How is variance calculated in a dataset?

Variance is a statistical measurement that reflects how far a set of numbers is spread out from their average value (mean). To calculate variance, the correct approach involves several key steps, which align with the chosen answer.

First, you find the mean of the dataset. Then, for each data point, you calculate the difference between that data point and the mean. This difference is known as the deviation from the mean. Next, you square each of these deviations. Squaring is important because it ensures that negative and positive deviations do not cancel each other out and also emphasizes larger deviations.

After squaring the differences, you calculate the average of these squared differences. This average gives you the variance of the dataset. In summary, variance is defined mathematically as the average of the squared deviations from the mean.

The choice that states to "square the differences from the mean, average them, then square root the total" represents a misunderstanding of the variance concept. Variance itself does not include taking the square root; that step leads to the standard deviation, which is a different measure that gives the dispersion of the dataset in the same units as the original data. The other choices also misrepresent the correct mathematical processes involved in calculating variance: one suggests incorrect operations that do