The variance of a given set of numbers is defined as the

Analyze the question: You are asked how variance relates to other measures of dispersion (spread).

Concept: Variance measures how far the values in a data set are spread out from the mean. It is calculated as the average of the squared deviations from the mean:

σ² = Σ(x − x̄)² / n

The standard deviation is defined as the square root of the variance:

σ = √(variance)

Working it out:

1. Start from the standard deviation: σ = √(variance).
2. Square both sides: σ² = variance.
3. So variance = (standard deviation)².

Checking the options:

• A. Absolute value of the standard deviation: wrong, because that would just be the standard deviation itself.
• B. Square of the standard deviation: correct.
• C. Square root of the standard deviation: wrong. The square root of the variance gives the standard deviation, not the other way round.
• D. Square of the mean deviation: wrong. The mean deviation is a different measure, based on absolute deviations, and its square is not the variance.
• E. Square root of the mean deviation: wrong, for the same reason.

Exam tip: Remember "Variance is the square, Standard deviation is the root." The standard deviation is in the same units as the data, while the variance is in squared units. This is why the standard deviation is used more often when interpreting results.