Question

The following transformation was made on 79 values of a variable W. U=W-54.5/6. Statistics computed from U were U bar = 6.8, variance of u = 1.8. Find W bar and variance of W.
U =W-54.5/6. Statistics computed Mean of U as 6.8 and Variance as 1.8. Find mean of w and variance of w

Answer 1

solution:

If U=W-(54.5/6) then W=U+(54.5/6).

Assuming a one-for-one transformation, the mean for W is found by adding all the W data together then dividing by 79.

That is, Wbar=(w1+w2+w3+...+w79)/79.

But w1=u1+54.5/6, w2=u2+54.5/6, etc.

So Wbar=(u1+u2+...+u79)/79+(79×54.5/6)/79=Ubar+54.5/6=6.8+54.5/6=15.8833 approx.

The variance is unaffected by the transformation since variance is simply the spread of the data which doesn’t change.

Wbar=Ubar=1.8.