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Find the Variance 21 , 12 , 6 , 7 , 9

21 , 12 , 6 , 7 , 9

Step 1
The mean of a set of numbers is the sum divided by the number of terms.
x=21+12+6+7+95

Step 2
Simplify the numerator.

Add 21 and 12.
x=33+6+7+95
Add 33 and 6.
x=39+7+95
Add 39 and 7.
x=46+95
Add 46 and 9.
x=555
x=555

Step 3
Divide 55 by 5.
x=11

Step 4
Set up the formula for variance. The variance of a set of values is a measure of the spread of its values.
s2=ni=1(xi-xavg)2n-1

Step 5
Set up the formula for variance for this set of numbers.
s=(21-11)2+(12-11)2+(6-11)2+(7-11)2+(9-11)25-1

Step 6
Simplify the result.

Simplify the numerator.

Subtract 11 from 21.
s=102+(12-11)2+(6-11)2+(7-11)2+(9-11)25-1
Raise 10 to the power of 2.
s=100+(12-11)2+(6-11)2+(7-11)2+(9-11)25-1
Subtract 11 from 12.
s=100+12+(6-11)2+(7-11)2+(9-11)25-1
One to any power is one.
s=100+1+(6-11)2+(7-11)2+(9-11)25-1
Subtract 11 from 6.
s=100+1+(-5)2+(7-11)2+(9-11)25-1
Raise -5 to the power of 2.
s=100+1+25+(7-11)2+(9-11)25-1
Subtract 11 from 7.
s=100+1+25+(-4)2+(9-11)25-1
Raise -4 to the power of 2.
s=100+1+25+16+(9-11)25-1
Subtract 11 from 9.
s=100+1+25+16+(-2)25-1
Raise -2 to the power of 2.
s=100+1+25+16+45-1
Add 100 and 1.
s=101+25+16+45-1
Add 101 and 25.
s=126+16+45-1
Add 126 and 16.
s=142+45-1
Add 142 and 4.
s=1465-1
s=1465-1
Reduce the expression by cancelling the common factors.

Subtract 1 from 5.
s=1464
Cancel the common factor of 146 and 4.

Factor 2 out of 146.
s=2(73)4
Cancel the common factors.

Factor 2 out of 4.
s=27322
Cancel the common factor.
s=27322
Rewrite the expression.
s=732
s=732
s=732
s=732
s=732

Step 7
Approximate the result.
s236.5