Question

why is the standard deviation used more frequently than the variance?

choose the correct answer below.

a. the standard deviation requires less entries from the data set.
b. the units of variance are squared. its units are meaningless.
c. the standard deviation is easier to compute.

Explanation:

Analyze the relationship between variance and standard deviation

We are comparing standard deviation and variance, which are key Measures of Variation. The variance of a dataset is calculated by squaring the deviations of each data value from the mean and finding their average. Because of this squaring process, the units of variance are also squared (for example, if the data is in dollars, the variance is in squared dollars).

Evaluate the physical meaning of units

Using the Measures of Variation concept, we know that standard deviation is the square root of the variance. Taking the square root returns the measure of spread back to the original units of the data (such as dollars instead of squared dollars). Squared units are often difficult to interpret or practically meaningless in real-world contexts, which is why standard deviation is preferred for describing data spread.

Evaluate the given multiple-choice options

• Option A: Incorrect. Both calculations require using every single entry from the dataset.
• Option B: Correct. The units of variance are squared, making them difficult to interpret or practically meaningless compared to the original units.
• Option C: Incorrect. Standard deviation actually requires an extra step (taking the square root of the variance), making it slightly more complex to compute, not easier.

Answer:

• A. The standard deviation requires less entries from the data set.
• B. The units of variance are squared. Its units are meaningless. (Correct answer)
• C. The standard deviation is easier to compute.