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Find the Variance 90 , 90 , 91 , 89 , 91 , 89 , 90 , 90

90 , 90 , 91 , 89 , 91 , 89 , 90 , 90
Step 1
The mean of a set of numbers is the sum divided by the number of terms.
‾x=90+90+91+89+91+89+90+908

Step 2
Simplify the numerator.

Add 90 and 90.
‾x=180+91+89+91+89+90+908
Add 180 and 91.
‾x=271+89+91+89+90+908
Add 271 and 89.
‾x=360+91+89+90+908
Add 360 and 91.
‾x=451+89+90+908
Add 451 and 89.
‾x=540+90+908
Add 540 and 90.
‾x=630+908
Add 630 and 90.
‾x=7208
‾x=7208

Step 3
Divide 720 by 8.
‾x=90

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=n∑i=1(xi-xavg)2n-1

Step 5
Set up the formula for variance for this set of numbers.
s=(90-90)2+(90-90)2+(91-90)2+(89-90)2+(91-90)2+(89-90)2+(90-90)2+(90-90)28-1

Step 6
Simplify the result.

Simplify the numerator.

Subtract 90 from 90.
s=02+(90-90)2+(91-90)2+(89-90)2+(91-90)2+(89-90)2+(90-90)2+(90-90)28-1
Raising 0 to any positive power yields 0.
s=0+(90-90)2+(91-90)2+(89-90)2+(91-90)2+(89-90)2+(90-90)2+(90-90)28-1
Subtract 90 from 90.
s=0+02+(91-90)2+(89-90)2+(91-90)2+(89-90)2+(90-90)2+(90-90)28-1
Raising 0 to any positive power yields 0.
s=0+0+(91-90)2+(89-90)2+(91-90)2+(89-90)2+(90-90)2+(90-90)28-1
Subtract 90 from 91.
s=0+0+12+(89-90)2+(91-90)2+(89-90)2+(90-90)2+(90-90)28-1
One to any power is one.
s=0+0+1+(89-90)2+(91-90)2+(89-90)2+(90-90)2+(90-90)28-1
Subtract 90 from 89.
s=0+0+1+(-1)2+(91-90)2+(89-90)2+(90-90)2+(90-90)28-1
Raise -1 to the power of 2.
s=0+0+1+1+(91-90)2+(89-90)2+(90-90)2+(90-90)28-1
Subtract 90 from 91.
s=0+0+1+1+12+(89-90)2+(90-90)2+(90-90)28-1
One to any power is one.
s=0+0+1+1+1+(89-90)2+(90-90)2+(90-90)28-1
Subtract 90 from 89.
s=0+0+1+1+1+(-1)2+(90-90)2+(90-90)28-1
Raise -1 to the power of 2.
s=0+0+1+1+1+1+(90-90)2+(90-90)28-1
Subtract 90 from 90.
s=0+0+1+1+1+1+02+(90-90)28-1
Raising 0 to any positive power yields 0.
s=0+0+1+1+1+1+0+(90-90)28-1
Subtract 90 from 90.
s=0+0+1+1+1+1+0+028-1
Raising 0 to any positive power yields 0.
s=0+0+1+1+1+1+0+08-1
Add 0+0+1+1+1+1+0 and 0.
s=0+0+1+1+1+1+08-1
Add 0+0+1+1+1+1 and 0.
s=0+0+1+1+1+18-1
Add 0 and 0.
s=0+1+1+1+18-1
Add 0 and 1.
s=1+1+1+18-1
Add 1 and 1.
s=2+1+18-1
Add 2 and 1.
s=3+18-1
Add 3 and 1.
s=48-1
s=48-1
Subtract 1 from 8.
s=47
s=47

Step 7
Approximate the result.
s2≈0.5714


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