Understand the idea.
Centre is only part of a comparison
Compare both centre and spread. Two groups can share a mean or median while having very different ranges. State the context and units so that “same centre” does not become a claim that all observations are the same.
Use compatible scales when comparing plots. Group size also matters: a larger total can arise simply because more people were recorded. For unequal groups, proportions or appropriately defined numerical summaries usually support a fairer comparison than raw totals.
| Group | Scores |
|---|---|
| A | 18, 19, 20, 20, 23 |
| B | 14, 18, 20, 22, 26 |
Choose the average for its meaning
Choose an average for its meaning. The mean describes equal sharing and uses every value. The median describes a middle position and can be more useful for a typical observation when extremes pull the mean away from the main group.
The mode identifies a most common value or category, including favourite sports where numerical averaging makes no sense. Explain your choice and keep the claim within the data: matching or different averages alone do not establish what caused a group’s results.
See the method in action.
Same centre, different spread
Compare the quiz scores in Groups A and B.
| Group | Scores |
|---|---|
| A | 18, 19, 20, 20, 23 |
| B | 14, 18, 20, 22, 26 |
Worked solution
- 1
Calculate the means for both groups.
Both groups total one hundred points across five observations.
- 2
Read the middle ordered scores.
Each ordered group has twenty in the third position.
- 3
Compare the ranges.
Group B spans twelve points, compared with five points for A.
- 4
State the comparison in context.
Both means and medians are twenty points, but B has greater spread as measured by its range.
Both means and medians are 20 points. Group B varies more: range 12 compared with 5.
A typical weekly amount
Five weekly earnings, in dollars, are 350, 380, 400, 420 and 2450. Choose a useful summary of a typical earner.
Worked solution
- 1
Calculate the equal-share summary.
The high earning contributes to the total of four thousand dollars.
- 2
Locate the middle earning.
Four hundred is the third of the five ordered amounts.
- 3
Choose a summary for a typical person in this group.
The median is more representative here because four earnings lie between three hundred and fifty and four hundred and twenty dollars. The mean remains the correct equal-share amount.
Median 400 dollars is more representative of a typical person in this small group. Mean 800 dollars remains the correct equal-share summary.
Try it yourself.
Check your understanding
Which average can describe the most common favourite sport?
Show answer & reasoning
The mode.
The mode identifies the most frequently named sport. Favourite sport is categorical, so calculating a numerical mean or median of its labels would not describe it.
Keep practising
6 worksheet questions · 12 marks
Read the questions online
- Group A has mean 15 and range 4. Group B has mean 15 and range 14. State one similarity and one difference.2 marks
- A dataset has several very high prices and many modest prices. Which of mean or median is usually more useful for a typical price? Explain.2 marks
- Which summary would help a shop order its most popular T-shirt colour?2 marks
- Two bar graphs show the same frequencies, but one scale runs 0–20 and the other 0–200. Can bar height in centimetres alone compare frequencies?2 marks
- Scores are 6, 8, 8, 10, 13. Give the median and range, then explain why these do not describe everything.2 marks
- In Group A, 12 of 40 students catch a bus. In Group B, 8 of 20 do. Which has the greater proportion of bus travellers?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Group A has mean 15 and range 4. Group B has mean 15 and range 14. State one similarity and one difference.2 marks
Both centres measured by the mean are 15.
14 is a larger range than 4.
Same mean; Group B has the wider spread. - A dataset has several very high prices and many modest prices. Which of mean or median is usually more useful for a typical price? Explain.2 marks
The high extremes can pull the mean upwards; the median describes the middle position.
Median, with an explanation of the high prices. - Which summary would help a shop order its most popular T-shirt colour?2 marks
Colours are categories; the highest-frequency category is relevant.
The modal colour. - Two bar graphs show the same frequencies, but one scale runs 0–20 and the other 0–200. Can bar height in centimetres alone compare frequencies?2 marks
The scales differ. Read labelled values or redraw using a common scale.
No. - Scores are 6, 8, 8, 10, 13. Give the median and range, then explain why these do not describe everything.2 marks
The middle value is 8.
.
Different datasets can share those summaries.
Median 8; range 7. A list or plot is still needed to show all frequencies and shape. - In Group A, 12 of 40 students catch a bus. In Group B, 8 of 20 do. Which has the greater proportion of bus travellers?2 marks
A: .
B: .
40% is greater than 30%, even though A has more bus travellers in total.
Group B.
Curriculum reference & lesson scope
Australian Curriculum v9 / South Australian Mathematics Curriculum
Year 7 statistical variables, representations, summary statistics, outliers and an original small investigation; deeper sampling methods develop in Year 8.
Official curriculum source ↗