Primary 5 · Mathematics · Statistics
Interpreting data displays
Collect categorical and numerical data, represent it in tables and graphs, and write statements comparing what the data shows.
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These lessons were written around Australian Curriculum strands and matched to Singapore levels by age (Primary 1 is the first year of primary school). They are not aligned to MOE syllabuses or the PSLE, so check them against the syllabus your child is working towards.
Learning goals
Learners will
- Tell the difference between categorical and numerical data.
- Represent data in tables, column graphs, dot plots and line graphs.
- Write statements that compare and describe what a data display shows.
Success looks like
- I can say whether data is categorical (words or groups) or numerical (numbers or measurements).
- I can choose a suitable graph and draw it with a title, labels and an even scale.
- I can write comparing statements such as “twice as many people chose…” using the data.
The big idea
Data comes in two main types. Categorical data puts things into groups, such as favourite fruit or type of pet. Numerical data is made of numbers that count or measure, such as the number of books read or the temperature.
The type of data helps us choose a display:
- A column graph suits categorical data, such as how many people chose each sport.
- A dot plot suits small sets of numerical data. Draw a number line and place a dot above each value. Stacks of dots show which values are most common.
- A line graph suits data that changes over time, such as the temperature each hour of a day.
Every good graph has a title, labelled axes and a scale that goes up in equal steps. If the scale counts in 2s, a column that stops halfway between 8 and 10 shows 9.
Reading a graph is only the start. We also interpret it by writing statements. Useful statements include: which category or value is most or least common, how much bigger one group is than another, the total, and any patterns or surprises.
Try to use comparing words: “6 more people chose swimming than tennis”, “twice as many people walked as rode a bike”, or “the temperature rose steadily from 7 am to 2 pm, then fell”.
Worked examples
Categorical or numerical?
Sort these survey questions into categorical or numerical data: “What is your favourite colour?”, “How many pets do you have?”, “What is your height in centimetres?”, “Which month were you born in?”
- Favourite colour gives words, so it is categorical.
- Number of pets is a count, so it is numerical.
- Height in centimetres is a measurement, so it is numerical.
- Month of birth puts people into 12 groups, so it is categorical.
Answer: Categorical: favourite colour, birth month. Numerical: number of pets, height.
Making a dot plot
Ten learners recorded how many books they read in a month: 2, 3, 3, 4, 4, 4, 5, 6, 6, 8. Draw a dot plot and describe it.
- Draw a number line from 0 to 8 (or 2 to 8) with equal gaps.
- Place one dot above the number for each value: 1 dot at 2, 2 dots at 3, 3 dots at 4, 1 dot at 5, 2 dots at 6 and 1 dot at 8.
- The tallest stack is above 4, so 4 books was the most common.
- The values go from 2 to 8, and most learners read between 3 and 6 books.
Answer: The most common number of books was 4. Results ranged from 2 to 8 books, with most between 3 and 6.
Interpreting a line graph
A line graph shows the temperature: 9 am 14 °C, 11 am 18 °C, 1 pm 22 °C, 3 pm 21 °C, 5 pm 17 °C. Describe what it shows.
- Find the highest point: 22 °C at 1 pm.
- Describe the trend: the temperature rose from 9 am to 1 pm, then fell.
- Compare: from 9 am to 1 pm the temperature rose by 22 − 14 = 8 degrees.
Answer: The day warmed up by 8 degrees to a high of 22 °C at 1 pm, then cooled down during the afternoon.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
Which of these is numerical data?
Number of siblings — Number of siblings is a count, so it is numerical. The others sort people into groups, so they are categorical.
Which of these is categorical data?
Favourite fruit — Favourite fruit sorts people into groups such as apple or banana. The others are numbers.
Books read in a month: Ava 6, Ben 9, Chloe 4, Dev 9, Eli 7. Who read the fewest books?
Chloe — Chloe read 4 books, which is fewer than everyone else.
Books read in a month: Ava 6, Ben 9, Chloe 4, Dev 9, Eli 7. How many books did they read altogether?
35 — 6 + 9 + 4 + 9 + 7 = 35 books.
Books read in a month: Ava 6, Ben 9, Chloe 4, Dev 9, Eli 7. How many more books did Ben read than Chloe?
5 — 9 − 4 = 5, so Ben read 5 more books than Chloe.
Which display is best for showing how the temperature changes during one day?
A line graph — A line graph shows how something changes over time, so it is best for temperatures through a day.
Here are the numbers of goals scored in 7 games: 3, 5, 5, 6, 7, 5, 2. Which number of goals appears most often?
5 — 5 appears three times, more than any other value.
The scale on a column graph goes up in 2s. A column stops exactly halfway between 8 and 10. What value does it show?
9 — Halfway between 8 and 10 is 9.
Watch out for
- Thinking that any data with numbers is numerical. Postcodes or jersey numbers are labels, not amounts, so they are really categorical. Ask “Does it make sense to add these numbers?”
- Reading a column graph as if every gridline is 1 when the scale counts by 2s, 5s or 10s. Always read the scale first.
- Writing statements that just repeat one number (“Ben read 9 books”). Encourage comparing statements that use more than one piece of data.
Tips for parents
- Look for graphs in newspapers, weather reports and sports results, and ask the learner what each one shows.
- Let the learner choose a question they are curious about, collect the data and decide how to display it.
- Ask “How do you know?” after each statement so the learner points to the evidence in the graph.
Go further
- Measure the temperature outside every two hours during one day and draw a line graph. Describe when it was warmest and coolest.
- Record the number of letters in the first 30 words of a book and draw a dot plot. Which word length is most common?
- Collect the same data from two groups (such as adults and children) and write five statements comparing them.
About 45 minutes
You'll need
- Grid paper, a ruler and a pencil
- Coloured pencils
- A thermometer (optional, for measuring temperature through a day)
- Family members or friends to survey
Key words
- Categorical data
- Data that sorts things into groups or categories, such as favourite sport or eye colour.
- Numerical data
- Data made up of numbers that count or measure, such as number of siblings or height in centimetres.
- Dot plot
- A graph that shows each piece of numerical data as a dot above a number line.
- Line graph
- A graph that uses points joined by lines to show how something changes over time.
- Scale
- The numbers along an axis of a graph, which must go up in equal steps.
Still tricky?
For parents
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