The idea, step by step
Four different summaries
The mean is total divided by observation count. The median is the middle of ordered data; for an even count, average the two middle observations. The mode occurs most often. The range is largest minus smallest. In a frequency table, multiply each value by its frequency before adding; do not average just the distinct values.
A suitable picture
Column graphs suit categories or discrete values; a line graph can show change over ordered time. Dot plots and stem-and-leaf displays retain individual values. Label axes and units consistently. Compare centre, spread, shape and unusual observations. A zero baseline is important for fair visual comparisons of column heights.
A common trap
The median is halfway between the smallest and largest values.
Instead: The median comes from the middle observations after ordering; halfway between extremes is a different measure.
See the thinking
Worked example 1
Find mean, median, mode and range for 2,3,3,4,8.
- Total 20; mean 20÷5=4.
- The middle ordered value is 3; 3 occurs most often.
- Range 8−2=6.
Worked example 2
Use the supplied table to find mean books read.
| Books | Frequency |
|---|---|
| 0 | 1 |
| 1 | 2 |
| 2 | 4 |
| 3 | 2 |
| 4 | 1 |
- Total frequency=1+2+4+2+1=10.
- Weighted total=0×1+1×2+2×4+3×2+4×1=20.
- Mean=20÷10=2.
Check your understanding
Find the median of 2,4,7,9.
Show answer
5.5.
The middle observations are 4 and 7, so (4+7)÷2=5.5.
Your turn
6 questions · 16 marks · Work at your own pace.
Read the questions online
- Find the mean, median, mode and range of 5,6,6,7,11.4 marks
- How many students read at least 3 books in the supplied table?2 marks
Example data: books read in one week Books Frequency 0 1 1 2 2 4 3 2 4 1 - Find the median books read from the supplied table.2 marks
Example data: books read in one week Books Frequency 0 1 1 2 2 4 3 2 4 1 - A stem-and-leaf display has rows 1|246 and 2|03, with key 1|2=12. List the data and range.3 marks
- Choose a display for rainfall measured daily across a fortnight. Explain.2 marks
- Columns for counts 45 and 50 start their vertical axis at 40. Explain the distortion.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find the mean, median, mode and range of 5,6,6,7,11.4 marks
Total 35; 35÷5=7.
Middle value 6; 6 occurs twice; 11−5=6.
Mean 7; median 6; mode 6; range 6. - How many students read at least 3 books in the supplied table?2 marks
Example data: books read in one week Books Frequency 0 1 1 2 2 4 3 2 4 1 Add frequencies for 3 and 4 books: 2+1=3.
3 students. - Find the median books read from the supplied table.2 marks
Example data: books read in one week Books Frequency 0 1 1 2 2 4 3 2 4 1 The fifth and sixth observations are both 2.
2 books. - A stem-and-leaf display has rows 1|246 and 2|03, with key 1|2=12. List the data and range.3 marks
Read place values from the key; 23−12=11.
12,14,16,20,23; range 11. - Choose a display for rainfall measured daily across a fortnight. Explain.2 marks
Ordered time allows day-to-day change to be seen.
A line graph with day horizontally and rainfall in millimetres vertically. - Columns for counts 45 and 50 start their vertical axis at 40. Explain the distortion.3 marks
Use a zero baseline for fair column-height comparisons.
Displayed heights 5 and 10 make 50 look twice 45, although actual counts differ by only 5.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum
Population, census and sample; observational versus experimental data; random and non-random sampling; primary/secondary data; reviewing numerical displays and summary statistics; comparing samples and sample sizes; bias, variation and uncertainty; planning, conducting and reporting a fair investigation.
Official curriculum source ↗