# Find the Standard Deviation 66 , 36 , 18 66 , 36 , 18
Find the mean.
The mean of a set of numbers is the sum divided by the number of terms.
x&OverBar;=66+36+183
Cancel the common factor of 66+36+18 and 3.
Factor 3 out of 66.
x&OverBar;=3⋅22+36+183
Factor 3 out of 36.
x&OverBar;=3⋅22+3⋅12+183
Factor 3 out of 3⋅22+3⋅12.
x&OverBar;=3⋅(22+12)+183
Factor 3 out of 18.
x&OverBar;=3⋅(22+12)+3⋅63
Factor 3 out of 3⋅(22+12)+3(6).
x&OverBar;=3⋅(22+12+6)3
Cancel the common factors.
Factor 3 out of 3.
x&OverBar;=3⋅(22+12+6)3(1)
Cancel the common factor.
x&OverBar;=3⋅(22+12+6)3⋅1
Rewrite the expression.
x&OverBar;=22+12+61
Divide 22+12+6 by 1.
x&OverBar;=22+12+6
x&OverBar;=22+12+6
x&OverBar;=22+12+6
Simplify by adding numbers.
Add 22 and 12.
x&OverBar;=34+6
Add 34 and 6.
x&OverBar;=40
x&OverBar;=40
x&OverBar;=40
Simplify each value in the list.
Convert 66 to a decimal value.
66
Convert 36 to a decimal value.
36
Convert 18 to a decimal value.
18
The simplified values are 66,36,18.
66,36,18
66,36,18
Set up the formula for sample standard deviation. The standard deviation of a set of values is a measure of the spread of its values.
s=∑i=1n⁡(xi-xavg)2n-1
Set up the formula for standard deviation for this set of numbers.
s=(66-40)2+(36-40)2+(18-40)23-1
Simplify the result.
Subtract 40 from 66.
s=262+(36-40)2+(18-40)23-1
Raise 26 to the power of 2.
s=676+(36-40)2+(18-40)23-1
Subtract 40 from 36.
s=676+(-4)2+(18-40)23-1
Raise -4 to the power of 2.
s=676+16+(18-40)23-1
Subtract 40 from 18.
s=676+16+(-22)23-1
Raise -22 to the power of 2.
s=676+16+4843-1
Add 676 and 16.
s=692+4843-1
Add 692 and 484.
s=11763-1
Subtract 1 from 3.
s=11762
Divide 1176 by 2.
s=588
Rewrite 588 as 142⋅3.
Factor 196 out of 588.
s=196(3)
Rewrite 196 as 142.
s=142⋅3
s=142⋅3
Pull terms out from under the radical.
s=143
s=143
The standard deviation should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.
24.2
Find the Standard Deviation 66 , 36 , 18

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