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? 

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

Hint:

To find the median of an odd-sized dataset, sort the data and pick the middle value. Always compare values carefully—especially medians vs. averages—as they can be equal or different depending on distribution.

Answer 1

The Correct Option is B

First, sort the scores for both students:


So, the medians are not the same, making option (2) incorrect.

Let us verify the other options:
Average of P:
\[ \frac{22 + 89 + 50 + 45 + 78 + 60 + 39}{7} = \frac{383}{7} \approx 54.71 \]
Average of Q:
\[ \frac{35 + 65 + 60 + 56 + 81 + 45 + 50}{7} = \frac{392}{7} = 56 \]
Hence, average of P is less than Q. Option (1) is correct.

Range of P: \( 89 - 22 = 67 \)
Range of Q: \( 81 - 35 = 46 \)
So, option (3) is correct.

Option (4):
We already found median of Q = 56, and average of Q = 56.
So, option (4) is also correct.