What is the purpose of measuring variance in statistics?

The purpose of measuring variance in statistics is to assess the degree of spread in individual data points from the mean. Variance quantifies how far each data point in the set deviates from the mean, providing insight into the distribution and variability within the dataset. A higher variance indicates a wider spread of values, while a lower variance suggests that the data points are closer to the mean. Understanding this spread is crucial for interpreting data, making predictions, and performing further statistical analyses.

Some options, while related to statistics, do not capture the specific role of variance. For instance, identifying the average of a dataset pertains to calculating the mean, which does not reflect variability. Determining the trend of a dataset relates more to analyzing its direction or movement over time rather than its spread around the mean. Similarly, calculating the total sum of variables focuses on aggregating values rather than evaluating their dispersion. Thus, the focus on assessing the spread from the mean makes the selected answer accurate and relevant in the context of statistics.