Mathematics • Year 7 • Unit 4 • Lesson 11
Comparing Data Sets — Mixed Challenge
Bring together mean, median, range, the outlier effect and back-to-back stem-and-leaf plots. Then spot a flawed comparison and design your own pair of data sets.
1. Mixed problems
Apply centre, spread and stem-plot reading. Justify briefly. 2 marks each
1.1 Group A: mean = 50, range = 6. Group B: mean = 50, range = 22. State which is more consistent and explain why in one sentence.
1.2 Calculate the mean and range of: 14, 16, 18, 20, 22.
1.3 Two surfers' wave-height records (m): Surfer P: 1.4, 1.5, 1.6, 1.7, 1.8. Surfer Q: 0.5, 1.0, 1.6, 2.2, 2.7. Show both means equal 1.6, then compare the ranges.
1.4 Below is a back-to-back stem plot of two classes' quiz marks out of 50.
Class L | Stem | Class M
8 4 | 1 | 2 5
7 3 | 2 | 0 6 8
5 0 | 3 | 4 7
1 | 4 | 2
Key: Class L 1|4 means 14. Class M 1|2 means 12.
Write out Class L's full list of scores.
1.5 Outlier check: data set is 4, 6, 8, 10, 90. (i) Calculate the mean. (ii) Calculate the median. (iii) Which value (mean or median) better represents the typical value, and why?
1.6 A coach has two sets of 30 sprint times. Set X has range 1.0 s, Set Y has range 4.5 s. Both have the same mean. Sample size is the same. In one sentence, write a conclusion the coach could use.
2. Find the mistake
A Year 7 student wrote the following analysis of two cricket batters' scores. Exactly one line contains a serious comparison error. Spot it, explain why it is wrong, then rewrite the conclusion correctly. 3 marks
Student's analysis: Batter X scores: 30, 35, 40, 45, 50 (mean 40, range 20). Batter Y scores: 10, 20, 40, 60, 70 (mean 40, range 60).
Line 1: Both batters average the same number of runs (mean = 40 each).
Line 2: Batter X has a range of 20; Batter Y has a range of 60.
Line 3: Because Batter Y has a larger range, Batter Y is more consistent.
Line 4: For a one-day final where steady scoring matters, the team should choose Batter X.
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write the corrected conclusion.
Stuck? Recall the rule: smaller range means MORE consistent, not less.3. Open-ended challenge — design a fair comparison
This question has many correct answers. Show your work clearly. 4 marks
3.1 You are choosing between two rideshare drivers based on past trip times to school (minutes). Both drivers' data sets must have exactly 5 trips and the same mean of 18 minutes.
- Design Driver A's 5 trip times so they are very consistent (small range).
- Design Driver B's 5 trip times so they have a large range due to one outlier.
For each driver: (i) list the 5 trip times, (ii) calculate the mean (must equal 18), (iii) calculate the range, (iv) write one sentence saying which driver you would pick and why.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Same mean, different range
Group A is more consistent because its range (6) is much smaller than Group B's (22) — Group A's values cluster much tighter around the mean.
1.2 — Mean and range
Mean = (14+16+18+20+22) ÷ 5 = 90 ÷ 5 = 18. Range = 22 − 14 = 8.
1.3 — Surfers
Surfer P mean = (1.4+1.5+1.6+1.7+1.8) ÷ 5 = 8.0 ÷ 5 = 1.6 m. Range = 1.8 − 1.4 = 0.4 m.
Surfer Q mean = (0.5+1.0+1.6+2.2+2.7) ÷ 5 = 8.0 ÷ 5 = 1.6 m. Range = 2.7 − 0.5 = 2.2 m.
Same mean. Surfer P is far more consistent (range 0.4 vs 2.2).
1.4 — Reading the stem plot
Class L scores (left side reads right-to-left from stem): 14, 18, 23, 27, 30, 35, 41.
1.5 — Outlier check
(i) Mean = (4+6+8+10+90) ÷ 5 = 118 ÷ 5 = 23.6.
(ii) Median (ordered 4, 6, 8, 10, 90) = 8.
(iii) The median (8) better represents the typical value. The single value 90 is an outlier that pulls the mean up to 23.6, which is higher than 4 of the 5 actual values.
1.6 — Conclusion in context
Sample answer: "Although both sprint groups have the same mean time, Set X is far more consistent (range 1.0 s vs 4.5 s), so Set X athletes are more reliable for race-day performance."
2 — Find the mistake
(a) The mistake is on Line 3.
(b) A LARGER range means LESS consistent, not more. Batter Y's wider spread (range 60) means his scores are much more variable than Batter X's (range 20).
(c) Corrected: Because Batter X has a smaller range, Batter X is more consistent. For a one-day final where steady scoring matters, the team should choose Batter X. (Line 4 was correct, but for the right reason — Batter X's smaller range, not Batter Y's larger one.)
3 — Driver comparison (sample design)
Driver A (consistent): 17, 17, 18, 19, 19 minutes. Mean = 90 ÷ 5 = 18. Range = 19 − 17 = 2.
Driver B (one outlier): 14, 15, 16, 17, 28 minutes. Mean = 90 ÷ 5 = 18. Range = 28 − 14 = 14.
Pick: I would choose Driver A because both drivers have the same average (18 min), but Driver A is far more predictable — they almost never deviate from 18 minutes, while Driver B has occasional very long trips that would make me late for school.
Marking: 1 for each driver with correct mean of 18 and stated range; 1 for clearly different ranges; 1 for a one-sentence justified choice.