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).