between each age and the mean.
The mean is computed as the average of the total data value.
The ages of people in a particular region = 55 + 42 + 13 + 62 + 51
The number of people = 5
Mean = (55 + 42 + 13 + 62 + 51) / 5 Mean = 223 / 5 Mean = 44.6
The squared differences between each age and the mean:
(55 - 44.6)^2 = 110.25
(42 - 44.6)^2 = 7.84
(13 - 44.6)^2 = 1017.64
(62 - 44.6)^2 = 303.61
(51 - 44.6)^2 = 40.96
The average of these squared differences:
Average = (110.25 + 7.84 + 1017.64 + 303.61 + 40.96) / 5
Average = 496.26 / 5
Average = 99.252
Taking the square root of the above average gives the standard deviation:
Standard deviation = √99.252
Standard deviation ≈ 9.96
Thus, the standard deviation of the ages in the region is approximately 9.96.
Complete Question:
A study is published with information about ages of people in a particular region.
55 42 13 62 51
Determine the standard deviation.