Why is standard deviation a useful measure in comparing two data sets?

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Question: Why is standard deviation a useful measure in comparing two data sets?

Option a: It measures the spread of data around the mean, allowing for comparison of variability. This is correct. Standard deviation quantifies how far data points typically lie from the mean, giving a sense of dispersion or variability in each data set, which can then be compared across sets.

Option b: It eliminates all outliers from the calculation. This is incorrect. Standard deviation does not automatically remove outliers; unless you explicitly handle outliers beforehand, they influence the measure of spread and can distort the SD.

Option c: It is always smaller than the variance. This statement is false. The standard deviation is the square root of the variance, so it can be smaller than the variance, but not necessarily always smaller in all cases (e.g., if the variance is less than 1, the SD will be greater than the variance).

Option d: It shows whether the means of the data sets are equal. This is not correct. The standard deviation describes dispersion, not whether the central tendencies (means) are equal. To compare means, you would typically examine the mean values themselves or use a hypothesis test (e.g., t-test).

In summary, option a accurately describes the purpose of standard deviation for comparing variability between data sets, while options b, c, and d mischaracterize its properties or purpose.

MDM4U - Mathematics of Data Management 12 (2025-26) - A

Why is standard deviation a useful measure in comparing two data sets?

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