Chapter 3, Problem 1.1HD

To determine

Explain the relation between Z score and raw score.

Explanation of Solution

Z score:

The Z score is the number of standard deviations that a score is above or below the mean of a given distribution.

The formula for Z score is obtained as,

$Z=\frac{X-M}{SD}$, where X is the score value, M is the mean and SD is the standard deviation of the set of scores.

Raw score:

A raw score is an ordinary score which represents any number in a distribution before it is converted to a Z score.

A raw score can be obtained as by multiplying the Z score with standard deviation and add the result with mean.

Thus, $X=Z\left(SD\right)+M$.