Mathematics • Year 7 • Unit 4 • Lesson 7
Stem-and-Leaf and Dot Plots — Mixed Challenge
Combine every plotting skill: building plots from raw data, reading median, mode and range, identifying clusters, gaps and outliers, choosing between stem-and-leaf and dot plots. Then spot one plausible student error, and design your own data display.
1. Mixed problems — apply every skill
Each question uses a different idea from the lesson. Show working. 2 marks each
1.1 Build an ordered stem-and-leaf plot for 9 reaction times (milliseconds): 224, 238, 215, 231, 247, 220, 215, 240, 219. Include a key.
1.2 A dot plot has 4 dots above 7, 2 dots above 8, 1 dot above 9 and 1 dot above 12. State the mode, the range, and n (total data values).
1.3 From a stem-and-leaf plot of test scores, you read: 3 | 1 means 31, 3 | 4 means 34, and 5 | 8 means 58. (a) Which value is bigger: 4 | 9 or 5 | 0? (b) Explain in one sentence why this is the right comparison even though "9 > 0".
1.4 Use the plot from 1.1 to find the median (n = 9) and identify any repeated value (the mode).
1.5 For each dataset below, choose whether a stem-and-leaf plot or a dot plot is more appropriate, and give a one-line reason: (a) 60 students' heights in cm (range 145–185); (b) 15 students' number of pets (0–4); (c) 25 maths scores out of 100 (range 30–95).
1.6 Two classes both have 15 students. From a stem-and-leaf plot, you see Class A leaves are tightly clustered on one stem; Class B leaves are spread across 4 stems with a gap and one outlier. Without calculating anything, what can you conclude about the SPREAD of each class compared to the other?
2. Find the mistake
Another Year 7 student answered the prompt: "Build an ordered stem-and-leaf plot for: 42, 38, 51, 47, 35, 29, 47, 56." Their plot has exactly one error. Spot it, explain why it's wrong, then write the corrected plot. 3 marks
Student's plot:
2 | 9
3 | 5 8
4 | 7 7 2
5 | 1 6
Key: 4 | 7 = 47 (Leaf count: 1 + 2 + 3 + 2 = 8 ✓)
(a) Which row contains the mistake?
(b) Explain in one sentence why that row is wrong.
(c) Write the corrected row (and the full corrected plot if you wish).
Stuck? Check whether the leaves in each row are sorted ascending. One row is out of order.3. Open-ended challenge — design your own data display
This question has many correct answers. Show your work clearly. 4 marks
3.1 You are to design a one-page data report on YOUR class. Collect (or invent) two datasets:
- (A) A two-digit numerical variable for at least 10 students (e.g. shoe size in EU sizes, height in cm, last test score out of 100) — display this as a stem-and-leaf plot.
- (B) A small whole-number variable for at least 10 students (e.g. number of pets, number of siblings, number of subjects you take) — display this as a dot plot.
For each: (i) write the variable and how you would collect it, (ii) invent 10+ realistic values, (iii) sketch the display with a key (for the stem-and-leaf), (iv) state the median, mode and range, and (v) describe the SHAPE (cluster, gap, outliers) in one sentence.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Reaction times plot
Sorted: 215, 215, 219, 220, 224, 231, 238, 240, 247. Stems = 21, 22, 23, 24.
21 | 5 5 9
22 | 0 4
23 | 1 8
24 | 0 7 Key: 22 | 4 = 224 ms. (9 leaves ✓.)
1.2 — Dot plot reading
Mode = 7 (highest stack, 4 dots). Range = 12 − 7 = 5. n = 4 + 2 + 1 + 1 = 8.
1.3 — Comparing 4|9 vs 5|0
(a) 5 | 0 = 50 is bigger (because 4 | 9 = 49).
(b) The stem is the tens digit and matters more than the leaf — a value with stem 5 is at least 50, and 49 (stem 4) is less than 50 no matter what the leaf is.
1.4 — Median and mode of 1.1
n = 9 (odd), middle = 5th value. Ordered list: 215, 215, 219, 220, 224, 231, 238, 240, 247. Median = 224 ms. Mode = 215 ms (only repeated value, leaf 5 appears twice on stem 21).
1.5 — Which display?
(a) Stem-and-leaf — 2-3 digit data, large dataset (60) needs the shape and exact values.
(b) Dot plot — small whole numbers (0–4), small dataset (15).
(c) Stem-and-leaf — two-digit data with a wide spread (30–95), medium dataset.
1.6 — Comparing spreads visually
Class A has a small spread — all 15 students scored similarly (tight cluster on one stem). Class B has a much larger spread — students are varied, with a clear gap (suggesting two sub-groups) and at least one student well above or below the rest.
2 — Find the mistake
(a) Row 4 — the leaves on stem 4 are out of order.
(b) Leaves must always be in ascending order. The student wrote "7 7 2" but 2 is smaller than 7, so 2 should come first.
(c) Corrected row: 4 | 2 7 7. (Full corrected plot: 2|9, 3|5 8, 4|2 7 7, 5|1 6, Key: 4|7 = 47.)
3 — Data display project (sample answer)
(A) Height in cm. Measured each student against the wall.
Values (10 students): 142, 148, 151, 154, 154, 158, 160, 163, 167, 172.
14 | 2 8 15 | 1 4 4 8 16 | 0 3 7 17 | 2 Key: 15 | 4 = 154.
Median (n=10, even): (158 + 154) ÷ 2 = wait — sort first then take 5th + 6th: (154 + 158) ÷ 2 = 156 cm. Mode = 154 cm. Range = 172 − 142 = 30 cm. Shape: cluster around 150–160 cm, no obvious gap, slight tall outlier at 172.
(B) Number of pets. Asked each student.
Values: 0, 1, 0, 2, 1, 0, 1, 3, 1, 2.
Dot plot: above 0 → 3 dots, above 1 → 4 dots, above 2 → 2 dots, above 3 → 1 dot.
Median (n=10): 5th & 6th values in sorted list (0,0,0,1,1,1,1,2,2,3) = (1 + 1) ÷ 2 = 1 pet. Mode = 1 pet. Range = 3 − 0 = 3. Shape: most students have 0–1 pets; 3 pets is a mild outlier.
Marking: 1 mark each for (i)+(ii), (iii) plot with key, (iv) stats, (v) shape description.