Using the direct method, the initial sum of the 15 observations is 15 multiplied by 15, giving 225, and the sum of squares is 15 multiplied by 5 plus 225 squared, yielding 5100. When you remove the observation 15, the sum becomes 210 and the sum of squares becomes 4875. Adding the observations 6 and 8 makes the new sum 224 and the new sum of squares 4995 for the 16 total observations. The new mean is 224 divided by 16, which is 14, and the new variance is calculated as the sum of squares divided by n minus the mean squared, so 4995 divided by 16 minus 14 squared gives 312.1875 minus 196, resulting in a variance of 11.8125.