# Find the Variance 28 , 42

28 , 42
The mean of a set of numbers is the sum divided by the number of terms.
x&OverBar;=28+422
Cancel the common factor of 28+42 and 2.
Factor 2 out of 28.
x&OverBar;=2⋅14+422
Factor 2 out of 42.
x&OverBar;=2⋅14+2⋅212
Factor 2 out of 2⋅14+2⋅21.
x&OverBar;=2⋅(14+21)2
Cancel the common factors.
Factor 2 out of 2.
x&OverBar;=2⋅(14+21)2(1)
Cancel the common factor.
x&OverBar;=2⋅(14+21)2⋅1
Rewrite the expression.
x&OverBar;=14+211
Divide 14+21 by 1.
x&OverBar;=14+21
x&OverBar;=14+21
x&OverBar;=14+21
Add 14 and 21.
x&OverBar;=35
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=(28-35)2+(42-35)22-1
Simplify the result.
Simplify the numerator.
Subtract 35 from 28.
s=(-7)2+(42-35)22-1
Raise -7 to the power of 2.
s=49+(42-35)22-1
Subtract 35 from 42.
s=49+722-1
Raise 7 to the power of 2.
s=49+492-1
Add 49 and 49.
s=982-1
s=982-1
Simplify the expression.
Subtract 1 from 2.
s=981
Divide 98 by 1.
s=98
s=98
s=98
Approximate the result.
s2≈98
Find the Variance 28 , 42
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