Question

Is it possible to construct a dataset where the mean is 30.0, the range is 10.0 and the variance is 40?

Answer 1

Let, X be a random variables with values between [a,b]

Let us define,

Since X and Y differ by a constant, Var(X)=Var(Y).

Since,

Thus,Var(X)=Var(Y)=E(Y²)-E(Y)²

E(Y²)

......................(i)

Range=(b-a)

In this problem, Range=10

Variance=40

So, Variance= 40

(Range)²/4=(10)²/4=25

So it does not satisfy equation (i), so we can conclude that "It is impossible to form a dataset with the given information".

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