Common Core Standards: Math
3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.
By the time they're in seventh grade, students have a whole smorgasbord of statistical tricks at their fingertips. They can describe the center of a distribution using the mean and median, its variation with the mean absolute deviation and interquartile range, and even whip out a box plot, dot plot, or histogram on their sketchpad. With so many statistical tools on hand, they're like little Tim "The Tool Man" Talyors of stats.
Unlike working with a pair of power saws, though, this standard expects students to use their stats toolset to juggle two data distributions at once. Specifically, they'll be comparing the graphs of distributions that have a similar spread.
You might think that because the two distributions have similar spreads, that all we can do is check which one has the larger mean, and then—bam! we're done. Well—bam!—we're not. Instead, students will compare distributions in terms of their variation. This is the same kind of logic they'll use in later grades when they find the number of standard deviations a data value is from the mean, which is kind of a big deal when working with the normal distribution.
For now, we'll stick to using the mean absolute deviation (MAD), instead, since it's easier to calculate. (Or we can work with the median and the interquartile range, if we're feeling particularly saucy.) Suppose African woodchucks can chuck an average of 5 logs per minute (lpm), compared to European woodchucks chucking 7 lpm. If they both have a MAD of 1 lpm, then the difference in their means is around two MAD worth.
Of course, with all of these comparisons being thrown around, combining this standard with 7.SP.4, to draw conclusions about the two distributions, is a natural fit. If you want students to get off their keisters, well, any type of activity where students gather two samples of similar data will do the trick.