Cogito
AP Statistics · Chapter 1 · Lesson 3
Comparing Distributions
Saying how two groups differ.
12 problems · about 21 minutes · UNC-1.S, UNC-1.T
What this lesson teaches
The student compares distributions using shape, centre, spread and outliers in context.
- Compare shape, centre, spread and outliers.
- Use comparative language and name the variable in context.
- Let the shape decide whether to quote means or medians.
Warm Up
Straightforward practice. Get the method working first.
5 problemsQ1 = 15, Q3 = 35. What is the IQR?
Answer 20
Why 20.
What makes a comparison complete on the exam?
Answer Shape, centre, spread and outliers, in context and with comparative language.
Why All four features, compared explicitly.
How many features should a comparison mention?
Answer 4
Why Shape, centre, spread, outliers.
Q1 = 12, Q3 = 30. What is the IQR?
Answer 18
Why 30 − 12.
Symmetric data with no outliers. Which centre? 1 mean, 2 median.
Answer 1
Why The mean is fine here.
Build It Up
The same ideas with more to keep track of.
3 problemsGroup A median 25, Group B median 18. Which is higher? 1 A, 2 B.
Answer 1
Why 25 against 18.
Is listing two separate descriptions a comparison? 1 yes, 0 no.
Answer 0
Why Comparative language is required.
Skewed right. Is the mean above or below the median? 1 above, 2 below.
Answer 1
Why The tail drags the mean.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsWhich belong in a full comparison?
Answer Shape; Centre and spread; Unusual features such as outliers
Why Sample size is worth noting but is not one of the four features.
Q1 = 20, Q3 = 26. What is the IQR?
Answer 6
Why 26 − 20.
The Spread: Group A has IQR 10 and Group B has IQR 22. Which has greater spread? 1 A, 2 B.
Answer 2
Why Group B.
The Choice: Both distributions are strongly skewed. Which centre should be compared? 1 mean, 2 median.
Answer 2
Why The median.