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

Stem-and-Leaf Plots

Construct and interpret stem-and-leaf plots to display and compare distributions while preserving raw data.

Today's hook:
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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 someone gave you a list of 50 test scores, how would you quickly find the highest and lowest without a calculator?

Q2 · What is the advantage of showing data in order from smallest to largest rather than in the order it was collected?

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From the lesson
Intentions

Learning Intentions

Know

  • A stem-and-leaf plot separates each value into a stem (leading digit) and a leaf (trailing digit).

Understand

  • Why stem-and-leaf plots preserve the original data values while still showing the distribution shape.

Can Do

  • Create back-to-back stem-and-leaf plots and use them to compare two data sets.
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From the lesson
Key Terms

Key Terms

Stem — The leading digit(s) of a number, displayed in a column.
Leaf — The trailing digit of a number, displayed in a row next to its stem.
Back-to-back — Two stem-and-leaf plots sharing a common stem for comparing distributions.
Key — A statement explaining what the stem and leaf represent, e.g. 3 | 2 = 32.
Ordered stem-and-leaf — A plot where leaves are arranged in ascending order.
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From the lesson
Misconceptions

Misconceptions to Fix

✗

Wrong: Leaves in a stem-and-leaf plot can be in any order.

✓

Right: An ordered stem-and-leaf plot requires leaves in ascending order from the stem outward. Unordered leaves make the plot difficult to read and cannot be used to find the median directly.

✗

Wrong: A back-to-back plot with more leaves on one side always has a higher mean.

✓

Right: More leaves on one side indicates more data values in that range, but the mean depends on all values, not just the count.

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From the lesson
Content

Stem-and-Leaf Plots

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

Remember Mean = (sum of all values) / (number of values). For frequency tables: Mean = (sum of value × frequency) / (total frequency).
HSC Note Always check whether your calculated mean is reasonable. If the data ranges from 10 to 50, a mean of 200 is clearly wrong.
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From the lesson
Activity
✏ Activity 1 — Calculate the Mean

Calculate the mean for each data set:

  1. 12, 15, 18, 21, 24
  2. 4, 8, 12, 16, 20, 24, 28
  3. The following frequency table: Value 5 (freq 3), Value 10 (freq 5), Value 15 (freq 2).
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From the lesson
Worked Example

Worked Example

Step-by-step
Find the mean of the following data set: 12, 15, 18, 21, 24, 27, 30.
  1. 1
    Step 1: Sum all values. 12 + 15 + 18 + 21 + 24 + 27 + 30 = 167.
  2. 2
    Step 2: Count the number of values. n = 7.
  3. 3
    Step 3: Divide the sum by the count. Mean = 167 / 7 = 23.86 (2 d.p.).
  4. 4
    Check: The mean (23.86) lies between the minimum (12) and maximum (30), so it is reasonable.
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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 In the stem-and-leaf plot key 2 | 5 = 25, the stem is:

1 mark A back-to-back stem-and-leaf plot is useful for:

1 mark The advantage of a stem-and-leaf plot over a histogram is that it:

1 mark In an ordered stem-and-leaf plot, the leaves should be:

1 mark The median can be found from a stem-and-leaf plot by:

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From the lesson
Short Answer

Short Answer

Show all working and justify your answers.

1. 4 marks The test scores of 8 students are: 56, 62, 68, 74, 80, 86, 92, 98.
(a) Calculate the mean.
(b) If each student scores 5 bonus marks, what is the new mean?
(c) Explain why adding a constant to every value changes the mean by that constant.

2. 3 marks The following frequency table shows the number of books read by students in a term:
0 books: 4 students, 1 book: 8 students, 2 books: 12 students, 3 books: 6 students.
Calculate the mean number of books read.

3. 2 marks A data set has a mean of 24. One value of 100 is added to the data set. Explain whether the new mean will be greater than, less than, or equal to 24.

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

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