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

Math
85 , 65 , 72 , 73 , 53
The mean of a set of numbers is the sum divided by the number of terms.
x‾=85+65+72+73+535
Simplify the numerator.
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Add 85 and 65.
x‾=150+72+73+535
Add 150 and 72.
x‾=222+73+535
Add 222 and 73.
x‾=295+535
Add 295 and 53.
x‾=3485
x‾=3485
Divide.
x‾=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.
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Simplify the numerator.
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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
Add 237.16 and 21.16.
s=258.32+5.76+11.56+275.565-1
Add 258.32 and 5.76.
s=264.08+11.56+275.565-1
Add 264.08 and 11.56.
s=275.64+275.565-1
Add 275.64 and 275.56.
s=551.25-1
s=551.25-1
Simplify the expression.
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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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