Question

Given a set of data with a mean of 25.7 and a standard deviation of 5.2, calculate the Z score equivalents of the following raw scores:

(a) 21.6

Answer 1

The Z score for a raw score of 21.6 with a mean of 25.7 and a standard deviation of 5.2 is approximately -0.79, indicating it lies 0.79 standard deviations below the mean.

Step-by-step explanation:

To calculate the Z score for a given raw score, you use the formula:

Z = (X - μ) / σ

Where X is the raw score, μ is the mean, and σ is the standard deviation. Using the data provided with a mean of 25.7 and a standard deviation of 5.2, we can calculate the Z score for a raw score of 21.6 as follows:

Z = (21.6 - 25.7) / 5.2

Z = -4.1 / 5.2

Z = -0.7885 (rounded to four decimal places)

This Z score of approximately -0.79 indicates that the raw score of 21.6 is about 0.79 standard deviations below the mean.