Mathematics • Year 7 • Unit 4 • Lesson 7
Stem-and-Leaf and Dot Plots — Real World
Apply stem-and-leaf and dot plots to real situations: a PE class sprint test, a school canteen survey, ages at a family party, weekly homework time, and resting heart rate. Build the plot, then use it to answer a real question — what's typical, what's unusual, what's the spread?
1. Word problems
Each scenario uses real-world data. Build the plot first, then answer the questions.
1.1 — PE sprint test. Mr Park times the 100 m sprint for 11 students (seconds, to the nearest whole second): 18, 15, 14, 19, 17, 14, 16, 21, 13, 17, 15.
(a) Build an ordered stem-and-leaf plot with a key. (b) State the median and the mode. (c) Identify the slowest sprinter (highest time) and state whether 21 s looks like an outlier compared to the rest. 5 marks
1.2 — Canteen survey. The canteen records how many pieces of fruit each of 15 students bought in one week: 0, 1, 2, 3, 1, 0, 2, 4, 1, 2, 0, 1, 5, 2, 3.
(a) Why is a DOT PLOT (not a stem-and-leaf plot) better here? (b) Draw the dot plot. (c) State the mode and the range. (d) The canteen wants to promote fruit eating — describe what the dot plot tells them about typical purchasing. 5 marks
1.3 — Family party. The ages (in years) of the 14 people at a family party: 8, 12, 35, 42, 38, 11, 9, 67, 41, 35, 16, 33, 70, 45.
(a) Build an ordered stem-and-leaf plot with a key. (b) Identify any visible CLUSTERS (groups of ages). (c) Are there any GAPS that suggest a "missing generation"? 4 marks
1.4 — Weekly homework time. 10 Year 7 students each report total homework time per week (minutes): 95, 120, 85, 110, 130, 90, 100, 125, 105, 240.
(a) Build an ordered stem-and-leaf plot using stems 8, 9, 10, 11, 12, 13, ..., 24 — OR using class intervals of 20 (your choice; justify). (b) Identify the outlier and suggest a real-world explanation for it. (c) Calculate the range with and without the outlier. 5 marks
1.5 — Resting heart rate. A Year 7 PE class measures resting heart rates (beats per minute) for 12 students: 68, 72, 75, 65, 70, 80, 72, 68, 75, 90, 72, 70.
(a) Build an ordered stem-and-leaf plot. (b) State the median, mode and range. (c) The "normal" adult range is 60–100 bpm — is any student outside this range? 4 marks
2. Explain your thinking
Communication matters. Use full sentences. 4 marks
2.1 A Year 7 student claims: "I always prefer a bar chart to a stem-and-leaf plot, because bar charts look nicer." Explain (i) ONE piece of information a stem-and-leaf plot shows that a bar chart hides, (ii) ONE situation where a dot plot would be the better choice than either, and (iii) why scientists and statisticians often start by drawing a stem-and-leaf plot of a new dataset.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Sprint test
Sorted: 13, 14, 14, 15, 15, 16, 17, 17, 18, 19, 21. Stems 1, 2.
1 | 3 4 4 5 5 6 7 7 8 9
2 | 1 Key: 1 | 3 = 13 s. (11 leaves ✓.)
(b) Median: n = 11 (odd), middle = 6th value = 16 s. Mode: leaves 4, 5 and 7 each appear twice → multimodal: 14, 15 and 17 s.
(c) Slowest = 21 s. It IS a likely outlier — it sits 2 s above the next slowest (19 s) and is the only value in stem 2, with 10 others bunched in stem 1.
1.2 — Canteen fruit survey
(a) Dot plot is better because the data is small (15 values), uses small whole numbers (0–5), and a stem-and-leaf plot needs at least two-digit data to be useful.
(b) Dot plot: above 0 — 3 dots; above 1 — 4 dots; above 2 — 4 dots; above 3 — 2 dots; above 4 — 1 dot; above 5 — 1 dot.
(c) Mode = 1 and 2 (bimodal, each appears 4 times). Range = 5 − 0 = 5.
(d) Most students buy 1–2 pieces of fruit per week, with 3 students buying none at all. To promote fruit eating, the canteen could focus on the 3 zero-fruit students and try to lift the typical purchase from 1–2 to 3+.
1.3 — Family party ages
(a) Sorted: 8, 9, 11, 12, 16, 33, 35, 35, 38, 41, 42, 45, 67, 70. Stems 0, 1, 2, 3, 4, 5, 6, 7.
0 | 8 9
1 | 1 2 6
2 | (empty)
3 | 3 5 5 8
4 | 1 2 5
5 | (empty)
6 | 7
7 | 0 Key: 3 | 5 = 35. (14 leaves ✓.)
(b) Clusters: children (8–16), parents/adults (33–45), and grandparents (67–70).
(c) Yes — empty stem 2 (no one in their 20s) and empty stem 5 (no one in their 50s) point to two "missing generations" at this party.
1.4 — Homework time
(a) Using stems of the first two digits (i.e. tens of minutes):
8 | 5 9 | 0 5 10 | 0 5 11 | 0 12 | 0 5 13 | 0 (empty stems 14–23) 24 | 0
Key: 10 | 5 = 105. (10 leaves ✓.) Justification: keeping individual minutes preserves all data.
(b) Outlier = 240 min (4 hours). Real-world cause: an assessment week, a major assignment due, or one student catching up on missed homework.
(c) Range with outlier = 240 − 85 = 155 min. Without outlier: max = 130, range = 130 − 85 = 45 min. The outlier roughly triples the range.
1.5 — Resting heart rate
(a) Sorted: 65, 68, 68, 70, 70, 72, 72, 72, 75, 75, 80, 90. Stems 6, 7, 8, 9.
6 | 5 8 8
7 | 0 0 2 2 2 5 5
8 | 0
9 | 0 Key: 7 | 2 = 72 bpm. (12 leaves ✓.)
(b) Median: n = 12, middle = 6th and 7th = 72 and 72. Median = 72 bpm. Mode: leaf 2 on stem 7 appears 3 times → mode = 72 bpm. Range = 90 − 65 = 25 bpm.
(c) All values are between 65 and 90 — every student is within the normal 60–100 bpm range.
2.1 — Explain your thinking (sample response)
(i) A stem-and-leaf plot shows every individual data value, including its exact units digit; a bar chart usually shows only the count or the total per interval, hiding the original numbers. (ii) A dot plot is best when the dataset is small and the values are small whole numbers (for example, "number of siblings" or "number of pets per household") — stem-and-leaf would be overkill for one-digit data. (iii) Statisticians often start with a stem-and-leaf plot of new data because it reveals the SHAPE (symmetric or skewed?), any clusters or gaps, AND any outliers — all in one quick handwritten diagram, before any calculations.
Marking: 1 mark per part (i), (ii), (iii); 1 final mark for using the lesson vocabulary (shape, cluster, gap, outlier).