What must be done to each number in a data set to calculate variance?

To calculate variance, the correct process involves determining the differences between each number in the data set and the mean of the data set. Specifically, you first find the mean, and then for each number in the data set, you subtract the mean from that number to calculate the difference.

Once you have these differences, the next step is to square each of those differences. This is where the choice about squaring the difference from the mean becomes crucial. Squaring ensures that all differences are non-negative, which is important for accurately measuring the spread of the data around the mean. After squaring each difference, you then average those squared differences to find the variance.

Therefore, squaring the difference from the mean is the essential step in calculating variance, which corroborates why this answer is correct. The other processes listed—dividing each number by the mean, adding the numbers together, and multiplying each number by the mean—do not represent the necessary steps for calculating variance. These alternatives do not provide the required information about the dispersion of the data around the mean, which is what variance is intended to measure.