1. Variability Mechanics

2. The Average Deviation Another approach to estimating variance is to directly measure the degree to which individual data points differ from the mean and then average those deviations. That is:

3. The Average Deviation (cont.) However, if we try to do this with real data, the result will always be zero:

4. Average Deviation One way to get around the problem with the average deviation is to use the absolute value of the differences, instead of the differences themselves. The absolute value of some number is just the number without any sign: –For Example: |-3| = 3

5. Average Deviation Thus, we could re-write and solve our average deviation question as follows: The data set in question has a mean of 5 and a mean absolute deviation of 2.25.

6. Variance Example X = 2,3,3,4,4,6,6,12

7. An equivalent formula that is easier to work with when calculating variances by hand is: Although this second formula may look more intimidating, a few examples will show you that it is actually easier to work with.

8. Median Absolute Deviation X = 2,3,3,4,4,6,6,12 Deviations from the median of 4 – -2 -1 -1 0 0 2 2 8 Absolute values –2 1 1 0 0 2 2 8 Order –0 0 1 1 2 2 2 8 Mad = 1.5

9. Coefficient of Variation This one’s pretty simple, just a ratio of standard deviation to the sample mean Can give a sense of relative variability even with different means