Three averages are available — choose the most appropriate one for the context. When comparing two datasets, always calculate the same average for both and then comment on what the difference means.
Key insight: Two datasets can have the same mean but very different spreads. You must comment on both an average and the range to give a complete comparison.
✔ Quick Check compds1 — Choosing averages
Question 1 of 10
Comparing Spread Using the Range
You met the range and what it shows about consistency in Lesson 18.4 — Range: a larger range means the data is more spread out (less consistent), a smaller range means more consistent. What's new here is putting that into a proper comparison statement — always quote the actual numbers and say what they mean in context.
Range = Maximum value − Minimum value
Example — Comparing Class A and Class B test scores
Data
Class A: mean 65, range 40. Class B: mean 63, range 12.
Compare averages
"Class A has a higher mean score (65 vs 63), suggesting slightly better overall performance on average."
Compare spread
"However, Class B has a much smaller range (12 vs 40), showing far more consistent results — students in Class B performed more similarly to each other."
✔ Quick Check compds2 — Range and written comparisons
Question 1 of 10
Full Comparison in Exam Conditions
Exam questions that say "compare" the two datasets require you to comment on both an average AND the spread, with actual values quoted and interpreted in context. Missing any part costs marks.
Full Comparison — Employee A vs Employee B daily sales
Data
Employee A: mean £420, range £180. Employee B: mean £380, range £45.
Average comparison
"Employee A has a higher mean daily sales figure (£420 vs £380), suggesting that on average Employee A generates more revenue per day."
Spread comparison
"However, Employee B has a much smaller range (£45 vs £180), meaning their sales are far more consistent and predictable from day to day. Employee A's results are more variable."
Conclusion (optional)
"Overall, Employee A earns more on average but Employee B is more reliable. The choice depends on whether you value higher average sales or consistency."
✔ Quick Check compds3 — Full comparisons in exam conditions
Question 1 of 10
Practice: Compare Team A and Team B
Use the datasets below. Calculate the mean and range for each team, then answer the questions.
Team
Project completion times (days)
Team A
4, 6, 5, 8, 7, 6, 5
Team B
3, 9, 2, 10, 4, 8, 6
Q1. What is Team A's mean? (to 2 decimal places)
Q2. What is Team B's range?
Q3. Which team is more consistent? (type A or B)
Q4. What is Team A's range?
Q5. What is Team B's mean? (to 2 decimal places)
Q6. What is Team A's median?
Q7. What is Team B's median?
Q8. By how many days does Team B's range exceed Team A's range?
Q9. What is the difference between Team A and Team B's means? (to 2 decimal places)
Q10. If Team A's slowest time (8) improved to 6 days, what would the new range be?
⚠ Things to Watch Out For
Only comparing one measure: A full comparison requires both an average AND the range (or other measure of spread). Commenting on just the mean loses marks.
Not quoting figures: Say "Team A has a higher mean (5.86 vs 6.0)" — always include the actual values in your comparison statement.
Not interpreting in context: Don't just say "A has a higher mean." Say what that MEANS — "suggesting Team A completes projects faster on average."
Confusing "consistent" with "better": A smaller range means MORE consistent, but not necessarily better. A consistently low score is consistent but poor.
Comparing different averages: Compare like with like — mean vs mean, or median vs median. Don't compare the mean of one dataset with the median of another.