"Data Interpretation" — Practice

Question 1

A district education officer, wanting fresh data on mid-day meal attendance, sends field staff to personally record attendance at 50 schools over one week. This data is:
(a) Primary data  (b) Secondary data  (c) Qualitative data only  (d) An index number

Accepted Answer

The data is collected firsthand, by the officer's own staff, specifically for this attendance study — the defining feature of primary data.

Answer: (a) Primary data. Trap (b) would apply only if the officer instead reused attendance figures already published for some other purpose. Trap (c) is wrong because attendance counts are numerical, making this quantitative, not qualitative, data. Trap (d) misapplies an unrelated statistical concept (an index number measures relative change over a base period) to a plain data-collection scenario.

Question 2

Which of the following is an example of qualitative data collected in an educational survey?
(a) Number of students enrolled in a college  (b) Average attendance percentage of a class  (c) Students' self-reported satisfaction rated as 'poor', 'average', or 'good'  (d) Total marks scored by a student in an examination

Accepted Answer

Qualitative data is categorical or descriptive rather than a natural quantity. A satisfaction rating recorded as a category label ('poor'/'average'/'good') is qualitative, even though it can later be coded numerically for analysis.

Answer: (c) Students' self-reported satisfaction. Trap (a), trap (b), and trap (d) are all inherently numerical counts or measurements — enrolment numbers, a percentage, and a total mark — making all three quantitative data.

Question 3

Which of the following is an example of continuous data?
(a) Number of research papers published by a department in a year  (b) Number of students who cleared an examination  (c) Number of colleges affiliated to a university  (d) Time taken by a student to complete an examination paper

Accepted Answer

Time can take any value within a range, including fractional values (such as 92.5 minutes), which is the defining feature of continuous data.

Answer: (d) Time taken to complete an examination paper. Trap (a), trap (b), and trap (c) are all counts that take only whole-number values with no meaningful in-between value, making all three discrete data, not continuous.

Question 4

In the standard format of a statistical table, the row headings that describe what each row of the table records are called the:
(a) Caption  (b) Stub  (c) Body  (d) Footnote

Accepted Answer

The stub is the specific term for a table's row headings; the corresponding term for column headings is the caption.

Answer: (b) Stub. Trap (a) names the column headings, not the row headings, the reverse of what the question asks. Trap (c) names the numerical data itself, not any heading. Trap (d) names the clarifying note on units or source, unrelated to headings altogether.

Question 5

A survey records the number of students enrolled in five unrelated undergraduate programmes (B.A., B.Sc., B.Com., B.Ed., BBA) at a college. The most appropriate chart to represent this data is a:
(a) Bar diagram  (b) Histogram  (c) Ogive  (d) Frequency polygon

Accepted Answer

The five programmes are discrete, unrelated categories, not a continuous frequency distribution over class intervals — exactly the situation a bar diagram, drawn with gaps between bars, is designed for.

Answer: (a) Bar diagram. Trap (b) would only be correct if the categories were continuous class intervals rather than unrelated named programmes. Trap (c) and trap (d) are both tools for a continuous frequency distribution's cumulative or shape-based reading, neither of which applies to five unrelated categories.

Question 6

To visually compare the shape of the marks distributions of two different sections of a class on the same set of axes, without the clutter of overlapping bars, the appropriate chart is a:
(a) Pie chart  (b) Ogive  (c) Bar diagram  (d) Frequency polygon

Accepted Answer

A frequency polygon, formed by joining the midpoints of histogram bar-tops with straight lines, is specifically suited to overlaying two or more frequency distributions on shared axes for a direct shape comparison.

Answer: (d) Frequency polygon. Trap (b) names a related but distinct tool that plots cumulative, not plain, frequency, and is used to locate the median rather than compare distribution shapes. Trap (a) and trap (c) are chart types unrelated to overlaying continuous frequency distributions at all.

