Extra: mean absolute deviation
See each dot's distance from the mean, average those distances, find out why signed differences always add up to zero, and compare two data sets by their spread.
- France: grade 8
- Germany: grade 7
- Afghanistan: grade 9
- Syria: grade 11
- Palestine: grade 8
- Russia: grade 7
Guide
This is an extra studio: the mean deviation is taught in the Afghan grade 9 book, not in the KS3 or GCSE programme. It suits a learner who already knows the mean and the range.
The mean absolute deviation tells you how far, on average, the values are from the mean: write each value's distance from the mean (always positive), add the distances and divide by the number of values.
If you add the differences with their signs (some negative, some positive), you always get zero, because the mean is the balance point of the data. That is why we use distances, without signs.
The range only looks at the two ends; the mean absolute deviation uses every value. Two data sets can have the same range but different spread.
Ask: "If the mean absolute deviation is 0, what does the data look like?"