# Find the Standard Deviation 1314 , 795÷11 , 1

1314 , 795÷11 , 1
Find the mean.
Rewrite the division as a fraction.
x&OverBar;=1314,79511,1
The mean of a set of numbers is the sum divided by the number of terms.
x&OverBar;=1314+79511+13
Simplify the numerator.
To write 1314 as a fraction with a common denominator, multiply by 1111.
x&OverBar;=1314⋅1111+79511+13
Combine 1314 and 1111.
x&OverBar;=1314⋅1111+79511+13
Combine the numerators over the common denominator.
x&OverBar;=1314⋅11+79511+13
Simplify the numerator.
Multiply 1314 by 11.
x&OverBar;=14454+79511+13
x&OverBar;=1524911+13
x&OverBar;=1524911+13
Write 1 as a fraction with a common denominator.
x&OverBar;=1524911+11113
Combine the numerators over the common denominator.
x&OverBar;=15249+11113
x&OverBar;=15260113
x&OverBar;=15260113
Multiply the numerator by the reciprocal of the denominator.
x&OverBar;=1526011⋅13
Multiply 1526011⋅13.
Multiply 1526011 and 13.
x&OverBar;=1526011⋅3
Multiply 11 by 3.
x&OverBar;=1526033
x&OverBar;=1526033
Divide.
x&OverBar;=462.42‾
The mean 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.
x&OverBar;=462.4
x&OverBar;=462.4
Simplify each value in the list.
Convert 1314 to a decimal value.
1314
Convert 79511 to a decimal value.
72.27‾
Convert 1 to a decimal value.
1
The simplified values are 1314,72.27‾,1.
1314,72.27‾,1
1314,72.27‾,1
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=(1314-462.4)2+(72.27‾-462.4)2+(1-462.4)23-1
Simplify the result.
Subtract 462.4 from 1314.
s=851.62+(72.27‾-462.4)2+(1-462.4)23-1
Raise 851.6 to the power of 2.
s=725222.56+(72.27‾-462.4)2+(1-462.4)23-1
Subtract 462.4 from 72.27‾.
s=725222.56+(-390.127‾)2+(1-462.4)23-1
Raise -390.127‾ to the power of 2.
s=725222.56+152199.28892562+(1-462.4)23-1
Subtract 462.4 from 1.
s=725222.56+152199.28892562+(-461.4)23-1
Raise -461.4 to the power of 2.
s=725222.56+152199.28892562+212889.963-1
s=877421.84892562+212889.963-1
s=1090311.808925623-1
Subtract 1 from 3.
s=1090311.808925622
Divide 1090311.80892562 by 2.
s=545155.90446281
s=545155.90446281
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.
738.3
Find the Standard Deviation 1314 , 795÷11 , 1

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