# Find the Variance 5 , 10 , 15 , 20 5 , 10 , 15 , 20
The mean of a set of numbers is the sum divided by the number of terms.
x&OverBar;=5+10+15+204
Simplify the numerator.
Add 5 and 10.
x&OverBar;=15+15+204
Add 15 and 15.
x&OverBar;=30+204
Add 30 and 20.
x&OverBar;=504
x&OverBar;=504
Cancel the common factor of 50 and 4.
Factor 2 out of 50.
x&OverBar;=2(25)4
Cancel the common factors.
Factor 2 out of 4.
x&OverBar;=2⋅252⋅2
Cancel the common factor.
x&OverBar;=2⋅252⋅2
Rewrite the expression.
x&OverBar;=252
x&OverBar;=252
x&OverBar;=252
Divide.
x&OverBar;=12.5
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=(5-12.5)2+(10-12.5)2+(15-12.5)2+(20-12.5)24-1
Simplify the result.
Simplify the numerator.
Subtract 12.5 from 5.
s=(-7.5)2+(10-12.5)2+(15-12.5)2+(20-12.5)24-1
Raise -7.5 to the power of 2.
s=56.25+(10-12.5)2+(15-12.5)2+(20-12.5)24-1
Subtract 12.5 from 10.
s=56.25+(-2.5)2+(15-12.5)2+(20-12.5)24-1
Raise -2.5 to the power of 2.
s=56.25+6.25+(15-12.5)2+(20-12.5)24-1
Subtract 12.5 from 15.
s=56.25+6.25+2.52+(20-12.5)24-1
Raise 2.5 to the power of 2.
s=56.25+6.25+6.25+(20-12.5)24-1
Subtract 12.5 from 20.
s=56.25+6.25+6.25+7.524-1
Raise 7.5 to the power of 2.
s=56.25+6.25+6.25+56.254-1
Add 56.25 and 6.25.
s=62.5+6.25+56.254-1
Add 62.5 and 6.25.
s=68.75+56.254-1
Add 68.75 and 56.25.
s=1254-1
s=1254-1
Reduce the expression by cancelling the common factors.
Subtract 1 from 4.
s=1253
Cancel the common factor of 125 and 3.
Rewrite 125 as 1(125).
s=1(125)3
Cancel the common factors.
Rewrite 3 as 1(3).
s=1⋅1251⋅3
Cancel the common factor.
s=1⋅1251⋅3
Rewrite the expression.
s=1253
s=1253
s=1253
s=1253
s=1253
Approximate the result.
s2≈41.6667
Find the Variance 5 , 10 , 15 , 20

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