Find the Variance 68 , 67 , 74 , 63 , 71

Math
68 , 67 , 74 , 63 , 71
The mean of a set of numbers is the sum divided by the number of terms.
x‾=68+67+74+63+715
Simplify the numerator.
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Add 68 and 67.
x‾=135+74+63+715
Add 135 and 74.
x‾=209+63+715
Add 209 and 63.
x‾=272+715
Add 272 and 71.
x‾=3435
x‾=3435
Divide.
x‾=68.6
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=(68-68.6)2+(67-68.6)2+(74-68.6)2+(63-68.6)2+(71-68.6)25-1
Simplify the result.
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Simplify the numerator.
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Subtract 68.6 from 68.
s=(-0.6)2+(67-68.6)2+(74-68.6)2+(63-68.6)2+(71-68.6)25-1
Raise -0.6 to the power of 2.
s=0.36+(67-68.6)2+(74-68.6)2+(63-68.6)2+(71-68.6)25-1
Subtract 68.6 from 67.
s=0.36+(-1.6)2+(74-68.6)2+(63-68.6)2+(71-68.6)25-1
Raise -1.6 to the power of 2.
s=0.36+2.56+(74-68.6)2+(63-68.6)2+(71-68.6)25-1
Subtract 68.6 from 74.
s=0.36+2.56+5.42+(63-68.6)2+(71-68.6)25-1
Raise 5.4 to the power of 2.
s=0.36+2.56+29.16+(63-68.6)2+(71-68.6)25-1
Subtract 68.6 from 63.
s=0.36+2.56+29.16+(-5.6)2+(71-68.6)25-1
Raise -5.6 to the power of 2.
s=0.36+2.56+29.16+31.36+(71-68.6)25-1
Subtract 68.6 from 71.
s=0.36+2.56+29.16+31.36+2.425-1
Raise 2.4 to the power of 2.
s=0.36+2.56+29.16+31.36+5.765-1
Add 0.36 and 2.56.
s=2.92+29.16+31.36+5.765-1
Add 2.92 and 29.16.
s=32.08+31.36+5.765-1
Add 32.08 and 31.36.
s=63.44+5.765-1
Add 63.44 and 5.76.
s=69.25-1
s=69.25-1
Simplify the expression.
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Subtract 1 from 5.
s=69.24
Divide 69.2 by 4.
s=17.3
s=17.3
s=17.3
Approximate the result.
s2≈17.3
Find the Variance 68 , 67 , 74 , 63 , 71

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