Find the Variance 1 , 9 , 4 , 12 , 13 , 13

Math
1 , 9 , 4 , 12 , 13 , 13
The mean of a set of numbers is the sum divided by the number of terms.
x‾=1+9+4+12+13+136
Simplify the numerator.
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Add 1 and 9.
x‾=10+4+12+13+136
Add 10 and 4.
x‾=14+12+13+136
Add 14 and 12.
x‾=26+13+136
Add 26 and 13.
x‾=39+136
Add 39 and 13.
x‾=526
x‾=526
Cancel the common factor of 52 and 6.
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Factor 2 out of 52.
x‾=2(26)6
Cancel the common factors.
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Factor 2 out of 6.
x‾=2⋅262⋅3
Cancel the common factor.
x‾=2⋅262⋅3
Rewrite the expression.
x‾=263
x‾=263
x‾=263
Divide.
x‾=8.6‾
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‾=8.7
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=(1-8.7)2+(9-8.7)2+(4-8.7)2+(12-8.7)2+(13-8.7)2+(13-8.7)26-1
Simplify the result.
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Simplify the numerator.
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Subtract 8.7 from 1.
s=(-7.7)2+(9-8.7)2+(4-8.7)2+(12-8.7)2+(13-8.7)2+(13-8.7)26-1
Raise -7.7 to the power of 2.
s=59.29+(9-8.7)2+(4-8.7)2+(12-8.7)2+(13-8.7)2+(13-8.7)26-1
Subtract 8.7 from 9.
s=59.29+0.32+(4-8.7)2+(12-8.7)2+(13-8.7)2+(13-8.7)26-1
Raise 0.3 to the power of 2.
s=59.29+0.09+(4-8.7)2+(12-8.7)2+(13-8.7)2+(13-8.7)26-1
Subtract 8.7 from 4.
s=59.29+0.09+(-4.7)2+(12-8.7)2+(13-8.7)2+(13-8.7)26-1
Raise -4.7 to the power of 2.
s=59.29+0.09+22.09+(12-8.7)2+(13-8.7)2+(13-8.7)26-1
Subtract 8.7 from 12.
s=59.29+0.09+22.09+3.32+(13-8.7)2+(13-8.7)26-1
Raise 3.3 to the power of 2.
s=59.29+0.09+22.09+10.89+(13-8.7)2+(13-8.7)26-1
Subtract 8.7 from 13.
s=59.29+0.09+22.09+10.89+4.32+(13-8.7)26-1
Raise 4.3 to the power of 2.
s=59.29+0.09+22.09+10.89+18.49+(13-8.7)26-1
Subtract 8.7 from 13.
s=59.29+0.09+22.09+10.89+18.49+4.326-1
Raise 4.3 to the power of 2.
s=59.29+0.09+22.09+10.89+18.49+18.496-1
Add 59.29 and 0.09.
s=59.38+22.09+10.89+18.49+18.496-1
Add 59.38 and 22.09.
s=81.47+10.89+18.49+18.496-1
Add 81.47 and 10.89.
s=92.36+18.49+18.496-1
Add 92.36 and 18.49.
s=110.85+18.496-1
Add 110.85 and 18.49.
s=129.346-1
s=129.346-1
Simplify the expression.
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Subtract 1 from 6.
s=129.345
Divide 129.34 by 5.
s=25.868
s=25.868
s=25.868
Approximate the result.
s2≈25.868
Find the Variance 1 , 9 , 4 , 12 , 13 , 13

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