Scholarship Results Across Four Centres: Reading a Two-Year Table
A coaching chain tabulates results for a scholarship test held in 2019 and again in 2023. For each centre the table gives the number of students who actually appeared for the test and, among them, the number who qualified for a fee waiver. Total enrolment across the four centres rose from 1,940 in 2019 to 2,090 in 2023, with the sharpest rise at the newly opened East centre. Conversion from enrolment to appearance was roughly stable in every centre over the period. The board will review the table at its annual meeting and has asked for a one-page note that is defensible line by line.
| Centre | Appeared 2019 | Qualified 2019 | Appeared 2023 | Qualified 2023 |
|---|---|---|---|---|
| North | 384 | 96 | 510 | 153 |
| South | 512 | 64 | 476 | 119 |
| East | 240 | 48 | 405 | 90 |
| West | 442 | 78 | 408 | 102 |
The regional head writes in her review: "Since overall enrolment has fallen, our results have clearly deteriorated; we must therefore be doing something wrong on the academic side." The academic coordinator disputes both halves of that sentence.
1. Compute the qualification rate (qualified ÷ appeared) for every centre in both years and identify which centre improved by the largest number of percentage points.
Read the worked answer
| Centre | 2019 rate | 2023 rate | Change |
|---|---|---|---|
| North | 96/384 = 25.00% | 153/510 = 30.00% | +5.00 pp |
| South | 64/512 = 12.50% | 119/476 = 25.00% | +12.50 pp |
| East | 48/240 = 20.00% | 90/405 = 22.22% | +2.22 pp |
| West | 78/442 = 17.65% | 102/408 = 25.00% | +7.35 pp |
South improved the most, by 12.5 percentage points - it doubled its rate, even though the number of candidates appearing there actually fell from 512 to 476. Note that a percentage-point change and a percentage change are different: South's rate rose by 12.5 pp but by 100% in relative terms. Only the pp measure ranks the centres correctly here, because all four start from different bases.
2. By what percentage did the total number of qualified students change between 2019 and 2023? Which centre contributed the largest share of the 2023 total?
Read the worked answer
Totals
- Qualified 2019 = 96 + 64 + 48 + 78 = 286.
- Qualified 2023 = 153 + 119 + 90 + 102 = 464.
- Absolute increase = 178.
- Percentage increase = 178/286 × 100 = ≈ 62.2%.
Share of the 2023 total
- North 153/464 = 32.97%
- South 119/464 = 25.65%
- East 90/464 = 19.40%
- West 102/464 = 21.98%
North contributed the largest single share, about 33%. But note that North also appeared with the largest 2023 cohort (510), so a share-of-total argument flatters big centres; the rate table from the previous task is the fairer basis for judging teaching quality.
3. Evaluate the regional head's statement using the table and the enrolment figures. Is the academic coordinator right to dispute both halves of it?
Read the worked answer
First half - "overall enrolment has fallen": false. Enrolment went from 1,940 to 2,090, a rise of 150 students, i.e. +7.73%. The head has the direction of the change backwards.
Second half - "results have clearly deteriorated": also unsupported. Qualified numbers rose from 286 to 464 (+62.2%), and every single centre improved its qualification rate (North +5 pp, South +12.5 pp, East +2.22 pp, West +7.35 pp). Not one centre shows a decline.
So the coordinator is right on both counts. Two caveats worth putting in the note, because a good answer states the limits of its own evidence:
- The rates are computed on appeared, not enrolled students. Since we are told enrolment-to-appearance conversion was roughly stable, this is not fatal - but per-centre enrolment for 2023 is not in the table, so no centre-level claim about enrolment can be made.
- South's improvement rests on a shrinking base of candidates; sustaining a 25% rate as numbers recover is the open question, not a settled achievement.