Question

The WBC count of a group of athletes in a team was estimated to be 7900, 9000, 7800, 8300, 2900, 4545, 5100, 3700, 9900 and 4545 per mm3 of blood. Calculate the median WBC count of this group of individuals.

• A. 2900 per mm\(^3\)
• B. 4545 per mm\(^3\)
• C. 6369 per mm\(^3\)
• D. 6450 per mm\(^3\)

Hint:

The most common mistake when calculating the median is forgetting to order the data first. Always arrange the numbers from smallest to largest before finding the middle value.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The median is the middle value in a dataset that has been arranged in order of magnitude. It divides the dataset into two equal halves.

Step 2: Key Formula or Approach:
1. Arrange the data in ascending or descending order.
2. Count the number of observations, N.
3. If N is odd, the median is the \(\left(\frac{N+1}{2}\right)\)th value.
4. If N is even, the median is the average of the \(\left(\frac{N}{2}\right)\)th and \(\left(\frac{N}{2}+1\right)\)th values.

Step 3: Detailed Calculation:
1. The given dataset is: 7900, 9000, 7800, 8300, 2900, 4545, 5100, 3700, 9900, 4545.
2. Number of observations (N) = 10.
3. Arrange the data in ascending order:
2900, 3700, 4545, 4545, 5100, 7800, 7900, 8300, 9000, 9900
4. Calculate the median: Since N is even (10), the median is the average of the 5th and 6th values.
- 5th value = 5100
- 6th value = 7800
\[ \text{Median} = \frac{5100 + 7800}{2} = \frac{12900}{2} = 6450 \]
Step 4: Final Answer:
The median WBC count of the group is 6450 per mm\(^3\). Therefore, option (D) is correct.