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.