# Find the Variance 85 , 65 , 72 , 73 , 53

85 , 65 , 72 , 73 , 53
The mean of a set of numbers is the sum divided by the number of terms.
x&OverBar;=85+65+72+73+535
Simplify the numerator.
x&OverBar;=150+72+73+535
x&OverBar;=222+73+535
x&OverBar;=295+535
x&OverBar;=3485
x&OverBar;=3485
Divide.
x&OverBar;=69.6
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=(85-69.6)2+(65-69.6)2+(72-69.6)2+(73-69.6)2+(53-69.6)25-1
Simplify the result.
Simplify the numerator.
Subtract 69.6 from 85.
s=15.42+(65-69.6)2+(72-69.6)2+(73-69.6)2+(53-69.6)25-1
Raise 15.4 to the power of 2.
s=237.16+(65-69.6)2+(72-69.6)2+(73-69.6)2+(53-69.6)25-1
Subtract 69.6 from 65.
s=237.16+(-4.6)2+(72-69.6)2+(73-69.6)2+(53-69.6)25-1
Raise -4.6 to the power of 2.
s=237.16+21.16+(72-69.6)2+(73-69.6)2+(53-69.6)25-1
Subtract 69.6 from 72.
s=237.16+21.16+2.42+(73-69.6)2+(53-69.6)25-1
Raise 2.4 to the power of 2.
s=237.16+21.16+5.76+(73-69.6)2+(53-69.6)25-1
Subtract 69.6 from 73.
s=237.16+21.16+5.76+3.42+(53-69.6)25-1
Raise 3.4 to the power of 2.
s=237.16+21.16+5.76+11.56+(53-69.6)25-1
Subtract 69.6 from 53.
s=237.16+21.16+5.76+11.56+(-16.6)25-1
Raise -16.6 to the power of 2.
s=237.16+21.16+5.76+11.56+275.565-1
s=258.32+5.76+11.56+275.565-1
s=264.08+11.56+275.565-1
s=275.64+275.565-1
s=551.25-1
s=551.25-1
Simplify the expression.
Subtract 1 from 5.
s=551.24
Divide 551.2 by 4.
s=137.8
s=137.8
s=137.8
Approximate the result.
s2≈137.8
Find the Variance 85 , 65 , 72 , 73 , 53

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