Calculating Variance Given Arithmetic Mean

To calculate the variance given an arithmetic mean, there are a few steps that need to be followed:

1. Find the deviations from the mean of each number in the data set.
2. Square each deviation.
3. Add up all the squared deviations.
4. Divide the sum of squared deviations by the number of observations in the data set.

Example Calculation

Suppose we have the following data set:

8, 4, 12, 6, 10

And the arithmetic mean is:

AM = (8 + 4 + 12 + 6 + 10) / 5 = 8

To calculate the variance, we first need to find the deviations from the mean:

8 - 8 = 0
4 - 8 = -4
12 - 8 = 4
6 - 8 = -2
10 - 8 = 2

Next, we need to square each deviation:

0^2 = 0
(-4)^2 = 16
4^2 = 16
(-2)^2 = 4
2^2 = 4

Then, we add up all the squared deviations:

0 + 16 + 16 + 4 + 4 = 40

Finally, we divide the sum of squared deviations by the number of observations in the data set:

40 / 5 = 8

Therefore, the variance of the data set is 8.

Conclusion

To calculate the variance given an arithmetic mean, we need to find the deviations from the mean, square each deviation, add up all the squared deviations, and divide the sum of squared deviations by the number of observations in the data set.