Find the Variance 64 , 65 , 71 , 75 , 69

Math
64 , 65 , 71 , 75 , 69
The mean of a set of numbers is the sum divided by the number of terms.
x‾=64+65+71+75+695
Simplify the numerator.
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Add 64 and 65.
x‾=129+71+75+695
Add 129 and 71.
x‾=200+75+695
Add 200 and 75.
x‾=275+695
Add 275 and 69.
x‾=3445
x‾=3445
Divide.
x‾=68.8
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=(64-68.8)2+(65-68.8)2+(71-68.8)2+(75-68.8)2+(69-68.8)25-1
Simplify the result.
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Simplify the numerator.
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Subtract 68.8 from 64.
s=(-4.8)2+(65-68.8)2+(71-68.8)2+(75-68.8)2+(69-68.8)25-1
Raise -4.8 to the power of 2.
s=23.04+(65-68.8)2+(71-68.8)2+(75-68.8)2+(69-68.8)25-1
Subtract 68.8 from 65.
s=23.04+(-3.8)2+(71-68.8)2+(75-68.8)2+(69-68.8)25-1
Raise -3.8 to the power of 2.
s=23.04+14.44+(71-68.8)2+(75-68.8)2+(69-68.8)25-1
Subtract 68.8 from 71.
s=23.04+14.44+2.22+(75-68.8)2+(69-68.8)25-1
Raise 2.2 to the power of 2.
s=23.04+14.44+4.84+(75-68.8)2+(69-68.8)25-1
Subtract 68.8 from 75.
s=23.04+14.44+4.84+6.22+(69-68.8)25-1
Raise 6.2 to the power of 2.
s=23.04+14.44+4.84+38.44+(69-68.8)25-1
Subtract 68.8 from 69.
s=23.04+14.44+4.84+38.44+0.225-1
Raise 0.2 to the power of 2.
s=23.04+14.44+4.84+38.44+0.045-1
Add 23.04 and 14.44.
s=37.48+4.84+38.44+0.045-1
Add 37.48 and 4.84.
s=42.32+38.44+0.045-1
Add 42.32 and 38.44.
s=80.76+0.045-1
Add 80.76 and 0.04.
s=80.85-1
s=80.85-1
Simplify the expression.
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Subtract 1 from 5.
s=80.84
Divide 80.8 by 4.
s=20.2
s=20.2
s=20.2
Approximate the result.
s2≈20.2
Find the Variance 64 , 65 , 71 , 75 , 69

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