GATE 2020 IN GA Q.10: solution and answer

GATE 2020 · INGA Q.10 · 2 marks · MCQ

The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q, R and S. The average of success rates (in percentage) of these four schools is ______.

GATE 2020 IN GA question 10: Grouped (clustered) vertical bar chart titled "Performance of Schools P, Q, R and S". — Figure from the GATE 2020 IN paper. It is part of the question.

(A)
58.5 %
(B)
58.8 %
(C)
59.0 %
(D)
59.3 %

Answer and solution

ANSWER

The average of the four schools' success rates is 59.0 %. The answer is (C).

Official answer: CSource: Official answer key, GATE 2020 IN (IIT Delhi)

Read the chart: School P, 500 appeared and 280 passed. School Q, 600 and 330. School R, 700 and 455. School S, 400 and 240.
A school's success rate is $\frac{passed}{appeared} \times 100$ . For P: $\frac{280}{500} \times 100 = 56%$ .
For Q: $\frac{330}{600} \times 100 = 55%$ .
For R: $\frac{455}{700} \times 100 = 65%$ .
For S: $\frac{240}{400} \times 100 = 60%$ .
The question asks for the average of the four success rates, so take the arithmetic mean of the four percentages, with each school counted once: $\frac{56 + 55 + 65 + 60}{4} = \frac{236}{4} = 59.0%$
This is option (C).

KEY IDEA

"Average of success rates" means the simple mean of each school's own rate (passed / appeared x 100), with every school weighted equally. It is not the success rate of all four schools pooled together.

WATCH OUT FOR

Pooling the totals: total passed / total appeared = $\frac{1305}{2200} \times 100 \approx 59.3%$ . That gives option (D), a distractor. Pooling weights each school by how many students it has, so the large School R (65 %) pulls the figure up. The question asks for the average of the four rates.

From the GATE 2020 IN paper. Every question of this paper · Download the full paper · All 9 Data interpretation questions, with notes

GATE 2020 IN GA Q.10: solution and answer

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