Find the Variance 92 , 97 , 53 , 90 , 95 , 98

Math
92 , 97 , 53 , 90 , 95 , 98
The mean of a set of numbers is the sum divided by the number of terms.
x‾=92+97+53+90+95+986
Simplify the numerator.
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Add 92 and 97.
x‾=189+53+90+95+986
Add 189 and 53.
x‾=242+90+95+986
Add 242 and 90.
x‾=332+95+986
Add 332 and 95.
x‾=427+986
Add 427 and 98.
x‾=5256
x‾=5256
Cancel the common factor of 525 and 6.
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Factor 3 out of 525.
x‾=3(175)6
Cancel the common factors.
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Factor 3 out of 6.
x‾=3⋅1753⋅2
Cancel the common factor.
x‾=3⋅1753⋅2
Rewrite the expression.
x‾=1752
x‾=1752
x‾=1752
Divide.
x‾=87.5
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=(92-87.5)2+(97-87.5)2+(53-87.5)2+(90-87.5)2+(95-87.5)2+(98-87.5)26-1
Simplify the result.
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Simplify the numerator.
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Subtract 87.5 from 92.
s=4.52+(97-87.5)2+(53-87.5)2+(90-87.5)2+(95-87.5)2+(98-87.5)26-1
Raise 4.5 to the power of 2.
s=20.25+(97-87.5)2+(53-87.5)2+(90-87.5)2+(95-87.5)2+(98-87.5)26-1
Subtract 87.5 from 97.
s=20.25+9.52+(53-87.5)2+(90-87.5)2+(95-87.5)2+(98-87.5)26-1
Raise 9.5 to the power of 2.
s=20.25+90.25+(53-87.5)2+(90-87.5)2+(95-87.5)2+(98-87.5)26-1
Subtract 87.5 from 53.
s=20.25+90.25+(-34.5)2+(90-87.5)2+(95-87.5)2+(98-87.5)26-1
Raise -34.5 to the power of 2.
s=20.25+90.25+1190.25+(90-87.5)2+(95-87.5)2+(98-87.5)26-1
Subtract 87.5 from 90.
s=20.25+90.25+1190.25+2.52+(95-87.5)2+(98-87.5)26-1
Raise 2.5 to the power of 2.
s=20.25+90.25+1190.25+6.25+(95-87.5)2+(98-87.5)26-1
Subtract 87.5 from 95.
s=20.25+90.25+1190.25+6.25+7.52+(98-87.5)26-1
Raise 7.5 to the power of 2.
s=20.25+90.25+1190.25+6.25+56.25+(98-87.5)26-1
Subtract 87.5 from 98.
s=20.25+90.25+1190.25+6.25+56.25+10.526-1
Raise 10.5 to the power of 2.
s=20.25+90.25+1190.25+6.25+56.25+110.256-1
Add 20.25 and 90.25.
s=110.5+1190.25+6.25+56.25+110.256-1
Add 110.5 and 1190.25.
s=1300.75+6.25+56.25+110.256-1
Add 1300.75 and 6.25.
s=1307+56.25+110.256-1
Add 1307 and 56.25.
s=1363.25+110.256-1
Add 1363.25 and 110.25.
s=1473.56-1
s=1473.56-1
Simplify the expression.
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Subtract 1 from 6.
s=1473.55
Divide 1473.5 by 5.
s=294.7
s=294.7
s=294.7
Approximate the result.
s2≈294.7
Find the Variance 92 , 97 , 53 , 90 , 95 , 98

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