Find the Variance 88 , 102 , 106 , 116 , 128 , 134 , 166

Math
88 , 102 , 106 , 116 , 128 , 134 , 166
The mean of a set of numbers is the sum divided by the number of terms.
x‾=88+102+106+116+128+134+1667
Simplify the numerator.
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Add 88 and 102.
x‾=190+106+116+128+134+1667
Add 190 and 106.
x‾=296+116+128+134+1667
Add 296 and 116.
x‾=412+128+134+1667
Add 412 and 128.
x‾=540+134+1667
Add 540 and 134.
x‾=674+1667
Add 674 and 166.
x‾=8407
x‾=8407
Divide 840 by 7.
x‾=120
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=(88-120)2+(102-120)2+(106-120)2+(116-120)2+(128-120)2+(134-120)2+(166-120)27-1
Simplify the result.
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Simplify the numerator.
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Subtract 120 from 88.
s=(-32)2+(102-120)2+(106-120)2+(116-120)2+(128-120)2+(134-120)2+(166-120)27-1
Raise -32 to the power of 2.
s=1024+(102-120)2+(106-120)2+(116-120)2+(128-120)2+(134-120)2+(166-120)27-1
Subtract 120 from 102.
s=1024+(-18)2+(106-120)2+(116-120)2+(128-120)2+(134-120)2+(166-120)27-1
Raise -18 to the power of 2.
s=1024+324+(106-120)2+(116-120)2+(128-120)2+(134-120)2+(166-120)27-1
Subtract 120 from 106.
s=1024+324+(-14)2+(116-120)2+(128-120)2+(134-120)2+(166-120)27-1
Raise -14 to the power of 2.
s=1024+324+196+(116-120)2+(128-120)2+(134-120)2+(166-120)27-1
Subtract 120 from 116.
s=1024+324+196+(-4)2+(128-120)2+(134-120)2+(166-120)27-1
Raise -4 to the power of 2.
s=1024+324+196+16+(128-120)2+(134-120)2+(166-120)27-1
Subtract 120 from 128.
s=1024+324+196+16+82+(134-120)2+(166-120)27-1
Raise 8 to the power of 2.
s=1024+324+196+16+64+(134-120)2+(166-120)27-1
Subtract 120 from 134.
s=1024+324+196+16+64+142+(166-120)27-1
Raise 14 to the power of 2.
s=1024+324+196+16+64+196+(166-120)27-1
Subtract 120 from 166.
s=1024+324+196+16+64+196+4627-1
Raise 46 to the power of 2.
s=1024+324+196+16+64+196+21167-1
Add 1024 and 324.
s=1348+196+16+64+196+21167-1
Add 1348 and 196.
s=1544+16+64+196+21167-1
Add 1544 and 16.
s=1560+64+196+21167-1
Add 1560 and 64.
s=1624+196+21167-1
Add 1624 and 196.
s=1820+21167-1
Add 1820 and 2116.
s=39367-1
s=39367-1
Simplify the expression.
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Subtract 1 from 7.
s=39366
Divide 3936 by 6.
s=656
s=656
s=656
Approximate the result.
s2≈656
Find the Variance 88 , 102 , 106 , 116 , 128 , 134 , 166

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