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).
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-leaf2-3 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.
Sorted: 142, 148, 151, 154, 154, 158, 160, 163, 167, 172. Median (n=10, even): 5th and 6th values = 154 and 158. Median = (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.