Question

If an entire population of N = 20 scores is transformed into z-scores, the set of 20 z-scores will have μX = 0. True or False?

Answer 1

A population has N=20 scores.

All of them are transformed into z-scores.

So, our data set was

.

Now, we transformed them into the z-scores.

We know that,

Where, m is the mean of the original data set, and s is the standard deviation.

ie.

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

We have to find the mean of the new data set, ie. the data set of z-scores.

ie. to find

From equation (i), we have

So, the value of the mean is 0.

Thus, as we prove that the mean of the z-scores is 0, so the given statement is TRUE.