Mathematics • Year 7 • Unit 4 • Lesson 7
Stem-and-Leaf and Dot Plots
Build fluency with the four-step recipe for a stem-and-leaf plot: List stems → Draft leaves → Sort ascending → Write key. For dot plots: one dot per value, stacked. Both displays show every individual value AND the shape of the data.
1. I do — fully worked example
Read every line. Each step shows the question to ask and the reason for the answer.
Problem. Build an ordered stem-and-leaf plot for the 10 test scores: 34, 41, 28, 52, 37, 41, 29, 33, 45, 55.
Step 1 — List the stems (tens digits).
Smallest = 28 (tens = 2). Largest = 55 (tens = 5). Stems needed: 2, 3, 4, 5.
Reason: include every tens value between the min and max — even if no leaves land there.
Step 2 — Draft the leaves (any order).
2 | 8 9 3 | 4 7 3 4 | 1 1 5 5 | 2 5
Reason: write the units digit of each value next to its stem in the order you read the data.
Step 3 — Sort the leaves into ascending order.
2 | 8 9 3 | 3 4 7 4 | 1 1 5 5 | 2 5
Reason: ordered leaves reveal the shape and make the median easy to read.
Step 4 — Add a key and check the count.
Key: 3 | 4 = 34. Leaf count = 2 + 3 + 3 + 2 = 10 ✓ (matches n).
Reason: every plot must have a key. The count check catches missing leaves.
Answer: 2|8 9, 3|3 4 7, 4|1 1 5, 5|2 5 with Key: 3|4 = 34.
2. We do — fill in the missing steps
Read the median and mode from a completed stem-and-leaf plot. Fill in each blank. 5 marks
Given plot (n = 8 values):
2 | 3 3 8
3 | 1 7
4 | 2 5
5 | 1 Key: 2 | 3 = 23
Step 1 — List all values in order from the plot: 23, 23, 28, ____, ____, 42, ____, ____.
Step 2 — Find the middle position(s): n = 8 (even). The two middle positions are ___ and ___.
Step 3 — Calculate the median: Median = (___ + ___) ÷ 2 = _______.
Step 4 — Identify the mode: The only repeated leaf is on stem ___, leaf ___. So mode = _______.
Step 5 — Calculate the range: Max = ____, Min = ____, Range = _______.
3. You do — independent practice
Eight graduated problems. Use the methods from sections 1 and 2.
Foundation — basic plotting
3.1 What does "3 | 7" mean in a stem-and-leaf plot with key 3|7 = 37? 1 mark
3.2 Build an ordered stem-and-leaf plot for: 14, 22, 18, 25, 11, 19, 23, 16. Include a key. 2 marks
3.3 For data 3, 5, 3, 7, 5, 3, 8: how many dots should sit above the value 3 on a dot plot? 1 mark
3.4 From the plot in 3.2, find (a) the minimum value, (b) the maximum value, (c) the range. 2 marks
Standard — read and interpret
3.5 From the plot in 3.2 (n = 8): find the median. Show the two middle values you average. 2 marks
3.6 Draw a dot plot for: 2, 5, 4, 4, 5, 6, 4, 7, 5. Describe the shape in one sentence (mention clusters, gaps and outliers if any). 3 marks
Extension — push your thinking
3.7 A class has these 12 maths scores: 47, 52, 58, 51, 60, 49, 65, 53, 50, 71, 55, 50. (a) Build an ordered stem-and-leaf plot with a key. (b) Find the mode and median. (c) Identify any outlier and justify in one sentence. 4 marks
3.8 The lesson says: "Always include empty stems with no leaves." Why? Give an example: list a small dataset where leaving out an empty stem would HIDE a gap. 3 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — Reading the plot (We do)
Step 1: 23, 23, 28, 31, 37, 42, 45, 51.
Step 2: n = 8, middle positions = 4th and 5th.
Step 3: Median = (31 + 37) ÷ 2 = 34.
Step 4: repeated leaf on stem 2, leaf 3 → mode = 23.
Step 5: Max = 51, Min = 23, Range = 28.
3.1 — Meaning of 3|7
3|7 = 37. The stem (3) is the tens digit; the leaf (7) is the units digit. Stem always read first.
3.2 — Build the plot
Sorted data: 11, 14, 16, 18, 19, 22, 23, 25. Stems = 1, 2.
1 | 1 4 6 8 9
2 | 2 3 5
Key: 1 | 1 = 11. (Count: 5 + 3 = 8 leaves ✓.)
3.3 — Dots above 3
Value 3 appears three times in the data, so 3 stacked dots above 3.
3.4 — Min, max, range
(a) Min = 11 (top row, first leaf). (b) Max = 25 (bottom row, last leaf). (c) Range = 25 − 11 = 14.
3.5 — Median
n = 8 (even), middle positions 4 and 5. From the ordered list (11, 14, 16, 18, 19, 22, 23, 25), the 4th = 18 and 5th = 19. Median = (18 + 19) ÷ 2 = 18.5.
3.6 — Dot plot for {2, 5, 4, 4, 5, 6, 4, 7, 5}
Number line from 2 to 7. Above 2: 1 dot. Above 4: 3 dots. Above 5: 3 dots. Above 6: 1 dot. Above 7: 1 dot. (Nothing above 3.)
Shape: Cluster at 4 and 5 (the bulk of the data); a small gap at 3; values 2, 6 and 7 are tails, not strong outliers.
3.7 — Class scores plot
(a) Sorted: 47, 49, 50, 50, 51, 52, 53, 55, 58, 60, 65, 71. Stems 4, 5, 6, 7.
4 | 7 9
5 | 0 0 1 2 3 5 8
6 | 0 5
7 | 1 Key: 5 | 0 = 50. (Count: 2 + 7 + 2 + 1 = 12 ✓.)
(b) Mode = 50 (repeated leaf 0 on stem 5). Median: n = 12, middle = 6th and 7th values = 52 and 53. Median = (52 + 53) ÷ 2 = 52.5.
(c) 71 is a possible outlier — it sits 6 marks above the next highest value (65) and is the only value in stem 7.
3.8 — Empty stems (sample)
Empty stems show that no data lies in that range — that's important information, not a typo. Example: {12, 13, 41, 42}. With empty stems:
1 | 2 3
2 | (empty)
3 | (empty)
4 | 1 2
The empty stems make the GAP between teens and forties obvious. Without them (just "1 | 2 3" then "4 | 1 2"), readers might think the data is evenly spread — hiding a real gap of 27 between 13 and 41.