If the number of observations n is even, then median is

Options

A. `((n+1)/2)^("th")` term
B. `(n/2)^("th")` term
C. Mean of `(n/2)^("th")` and `(n/2+1)^("th")` term
D. None of these

Answer

To find the median when the number of observations \( n \) is even, follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Observations**:
- Let \( n \) be the total number of observations. Since \( n \) is even, we can express it as \( n = 2k \) for some integer \( k \).

2. **Determine the Position of the Median**:
- The median is defined as the average of the two middle values when the data set is arranged in ascending order.
- For an even number of observations, the two middle positions are:
- \( \frac{n}{2} \)th term
- \( \left(\frac{n}{2} + 1\right) \)th term

3. **Calculate the Median**:
- The median \( M \) can be calculated using the formula:
\[ M = \frac{\text{Value at } \frac{n}{2} \text{th term} + \text{Value at } \left(\frac{n}{2} + 1\right) \text{th term}}{2} \]
- This means you add the values at the two middle positions and then divide by 2.

4. **Conclusion**:
- Therefore, when \( n \) is even, the median is the average of the \( \frac{n}{2} \)th term and the \( \left(\frac{n}{2} + 1\right) \)th term.

### Final Answer:
If the number of observations \( n \) is even, then the median is given by:
\[ M = \frac{\text{Value at } \frac{n}{2} \text{th term} + \text{Value at } \left(\frac{n}{2} + 1\right) \text{th term}}{2} \]