Mathematics • Year 8 • Unit 4 • Lesson 11
Comparing Data Sets
Build fluency with the four numbers that drive comparison: mean, median, mode, and range. One worked example, one guided example with blanks, then eight independent problems from quick recall to writing full comparative statements.
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. Two basketball teams played 5 games each. Compare them using centre AND spread.
Team A: 70, 78, 82, 84, 90 Team B: 55, 65, 82, 95, 105
Step 1 — Find the mean of each team.
Team A: (70 + 78 + 82 + 84 + 90) ÷ 5 = 404 ÷ 5 = 80.8
Team B: (55 + 65 + 82 + 95 + 105) ÷ 5 = 402 ÷ 5 = 80.4
Reason: mean = sum ÷ count. Use this for the "average performance" of each team.
Step 2 — Find the range of each team.
Team A: max − min = 90 − 70 = 20
Team B: max − min = 105 − 55 = 50
Reason: range measures spread. A small range means the team scored consistently.
Step 3 — Compare centre and compare spread.
Centre: means are almost identical (80.8 vs 80.4) — both teams scored about the same on average.
Spread: Team A's range (20) is much smaller than Team B's range (50).
Step 4 — Write a full comparative statement.
Answer: "Both teams averaged a similar score (mean 80.8 vs 80.4), but Team A had a much smaller range (20 vs 50), so Team A is more consistent overall."
2. We do — fill in the missing steps
Same shape as Section 1, but the working is faded. Fill in each blank. 5 marks
Problem. Two Year 8 maths classes sat the same test. Compare them.
Class P: 64, 70, 72, 74, 80 Class Q: 50, 60, 72, 84, 94
Step 1 — Mean of each class:
Class P: (64 + 70 + 72 + 74 + 80) ÷ 5 = ______ ÷ 5 = ______
Class Q: (50 + 60 + 72 + 84 + 94) ÷ 5 = ______ ÷ 5 = ______
Step 2 — Range of each class:
Class P: ______ − ______ = ______
Class Q: ______ − ______ = ______
Step 3 — Compare centre and spread:
The means are __________________ (similar / very different). The range of Class P is __________ than Class Q.
Step 4 — Write the comparative statement:
"Both classes had about the same mean (______ vs ______), but Class ______ had a smaller range (______ vs ______), so Class ______ was more consistent."
3. You do — independent practice
Show your working in the space under each problem. The first four are foundation (single skill). The middle two are standard (two steps). The last two are extension (write the full comparison).
Foundation — single calculations
3.1 Find the mean of: 6, 8, 10, 12, 14. 1 mark
3.2 Find the median of: 18, 25, 12, 15, 20. (Order them first.) 1 mark
3.3 Find the range of: 3, 7, 5, 11, 4, 9. 1 mark
3.4 Define consistent in one sentence using the word "range". 1 mark
Standard — calculate mean and range for two groups
3.5 Two groups completed a 100 m sprint (time in seconds).
Group X: 13.0, 13.4, 13.6, 14.0, 14.5 Group Y: 12.5, 13.2, 13.6, 14.8, 15.4
Calculate the mean and range for each group. 2 marks
3.6 Two students recorded daily steps over 5 days.
Sam: 7 200, 8 000, 8 500, 9 100, 9 200 Lee: 4 000, 6 500, 8 500, 10 000, 12 000
Calculate the mean and median for each student. 2 marks
Extension — write the full comparison
3.7 Class A: mean 72, range 30. Class B: mean 65, range 12. Write ONE comparative statement that mentions both centre AND spread, gives both values, and draws a conclusion about which class performed better overall. 2 marks
3.8 A back-to-back stem-and-leaf plot shows Year 8 and Year 9 test marks (leaves = units):
Year 8 (read right to left) | Stem | Year 9
9 8 5 | 5 | 2 4 7
7 4 2 1 | 6 | 0 3 5 8
6 3 | 7 | 1 4 6
5 | 8 | 2
(a) Find the median of each year group. (b) Find the range of each year group. (c) Which year is more consistent? 3 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (Class P vs Class Q)
Step 1: Class P sum = 360, mean = 360 ÷ 5 = 72. Class Q sum = 360, mean = 360 ÷ 5 = 72.
Step 2: Class P range = 80 − 64 = 16. Class Q range = 94 − 50 = 44.
Step 3: Means are identical; Class P range is much smaller than Class Q.
Step 4: "Both classes had about the same mean (72 vs 72), but Class P had a smaller range (16 vs 44), so Class P was more consistent."
3.1 — Mean of 6, 8, 10, 12, 14
Sum = 50, count = 5. Mean = 50 ÷ 5 = 10.
3.2 — Median of 18, 25, 12, 15, 20
Ordered: 12, 15, 18, 20, 25. The middle (3rd) value is 18.
3.3 — Range of 3, 7, 5, 11, 4, 9
Max = 11, min = 3. Range = 11 − 3 = 8.
3.4 — Define consistent
A data set is consistent when it has a small range — the values are close together and don't vary much from one to the next.
3.5 — Sprint times
Group X: sum = 68.5, mean = 68.5 ÷ 5 = 13.7 s. Range = 14.5 − 13.0 = 1.5 s.
Group Y: sum = 69.5, mean = 69.5 ÷ 5 = 13.9 s. Range = 15.4 − 12.5 = 2.9 s.
3.6 — Daily steps
Sam: sum = 42 000, mean = 8 400 steps. Already ordered → median = 8 500 (middle value).
Lee: sum = 41 000, mean = 8 200 steps. Already ordered → median = 8 500 (middle value).
3.7 — Class A vs Class B comparison
Sample answer: "On average, Class A scored higher (mean 72 vs 65). However, Class B was more consistent (range 12 vs 30). Class A performed better overall on average, but Class B's scores were more tightly clustered, making them more reliable."
3.8 — Stem-and-leaf comparison
Year 8 values ordered: 55, 58, 59, 61, 62, 64, 67, 73, 76, 85. (a) median = average of 5th and 6th = (62 + 64) ÷ 2 = 63. (b) range = 85 − 55 = 30.
Year 9 values ordered: 52, 54, 57, 60, 63, 65, 68, 71, 74, 76, 82. (a) median = 6th value = 65. (b) range = 82 − 52 = 30.
(c) Ranges are identical (30), so consistency is roughly equal — neither year is more consistent on the range measure. Year 9's median (65) is slightly higher than Year 8's (63), so Year 9 performed marginally better overall.