# Common Core Standards: Math

### Statistics and Probability 7.SP.B.4

4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

Students know that random sampling is the bee's knees, the cat's pajamas (and its meow), and totally necessary for drawing valid conclusions about a population. It's not enough to just take a sample and describe a population, though.

Seventh graders are competitive. They don't just want to know their grades; they want to know if they're better than their rival, Johnny Poindexter. Who's the better dodge ball player? And they just know that their dad could beat Johnny's dad in a bear-wrestling contest. In short, seventh graders want to make comparisons between one thing and another, and statistics is no different.

For this standard, students need to pull out their whole bag of tricks—mean, median, range, interquartile range, and mean absolute deviation—on two sets of samples at once. As long as both samples are random samples, they can use those numbers to draw some conclusions. Sorry, but Johnny has the higher grade point average and more points per game. Unfortunately, the bears were the only winners in the wrestling contest, so that one's a draw.

In later statistics class, students will learn about "statistically significant" results. Well, they don't need to worry about that right now. They're drawing informal conclusions here, so just noticing that there is a difference between the groups is good enough. However, always be sure to pull things around to asking what the real-world significance of a result is. If Johnny's grade is 0.00001 points higher than yours, he doesn't really get any bragging rights.

This standard goes together with 7.SP.3 like peanut butter and jelly. That one has students looking at and comparing the graphs of two distributions, while this one brings in all the crunchy numbers for them to draw conclusions with. It's like the standards come to us with the crusts already cut off. Lucky us.