What does variance measure in a dataset?

Variance is a statistical measurement that quantifies the degree to which data points in a dataset differ from the mean of that dataset. It is computed by averaging the squared differences between each data point and the mean. This process captures how much the values in a dataset vary, or spread out, around the mean. A high variance indicates that the data points are widely spread out from the mean, while a low variance signifies that they are closer together.

In this context, the other options do not accurately describe what variance measures. The average of the data values pertains to the mean, not variance. The total number of data points refers to the count of observations within the dataset, which is not related to variance. Lastly, the shape of the data distribution could relate to other aspects of data analysis, such as skewness or kurtosis, but it does not directly represent the concept of variance. Therefore, focusing on how variance reflects the dispersion of data values around the mean clarifies its significance within statistical analysis.