Cogito
Probability and Statistics · Chapter 1 · Lesson 3
Box Plots and the Five-Number Summary
Five numbers describing a whole data set.
12 problems · about 21 minutes · TEKS P.S.1.C, S-ID.A.1
What this lesson teaches
The student builds a box plot from the five-number summary and identifies outliers using the IQR rule.
- The five-number summary is minimum, Q1, median, Q3 and maximum.
- The IQR measures the middle half and ignores extremes.
- A value beyond 1.5 IQRs past a quartile counts as an outlier.
Warm Up
Straightforward practice. Get the method working first.
5 problemsQ1 = 12, Q3 = 20. What is the IQR?
Answer 8
Why 8.
What does a wide section of a box plot mean?
Answer Those values are spread thin, though the count is the same.
Why Width shows spread, not count.
Q1 = 10, Q3 = 22. What is the IQR?
Answer 12
Why 22 − 10.
Data 3, 5, 7, 8, 9, 13, 19. What is the median?
Answer 8
Why The middle value of seven.
Same data. What is Q1?
Answer 5
Why The middle of 3, 5, 7.
Build It Up
The same ideas with more to keep track of.
3 problemsSame data. What is Q3?
Answer 13
Why The middle of 9, 13, 19.
Q1 = 4, IQR = 6. What is the lower outlier fence?
Answer -5
Why 4 − 1.5 × 6.
What fraction of the data lies in the box, as a decimal?
Answer 0.5
Why Two of the four sections.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsMatch each part of the summary with what it reports.
Answer Median → The centre value; IQR → The spread of the middle half; Range → Maximum minus minimum
Why Only one of these ignores the extremes.
A box section is very wide. Does it hold more points or the same? 1 more, 2 the same.
Answer 2
Why Every section holds a quarter.
The Spread: Lower quartile 5, upper quartile 13. What is the IQR?
Answer 8
Why 8.
The Fence: IQR 8 and upper quartile 13. What is the upper outlier fence?
Answer 25
Why 25.