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Cogito

AP Statistics · Chapter 1 · Lesson 3

Practice Worksheet

Comparing Distributions

Saying how two groups differ.

12 problems · about 21 minutes · UNC-1.S, UNC-1.T

NameDate

Figure — use these to answer the problems

Change the values and watch the box move. Comparing two of these means comparing centre, spread and shape.
020
  • Minimum4
  • Lower quartile6
  • Median9
  • Upper quartile13
  • Maximum18
  • Interquartile range7
Value 14
Value 26
Value 38
Value 49
Value 511
Value 613
Value 718
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Q1 = 15, Q3 = 35. What is the IQR?

    Answer

  2. What makes a comparison complete on the exam?

    • Shape, centre, spread and outliers, in context and with comparative language.
    • Naming which centre is larger.

  3. How many features should a comparison mention?

    Answer

  4. Q1 = 12, Q3 = 30. What is the IQR?

    Answer

  5. Symmetric data with no outliers. Which centre? 1 mean, 2 median.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Group A median 25, Group B median 18. Which is higher? 1 A, 2 B.

    Answer

  2. Is listing two separate descriptions a comparison? 1 yes, 0 no.

    Answer

  3. Skewed right. Is the mean above or below the median? 1 above, 2 below.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Which belong in a full comparison?

    • Shape
    • Centre and spread
    • Unusual features such as outliers
    • The sample size alone
    • Tick every box that applies.

  2. Q1 = 20, Q3 = 26. What is the IQR?

    Answer

  3. The Spread

    Group A has IQR 10 and Group B has IQR 22. Which has greater spread? 1 A, 2 B.

    Answer

  4. The Choice

    Both distributions are strongly skewed. Which centre should be compared? 1 mean, 2 median.

    Answer