Z Scores Overview

These flashcards cover key concepts and definitions related to z-scores and their properties in statistics.

What is the purpose of z-scores in statistics?

To transform X values into scores that indicate their exact location within a distribution.

How do z-scores use the mean and standard deviation?

Z-scores use the mean as a reference point and standard deviation as a measure of how much an individual score differs from the mean.

What does a positive z-score indicate?

The score is above the mean.

What does a negative z-score indicate?

The score is below the mean.

What properties does a distribution of z-scores have compared to the original scores?

It has the same shape, but the mean is 0 and standard deviation is 1.

How is a z-score computed?

Using the formula z = (X - μ) / σ.

If the mean is 60 and the standard deviation is 8, what is the z-score for an X value of 54?

z = (54 - 60) / 8 = -0.75.

What effect does transforming raw scores into z-scores have on individual scores' positions?

It does not change their positions; it relabels them while preserving their relative distances.

Why is it useful to standardize distributions using z-scores?

It allows for the comparison of scores from different distributions.

What are the values of mean and standard deviation for standardized distributions?

The mean is 0 and the standard deviation is 1.