Mathematics • Year 8 • Unit 4 • Lesson 4
Dot Plots and Stem-and-Leaf
Build fluency with dot plots and ordered stem-and-leaf plots: reading mode, median and range; identifying outliers; and constructing each display from raw data.
1. I do — fully worked example
Read every line. Each step has a short reason so you can see why we do it, not just what we do.
Problem. Data (n = 11): 34, 38, 41, 45, 45, 48, 52, 56, 59, 63, 67. Construct an ordered stem-and-leaf plot, include a key, and find the median.
Step 1 — Identify the stems (tens digit).
Values are in the 30s, 40s, 50s, 60s → stems = 3, 4, 5, 6.
Reason: the stem column lists every tens-digit that appears in the data.
Step 2 — Write each leaf (units digit) beside its stem in ascending order.
3 | 4 8 4 | 1 5 5 8 5 | 2 6 9 6 | 3 7
Reason: ordered leaves make finding the median quick — just count to the middle position.
Step 3 — Add a Key so any reader can decode the plot.
Key: 3 | 4 = 34
Step 4 — Find the median (n = 11, odd → position (n+1)÷2 = 6th value).
Counting through ordered leaves: 34, 38, 41, 45, 45, 48 ← 6th value.
Answer: Median = 48.
2. We do — fill in the missing steps
Same shape as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. Data (n = 9): 23, 25, 31, 34, 38, 42, 44, 47, 51. Construct an ordered stem-and-leaf plot, include a key, and find the median.
Step 1 — Identify the stems:
Stems = ______, ______, ______, ______
Step 2 — Write each leaf beside its stem in ascending order:
2 | ______ 3 | ______ 4 | ______ 5 | ______
Step 3 — Add the Key:
Key: 2 | 3 = ______
Step 4 — Median (n = 9, position (9+1)÷2 = 5th value):
5th value = ______
3. You do — independent practice
Show your working in the space under each problem. The first four are foundation. The middle two are standard. The last two are extension.
Foundation — quick recall
3.1 A dot plot shows: 5 (1 dot), 6 (2), 7 (4), 8 (3), 9 (1). State the mode and the range. 1 mark
3.2 In a stem-and-leaf plot, what is the value when stem = 4 and leaf = 7? 1 mark
3.3 Write the stem-and-leaf entry (ordered) for these values: 61, 67, 73, 79, 75. Include a key. 1 mark
3.4 From the stem-and-leaf plot 4 | 2 5 8 5 | 0 3 3 7 6 | 1 4, how many values are there in total and what is the range? 1 mark
Standard — two-step problems
3.5 Puzzle times (minutes) for 15 students: 8, 12, 9, 11, 14, 10, 8, 13, 9, 11, 15, 10, 12, 9, 7. State the mode, the range, and describe the shape in one sentence. 2 marks
3.6 Construct an ordered stem-and-leaf plot for: 43, 27, 55, 48, 31, 62, 35, 51, 29, 46, 58, 37. Include a key. Find the median. 2 marks
Extension — analyse a display
3.7 A dot plot shows values 12, 13, 14, 14, 15, 16, 17, 18, 42. (a) State the range. (b) Identify any outlier. (c) Explain in one sentence how the outlier affects the range. 2 marks
3.8 A back-to-back stem-and-leaf shows Group A leaves on the left: "8 6 3 | 5 | 1 4 7". (a) List all of Group A's values for the stem-5 row. (b) List all of Group B's values for the stem-5 row. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (data: 23, 25, 31, 34, 38, 42, 44, 47, 51)
Step 1: Stems = 2, 3, 4, 5.
Step 2: 2 | 3 5 3 | 1 4 8 4 | 2 4 7 5 | 1.
Step 3: Key: 2 | 3 = 23.
Step 4: 5th value = 38.
3.1 — Mode and range from dot plot
Mode = 7 (tallest stack, 4 dots). Range = 9 − 5 = 4.
3.2 — Stem 4, Leaf 7
Value = 47.
3.3 — Stem-and-leaf for 61, 67, 73, 79, 75
6 | 1 7 7 | 3 5 9. Key: 6 | 1 = 61.
3.4 — Total and range
Total = 3 + 4 + 2 = 9 values. Min = 42, Max = 64. Range = 22.
3.5 — Puzzle times
Sorted: 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 12, 12, 13, 14, 15. Mode = 9 (3 times). Range = 15 − 7 = 8. Shape: roughly symmetric with a small cluster around 9–12, no outliers.
3.6 — Stem-and-leaf for 12 values
Sorted: 27, 29, 31, 35, 37, 43, 46, 48, 51, 55, 58, 62.
2 | 7 9 3 | 1 5 7 4 | 3 6 8 5 | 1 5 8 6 | 2. Key: 2 | 7 = 27.
Median: n = 12 (even) → average of 6th and 7th = (43 + 46) ÷ 2 = 44.5.
3.7 — Outlier from dot plot
(a) Range = 42 − 12 = 30.
(b) Outlier = 42 — isolated far above the cluster 12–18.
(c) The single outlier inflates the range from what would otherwise be 18 − 12 = 6 up to 30, making the data look five times more spread out than it actually is.
3.8 — Back-to-back stem-5 row
(a) Group A: leaves 3, 6, 8 (reading outward from the stem) → values 53, 56, 58.
(b) Group B: leaves 1, 4, 7 (reading left-to-right) → values 51, 54, 57.