To calculate the variance of a data set, follow these steps:
Calculate the mean (average) of the data set. In this case, the mean is (1 + 5 + 6 + 8) / 4 = 20 / 4 = 5.
Subtract the mean from each data point and square the result. The differences squared are (1-5)^2 = 16, (5-5)^2 = 0, (6-5)^2 = 1, (8-5)^2 = 9.
Calculate the sum of all the squared differences. The sum is 16 + 0 + 1 + 9 = 26.
Divide the sum by the number of data points. Since there are 4 data points, the variance is 26 / 4 = 6.5.
Therefore, the variance of the data set 1, 5, 6, 8 is 6.5.
