# Find the Standard Deviation 732 , 178+167-542 , 137

732 , 178+167-542 , 137
Find the mean.
x&OverBar;=732,345-542,137
Subtract 542 from 345.
x&OverBar;=732,-197,137
The mean of a set of numbers is the sum divided by the number of terms.
x&OverBar;=732-197+1373
Simplify the numerator.
Subtract 197 from 732.
x&OverBar;=535+1373
x&OverBar;=6723
x&OverBar;=6723
Divide 672 by 3.
x&OverBar;=224
x&OverBar;=224
Simplify each value in the list.
Convert 732 to a decimal value.
732
Convert -197 to a decimal value.
-197
Convert 137 to a decimal value.
137
The simplified values are 732,-197,137.
732,-197,137
732,-197,137
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=(732-224)2+(-197-224)2+(137-224)23-1
Simplify the result.
Subtract 224 from 732.
s=5082+(-197-224)2+(137-224)23-1
Raise 508 to the power of 2.
s=258064+(-197-224)2+(137-224)23-1
Subtract 224 from -197.
s=258064+(-421)2+(137-224)23-1
Raise -421 to the power of 2.
s=258064+177241+(137-224)23-1
Subtract 224 from 137.
s=258064+177241+(-87)23-1
Raise -87 to the power of 2.
s=258064+177241+75693-1
s=435305+75693-1
s=4428743-1
Subtract 1 from 3.
s=4428742
Divide 442874 by 2.
s=221437
s=221437
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.
470.6
Find the Standard Deviation 732 , 178+167-542 , 137

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