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📖 Lesson 9 ⏱ ~30 min Year 10 · Unit 4 ⚡ +50 XP

Box Plots

Construct and interpret box plots (box-and-whisker plots) to compare distributions using the five-number summary.

Today's hook:
0/5QUESTS

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Core learning
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From the lesson
Worksheet

Worksheet

Use the worksheet to complete this lesson in your book or digitally.

Warm-up
Think First
+5 XP each

Q1 · If you had to describe a whole data set using just five numbers, which five would you choose and why?

Q2 · How could you tell from a single diagram whether one group of students is much more spread out than another?

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From the lesson
Intentions

Learning Intentions

Know

  • A box plot displays the minimum, Q1, median, Q3 and maximum. It shows spread and skewness at a glance.

Understand

  • How box plots allow quick visual comparison of centres, spreads and skewness between data sets.

Can Do

  • Draw box plots from the five-number summary and compare distributions using parallel box plots.
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From the lesson
Key Terms

Key Terms

Five-number summary — Minimum, Q1, median, Q3, and maximum of a data set.
Box plot — A display showing the five-number summary as a box with whiskers.
Whisker — A line extending from the box to the minimum and maximum (or to non-outlier extremes).
Parallel box plots — Two or more box plots drawn on the same scale for easy comparison.
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From the lesson
Misconceptions

Misconceptions to Fix

✗

Wrong: The box in a box plot shows the full range of the data.

✓

Right: The box shows the IQR (from Q1 to Q3) — the middle 50% of data. The WHISKERS show the range (from minimum to maximum, excluding outliers).

✗

Wrong: A longer box means the data values are higher.

✓

Right: A longer box means greater SPREAD in the middle 50% — it says nothing about the absolute level of the data. Two data sets can have the same IQR but very different medians.

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From the lesson
Content

Box Plots

Work through the content, activities and worked examples below. Test your understanding with the questions in the Questions phase.

Remember Always include a key with your stem-and-leaf plot. For example: 2 | 3 means 23 (or 2.3, depending on the context).
Exam Tip When finding the median from a stem-and-leaf plot, count the total number of leaves and find the middle position. Do not count the number of stems.
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From the lesson
Activity
✏ Activity 1 — Build a Stem-and-Leaf Plot

Construct a stem-and-leaf plot for each data set:

  1. 23, 25, 28, 31, 32, 35, 38, 41, 42, 45
  2. 5.2, 5.4, 5.6, 5.8, 6.1, 6.3, 6.5, 6.7, 6.9
  3. 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42
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From the lesson
Worked Example

Worked Example

Step-by-step
Construct a stem-and-leaf plot for the following data: 23, 25, 28, 31, 32, 35, 38, 41, 42, 45.
  1. 1
    Step 1: Choose the stem. Here, the tens digit is the stem: 2, 3, 4.
  2. 2
    Step 2: Write the stems in a column from smallest to largest.
  3. 3
    Step 3: Write each leaf (units digit) next to its stem.
  4. 4
    Step 4: Add a key: 2 | 3 = 23. Order the leaves for clarity.
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From the lesson
Revisit

Revisit Your Thinking

Look back at your Think First response. What new understanding do you have now?

Reflect
Revisit your thinking
reflect

Earlier you were asked: What was your first thought on this topic?

Now that you've worked through the lesson, write a fuller answer. What changed in your thinking?

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From the lesson
Multiple Choice

Multiple Choice

Select the best answer for each question.

1 mark A box plot does NOT show:

1 mark In a box plot, the box represents:

1 mark If a box plot has a longer whisker above the box than below, the data is:

1 mark Parallel box plots are used to:

1 mark The five-number summary includes:

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From the lesson
Short Answer

Short Answer

Show all working and justify your answers.

1. 4 marks The following stem-and-leaf plot shows the ages of people at a concert:
1 | 2 3 5 8
2 | 0 1 4 5 6 9
3 | 1 2 5 8
Key: 2 | 5 = 25 years
(a) How many people were at the concert?
(b) Find the median age.
(c) Find the range.

2. 3 marks Construct a back-to-back stem-and-leaf plot to compare these two data sets:
Class A: 12, 15, 18, 21, 24, 27, 30
Class B: 10, 14, 19, 22, 26, 29, 32

3. 2 marks Explain one advantage of a stem-and-leaf plot over a histogram.

Marking guidance: 1 mark each for MCQs. See mark allocations for each short answer question.

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