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

1 , 9 , 4 , 12 , 13 , 13
The mean of a set of numbers is the sum divided by the number of terms.
x&OverBar;=1+9+4+12+13+136
Simplify the numerator.
x&OverBar;=10+4+12+13+136
x&OverBar;=14+12+13+136
x&OverBar;=26+13+136
x&OverBar;=39+136
x&OverBar;=526
x&OverBar;=526
Cancel the common factor of 52 and 6.
Factor 2 out of 52.
x&OverBar;=2(26)6
Cancel the common factors.
Factor 2 out of 6.
x&OverBar;=2⋅262⋅3
Cancel the common factor.
x&OverBar;=2⋅262⋅3
Rewrite the expression.
x&OverBar;=263
x&OverBar;=263
x&OverBar;=263
Divide.
x&OverBar;=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&OverBar;=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.
Simplify the numerator.
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
s=59.38+22.09+10.89+18.49+18.496-1
s=81.47+10.89+18.49+18.496-1
s=92.36+18.49+18.496-1
s=110.85+18.496-1
s=129.346-1
s=129.346-1
Simplify the expression.
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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