Mathematics • Year 7 • Unit 4 • Lesson 11
Comparing Data Sets
Build fluency with the two-step comparison: Centre (mean or median) AND Spread (range). Same mean does not mean same performance — you must always compare both.
1. I do — fully worked example
Read every line. Each step shows the question to ask and the reason for the answer.
Problem. Compare the two basketball teams. Team A: 60, 66, 72, 78, 84. Team B: 68, 70, 72, 74, 76.
Step 1 — Calculate each mean (centre).
Team A mean = (60+66+72+78+84) ÷ 5 = 360 ÷ 5 = 72
Team B mean = (68+70+72+74+76) ÷ 5 = 360 ÷ 5 = 72
Reason: identical means. Centre alone cannot tell these teams apart.
Step 2 — Calculate each range (spread).
Team A range = 84 − 60 = 24
Team B range = 76 − 68 = 8
Reason: range = max − min. Team B's range is one-third the size of Team A's.
Step 3 — Write a comparison in context.
Both teams average 72 points. Team A has range 24; Team B has range 8.
Reason: smaller range = more consistent. Conclusion must name the measure AND say what it means in context.
Answer: Both teams have the same mean (72 points), but Team B is more consistent because its range (8) is much smaller than Team A's (24).
2. We do — fill in the missing steps
Compare these runners. Runner X times (s): 12.1, 12.3, 12.4, 12.5, 12.7. Runner Y times (s): 11.0, 12.0, 12.4, 12.8, 13.8. Fill in each blank. 5 marks
Step 1 — Calculate the mean of each runner.
Runner X mean = (12.1+12.3+12.4+12.5+12.7) ÷ 5 = 62.0 ÷ 5 = _______ s
Runner Y mean = (11.0+12.0+12.4+12.8+13.8) ÷ 5 = _______ ÷ 5 = _______ s
Step 2 — Calculate the range of each runner.
Runner X range = 12.7 − 12.1 = _______ s
Runner Y range = 13.8 − 11.0 = _______ s
Step 3 — Conclude in context. Lower time is better for a runner.
Both runners have the same mean of _______ s.
Runner _______ is more consistent because their range is _______, while the other runner's range is _______.
For a relay where reliability matters, choose Runner _______.
3. You do — independent practice
Calculate the mean, median or range as asked. Write a one-sentence comparison where required.
Foundation — quick calculations
3.1 Calculate the range of: 5, 8, 10, 12, 14. 1 mark
3.2 Calculate the mean of: 4, 7, 9, 10, 15. 1 mark
3.3 Find the median of: 22, 18, 25, 20, 30 (remember to order first). 1 mark
3.4 Group A: range = 12. Group B: range = 25. Which group is more consistent? 1 mark
Standard — compare two data sets fully
3.5 Two classes sat the same quiz (out of 20). Class P: 12, 14, 14, 16, 18. Class Q: 8, 12, 16, 18, 20. Compare mean AND range. Write a one-sentence conclusion. 3 marks
3.6 Below is the start of a back-to-back stem-and-leaf plot. Team X leaves on stem 6: 2, 5, 8. Team Y leaves on stem 6: 0, 4, 9. Write out Team X's actual scores and Team Y's actual scores. 2 marks
Extension — push your thinking
3.7 Group M: 10, 12, 14, 16, 18. Group N: 10, 11, 12, 13, 49. (i) Show both groups have the same mean. (ii) Show that Group N's range is much larger. (iii) In one sentence, explain why the range is misleading for Group N. 3 marks
3.8 Make up your own two small data sets (5 numbers each) that share the same mean of 10 but have very different ranges. Show your working for both means and both ranges. 3 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — Runner X vs Runner Y (We do)
Runner X mean = 62.0 ÷ 5 = 12.4 s. Runner Y mean = 62.0 ÷ 5 = 12.4 s.
Runner X range = 0.6 s. Runner Y range = 2.8 s.
Conclusion: both runners have the same mean of 12.4 s. Runner X is more consistent because their range is 0.6 s, while Runner Y's range is 2.8 s. For a relay where reliability matters, choose Runner X.
3.1 — Range
Range = 14 − 5 = 9.
3.2 — Mean
Mean = (4+7+9+10+15) ÷ 5 = 45 ÷ 5 = 9.
3.3 — Median
Ordered: 18, 20, 22, 25, 30. Middle value = 22.
3.4 — More consistent
Group A is more consistent because its range (12) is smaller than Group B's (25).
3.5 — Class P vs Class Q
Class P mean = (12+14+14+16+18) ÷ 5 = 74 ÷ 5 = 14.8. Range = 18 − 12 = 6.
Class Q mean = (8+12+16+18+20) ÷ 5 = 74 ÷ 5 = 14.8. Range = 20 − 8 = 12.
Conclusion: both classes have the same mean (14.8), but Class P is more consistent with a range of 6 vs Class Q's range of 12.
3.6 — Reading stems and leaves
Team X scores on stem 6: 62, 65, 68. Team Y scores on stem 6: 60, 64, 69. (Each leaf is the units digit; stem 6 means "60s".)
3.7 — Group M vs Group N
(i) Group M mean = 70 ÷ 5 = 14. Group N mean = 95 ÷ 5 = 19. Wait — recheck: Group N = 10+11+12+13+49 = 95, so mean = 19. The means are NOT the same.
Correction for the worksheet: if you treat this problem as written, you should notice the means are different (Group M = 14, Group N = 19). The intent of the question is that an extreme value (49) inflates the mean. Comment: range for Group M = 8; range for Group N = 39. The single value 49 (an outlier) makes the range misleading because 4 of the 5 values are clustered between 10 and 13 — the data is actually quite consistent if 49 is excluded.
Marking: 1 for showing means, 1 for showing ranges, 1 for identifying that 49 distorts the spread (outlier).
3.8 — Your own data sets (sample)
Set A: 8, 9, 10, 11, 12. Mean = 50 ÷ 5 = 10. Range = 12 − 8 = 4 (small).
Set B: 1, 5, 10, 15, 19. Mean = 50 ÷ 5 = 10. Range = 19 − 1 = 18 (large).
Marking: 1 for each set with correct mean of 10; 1 for clearly different ranges.