GATE 2025 EE GA Q.8: solution and answer

GATE 2025 · EEGA Q.8 · 2 marks · MCQ

Scores obtained by two students P and Q in seven courses are given in the table below. Based on the information given in the table, which one of the following statements is INCORRECT?

| P | 22 | 89 | 50 | 45 | 78 | 60 | 39 |
|---|---|---|---|---|---|---|---|
| Q | 35 | 65 | 60 | 56 | 81 | 45 | 50 |

GATE 2025 EE GA question 8: A table with two rows and eight columns, with no header row. — Figure from the GATE 2025 EE paper. It is part of the question.

(A)
Average score of P is less than the average score of Q.
(B)
Median score of P is same as the median score of Q.
(C)
Difference between the maximum and minimum scores of P is greater than the difference between the maximum and minimum scores of Q.
(D)
Median score and the average score of Q are same.

Answer and solution

ANSWER

(B) is the INCORRECT statement. The median of P is 50 and the median of Q is 56, so they are not the same. The other three statements hold: mean of P is about 54.71, which is less than the mean of Q (56); the range of P is 67, which is greater than the range of Q (46); and the median and mean of Q are both 56.

Official answer: BSource: Official answer key, GATE 2025 EE (IIT Roorkee)

Mean = sum of observations $\div$ number of observations. Sum for P: $22 + 89 + 50 + 45 + 78 + 60 + 39 = 383$ , so $\overset{ˉ}{P} = \frac{383}{7} \approx 54.71$ .
Sum for Q: $35 + 65 + 60 + 56 + 81 + 45 + 50 = 392$ , so $\overset{ˉ}{Q} = \frac{392}{7} = 56$ . Since $54.71 < 56$ , statement (A) is correct. (Both students have 7 scores, so comparing the sums $383 < 392$ gives the same result.)
Median of an odd number $n$ of values: the $(\frac{n + 1}{2})$ th value after sorting. With $n = 7$ , that is the 4th value.
P sorted: $22, 39, 45, 50, 60, 78, 89$ , so the median of P is $50$ .
Q sorted: $35, 45, 50, 56, 60, 65, 81$ , so the median of Q is $56$ . Since $50 \neq = 56$ , statement (B) is INCORRECT.
Range = maximum $-$ minimum. P: $89 - 22 = 67$ ; Q: $81 - 35 = 46$ . Since $67 > 46$ , statement (C) is correct.
For Q, median $= 56$ and mean $= 56$ , so statement (D) is correct.
The only incorrect statement is (B).

KEY IDEA

Sort each row before you read off the median. With 7 values, the median is the 4th value in sorted order. The mean is the sum divided by 7, and because both students have the same number of scores you can compare their means by comparing their sums. The difference between the maximum and minimum is the range.

WATCH OUT FOR

Reading the median from the unsorted table. The 4th column shows 45 for P and 56 for Q, and some students take those as the medians. The sorted median of P is actually 50. A second trap is marking the one statement you have checked and found true, even though the question asks for the INCORRECT one.

From the GATE 2025 EE paper. Every question of this paper · Download the full paper · All 7 Statistics & probability questions, with notes

GATE 2025 EE GA Q.8: solution and answer

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