Unit 7
Data and Percentage
About this unit
Read and interpret tables, bar charts, pie charts, and surveys — then use the data to calculate percentages, make comparisons, and answer multi-step numerical questions. This unit covers everything from reading a simple graph to computing layered percentage breakdowns.
What types of questions will you face?
- 1Calculate the percentage of a group from a bar or pie chart
- 2Compute the overall percentage when different-sized groups have different rates
- 3Find the "most improved" student or item using a ranked comparison table
- 4Determine a minimum score needed to guarantee winning a competition given partial results
- 5Read multi-column survey data and perform arithmetic across groups to find totals or percentages
Skills you will build
- Reading and extracting data accurately from tables, bar charts, and sector graphs
- Calculating percentages from fractions and whole numbers
- Combining percentages from groups of different sizes (weighted averages)
- Applying arithmetic and comparison logic to ranked data
- Performing multi-step calculations without a calculator
By the end of this unit, you will be able to
- Accurately extract numerical data from any graph or table format
- Calculate percentages across different group sizes without confusion
- Solve "minimum score needed" type competition problems by working backwards
- Interpret data to draw valid conclusions and avoid misleading readings
Difficulty profile
Easy difficulty (avg 2.46). Most questions are straightforward percentage and reading problems. The harder questions involve combining data from multiple-sized groups.
Exam tip: Data and Percentage
For percentage of a combined group: always multiply the proportion by the GROUP SIZE before adding. Never average percentages directly — a group of 1,000 at 50% contributes far more than a group of 10 at 90%.
Sample Questions
Data and table questions form a significant part of OC Thinking Skills, and the easiest ones simply reward careful, methodical reading — no complex formulas required, just a clear two-step process.
Ranking from a table with a specific selection rule (e.g. "take the better of two attempts") appears regularly in OC TS as an entry-level data question. The most common mistake is reading one row incorrectly and getting the entire ranking wrong as a result.
The examiner is testing whether you can correctly apply a selection rule to every row in a table, extract all the relevant values, and then rank them accurately — without mixing up the selection step and the ranking step.
A table of numerical results is given with a stated rule (e.g. "faster time counts"). You must apply that rule to every row, then order the extracted values from best to worst. The question asks for a specific placing — 1st, 2nd, or last.
Best approach: Do this in two clean passes. First pass: go through every row and write down the single selected value (the faster time, the higher score, etc.). Second pass: rank those extracted values. Never try to rank while simultaneously extracting — separating the two steps eliminates almost all errors.
Question
Eight swimmers each get two attempts at 50 m; the faster time counts as their result.
| Swimmer | Attempt 1 (s) | Attempt 2 (s) |
|---|---|---|
| 1 | 31.4 | 30.2 |
| 2 | 29.8 | 31.5 |
| 3 | 32.1 | 30.7 |
| 4 | 30.5 | 31.0 |
| 5 | 29.5 | 30.8 |
| 6 | 30.9 | 31.4 |
| 7 | 31.8 | 29.6 |
| 8 | 30.3 | 30.1 |
Who finishes 2nd (silver medal)?
- ASwimmer 2
- BSwimmer 5
- CSwimmer 7
- DSwimmer 8
Decided on your answer? Check how you went below.
Two tables, one prize. The trap in this question is that the Year 10 table is sorted by final score — so the student at the top looks like the obvious winner. But the prize is for biggest IMPROVEMENT, not highest score. Always re-read the rule before looking at the data, or you will answer a completely different question to the one being asked.
Two-table comparison questions where you must compute a derived value (difference, ratio, percentage change) appear regularly in OC TS data questions. The examiner always sorts or presents one table in a way that tempts you to pick the wrong answer — highest score, most recent result, etc. — instead of applying the actual stated rule.
The examiner is checking two things: (1) that you read and apply the correct rule (biggest improvement, not highest score), and (2) that you perform the subtraction for EVERY student before comparing — not just the ones who appear most impressive at a glance.
Two tables of the same group of people across two time points are given. A selection rule is stated (e.g. "biggest improvement", "highest percentage increase"). You must compute the relevant value for each person, rank them, and identify the winner. The order of one table will be misleading.
Best approach: Make a third column in your working. Write each student's name, then Year 9 mark, then Year 10 mark, then calculate the difference (Year 10 minus Year 9) for each one. Rank those differences — the largest positive difference is the winner. Never try to eyeball the improvement from two separate tables; always write the subtraction out for every student.
Question
At a school, exams are held at the end of each year. A prize is awarded in each subject to the student who has made the biggest improvement in his/her exam mark since the previous year. In Year 9, the marks achieved by the six students in the Mathematics class were as follows:
| Student | Year 9 mark |
|---|---|
| Uma | 84 |
| Finn | 82 |
| Lily | 75 |
| Arlo | 73 |
| Leon | 73 |
| Sophie | 69 |
At the end of Year 10, their marks were as follows:
| Student | Year 10 mark |
|---|---|
| Finn | 88 |
| Lily | 86 |
| Uma | 79 |
| Arlo | 78 |
| Sophie | 78 |
| Leon | 73 |
Which student won the Year 10 prize for Mathematics?
- AFinn
- BLily
- CUma
- DSophie
Decided on your answer? Check how you went below.
Now for the most demanding variant in this unit — a multi-layer calculation where you must work through five separate steps before reaching the final answer. One wrong step early on cascades into an incorrect total at the end.
Multi-step data questions combining group counts, different ratios, and secondary percentage applications are a fixture in the harder third of every OC TS test. The answer choices are almost always the results of stopping after the wrong step.
The examiner is testing whether you can calculate a missing group size, apply different ratios to different groups, find a secondary total, apply two different percentages to two different bases, and add only the right things together — without confusing the sub-totals along the way.
A population is split across several groups, each with a different checkout or participation rate. One group's size must be inferred from the "remaining" total. You then apply one percentage to the checking-out group and a different percentage to the non-checking-out group, and combine both figures.
Best approach: Work in a structured column format. Column 1: group size. Column 2: checkouts (apply each ratio). Foot of column 2: total checkouts. Non-checkouts = total − checkouts. Then apply the two percentages separately and add only at the very last line. The wrong-answer options are always the result of stopping one step too early.
Question
A school library recorded checkouts for 3,600 students across four year groups.
- Year 3 had 800 students, and 400 of them checked out a book.
- Year 4 had 1,000 students, and 3 out of every 5 checked out a book.
- Year 5 had 600 students, and 1 out of every 4 checked out a book.
- Year 6 had the remaining students, and 7 out of every 8 checked out a book.
If 50% of students who checked out a book preferred fiction and 40% of students who did NOT check out a book preferred audiobooks, how many students were in these two categories combined?
How many students were in these two categories combined?
- A1 100
- B1 400
- C1 660
- D2 200
Decided on your answer? Check how you went below.
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