Reading Data
Find the story hiding in numbers
Graphs, tables, and diagrams show you information visually. Your job is to extract the right numbers and calculate from there.
See It in Action
The Problem
A class of 30 students were surveyed. 18 play sport, 12 play an instrument, and 5 do both. How many do neither?
Common Mistake
18 + 12 = 30 students. So 0 do neither.
This double-counts the 5 students who do both (they've been counted in the 18 AND in the 12). The correct formula for two overlapping sets is: total in either = A + B − both.
Correct Approach
Students doing sport OR instrument = 18 + 12 − 5 = 25. (Subtract 5 to remove the double-count.) Students doing neither = 30 − 25 = 5.
Answer: 5 students do neither
Sport only: 13. Instrument only: 7. Both: 5. Neither: 5. Total: 13+7+5+5 = 30. ✓
The Core Concept
Data questions follow the same pattern every time: (1) read the title and axis labels, (2) identify exactly which values the question asks about, (3) extract those values carefully, (4) calculate. Most errors happen in steps 1 and 2 — rushing past the labels.
The most common data displays in NSW selective tests are: bar graphs, line graphs, two-way tables, timetables, Venn diagrams, and Carroll diagrams. Each shows the same kind of information differently. Know the vocabulary: "range" means highest minus lowest value (not the number of categories). In a Venn diagram, "only A" means inside circle A but not in the overlap region.
For two-way tables, row totals and column totals must all add up to the grand total. If a cell is missing, use the row or column total to find it by subtraction.
Common Mistakes to Avoid
Confusing "range" with "number of categories"
Range = highest value − lowest value. Not the count of items on an axis. In a data set {4, 7, 2, 9}, the range is 9 − 2 = 7.
Double-counting in Venn diagrams
Students in the overlap region belong to BOTH groups. When adding group sizes, subtract the overlap once: A + B − (A and B).
"Only A" vs "A" in Venn diagrams
"Students who play sport" includes those who also play instruments. "Students who only play sport" excludes those in the overlap. Read carefully.
Reading the wrong row or column in a table
Always trace the row label AND the column label before reading a value. Misreading the axis is very common under exam pressure.
Try It Yourself
A bar graph shows: Monday 15 books, Tuesday 22 books, Wednesday 18 books, Thursday 12 books. What is the range?
Hint: Range = highest − lowest. Find the biggest and smallest values first.
Key Tips
Before calculating, circle the two values the question is actually asking about.
For Venn diagrams: draw it out, fill in the overlap first, then work outward.
Remember: range = highest − lowest. It's always a subtraction, not a count.
Related Skills
Ready to practise Reading Data?
Reading is the start. The Maths Gym has exercises designed around this skill — with instant feedback and progress tracking.