What is the variance a measure of in a dataset?

What is the variance a measure of in a dataset?

• A. Measure of central tendency
• B. Average of squared deviations from the mean
• C. Covariance between variables
• D. A measure of data skewness

Answer: (B)

Variance represents how spread out the data are around the mean. It is defined as the average of the squared differences between each value and the mean. In a population, you divide by N; in a sample, by N−1. A small variance means observations cluster near the mean; a large variance means they’re more dispersed. The square root of variance is the standard deviation. This is different from a measure of central tendency (which describes the center, like the mean), covariance (which describes how two variables vary together), and skewness (which describes asymmetry). The description that defines variance as the average of squared deviations from the mean is the correct one.

Variance represents how spread out the data are around the mean. It is defined as the average of the squared differences between each value and the mean. In a population, you divide by N; in a sample, by N−1. A small variance means observations cluster near the mean; a large variance means they’re more dispersed. The square root of variance is the standard deviation. This is different from a measure of central tendency (which describes the center, like the mean), covariance (which describes how two variables vary together), and skewness (which describes asymmetry). The description that defines variance as the average of squared deviations from the mean is the correct one.