Understand the idea.
Compare like with like
Before comparing data, check that the groups measure the same variable in the same units under comparable conditions. Sort small lists. Use a measure of centre to describe a typical value and a measure of spread to describe variation.
The mean is the total divided by the count; the median is the middle ordered value; the range is maximum minus minimum. Interpret these in context: a smaller time may be favourable, whereas a higher score may be favourable.
| Group A | Group B |
|---|---|
| 10 | 11 |
| 12 | 12 |
| 12 | 13 |
| 14 | 14 |
| 17 | 15 |
Use evidence without overclaiming
Compare with numbers and a clear interpretation: one group might have a lower median but a larger range. Equal means do not imply equal medians, equal spread or identical observations. A common-scale display can reveal overlap that a single summary hides.
Limit claims to the evidence. Overlapping samples do not show that every observation in one group is better. Small samples, selection methods or different conditions may limit generalisation, and a descriptive difference does not by itself establish a cause.
See the method in action.
Equal means, different spread
Compare A: 10, 12, 12, 14, 17 and B: 11, 12, 13, 14, 15.
| Group A | Group B |
|---|---|
| 10 | 11 |
| 12 | 12 |
| 12 | 13 |
| 14 | 14 |
| 17 | 15 |
Worked solution
- 1
Calculate both means.
Both samples total and contain five observations.
- 2
Read the ordered middle values.
For five ordered observations, the third is the median.
- 3
Calculate the ranges.
Subtract the minimum from the maximum in each group.
- 4
Compare centre and spread.
A has the lower median; B has the smaller range. Their equal means do not make the samples identical, and the values overlap.
Both means 13; A median 12/range 7; B median 13/range 4.
Compare delivery times
Times in minutes: A: 18, 20, 20, 22, 25; B: 15, 19, 21, 23, 27.
Worked solution
- 1
Calculate the sample means.
Each total is minutes for five deliveries.
- 2
Read the sample medians.
The lists are ordered, so their third observations are the medians.
- 3
Calculate the ranges.
Range compares the full observed span of delivery times.
- 4
Interpret the comparison.
A has a one-minute lower sample median and less spread by range. The samples overlap, so this does not show that every A delivery is faster.
A has the lower sample median and smaller range.
Try it yourself.
Check your understanding
A has median 12/range 9. B has median 12/range 4. Compare them.
Show answer & reasoning
Equal medians; B is less spread out by range.
Both groups have median , so this measure of centre is equal. B has the smaller range, rather than , indicating less spread by range without proving the distributions are otherwise identical.
Keep practising
6 worksheet questions · 14 marks
Read the questions online
- Find mean, median and range for 3, 5, 5, 7, 10.3 marks
- A: 6, 7, 8, 9, 10. B: 4, 8, 8, 8, 12. Compare means and ranges.3 marks
- A: 11, 12, 13. B: 10, 14, 15. Does B's higher mean show every B score is higher?2 marks
- Two waiting-time samples have medians 8 and 11 minutes. Interpret the difference.2 marks
- Why is comparing raw totals from a five-minute test with a ten-minute test unfair?2 marks
- A sample of six has a higher median score than another sample of six. Write a cautious conclusion.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find mean, median and range for 3, 5, 5, 7, 10.3 marks
Total is 30, so mean .
The middle is 5; .
Mean 6; median 5; range 7. - A: 6, 7, 8, 9, 10. B: 4, 8, 8, 8, 12. Compare means and ranges.3 marks
Both totals are 40.
and , so A is less spread out.
Both means 8; A range 4, B range 8. - A: 11, 12, 13. B: 10, 14, 15. Does B's higher mean show every B score is higher?2 marks
A mean is 12 and B mean is 13.
A group mean does not imply a claim about all individuals.
No; B contains 10, below every A score. - Two waiting-time samples have medians 8 and 11 minutes. Interpret the difference.2 marks
minutes.
It does not mean each individual wait differs by 3 minutes.
The first sample's middle waiting time is 3 minutes shorter. - Why is comparing raw totals from a five-minute test with a ten-minute test unfair?2 marks
The longer test allows more events.
Use the same conditions or a suitable rate, explaining remaining differences.
The groups have different amounts of time or opportunity. - A sample of six has a higher median score than another sample of six. Write a cautious conclusion.2 marks
This evidence describes two small samples.
Sampling variation or other differences may explain the result.
The first sample has a higher median; larger fair samples are needed before generalising.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Year 9 sampling, comparative distributions, centre/spread/outliers, displays, critique and statistical investigations.
Official curriculum source ↗