Mathematics • Year 8 • Unit 4 • Lesson 4
Dot Plots and Stem-and-Leaf in the Real World
Apply dot plots and stem-and-leaf plots to real situations: sports times, student heights, exam comparisons, and weather records — read mode, median, range, and describe shape.
1. Word problems
Each problem uses ideas from Lesson 4. Show your working — a single answer with no working only earns half marks.
1.1 — Test scores dot plot. 14 students sit a 20-mark spelling test. Scores: 12, 15, 15, 16, 16, 17, 17, 17, 18, 18, 19, 19, 20, 20.
(a) Draw a dot plot in your workbook (use the number line 12 to 20).
(b) State the mode and the range.
(c) Describe the shape in one sentence. 4 marks
1.2 — Student heights stem-and-leaf. Heights (cm) of 14 Year 8 students: 152, 148, 161, 155, 158, 163, 170, 172, 175, 162, 165, 156, 153, 168.
(a) Construct an ordered stem-and-leaf plot. Use stems 14, 15, 16, 17 (treat the first two digits as the stem). Include a key.
(b) Find the median height.
(c) Find the range. 4 marks
1.3 — Sprint times. 9 athletes' 100 m times (seconds): 11.4, 11.6, 11.5, 11.8, 12.0, 11.9, 13.2, 11.7, 11.6. (Treat values to one decimal: stem = whole + tenths up to the dot is the integer part, leaves are tenths.)
(a) Construct a stem-and-leaf plot using stems 11, 12, 13 with leaves being the tenths digit. Include the key (e.g. 11 | 4 = 11.4).
(b) Identify any outlier.
(c) Find the median time. 3 marks
1.4 — Two classes back-to-back. Class A exam results: 42, 45, 47, 51, 53, 54, 56, 63. Class B exam results: 41, 43, 46, 50, 52, 55, 58, 67.
(a) Construct a back-to-back stem-and-leaf with Class A leaves on the left and Class B on the right.
(b) Find the median of each class.
(c) Which class performed better, on the median? 3 marks
1.5 — Daily rainfall dot plot. Rainfall (mm) over 10 days: 2, 3, 3, 4, 4, 4, 5, 5, 6, 18.
(a) Identify the outlier.
(b) State the range with the outlier and without.
(c) Which "range" gives a fairer picture of a typical day's rainfall? Explain in one sentence. 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate constructs a stem-and-leaf plot but leaves the leaves in the order the values appeared in the data set, instead of ascending order. In your own words, explain (i) why ordered leaves matter, (ii) one statistical task that is now harder to do, and (iii) one practical fix the classmate could apply. Use the term median in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Test scores dot plot
(b) Mode = 17 (3 dots — tallest stack). Range = 20 − 12 = 8.
(c) Shape: roughly symmetric / slightly skewed left — most students scored between 15 and 20, with one lower value at 12 stretching the left side.
1.2 — Student heights stem-and-leaf
Sorted: 148, 152, 153, 155, 156, 158, 161, 162, 163, 165, 168, 170, 172, 175.
14 | 8 15 | 2 3 5 6 8 16 | 1 2 3 5 8 17 | 0 2 5. Key: 15 | 2 = 152.
(b) Median: 7th and 8th values = (161 + 162) ÷ 2 = 161.5 cm.
(c) Range = 175 − 148 = 27 cm.
1.3 — Sprint times stem-and-leaf
Sorted: 11.4, 11.5, 11.6, 11.6, 11.7, 11.8, 11.9, 12.0, 13.2.
11 | 4 5 6 6 7 8 9 12 | 0 13 | 2. Key: 11 | 4 = 11.4 s.
(b) Outlier = 13.2 s (well above the cluster).
(c) Median (n = 9, 5th value) = 11.7 s.
1.4 — Two classes back-to-back
Both n = 8. Back-to-back (Class A left, outward; Class B right):
7 5 2 | 4 | 1 3 6
6 4 3 1 | 5 | 0 2 5 8
3 | 6 | 7
Key: 4 | 2 = 42 for Class A; 4 | 1 = 41 for Class B.
(b) Class A median = average of 4th & 5th = (51 + 53) ÷ 2 = 52. Class B median = (50 + 52) ÷ 2 = 51.
(c) Class A performed slightly better on the median (52 vs 51), but the difference is small.
1.5 — Daily rainfall
(a) Outlier = 18 mm (isolated far above the cluster 2–6).
(b) With outlier: range = 18 − 2 = 16 mm. Without: range = 6 − 2 = 4 mm.
(c) The range without the outlier (4 mm) better represents a typical day, because 9 of the 10 days had rainfall between 2 and 6 mm.
2.1 — Explain your thinking (sample response)
Ordered leaves matter because a stem-and-leaf plot is meant to act like a quick sorted list of the data. If the leaves are out of order, then finding the median becomes a guessing game — you can no longer just count across to the middle position. One statistical task that is harder is finding the median: you'd have to re-sort the whole data set first, which defeats the purpose of using the plot. A simple fix is to draft the plot with unordered leaves first, then rewrite it with each row sorted ascending before adding the Key.
Marking: 1 mark for explaining why order matters; 1 mark for naming a specific task (median) that needs ordered data; 1 mark for the suggested fix (draft + rewrite); 1 mark for clear full-sentence communication.