# Find the Variance 15 , 32 , 25 , 16 , 10

15 , 32 , 25 , 16 , 10
The mean of a set of numbers is the sum divided by the number of terms.
x&OverBar;=15+32+25+16+105
Simplify the numerator.
x&OverBar;=47+25+16+105
x&OverBar;=72+16+105
x&OverBar;=88+105
x&OverBar;=985
x&OverBar;=985
Divide.
x&OverBar;=19.6
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=(15-19.6)2+(32-19.6)2+(25-19.6)2+(16-19.6)2+(10-19.6)25-1
Simplify the result.
Simplify the numerator.
Subtract 19.6 from 15.
s=(-4.6)2+(32-19.6)2+(25-19.6)2+(16-19.6)2+(10-19.6)25-1
Raise -4.6 to the power of 2.
s=21.16+(32-19.6)2+(25-19.6)2+(16-19.6)2+(10-19.6)25-1
Subtract 19.6 from 32.
s=21.16+12.42+(25-19.6)2+(16-19.6)2+(10-19.6)25-1
Raise 12.4 to the power of 2.
s=21.16+153.76+(25-19.6)2+(16-19.6)2+(10-19.6)25-1
Subtract 19.6 from 25.
s=21.16+153.76+5.42+(16-19.6)2+(10-19.6)25-1
Raise 5.4 to the power of 2.
s=21.16+153.76+29.16+(16-19.6)2+(10-19.6)25-1
Subtract 19.6 from 16.
s=21.16+153.76+29.16+(-3.6)2+(10-19.6)25-1
Raise -3.6 to the power of 2.
s=21.16+153.76+29.16+12.96+(10-19.6)25-1
Subtract 19.6 from 10.
s=21.16+153.76+29.16+12.96+(-9.6)25-1
Raise -9.6 to the power of 2.
s=21.16+153.76+29.16+12.96+92.165-1
s=174.92+29.16+12.96+92.165-1
s=204.08+12.96+92.165-1
s=217.04+92.165-1
s=309.25-1
s=309.25-1
Simplify the expression.
Subtract 1 from 5.
s=309.24
Divide 309.2 by 4.
s=77.3
s=77.3
s=77.3
Approximate the result.
s2≈77.3
Find the Variance 15 , 32 , 25 , 16 , 10

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