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: 5, 8, 10, 11, 36. (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: 10+12+14+16+18 = 70 ÷ 5 = 14. Group N: 5+8+10+11+36 = 70 ÷ 5 = 14. Both means equal 14 ✓.
(ii) Group M range = 18 − 10 = 8. Group N range = 36 − 5 = 31. Group N's range is much larger.
(iii) The range is misleading for Group N because four of its five values (5, 8, 10, 11) are clustered tightly below 12, the single outlier value 36 drags the range up to 31, suggesting the data is very spread out when in fact most values are quite close together.
Marking: 1 for showing both means equal 14; 1 for showing both ranges; 1 for identifying the outlier (36) as the cause of the misleading range.
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.