Find the Variance 1/2 , 1/9 , 1/16

Math
12 , 19 , 116
The mean of a set of numbers is the sum divided by the number of terms.
x‾=12+19+1163
Simplify the numerator.
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To write 12 as a fraction with a common denominator, multiply by 99.
x‾=12⋅99+19+1163
To write 19 as a fraction with a common denominator, multiply by 22.
x‾=12⋅99+19⋅22+1163
Write each expression with a common denominator of 18, by multiplying each by an appropriate factor of 1.
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Multiply 12 and 99.
x‾=92⋅9+19⋅22+1163
Multiply 2 by 9.
x‾=918+19⋅22+1163
Multiply 19 and 22.
x‾=918+29⋅2+1163
Multiply 9 by 2.
x‾=918+218+1163
x‾=918+218+1163
Combine the numerators over the common denominator.
x‾=9+218+1163
Add 9 and 2.
x‾=1118+1163
To write 1118 as a fraction with a common denominator, multiply by 88.
x‾=1118⋅88+1163
To write 116 as a fraction with a common denominator, multiply by 99.
x‾=1118⋅88+116⋅993
Write each expression with a common denominator of 144, by multiplying each by an appropriate factor of 1.
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Multiply 1118 and 88.
x‾=11⋅818⋅8+116⋅993
Multiply 18 by 8.
x‾=11⋅8144+116⋅993
Multiply 116 and 99.
x‾=11⋅8144+916⋅93
Multiply 16 by 9.
x‾=11⋅8144+91443
x‾=11⋅8144+91443
Combine the numerators over the common denominator.
x‾=11⋅8+91443
Simplify the numerator.
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Multiply 11 by 8.
x‾=88+91443
Add 88 and 9.
x‾=971443
x‾=971443
x‾=971443
Multiply the numerator by the reciprocal of the denominator.
x‾=97144⋅13
Multiply 97144⋅13.
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Multiply 97144 and 13.
x‾=97144⋅3
Multiply 144 by 3.
x‾=97432
x‾=97432
Divide.
x‾=0.2245370‾
The mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.
x‾=0.2
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=(12-0.2)2+(19-0.2)2+(116-0.2)23-1
Simplify the result.
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Simplify the numerator.
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To write -0.2 as a fraction with a common denominator, multiply by 22.
s=(12-0.2⋅22)2+(19-0.2)2+(116-0.2)23-1
Combine -0.2 and 22.
s=(12+-0.2⋅22)2+(19-0.2)2+(116-0.2)23-1
Combine the numerators over the common denominator.
s=(1-0.2⋅22)2+(19-0.2)2+(116-0.2)23-1
Simplify the numerator.
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Multiply -0.2 by 2.
s=(1-0.42)2+(19-0.2)2+(116-0.2)23-1
Subtract 0.4 from 1.
s=(0.62)2+(19-0.2)2+(116-0.2)23-1
s=(0.62)2+(19-0.2)2+(116-0.2)23-1
Divide 0.6 by 2.
s=0.32+(19-0.2)2+(116-0.2)23-1
Raise 0.3 to the power of 2.
s=0.09+(19-0.2)2+(116-0.2)23-1
To write -0.2 as a fraction with a common denominator, multiply by 99.
s=0.09+(19-0.2⋅99)2+(116-0.2)23-1
Combine -0.2 and 99.
s=0.09+(19+-0.2⋅99)2+(116-0.2)23-1
Combine the numerators over the common denominator.
s=0.09+(1-0.2⋅99)2+(116-0.2)23-1
Simplify the numerator.
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Multiply -0.2 by 9.
s=0.09+(1-1.89)2+(116-0.2)23-1
Subtract 1.8 from 1.
s=0.09+(-0.89)2+(116-0.2)23-1
s=0.09+(-0.89)2+(116-0.2)23-1
Divide -0.8 by 9.
s=0.09+(-0.08‾)2+(116-0.2)23-1
Raise -0.08‾ to the power of 2.
s=0.09+0.00790123+(116-0.2)23-1
To write -0.2 as a fraction with a common denominator, multiply by 1616.
s=0.09+0.00790123+(116-0.2⋅1616)23-1
Combine -0.2 and 1616.
s=0.09+0.00790123+(116+-0.2⋅1616)23-1
Combine the numerators over the common denominator.
s=0.09+0.00790123+(1-0.2⋅1616)23-1
Simplify the numerator.
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Multiply -0.2 by 16.
s=0.09+0.00790123+(1-3.216)23-1
Subtract 3.2 from 1.
s=0.09+0.00790123+(-2.216)23-1
s=0.09+0.00790123+(-2.216)23-1
Divide -2.2 by 16.
s=0.09+0.00790123+(-0.1375)23-1
Raise -0.1375 to the power of 2.
s=0.09+0.00790123+0.018906253-1
Add 0.09 and 0.00790123.
s=0.09790123+0.018906253-1
Add 0.09790123 and 0.01890625.
s=0.116807483-1
s=0.116807483-1
Simplify the expression.
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Subtract 1 from 3.
s=0.116807482
Divide 0.11680748 by 2.
s=0.05840374
s=0.05840374
s=0.05840374
Approximate the result.
s2≈0.0584
Find the Variance 1/2 , 1/9 , 1/16
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