GATE Electrical 2025 | GA | Question: 8

Question

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?

$$\begin{array}{|c|c|c|c|c|c|c|c|} \hline \textbf{P} & 22 & 89 & 50 & 45 & 78 & 60 & 39 \\
\hline \textbf{Q} & 35 & 65 & 60 & 56 & 81 & 45 & 50 \\ \hline \end{array}$$

• 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 1

$\text{Average}_P = \frac{22 + 89 + 50 + 45 + 78 + 60 + 39}{7} = \frac{383}{7} = 54.71$

$\text{Average}_Q = \frac{35 + 65 + 60 + 56 + 81 + 45 + 50}{7} = \frac{392}{7} = 56$

A the average score of P is less than Q, which is correct 54.71 < 56

list the scores for P and Q in ascending order:

P: 22, 39, 45, 50, 60, 78, 89

Q: 35, 45, 50, 56, 60, 65, 81

Since there are 7 scores, the median is the 4th value in the ordered list.
Median_P = 50
Median_Q = 56

B the median score of P is the same as Q, which is incorrect 50 !=56.

Range_P = 89 - 22 = 67
Range_Q = 81 - 35 = 46
C the range of P is greater than Q, which is correct 67 > 46.

 

D the median score and the average score of Q are the same, which is correct 56 = 56.

Answer:
(B) Median score of P is same as the median score of Q.