What you'll learn
Interpreting data means reading information that has already been collected and working out what it actually tells you — and, just as importantly, what it does not. This topic covers reading values from tables, comparing and totalling them, spotting the largest and smallest, drawing fair conclusions, and recognising a claim that the data does not support. Statistics is worth 6 of the 40 items on the SEA Mathematics paper. The arithmetic in these questions is usually easy; the marks are won and lost on careful reading, which is why this is one of the most improvable topics on the paper.
Key terms and definitions
Data — information that has been collected, such as rainfall figures or the number of pupils choosing each sport.
Category — one of the groups the data is divided into, such as a day of the week or a type of sport.
Frequency — how many times something happened, or how many chose a particular option.
Total — all the frequencies added together. For a survey where each person chose once, this is the number of people asked.
Difference — the result of subtracting one value from another, used for "how many more" questions.
Trend — the general direction the data moves in over time: rising, falling, or staying about the same.
Conclusion — a statement the data supports.
Sample — the group actually asked. A survey of one village is a sample of that village, not of the whole country.
Core concepts
Reading a value from a table
Find the right row, then the right column, then read where they meet. Say both out loud as you go — "Green, then Track" — because most reading errors are landing in the wrong row.
| House | Track | Field | Total |
|---|---|---|---|
| Red | 34 | 21 | 55 |
| Blue | 28 | 30 | 58 |
| Green | 41 | 16 | 57 |
| Yellow | 25 | 27 | 52 |
Green's track score is 41. Green's field score is 16. They sit in the same row but different columns, and mixing them up is the commonest slip.
Largest, smallest and totals
To find the largest or smallest, compare within a single column. Blue has the highest total at 58; Yellow has the lowest at 52.
To find an overall total, add carefully and look for pairs that make round numbers. Adding 28 + 32 + 25 + 35 is easier as (28 + 32) + (25 + 35) = 60 + 60 = 120.
"How many more" always means subtract
If Thursday had 18 sales and Wednesday had 9, then Thursday had 18 − 9 = 9 more. Adding the two gives 27, which answers no question at all but appears as a wrong option in almost every such item.
Reading across columns
The interesting questions ask you to combine columns. In the table above, Green scored the most on the track with 41 but did not win overall, because Blue's strong field score of 30 carried it to 58 against Green's 57. A pupil who reads only the track column gets the wrong winner.
Always check which column the question is about before comparing anything.
Trends over time
When data is given by day, month or year, look at the direction of travel.
Rainfall: January 80 mm, February 60 mm, March 120 mm, April 40 mm.
March was the wettest and April the driest. But it would be wrong to say rainfall increased every month — it fell in February, rose in March, then fell again. Picking out the single largest value is not the same as describing a trend, and questions are written to catch exactly that.
Drawing fair conclusions
A conclusion is fair only if the data actually supports it. Three tests are worth applying.
Does the data mention it at all? If a survey records how pupils travel to school, it says nothing about what they eat for lunch. No conclusion about lunch can be drawn, however reasonable it sounds.
Is "most" really most? If 20 of 50 pupils walk, then walking is the largest single group only if no other group is bigger — and 20 out of 50 is fewer than half, so "most pupils walk" is false. Half of 50 is 25, and 20 is below it.
Who was actually asked? A survey of 200 people in one village describes that village. Reporting it as the view of the whole country is unfair, because the sample came from one place. A large sample taken from a single place is still a sample of that place.
Misleading presentation
A chart can be accurate and still mislead. Bars of different widths make a small value catch the eye; a scale that does not go up in equal steps stretches some parts of the data more than others. A fair chart has equal bar widths, an evenly spaced scale, labelled axes and a clear title.
Worked examples
Example 1: Reading and comparing across columns
Using the house points table above, which house scored the most track points, and did that house win overall?
Compare the Track column only: 34, 28, 41, 25. The largest is 41, so Green scored the most on the track.
Now compare the Total column: 55, 58, 57, 52. The largest is 58, which belongs to Blue.
So Green won the track but did not win overall. Blue's field score of 30 was the highest in that column, and it was enough to take the overall lead by a single point.
Example 2: A two-step conclusion
A school has 240 pupils. 25% play cricket and 30% play football. The rest play neither. How many play neither?
Find each group. 25% of 240: a quarter of 240 is 60 pupils. 30% of 240: 10% is 24, so 30% is 72 pupils.
Together that is 60 + 72 = 132 pupils who play a sport.
So 240 − 132 = 108 pupils play neither.
The figure 132 is offered as a wrong option in questions like this, because it answers the opposite question.
Example 3: Judging whether a claim is fair
In a survey, 20 pupils out of 50 said they walk to school. A newspaper reports that "most pupils walk to school". Is this fair?
Half of 50 is 25, and only 20 pupils walk, so fewer than half walk. In fact 50 − 20 = 30 pupils do not walk, which is the larger group.
The claim is not fair. Written as a percentage, 20 out of 50 is 40%, which is clearly below half.
What the data does support is that 40% of the pupils surveyed walk — and only for the pupils actually asked, not for every school in the country.
Common mistakes and how to avoid them
Adding when the question says "how many more". Fix: how many more, how many fewer and difference all mean subtract.
Reading the wrong column. Giving a field score when the track score was wanted. Fix: say the row and the column out loud before writing the number down.
Assuming the leader in one column wins overall. Fix: check the column the question actually names, then check the total separately.
Treating one high value as a trend. Saying rainfall increased every month because March was wettest. Fix: read the figures in order and describe what happens between each pair.
Saying "most" when it is fewer than half. Fix: work out half the total first, then compare.
Drawing conclusions the data cannot support. Fix: ask whether the survey actually asked about that. If not, no conclusion is possible.
How parents can help at home
This topic rewards conversation more than calculation, and you can practise it with anything printed.
Read a table together. Sports results, a weather forecast, a price list, a league table. Ask three questions: which is biggest, how much bigger than the next one, and what is the total?
Ask "does that follow?" When your child states something from the data, ask whether the numbers really say that. "The team scored most goals — did they win the league?" Not necessarily, and working out why teaches more than the answer does.
Challenge the word "most". If your child says most people did something, ask what half the total would be. This one habit prevents a whole family of errors.
Notice misleading claims in the world. Advertisements and headlines are full of them. Asking "who did they ask?" about a claim on television is exactly the skill the exam tests, and it is useful long after the exam is over.
Exam technique for interpreting data and drawing conclusions
Underline the row and column named in the question before you look at the table. Almost every reading error is prevented by that one mark on the page.
For "how many more" questions, write the subtraction out. It costs a moment and stops the addition slipping in under time pressure.
On conclusion questions, test each option against the data one at a time. Reject any option about something the data did not measure, however sensible it sounds — that is usually the distractor.
In multi-step problems, label each figure as you go: "cricket = 60, football = 72, both = 132, neither = 108". The question is then answered by choosing the right label, not by re-doing the arithmetic.
Quick revision summary
- Find the row, then the column, then read where they meet.
- "How many more" and "how many fewer" always mean subtract.
- Compare within the column the question names — the leader in one column may not lead overall.
- For a total, look for pairs of values that make round numbers.
- A trend is the direction over time, not the single largest value.
- "Most" means more than half — work out half the total before using the word.
- A conclusion is only fair if the data measured that thing.
- A sample from one place describes that place, however large the sample is.
- A fair chart has equal bar widths, an even scale, labelled axes and a title.