How do you calculate the variance of a data set?

To calculate the variance of a data set, find the average of the squared differences from the mean.

First, you need to find the mean (average) of your data set. Add up all the numbers in your data set and then divide by the number of data points. For example, if your data set is 2, 4, 6, 8, and 10, you would add these numbers to get 30, and then divide by 5 (the number of data points) to get a mean of 6.

Next, subtract the mean from each data point to find the difference for each one. Using our example, you would subtract 6 from each number: (2-6), (4-6), (6-6), (8-6), and (10-6), which gives you -4, -2, 0, 2, and 4.

Then, square each of these differences to get rid of any negative signs and to emphasise larger differences. Squaring the differences from our example, you get 16, 4, 0, 4, and 16.

After that, find the average of these squared differences. Add them up (16 + 4 + 0 + 4 + 16 = 40) and then divide by the number of data points. In this case, you divide 40 by 5 to get 8.

So, the variance of the data set 2, 4, 6, 8, and 10 is 8. This tells you how spread out the numbers in your data set are around the mean.