Example of Computing the Variance and Standard Deviation

Which measure of variability is defined as the mean of the squared differences between each score and the distribution's mean?

A researcher is calculating the variance ($SD^2$) for a set of data in a psychology study. Arrange the mathematical steps for finding the variance in the correct logical order.

A psychologist measuring social anxiety asks four participants to rate their discomfort in a crowd on a scale from 1 to 10. The ratings are: 3, 5, 7, and 9 (where the Mean = 6). Match each component of the variance calculation to its correct numerical value for this specific group of participants.

A researcher concludes that the variance ($SD^2$) is the most appropriate measure for a descriptive summary of participant scores because it expresses variability in the original units of measurement.

While variance ($SD^2$) is a foundational measure in inferential statistics, its square root—the standard deviation—is typically used in descriptive statistics.

Why do researchers square the differences between each individual score and the mean when calculating the variance ($SD^2$), rather than simply calculating the average of the raw differences?

A researcher analyzing scores on a psychological memory task finds that the distance of every participant's score from the mean is exactly doubled. The resulting variance ($SD^2$) will be _____ times larger than the original variance.