Find the Variance 15.0 , 15.9 , 15.3 , 15.3 , 15.5 , 15.9 , 15.9 , 15.0

Math
15 , 15.9 , 15.3 , 15.3 , 15.5 , 15.9 , 15.9 , 15
The mean of a set of numbers is the sum divided by the number of terms.
x‾=15+15.9+15.3+15.3+15.5+15.9+15.9+158
Simplify the numerator.
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Add 15 and 15.9.
x‾=30.9+15.3+15.3+15.5+15.9+15.9+158
Add 30.9 and 15.3.
x‾=46.2+15.3+15.5+15.9+15.9+158
Add 46.2 and 15.3.
x‾=61.5+15.5+15.9+15.9+158
Add 61.5 and 15.5.
x‾=77+15.9+15.9+158
Add 77 and 15.9.
x‾=92.9+15.9+158
Add 92.9 and 15.9.
x‾=108.8+158
Add 108.8 and 15.
x‾=123.88
x‾=123.88
Divide 123.8 by 8.
x‾=15.475
The mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.
x‾=15.48
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=(15-15.48)2+(15.9-15.48)2+(15.3-15.48)2+(15.3-15.48)2+(15.5-15.48)2+(15.9-15.48)2+(15.9-15.48)2+(15-15.48)28-1
Simplify the result.
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Simplify the numerator.
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Subtract 15.48 from 15.
s=(-0.48)2+(15.9-15.48)2+(15.3-15.48)2+(15.3-15.48)2+(15.5-15.48)2+(15.9-15.48)2+(15.9-15.48)2+(15-15.48)28-1
Raise -0.48 to the power of 2.
s=0.2304+(15.9-15.48)2+(15.3-15.48)2+(15.3-15.48)2+(15.5-15.48)2+(15.9-15.48)2+(15.9-15.48)2+(15-15.48)28-1
Subtract 15.48 from 15.9.
s=0.2304+0.422+(15.3-15.48)2+(15.3-15.48)2+(15.5-15.48)2+(15.9-15.48)2+(15.9-15.48)2+(15-15.48)28-1
Raise 0.42 to the power of 2.
s=0.2304+0.1764+(15.3-15.48)2+(15.3-15.48)2+(15.5-15.48)2+(15.9-15.48)2+(15.9-15.48)2+(15-15.48)28-1
Subtract 15.48 from 15.3.
s=0.2304+0.1764+(-0.18)2+(15.3-15.48)2+(15.5-15.48)2+(15.9-15.48)2+(15.9-15.48)2+(15-15.48)28-1
Raise -0.18 to the power of 2.
s=0.2304+0.1764+0.0324+(15.3-15.48)2+(15.5-15.48)2+(15.9-15.48)2+(15.9-15.48)2+(15-15.48)28-1
Subtract 15.48 from 15.3.
s=0.2304+0.1764+0.0324+(-0.18)2+(15.5-15.48)2+(15.9-15.48)2+(15.9-15.48)2+(15-15.48)28-1
Raise -0.18 to the power of 2.
s=0.2304+0.1764+0.0324+0.0324+(15.5-15.48)2+(15.9-15.48)2+(15.9-15.48)2+(15-15.48)28-1
Subtract 15.48 from 15.5.
s=0.2304+0.1764+0.0324+0.0324+0.022+(15.9-15.48)2+(15.9-15.48)2+(15-15.48)28-1
Raise 0.02 to the power of 2.
s=0.2304+0.1764+0.0324+0.0324+0.0004+(15.9-15.48)2+(15.9-15.48)2+(15-15.48)28-1
Subtract 15.48 from 15.9.
s=0.2304+0.1764+0.0324+0.0324+0.0004+0.422+(15.9-15.48)2+(15-15.48)28-1
Raise 0.42 to the power of 2.
s=0.2304+0.1764+0.0324+0.0324+0.0004+0.1764+(15.9-15.48)2+(15-15.48)28-1
Subtract 15.48 from 15.9.
s=0.2304+0.1764+0.0324+0.0324+0.0004+0.1764+0.422+(15-15.48)28-1
Raise 0.42 to the power of 2.
s=0.2304+0.1764+0.0324+0.0324+0.0004+0.1764+0.1764+(15-15.48)28-1
Subtract 15.48 from 15.
s=0.2304+0.1764+0.0324+0.0324+0.0004+0.1764+0.1764+(-0.48)28-1
Raise -0.48 to the power of 2.
s=0.2304+0.1764+0.0324+0.0324+0.0004+0.1764+0.1764+0.23048-1
Add 0.2304 and 0.1764.
s=0.4068+0.0324+0.0324+0.0004+0.1764+0.1764+0.23048-1
Add 0.4068 and 0.0324.
s=0.4392+0.0324+0.0004+0.1764+0.1764+0.23048-1
Add 0.4392 and 0.0324.
s=0.4716+0.0004+0.1764+0.1764+0.23048-1
Add 0.4716 and 0.0004.
s=0.472+0.1764+0.1764+0.23048-1
Add 0.472 and 0.1764.
s=0.6484+0.1764+0.23048-1
Add 0.6484 and 0.1764.
s=0.8248+0.23048-1
Add 0.8248 and 0.2304.
s=1.05528-1
s=1.05528-1
Simplify the expression.
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Subtract 1 from 8.
s=1.05527
Divide 1.0552 by 7.
s=0.15074285
s=0.15074285
s=0.15074285
Approximate the result.
s2≈0.1507
Find the Variance 15.0 , 15.9 , 15.3 , 15.3 , 15.5 , 15.9 , 15.9 , 15.0

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