Explanation
Given: 18∑i=1(xi−8)=9
18∑i=1(xi−8)2=45
Let X be a random variable taking values x1,........x18.
Then X−8 has the values x1−8,....,x18−8.
Now, E(X−8)=18∑i=1(xi−8)18
=918=12
And E[(X−8)2]=18∑i=1(xi−8)218
=4518=52
Thus, Var(X−8)=E[(X−8)2]−[E(X−8)]2
=52−(12)2
=52−14
=94
We know Var(1.X−8)=12Var(X), thus,
Var(X)=94
Standard deviation of X=√Var(X)
=√94=32
If the sum of squares of deviations of 15 observations from their mean 20 is 240, then what is the value of coefficient of variation (CV)?
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