Question

Consider the following table of the ages of our first six presidents

Ages of the first 6 presidents at inauguration

Washington 57
J. Adams 61
Jefferson 57
Madison 57
Monroe 58
JQ Adams 57

Find the mean of the data set
(57+61+57+57+58+57)/6 = 347/6 = 57.83

Find the standard deviation (showing all work)


How many of the presidentsÍ ages fall within one standard deviation of the mean?

Answer 1

`m=57.83 \\ \sigma= \sqrt{ (1)/(N) \sum_(i=1)^(N)(x_i-m)^2 } = \\= \sqrt{ ((57-57.83)^2+(61-57.83)^2+(57-57.83)^2+(57-57.83)^2+(58-57.83)^2+(57-57.83)^2)/(6) } \\= \sqrt{ (4(-0.83)^2+3.17^2+0.17^2)/(6) } \approx 1.46 \\ \\x=57.83 \pm 1.46 \\57.83-1.46 \leq x \leq 57.83+1.46 \\56.35 \leq x \leq 59.29`

Five presidents' ages fall within one standard deviation of the mean.