The idea, step by step
Frequency counts observations
Frequency is the number of observations in a category or at a numerical value. Each observation must be counted once. The frequencies must add to the number of valid responses. Tallying first can help you avoid missing or counting an observation twice.
For a categorical variable, separate bars compare category frequencies. Put the category names on one axis, frequency on the other and include an informative title. Equal-width bars and a clearly labelled scale help the reader compare fairly.
| Method | Frequency |
|---|---|
| Walk | 8 |
| Bus | 6 |
| Cycle | 4 |
| Car | 2 |
Choose the graph for the question
A dot plot is useful for a small numerical dataset because individual values remain visible. A bar graph suits categories. A line graph can show a measurement changing with ordered time, such as temperature measured each hour.
Do not connect unrelated categories with a line: that would suggest meaningful intermediate values between “bus” and “car”. Before drawing, decide what each axis represents, choose intervals that fit every value, and write units where appropriate.
A common trap
A line graph is suitable whenever any numbers appear in a table.
Instead: Choose according to the variable and purpose. Category codes do not become a continuous scale.
See the thinking
Complete a frequency table
The books borrowed by eight students are 0, 1, 1, 2, 2, 2, 3, 4. Give the frequencies.
| Books | Frequency |
|---|---|
| 0 | 1 |
| 1 | 2 |
| 2 | 3 |
| 3 | 1 |
| 4 | 1 |
- Count each possible value: 0 appears once; 1 twice; 2 three times; 3 once; 4 once.
- Check the total: 1+2+3+1+1=8.
A suitable time graph
A thermometer is read at 9 am, 10 am, 11 am and noon. The temperatures are 16°C, 18°C, 21°C and 23°C. Choose a display.
- The times are ordered and the variable is measured temperature.
- Use time on the horizontal axis and temperature in °C on the vertical axis.
- Plot the four observations. Joining them shows overall change, not extra measured readings.
Check your understanding
The frequencies in a survey of 18 students add to 20. Is the table ready to graph?
Show answer
No.
Check the records because a count, category rule or stated total is inconsistent.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- Make a frequency table for 1, 2, 2, 3, 3, 3, 4, 4.2 marks
- Using the travel table, how many more students walk than travel by car?2 marks
Travel to school: teaching data for 20 students Method Frequency Walk 8 Bus 6 Cycle 4 Car 2 - Using the travel table, what fraction of the students cycle? Give a simplest fraction.2 marks
Travel to school: teaching data for 20 students Method Frequency Walk 8 Bus 6 Cycle 4 Car 2 - Choose a display for favourite school subjects: a bar graph or line graph. Explain.2 marks
- Frequencies are 5, 7, 3 and one missing frequency. There are 21 responses. Find the missing frequency.2 marks
- A student draws the “Cycle” bar twice as wide as the others. Why could this mislead?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Make a frequency table for 1, 2, 2, 3, 3, 3, 4, 4.2 marks
Count each score once.
The frequencies total 8.
1:1, 2:2, 3:3, 4:2. - Using the travel table, how many more students walk than travel by car?2 marks
Travel to school: teaching data for 20 students Method Frequency Walk 8 Bus 6 Cycle 4 Car 2 8−2=6.
6 students. - Using the travel table, what fraction of the students cycle? Give a simplest fraction.2 marks
Travel to school: teaching data for 20 students Method Frequency Walk 8 Bus 6 Cycle 4 Car 2 4 of 20 cycle.
4/20=1/5.
1/5. - Choose a display for favourite school subjects: a bar graph or line graph. Explain.2 marks
School subjects are categories, so separate bars compare their frequencies.
A bar graph. - Frequencies are 5, 7, 3 and one missing frequency. There are 21 responses. Find the missing frequency.2 marks
Known frequencies total 5+7+3=15.
21−15=6.
6. - A student draws the “Cycle” bar twice as wide as the others. Why could this mislead?2 marks
Use equal bar widths and compare heights on the same frequency scale.
Its extra area can make the category look more important than its frequency justifies.
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 ↗