# Find the Variance 53 , 90 , 92 , 95 , 97 , 98 53 , 90 , 92 , 95 , 97 , 98
The mean of a set of numbers is the sum divided by the number of terms.
x&OverBar;=53+90+92+95+97+986
Simplify the numerator.
x&OverBar;=143+92+95+97+986
x&OverBar;=235+95+97+986
x&OverBar;=330+97+986
x&OverBar;=427+986
x&OverBar;=5256
x&OverBar;=5256
Cancel the common factor of 525 and 6.
Factor 3 out of 525.
x&OverBar;=3(175)6
Cancel the common factors.
Factor 3 out of 6.
x&OverBar;=3⋅1753⋅2
Cancel the common factor.
x&OverBar;=3⋅1753⋅2
Rewrite the expression.
x&OverBar;=1752
x&OverBar;=1752
x&OverBar;=1752
Divide.
x&OverBar;=87.5
Set up the formula for variance. The variance of a set of values is a measure of the spread of its values.
s2=∑i=1n⁡(xi-xavg)2n-1
Set up the formula for variance for this set of numbers.
s=(53-87.5)2+(90-87.5)2+(92-87.5)2+(95-87.5)2+(97-87.5)2+(98-87.5)26-1
Simplify the result.
Simplify the numerator.
Subtract 87.5 from 53.
s=(-34.5)2+(90-87.5)2+(92-87.5)2+(95-87.5)2+(97-87.5)2+(98-87.5)26-1
Raise -34.5 to the power of 2.
s=1190.25+(90-87.5)2+(92-87.5)2+(95-87.5)2+(97-87.5)2+(98-87.5)26-1
Subtract 87.5 from 90.
s=1190.25+2.52+(92-87.5)2+(95-87.5)2+(97-87.5)2+(98-87.5)26-1
Raise 2.5 to the power of 2.
s=1190.25+6.25+(92-87.5)2+(95-87.5)2+(97-87.5)2+(98-87.5)26-1
Subtract 87.5 from 92.
s=1190.25+6.25+4.52+(95-87.5)2+(97-87.5)2+(98-87.5)26-1
Raise 4.5 to the power of 2.
s=1190.25+6.25+20.25+(95-87.5)2+(97-87.5)2+(98-87.5)26-1
Subtract 87.5 from 95.
s=1190.25+6.25+20.25+7.52+(97-87.5)2+(98-87.5)26-1
Raise 7.5 to the power of 2.
s=1190.25+6.25+20.25+56.25+(97-87.5)2+(98-87.5)26-1
Subtract 87.5 from 97.
s=1190.25+6.25+20.25+56.25+9.52+(98-87.5)26-1
Raise 9.5 to the power of 2.
s=1190.25+6.25+20.25+56.25+90.25+(98-87.5)26-1
Subtract 87.5 from 98.
s=1190.25+6.25+20.25+56.25+90.25+10.526-1
Raise 10.5 to the power of 2.
s=1190.25+6.25+20.25+56.25+90.25+110.256-1
s=1196.5+20.25+56.25+90.25+110.256-1
s=1216.75+56.25+90.25+110.256-1
s=1273+90.25+110.256-1
s=1363.25+110.256-1
s=1473.56-1
s=1473.56-1
Simplify the expression.
Subtract 1 from 6.
s=1473.55
Divide 1473.5 by 5.
s=294.7
s=294.7
s=294.7
Approximate the result.
s2≈294.7
Find the Variance 53 , 90 , 92 , 95 , 97 , 98

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