Question

A sample with M = 85 and s = 12 is transformed into z-scores. After the transformation, what are the values for the mean and standard deviation for the sample of z-scores?

Answer 1

The mean (of the z-scores) will be zero (0), and the new std dev will be 12/n, where n is the number of scores.

Answer 2

The mean and standard deviation for the sample of z-score is 0 and 1 respectively.

Explanation:

We are given a sample mean, M = 85

Standard Deviation, s = 12

Let
`x_i's` be the sample.

Then, this sample can be transformed into z scores with the help of transformation:

`z_(score) = \displaystyle(x_i - M)/(s)`

This process is known as standardization.

Then, the mean of new obtained sample is 0 and the standard deviation is 1.