Mathematics • Year 10 • Unit 4 • Lesson 4
Stem-and-Leaf Plots — Skill Drill
Build fluency with the four parts of a stem-and-leaf plot from Lesson 4: the stem (leading digits), the leaf (trailing digit), the key (e.g. 3 | 2 = 32), and ordered leaves. Practise back-to-back plots for comparing two data sets.
1. I do — fully worked example
Read every step. Each one has a short reason on the right so you can see why, not just what.
Problem. Construct an ordered stem-and-leaf plot for the data set:
23, 17, 35, 41, 28, 22, 38, 17, 42, 31, 29, 34, 25, 19, 46.
Include a key.
Step 1 — Decide on stems and leaves.
Two-digit numbers → stem = tens digit, leaf = units digit.
Reason: Lesson 4 Key Terms — "stem = leading digit(s), leaf = trailing digit".
Step 2 — List the possible stems in order.
Smallest stem = 1 (for 17, 19); largest stem = 4 (for 41, 42, 46). Stems: 1, 2, 3, 4.
Reason: every stem in the range must appear, even if it has no leaves.
Step 3 — Place each leaf next to its stem.
1 | 7 7 9 2 | 3 8 2 9 5 3 | 5 8 1 4 4 | 1 2 6
Reason: each leaf preserves the original value. 2 | 3 means 23.
Step 4 — Order the leaves (ascending from the stem outward).
1 | 7 7 9 2 | 2 3 5 8 9 3 | 1 4 5 8 4 | 1 2 6
Reason: ordered leaves let us find the median directly. (Lesson 4 misconceptions card.)
Step 5 — Add the key.
Key: 2 | 3 = 23.
Answer: Ordered stem-and-leaf plot:
1 | 7 7 9
2 | 2 3 5 8 9
3 | 1 4 5 8
4 | 1 2 6 Key: 2 | 3 = 23.
2. We do — fill in the missing leaves
Same idea as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. Construct an ordered stem-and-leaf plot for the data set:
52, 64, 71, 58, 69, 73, 55, 67, 82, 60, 75, 88.
Step 1 — Stems. Two-digit data → stems = ______ digit.
Stems needed: ___, ___, ___, ___ (smallest to largest).
Step 2 — Unordered leaves.
5 | ____ ____ ____ 6 | ____ ____ ____ ____ 7 | ____ ____ ____ 8 | ____ ____
Step 3 — Ordered leaves.
5 | ____ ____ ____ 6 | ____ ____ ____ ____ 7 | ____ ____ ____ 8 | ____ ____
Step 4 — Key.
Key: 5 | ____ = 52.
Step 5 — Read off two things.
Smallest value = ______, largest value = ______.
3. You do — independent practice
Show your working under each problem. The first four are foundation (single small plot). The middle two are standard (read or use a plot). The last two are extension (back-to-back comparisons from Lesson 4's Can-Do intention).
Foundation — read off the values
3.1 In the key 2 | 5 = 25, the stem is ______. 1 mark
3.2 A stem-and-leaf plot shows the row 3 | 0 4 4 7 9 with key 3 | 0 = 30. List the five data values represented by this row. 1 mark
3.3 Construct an ordered stem-and-leaf plot for:
14, 22, 19, 28, 23, 31, 17, 26, 35. Include a key. 1 mark
3.4 A back-to-back stem-and-leaf plot is useful for: (a) showing one data set, (b) comparing two data sets, (c) displaying categorical data. Choose one and justify in one sentence. 1 mark
Standard — order, count and read
3.5 Re-order the leaves in this plot, then state how many data values there are in total.
4 | 7 3 9 1 5 | 6 2 8 5 0 6 | 1 9 4.
Key: 4 | 1 = 41. 2 marks
3.6 The ages of 12 people at a community event are: 23, 25, 31, 18, 47, 36, 42, 29, 33, 51, 24, 38. Build an ordered stem-and-leaf plot with a key. Then count how many people are in their thirties. 2 marks
Extension — back-to-back plots
3.7 Class 10A scores in a maths test (out of 100): 62, 78, 81, 55, 73, 67, 84, 91, 70, 58. Class 10B: 67, 72, 80, 76, 88, 65, 75, 82, 70, 90. Build a back-to-back stem-and-leaf plot with 10A's leaves on the left of the stem and 10B's leaves on the right. Include a key. 3 marks
3.8 Using your back-to-back plot from 3.7, write one sentence comparing the spread of the two classes and one sentence comparing which class has more high scores (in the 80s and 90s). 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (12-value plot)
Step 1: stems = tens digit. Stems needed: 5, 6, 7, 8.
Step 2: 5 | 2 8 5 6 | 4 9 7 0 7 | 1 3 5 8 | 2 8.
Step 3 (ordered): 5 | 2 5 8 6 | 0 4 7 9 7 | 1 3 5 8 | 2 8.
Step 4: Key: 5 | 2 = 52.
Step 5: Smallest = 52; largest = 88.
3.1 — Stem in 2 | 5 = 25
Stem = 2 (leading digit). The 5 is the leaf.
3.2 — Decode 3 | 0 4 4 7 9
Values: 30, 34, 34, 37, 39.
3.3 — Build the plot
1 | 4 7 9 2 | 2 3 6 8 3 | 1 5. Key: 1 | 4 = 14.
3.4 — Back-to-back plot
(b) Comparing two data sets. The shared stem lets the reader compare the two distributions side-by-side at a glance.
3.5 — Re-order leaves
Ordered: 4 | 1 3 7 9 5 | 0 2 5 6 8 6 | 1 4 9. Total = 4 + 5 + 3 = 12 data values.
3.6 — Ages at a community event
Ordered stem-and-leaf:
1 | 8
2 | 3 4 5 9
3 | 1 3 6 8
4 | 2 7
5 | 1 Key: 2 | 3 = 23.
People in their thirties = leaves in the 3 row = 4 people (31, 33, 36, 38).
3.7 — Back-to-back 10A vs 10B
(10A leaves, read outward) | stem | (10B leaves, read normally)
8 5 | 5 |
8 7 2 | 6 | 5 7
8 3 0 | 7 | 0 2 5 6
4 1 | 8 | 0 2 8
1 | 9 | 0 Key: 5 | 5 = 55.
Note: on the left side, leaves are written in ascending order out from the stem (so 5 | 5 closest to stem, 8 furthest).
3.8 — Comparison
Both classes span roughly the same range (mid 50s to low 90s), but 10A is more spread than 10B (10A reaches both the lowest value 55 and high values 91, while 10B's range starts in the mid-60s). 10B has more high scores in the 80s and 90s (4 students) compared to 10A (3 students), suggesting 10B performed slightly better at the top end.