How is the variance of a data set computed?

• A. By averaging the data points directly
• B. By finding the absolute differences from the mean
• C. By averaging the squared differences from the mean
• D. By summing all data points

Answer: (C)

The variance of a data set is computed by averaging the squared differences from the mean. This process involves several steps: first, you calculate the mean of the data set. Next, for each data point, you find the difference between that point and the mean, then square that difference. Finally, you take the average of all these squared differences to arrive at the variance.

By squaring the differences, you ensure that all values contribute positively to the final result, preventing issues that could arise from negative differences canceling out positive ones. This also emphasizes larger deviations from the mean, which can be particularly important in statistical analysis to assess the spread of the data. Therefore, the correct approach to finding the variance is indeed to average the squared differences from the mean, which is what choice C describes.