Question 7

A pie chart shows a university's annual research budget of ₹80 crore. The 'Equipment' sector has a central angle of 90°. The amount allocated to Equipment is:
(a) ₹15 crore  (b) ₹18 crore  (c) ₹20 crore  (d) ₹24 crore

Accepted Answer

Convert the angle to a percentage share first: 90°/360° = 25%. Applying that share to the total: 25% × ₹80 crore = ₹20 crore.

Answer: (c) ₹20 crore. Trap (a), trap (b), and trap (d) all result from either misconverting the angle to a percentage or applying the correct percentage to the wrong total.

Question 8

A university's library budget share fell from 12% in a 2022 pie chart to 10% in a 2023 pie chart. If the university's total annual budget rose from ₹50 crore in 2022 to ₹80 crore in 2023, the actual library budget:
(a) Fell, since the percentage share fell  (b) Rose, from ₹6 crore to ₹8 crore  (c) Stayed exactly the same in absolute terms  (d) Cannot be determined without knowing the number of sectors in each pie

Accepted Answer

Convert each year's share to an actual value using that year's own total: 12% of ₹50 crore = ₹6 crore in 2022, and 10% of ₹80 crore = ₹8 crore in 2023. The rupee amount rose even though the percentage share fell, because the total budget itself grew.

Answer: (b). Trap (a) is the classic two-pie-chart error — reading a falling percentage share as a falling actual value without checking whether the total changed. Trap (c) is simply the wrong arithmetic result. Trap (d) invents an irrelevant condition; the number of sectors in each pie has no bearing on this calculation.

Question 9

The table below shows student enrolment (in hundreds) in four affiliated colleges of a state university from 2021 to 2024:
College A: 12, 14, 15, 18
College B: 20, 19, 22, 21
College C: 8, 10, 13, 14
College D: 16, 18, 17, 20

The total enrolment (actual number of students, not in hundreds) across all four colleges in 2023 is:
(a) 6,100  (b) 6,400  (c) 6,600  (d) 6,700

Accepted Answer

Reading the 2023 column (the third figure in each list): College A = 15, College B = 22, College C = 13, College D = 17. Sum = 15+22+13+17 = 67, and since figures are in hundreds, the actual total is 67 × 100 = 6,700.

Answer: (d) 6,700. Trap (a), trap (b), and trap (c) all result from misreading a column, adding the wrong year's figures, or an arithmetic slip in the addition.

Question 10

Using the same enrolment table, the percentage increase in College C's enrolment from 2021 to 2024 is:
(a) 75%  (b) 60%  (c) 50%  (d) 80%

Accepted Answer

College C's enrolment rose from 8 (2021) to 14 (2024). % increase = [(14−8)/8] × 100 = (6/8) × 100 = 75%.

Answer: (a) 75%. Trap (b), trap (c), and trap (d) all result from dividing the increase by the wrong base value or a simple arithmetic slip.

Question 11

Using the same enrolment table, which college recorded the highest percentage growth in enrolment from 2021 to 2024 (not the highest absolute increase)?
(a) College A  (b) College C  (c) College B  (d) College D

Accepted Answer

Computing each college's own percentage change on its own 2021 base: College A rose from 12 to 18 (+50%), College B from 20 to 21 (+5%), College C from 8 to 14 (+75%), College D from 16 to 20 (+25%). College C has the highest percentage growth, even though College B has larger raw enrolment throughout.

Answer: (b) College C. Trap (c) (College B) has the smallest percentage growth of all four despite being the largest college by raw numbers — exactly the base-size trap this unit repeatedly tests. Trap (a) and trap (d) both post real but smaller percentage gains than College C.

Question 12

Using the same enrolment table, the ratio of College B's enrolment to College D's enrolment in 2024 is:
(a) 19:18  (b) 22:17  (c) 21:20  (d) 20:21

Accepted Answer

In 2024, College B's enrolment is 21 and College D's enrolment is 20, giving the ratio 21:20.

Answer: (c) 21:20. Trap (a) and trap (b) both use figures from the wrong year (2021 or 2023) instead of 2024. Trap (d) inverts the correct ratio, swapping which college comes first.

Practice — "Data Interpretation"

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