Find the Variance 14 , 12 , 16 , 20 , 10 , 18

Math
14 , 12 , 16 , 20 , 10 , 18
The mean of a set of numbers is the sum divided by the number of terms.
x‾=14+12+16+20+10+186
Cancel the common factor of 14+12+16+20+10+18 and 6.
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Factor 2 out of 14.
x‾=2(7)+12+16+20+10+186
Factor 2 out of 12.
x‾=2⋅7+2⋅6+16+20+10+186
Factor 2 out of 2⋅7+2⋅6.
x‾=2⋅(7+6)+16+20+10+186
Factor 2 out of 16.
x‾=2⋅(7+6)+2(8)+20+10+186
Factor 2 out of 2⋅(7+6)+2(8).
x‾=2⋅(7+6+8)+20+10+186
Factor 2 out of 20.
x‾=2⋅(7+6+8)+2(10)+10+186
Factor 2 out of 2⋅(7+6+8)+2(10).
x‾=2⋅(7+6+8+10)+10+186
Factor 2 out of 10.
x‾=2⋅(7+6+8+10)+2(5)+186
Factor 2 out of 2⋅(7+6+8+10)+2(5).
x‾=2⋅(7+6+8+10+5)+186
Factor 2 out of 18.
x‾=2⋅(7+6+8+10+5)+2(9)6
Factor 2 out of 2⋅(7+6+8+10+5)+2(9).
x‾=2⋅(7+6+8+10+5+9)6
Cancel the common factors.
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Factor 2 out of 6.
x‾=2⋅(7+6+8+10+5+9)2(3)
Cancel the common factor.
x‾=2⋅(7+6+8+10+5+9)2⋅3
Rewrite the expression.
x‾=7+6+8+10+5+93
x‾=7+6+8+10+5+93
x‾=7+6+8+10+5+93
Simplify the numerator.
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Add 7 and 6.
x‾=13+8+10+5+93
Add 13 and 8.
x‾=21+10+5+93
Add 21 and 10.
x‾=31+5+93
Add 31 and 5.
x‾=36+93
Add 36 and 9.
x‾=453
x‾=453
Divide 45 by 3.
x‾=15
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=(14-15)2+(12-15)2+(16-15)2+(20-15)2+(10-15)2+(18-15)26-1
Simplify the result.
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Simplify the numerator.
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Subtract 15 from 14.
s=(-1)2+(12-15)2+(16-15)2+(20-15)2+(10-15)2+(18-15)26-1
Raise -1 to the power of 2.
s=1+(12-15)2+(16-15)2+(20-15)2+(10-15)2+(18-15)26-1
Subtract 15 from 12.
s=1+(-3)2+(16-15)2+(20-15)2+(10-15)2+(18-15)26-1
Raise -3 to the power of 2.
s=1+9+(16-15)2+(20-15)2+(10-15)2+(18-15)26-1
Subtract 15 from 16.
s=1+9+12+(20-15)2+(10-15)2+(18-15)26-1
One to any power is one.
s=1+9+1+(20-15)2+(10-15)2+(18-15)26-1
Subtract 15 from 20.
s=1+9+1+52+(10-15)2+(18-15)26-1
Raise 5 to the power of 2.
s=1+9+1+25+(10-15)2+(18-15)26-1
Subtract 15 from 10.
s=1+9+1+25+(-5)2+(18-15)26-1
Raise -5 to the power of 2.
s=1+9+1+25+25+(18-15)26-1
Subtract 15 from 18.
s=1+9+1+25+25+326-1
Raise 3 to the power of 2.
s=1+9+1+25+25+96-1
Add 1 and 9.
s=10+1+25+25+96-1
Add 10 and 1.
s=11+25+25+96-1
Add 11 and 25.
s=36+25+96-1
Add 36 and 25.
s=61+96-1
Add 61 and 9.
s=706-1
s=706-1
Simplify the expression.
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Subtract 1 from 6.
s=705
Divide 70 by 5.
s=14
s=14
s=14
Approximate the result.
s2≈14
Find the Variance 14 , 12 , 16 , 20 , 10 , 18

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