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 presidents’ ages fall within one standard deviation of the mean?

Answer 1

so to find std dev it is the sq root of the variance and

variance = \[1/(n-1) \sum_{i =1}^{6} (x_i - \mu_x)^2 \]
and just sq root after

Answer 2

ok lol so what you do is \[\frac{ (57-57.83)^2+(61-57.83)^2+(57-57.83)^2+(57-57.83)^2+(58-57.83)^2+(57-57.83)^2 }{ 6- 1 }\]

Answer 3

then square root it and you will get the std dev

Answer 4

sorry I was off open study, thanks!

Answer 5

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

Answer 6

so the standard deviation would be 2.56668

Answer 7

actually its 1.6020861400062107

Answer 8

to see if it is 1 std. dev away you should take the numbers, subtract the mean then divide by the std
so the first one you do \[\frac{ 57-57.83 }{ 1.602 } = -0.52\]
since its greater than -1 and less than 1

might need someone to check on this though