Question

The run scored by Virat Kohli during IPL 2023 are as follows:
2, 45, 65, 7, 5, 14, 26, 46, 43, 112, 113, 9, 13, and 49. Find the median score.

• A. 36.0
• B. 34.5
• C. 34.0
• D. 7.5

Hint:

Always sort the data first before finding the median. If $N$ is even, average the two middle values. Here, the middle terms are 26 and 43, which average to 34.5.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The median is the middle value of a dataset when the observations are arranged in ascending or descending order.

Step 2: Detailed Explanation:
Let us list the raw scores: \[ 2, 45, 65, 7, 5, 14, 26, 46, 43, 112, 113, 9, 13, 49 \]
First, arrange the $N = 14$ observations in ascending order: \[ 2, 5, 7, 9, 13, 14, \mathbf{26}, \mathbf{43}, 45, 46, 49, 65, 112, 113 \]
Since the total number of observations ($N = 14$) is even, the median is calculated as the arithmetic mean of the two middle terms: the $(N/2)$-th term and the $(N/2 + 1)$-th term.
Identify the middle terms: \[ \frac{N}{2} = 7\text{-th term} = 26 \] \[ \frac{N}{2} + 1 = 8\text{-th term} = 43 \]
Calculate the median by taking the average of these two values: \[ \text{Median} = \frac{26 + 43}{2} = \frac{69}{2} = 34.5 \]

Step 3: Final Answer:
The median score is 34.5.