Chapter 4: Measures of Variability

Why are measures of central tendency alone incomplete?

They do not show how scores are distributed or varied around the center.

Range

The difference between the highest and lowest scores in a distribution.

What is the main limitation of the range?

It is highly sensitive to extreme outliers.

Inter-quartile range (IQR)

A measure of variability that manages the effects of extreme outliers.

Formula for Inter-quartile range (IQR)

Q₃ - Q₁

What does a larger Inter-quartile range (IQR) indicate?

Greater variability in the distribution.

Deviation

The distance of any given raw score from its mean.

Why are deviations squared when calculating variance?

To ensure the sum of deviations is non-negative.

Mean deviation (MD)

The sum of absolute deviations divided by the total number of scores.

Variance

The average of the squared deviations from the mean.

What level of measurement is required for variance and standard deviation?

Interval level variables.

Standard deviation

The square root of the variance.

Why is standard deviation preferred over variance for interpretation?

It removes squared units, returning the measure to the original scale.

What does standard deviation represent?

The average variability or average deviation of scores from the mean.

What is the benefit of the raw-score (computational) formula?

It provides an easier way to calculate variance and standard deviation.