# Find the Variance -21 , -35 , -17 , -31 , -18 , -2 , 5

-21 , -35 , -17 , -31 , -18 , -2 , 5
The mean of a set of numbers is the sum divided by the number of terms.
x&OverBar;=-21-35-17-31-18-2+57
Simplify the numerator.
Subtract 35 from -21.
x&OverBar;=-56-17-31-18-2+57
Subtract 17 from -56.
x&OverBar;=-73-31-18-2+57
Subtract 31 from -73.
x&OverBar;=-104-18-2+57
Subtract 18 from -104.
x&OverBar;=-122-2+57
Subtract 2 from -122.
x&OverBar;=-124+57
x&OverBar;=-1197
x&OverBar;=-1197
Divide -119 by 7.
x&OverBar;=-17
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=(-21+17)2+(-35+17)2+(-17+17)2+(-31+17)2+(-18+17)2+(-2+17)2+(5+17)27-1
Simplify the result.
Simplify the numerator.
s=(-4)2+(-35+17)2+(-17+17)2+(-31+17)2+(-18+17)2+(-2+17)2+(5+17)27-1
Raise -4 to the power of 2.
s=16+(-35+17)2+(-17+17)2+(-31+17)2+(-18+17)2+(-2+17)2+(5+17)27-1
s=16+(-18)2+(-17+17)2+(-31+17)2+(-18+17)2+(-2+17)2+(5+17)27-1
Raise -18 to the power of 2.
s=16+324+(-17+17)2+(-31+17)2+(-18+17)2+(-2+17)2+(5+17)27-1
s=16+324+02+(-31+17)2+(-18+17)2+(-2+17)2+(5+17)27-1
Raising 0 to any positive power yields 0.
s=16+324+0+(-31+17)2+(-18+17)2+(-2+17)2+(5+17)27-1
s=16+324+0+(-14)2+(-18+17)2+(-2+17)2+(5+17)27-1
Raise -14 to the power of 2.
s=16+324+0+196+(-18+17)2+(-2+17)2+(5+17)27-1
s=16+324+0+196+(-1)2+(-2+17)2+(5+17)27-1
Raise -1 to the power of 2.
s=16+324+0+196+1+(-2+17)2+(5+17)27-1
s=16+324+0+196+1+152+(5+17)27-1
Raise 15 to the power of 2.
s=16+324+0+196+1+225+(5+17)27-1
s=16+324+0+196+1+225+2227-1
Raise 22 to the power of 2.
s=16+324+0+196+1+225+4847-1
s=340+0+196+1+225+4847-1
s=340+196+1+225+4847-1
s=536+1+225+4847-1
s=537+225+4847-1
s=762+4847-1
s=12467-1
s=12467-1
Reduce the expression by cancelling the common factors.
Subtract 1 from 7.
s=12466
Cancel the common factor of 1246 and 6.
Factor 2 out of 1246.
s=2(623)6
Cancel the common factors.
Factor 2 out of 6.
s=2⋅6232⋅3
Cancel the common factor.
s=2⋅6232⋅3
Rewrite the expression.
s=6233
s=6233
s=6233
s=6233
s=6233
Approximate the result.
s2≈207.6667
Find the Variance -21 , -35 , -17 , -31 , -18 , -2 , 5

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