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

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.