To calculate the variance of a data set, you need to follow these steps:
Find the mean (average) of the data set. In this case, the mean is (3 + 4 + 6 + 9) / 4 = 5.5.
Subtract the mean from each data point and square the result. This gives you the squared deviations from the mean for each data point:
(3 - 5.5)^2 = 6.25 (4 - 5.5)^2 = 2.25 (6 - 5.5)^2 = 0.25 (9 - 5.5)^2 = 12.25
Find the sum of all the squared deviations:
6.25 + 2.25 + 0.25 + 12.25 = 21
Divide the sum by the number of data points. In this case, there are 4 data points, so:
21 / 4 = 5.25
Therefore, the variance of the data set {3, 4, 6, 9} is 5.25.
