Year 4 · Mathematics · Statistics
Data tables and graphs
Planning a survey, recording results in a tally table and showing them in a column graph or picture graph, then describing what the data shows.
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These lessons were written around Australian Curriculum strands and matched to UK year groups by age (Year 1 is the year a child turns 6 in England). They are not mapped to the National Curriculum in England or the curricula of Scotland, Wales or Northern Ireland, so check them against your own plans.
Learning goals
Learners will
- Plan a survey with a clear question and sensible choices.
- Record results in a tally table with a total for each choice.
- Show data in a column graph or picture graph and describe what it shows.
Success looks like
- I can write a survey question and plan who to ask.
- I can make a tally table and write the totals.
- I can draw a column graph with a title, labels and a scale, and write sentences about the results.
The big idea
A good survey starts with planning. Decide what you want to find out, write a clear question, choose 3 to 5 categories (including 'other' if needed) and decide who to ask. For example: 'How do you usually get to the park: walk, bike, car or bus?'
Record answers in a tally table. Draw three columns: the category, the tally marks and the total. Every fifth tally mark crosses the four before it, so the marks are easy to count in fives.
Count the tallies and write the total for each category. Add the totals to find how many people answered. This should match the number of people you asked — a useful check.
To draw a column graph, draw two axes. Write the categories along the horizontal axis and a scale up the vertical axis, starting at 0 and going up by the same amount each time (by 1s, or by 2s for bigger numbers). Draw a column for each category up to its total. Leave equal gaps between columns, and add a title and axis labels.
A picture graph uses a symbol for each answer, or sometimes one symbol for 2 answers. If a symbol stands for 2, a half symbol stands for 1. Always include a key that tells the reader what each symbol means.
Finally, describe the data. Good sentences compare categories: 'Walking was the most popular way, with 14 people.' 'Eight more people walked than rode a bike.' 'Twenty-six people answered.' Ask: what surprised you? What might the results be if you asked a different group?
- Plan the question and categories.
- Record with a tally table and totals.
- Show with a column or picture graph that has a title, labels and a scale.
- Describe the most, the least and the differences.
Worked examples
Totals in a tally table
Getting to the park: walk has two bundles of five and 4 lines, bike has one bundle and 1 line, car has 4 lines, bus has 2 lines. Find each total and the number of people surveyed.
- Walk: 5, 10, then 11, 12, 13, 14. Total 14.
- Bike: 5, then 6. Total 6.
- Car: 4. Bus: 2.
- Add the totals: 14 + 6 = 20, 20 + 4 = 24, 24 + 2 = 26.
Answer: Walk 14, bike 6, car 4, bus 2. 26 people were surveyed.
Drawing a column graph
Draw a column graph for walk 14, bike 6, car 4, bus 2.
- Title: 'How we get to the park'.
- Label the horizontal axis 'Way of travelling' and write the four categories.
- The biggest total is 14, so make the vertical scale go up in 2s from 0 to 14 and label it 'Number of people'.
- Draw each column up to its total: 14, 6, 4 and 2, with equal widths and gaps.
Answer: A labelled column graph with a scale in 2s and columns at 14, 6, 4 and 2.
Describing the data
Write two comparison sentences about walk 14, bike 6, car 4, bus 2.
- Find the most and least: walk is most (14), bus is least (2).
- Find a difference: walk 14 − bike 6 = 8.
Answer: Walking was the most popular and the bus was the least popular. Eight more people walked than rode a bike.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
A tally shows two bundles of five and 2 single lines. What is the total?
12 — Count the bundles by fives: 5, 10. Then count on 2: 11, 12.
Favourite sport totals: soccer 8, swimming 11, basketball 5, tennis 6. Which sport was most popular?
swimming — Swimming has the biggest total, 11.
Using the same totals (soccer 8, swimming 11, basketball 5, tennis 6), how many people were surveyed?
30 — 8 + 11 = 19, 19 + 5 = 24, 24 + 6 = 30.
Using the same totals (soccer 8, swimming 11, basketball 5, tennis 6), how many more people chose soccer than basketball?
3 — 8 − 5 = 3.
In a column graph, what does the height of each column show?
How many are in that category — Each column goes up to the total for its category, read from the scale.
A column graph's scale goes up in 2s. A column ends exactly halfway between 6 and 8. What number does it show?
7 — Halfway between 6 and 8 is 7.
In a picture graph, one ☺ stands for 2 people. How many people do ☺☺☺ show?
6 — Each symbol is 2 people: 2 + 2 + 2 = 6.
Which is the best survey question for making a tally table?
Which is your favourite fruit: apple, banana, orange or other? — It has clear categories that are easy to tally, plus 'other' for anyone whose favourite is not listed.
Watch out for
- Making a scale with uneven jumps (0, 1, 2, 5, 10). Show that each step on the scale must go up by the same amount.
- Forgetting the title, labels or key, so the reader cannot tell what the graph shows. Use a checklist before calling the graph finished.
- Reading a picture graph by counting symbols when each symbol stands for more than one. Always read the key first.
Tips for parents
- Let your child choose a real question to investigate — they will care more about the results.
- Check that the total of the tally table matches the number of people asked.
- Ask open questions about the graph: 'What does it tell us? What surprised you? What would you ask next?'
Go further
- Run the same survey with two groups (such as adults and children) and draw both results on one graph to compare.
- Keep a tally of the weather each day for two weeks and make a column graph at the end.
- Make a picture graph where one symbol stands for 2 votes, including half symbols for odd numbers.
About 40 minutes
You'll need
- Grid paper or a ruler and plain paper
- Pencils and coloured pencils
- A clipboard or notebook for recording
- A list of people to survey (family, friends, a sports team or club)
Key words
- survey
- A way of collecting data by asking people the same question.
- tally table
- A table that records data with tally marks and shows the total for each category.
- category
- One of the groups or choices in a set of data.
- column graph
- A graph that uses columns of different heights to show how many are in each category.
- axis
- A line along the side or bottom of a graph with labels or numbers.
- scale
- The numbers along an axis, which go up by the same amount each time.
Still tricky?
For parents
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