What does variance measure in a dataset?

Variance measures the spread of data from the mean. It quantifies how far each data point in a dataset is from the mean (the average) and, consequently, how much the data points differ from each other. A high variance indicates that the data points are spread out widely around the mean, while a low variance suggests that the data points are clustered closely to the mean.

This calculation is essential in statistics, as it helps determine the consistency and reliability of the data. Variance is calculated by averaging the squared differences between each data point and the mean, emphasizing larger deviations. Understanding variance is crucial for making inferences about population data and assessing the risk in various fields, such as finance and quality control.

Other choices do not accurately represent what variance measures. The difference between maximum and minimum reflects the range, not the distribution relative to the mean. The frequency of the mode pertains to the most common value in the dataset, which does not provide insight into the overall spread. The average of the dataset is simply the mean, which itself does not account for how spread out the data points are. Thus, the correct understanding of variance as a measure of the spread from the mean underscores its importance in statistical analysis.