What does variance measure in statistics?

Variance is a statistical measure that quantifies the degree to which individual data points in a set differ from the mean of the set. Specifically, it provides insight into the dispersion or spread of values. When calculating variance, you determine how much each value in the dataset deviates from the mean, square those deviations to remove any negative signs, and then average them. This process results in a numerical value that reflects the overall variability within the dataset.

The emphasis on the degree of spread is crucial. A low variance indicates that the data points tend to be close to the mean, while a high variance suggests that the data points are more spread out. This characteristic of variance makes it a valuable tool in various analyses, including identifying trends and understanding data distribution.

The options about the difference between the highest and lowest scores, the average spread of numbers, and the most frequently occurring score do not capture the comprehensive nature of variance as a measure of variability. They describe other statistical concepts that have distinct definitions and uses in data analysis.