Percentage Points or Per Cent? Fixing a Data-Interpretation Item
A B.Ed trainee at a coaching institute in Meerut is building data-interpretation items for a mock test. The table he has typed out gives pass percentages for two schools: School X - 2021: 20 per cent, 2022: 30 per cent; School Y - 2021: 60 per cent, 2022: 72 per cent. His draft question reads, 'Which school improved more between 2021 and 2022?' and the key marks School Y, because 12 percentage points is more than 10. In the trial, 14 of 30 students chose School X, calculating a 50 per cent rise for X against 20 per cent for Y. The institute's mock papers instruct candidates to 'choose the most appropriate option' and use four options with no negative marking. Three other DI items in the set already use the phrase 'percentage points'. The table has no column for the number of students who appeared. The paper goes to press in 90 minutes.
1. Diagnose the dispute. Which answer is correct, and why is the item defective?
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Both calculations are arithmetically correct but answer different questions. In percentage points: X rises from 20 to 30, a gain of 10; Y rises from 60 to 72, a gain of 12 - so Y. In relative terms: X gains 10/20 = 50 per cent; Y gains 12/60 = 20 per cent - so X.
The stem says only 'improved more'. For a percentage-valued variable the default reading in most papers is percentage points, which supports the key, but a candidate cannot be required to guess a convention the stem does not state. As written the item rewards guessing, not data handling, and would penalise the 14 students for correct relative-change reasoning.
Decision: the key is defensible only after the stem is fixed. Do not change the students' answers to fit it; change the wording so that only one computation is asked for.
2. Rewrite the stem as two unambiguous items and give the option set for each, with the reasoning behind the distractors.
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Version A (absolute): 'By how many percentage points did the pass percentage of School Y rise from 2021 to 2022?' Options: 8, 10, 12, 20 - key 12. Distractors: 20 is Y's 2022 value; 10 is X's gain, caught by a reader who does not check which school is asked about; 8 is a subtraction slip.
Version B (relative): 'The pass percentage of School X rose by what per cent from 2021 to 2022?' Options: 10, 15, 33.3, 50 - key 50. Distractors: 10 is the percentage-point gain (unit confusion); 33.3 comes from 10/30, using the later year as base; 15 is a pure arithmetic slip.
Rule for the remaining items in the set: every DI stem must carry its unit - 'percentage points', 'per cent', or 'students'. A stem using 'more' or 'faster' without a unit is an item defect, not a hard question.
3. A student asks why the number of students who appeared is missing. Explain what can and cannot be computed, and what one extra column would enable.
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With rates alone you can compute changes in rates - differences and relative changes - but nothing about counts. Sixty per cent of 200 students is 120 passes; 30 per cent of 2,000 is 600, so the school with the lower rate can produce far more successful students. Any claim about how many students improved, or which school helped more students, needs the base.
Adding one column, 'students appeared', enables: pass counts (rate x appeared), a combined pass rate for the two schools, and weighted comparisons. Adding 'students passed' instead would let the count be recovered, but it is redundant with the rate and creates a second chance for inconsistency between columns.
Teaching point for the student: percentage data hides base size, so a DI item that intends a count question must print the base - otherwise the correct answer is 'cannot be determined', which is a legitimate option that candidates often ignore.