Math 1 · Unit 12 · Lesson 5 · part 2 of 4
Five steps, and two classes with the same mean
Everything in this unit comes together when you compare two or more groups.
Five steps, and two classes with the same mean
Everything in this unit comes together when you compare two or more groups. Five steps, always in this order.
- 1Graph them on the same scale.Stacked box plots or histograms, one above the other, so they line up.
- 2Describe each one's shape.Symmetric, skewed right, skewed left. Any outliers?
- 3Choose the statistics that fit the shape.Roughly symmetric with no outliers: mean and standard deviation. Skewed, or with outliers: median and IQR. Use the same kind for both groups, so the comparison is fair.
- 4Compare the centers and the spreads.Which group is higher? Which is more consistent, with less spread?
- 5Write sentences in context.Numbers with the story around them.
Two Math 1 classes took the same unit test. Each list is the whole class, so the population standard deviation, σ, is the right one.
1st period: 92, 88, 95, 72, 85, 90, 34, 78, 96, 83, 88, 91, 70, 86, 94, 80, 89, 93, 75, 87.
4th period: 84, 79, 88, 82, 90, 76, 85, 81, 87, 83, 78, 86, 80, 89, 84, 82, 77, 85, 83, 81.
Here is the surprise. The means are almost the same, 83.3 and 83.0, so the mean alone says the two classes did equally well. But look at the shapes. 1st period is skewed left with an outlier: the 34 is below its lower fence of 60.25. So for 1st period the mean has been pulled down, and the right statistics are the median and the IQR. To keep the comparison fair, use the median and IQR for both.
| class | shape | mean | median | IQR | σ |
|---|---|---|---|---|---|
| 1st period | skewed left, one outlier (34) | 83.3 | 87.5 | 12.5 | 13.47 |
| 4th period | roughly symmetric, no outliers | 83.0 | 83 | 5 | 3.81 |