Frequency tables and appropriate displays | Year 11

01 / LEARN

The idea, step by step

Preserve counts

Frequencies count observations and must sum to the valid sample size. Relative frequency divides by that total; multiply by 100 for a percentage. State whether missing answers are excluded.

Numerical class intervals must not overlap. With $10 \leq t < 20$ , a time of 20 belongs to the next interval, not both.

Match the graph to the data

Separated bars compare categories. Adjacent histogram intervals represent grouped numerical data; use equal widths when heights are directly interpreted as frequencies. Dot plots retain individual small-sample values, while box plots summarise centre and spread.

A line graph suits observations ordered through time, not unrelated category labels. Supply variable names, units and an honest scale. A bar chart normally begins at zero.

Travel method for 25 students
Method	Walk	Cycle	Bus	Car
Frequency	6	4	10	5

A common trap

Histograms and bar charts are interchangeable.

Instead: A histogram represents numerical intervals, not category labels.

02 / WORKED EXAMPLES

See the thinking

Example 1

Relative frequency

Ten of 25 students use a bus. Find relative frequency and percentage.

$10 / 25 = 0.4$ .
$0.4 \times 100 = 40 %$ .

0.4, or 40%.

Example 2

Boundary values

Group 8, 10, 19, 20, 28 into $0 \leq t < 10$ , $10 \leq t < 20$ , $20 \leq t < 30$ .

8 enters the first interval.
10 and 19 enter the second; 20 and 28 the third.

Frequencies 1, 2, 2.

Check your understanding

Counts are 7, 12, 6. What is the total?

Show answer

25.

Add all valid frequencies.

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Counts are 6, 4, 10, 5. Find total and the third category’s percentage.
2 marks
Choose a display for favourite music genre.
2 marks
Choose a display for hourly temperature during one day.
2 marks
Group 3, 7, 10, 14, 19, 20 into intervals [0, 10), [10, 20), [20, 30).
2 marks
Why can starting a bar axis at 90 exaggerate differences?
2 marks
There are 18 valid and 2 missing replies. Nine valid replies choose A. Find A’s percentage among valid replies.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Counts are 6, 4, 10, 5. Find total and the third category’s percentage.
2 marks
Total 25; $10 / 25 \times 100 = 40 %$ .
25; 40%.
Choose a display for favourite music genre.
2 marks
The variable is categorical.
A bar chart.
Choose a display for hourly temperature during one day.
2 marks
Time is ordered and change is meaningful.
A time-series line graph.
Group 3, 7, 10, 14, 19, 20 into intervals [0, 10), [10, 20), [20, 30).
2 marks
Boundary values enter intervals starting there.
2, 3, 1.
Why can starting a bar axis at 90 exaggerate differences?
2 marks
Small numerical differences can appear proportionally huge.
Bar lengths omit most of the values below 90.
There are 18 valid and 2 missing replies. Nine valid replies choose A. Find A’s percentage among valid replies.
2 marks
$9 / 18 \times 100 = 50 %$ .
50%.

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Shape, centre and spread

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Curriculum reference & lesson scope

SACE Board of South Australia

Stage 1 General Mathematics: statistical investigation, univariate data, sampling, displays, summaries and interpretation.

Official curriculum source ↗

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