Mathematics K–6 · Years 3–4

From survey to column graph: a statistical investigation

Statistics and probability

PracticalLow risk

The idea

A question is answered by collecting data with a method that everyone follows, recording it in a frequency table and drawing a graph whose scale suits the numbers.

What you need

a survey sheet with one question and four to six categories (for example how many people live in your home, or which sport you play)
a frequency table and 1 cm grid paper
a spreadsheet on a tablet or computer (optional)
sticky dots for a dot plot

How to do it

Agree the question and the categories before asking anyone. Decide who will be asked and record every answer once on the survey sheet.
Transfer the answers to a frequency table with a tally column and a total column. Check the total equals the number of people asked.
Draw a column graph on the grid paper with a scale of one square per person, then redraw it with one square per two people and compare how the columns look.
Make a dot plot of the same data with sticky dots and a pictograph where one picture stands for two people.
Write three statements the data supports (the most common answer, a comparison of two categories, the total) and one question the data cannot answer.

What you should see

The frequency totals add up to the number of people surveyed. On a scale of one square per two people, an odd count such as 11 is shown as five and a half squares and five and a half pictures, so a half symbol is needed. The column graph, dot plot and pictograph all show the same tallest category and the same order. A statement such as most children in the class play soccer is supported only if the soccer count is more than half the total.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

A column graph with a bigger scale shows more people.
The tallest column always means more than half the group chose it.

Safety card

Low riskLearners carry it out

Hazards

none beyond ordinary classroom materials

Controls

keep survey answers to the agreed question; no names recorded

Note

No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA2-DATA-01 MA2-DATA-02 MAO-WM-01
Australian Curriculum v9AC9M3ST01AC9M3ST02AC9M3ST03AC9M4ST01

Sources

The pages the author read to write this activity.

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