# Find the Variance 9 , 8 , 2 , 5 , 5

9 , 8 , 2 , 5 , 5
The mean of a set of numbers is the sum divided by the number of terms.
x&OverBar;=9+8+2+5+55
Simplify the numerator.
Add 9 and 8.
x&OverBar;=17+2+5+55
Add 17 and 2.
x&OverBar;=19+5+55
Add 19 and 5.
x&OverBar;=24+55
Add 24 and 5.
x&OverBar;=295
x&OverBar;=295
Divide.
x&OverBar;=5.8
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=(9-5.8)2+(8-5.8)2+(2-5.8)2+(5-5.8)2+(5-5.8)25-1
Simplify the result.
Simplify the numerator.
Subtract 5.8 from 9.
s=3.22+(8-5.8)2+(2-5.8)2+(5-5.8)2+(5-5.8)25-1
Raise 3.2 to the power of 2.
s=10.24+(8-5.8)2+(2-5.8)2+(5-5.8)2+(5-5.8)25-1
Subtract 5.8 from 8.
s=10.24+2.22+(2-5.8)2+(5-5.8)2+(5-5.8)25-1
Raise 2.2 to the power of 2.
s=10.24+4.84+(2-5.8)2+(5-5.8)2+(5-5.8)25-1
Subtract 5.8 from 2.
s=10.24+4.84+(-3.8)2+(5-5.8)2+(5-5.8)25-1
Raise -3.8 to the power of 2.
s=10.24+4.84+14.44+(5-5.8)2+(5-5.8)25-1
Subtract 5.8 from 5.
s=10.24+4.84+14.44+(-0.8)2+(5-5.8)25-1
Raise -0.8 to the power of 2.
s=10.24+4.84+14.44+0.64+(5-5.8)25-1
Subtract 5.8 from 5.
s=10.24+4.84+14.44+0.64+(-0.8)25-1
Raise -0.8 to the power of 2.
s=10.24+4.84+14.44+0.64+0.645-1
Add 10.24 and 4.84.
s=15.08+14.44+0.64+0.645-1
Add 15.08 and 14.44.
s=29.52+0.64+0.645-1
Add 29.52 and 0.64.
s=30.16+0.645-1
Add 30.16 and 0.64.
s=30.85-1
s=30.85-1
Simplify the expression.
Subtract 1 from 5.
s=30.84
Divide 30.8 by 4.
s=7.7
s=7.7
s=7.7
Approximate the result.
s2≈7.7
Find the Variance 9 , 8 , 2 , 5 , 5

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