`P_(50) = D_5=Q_K = ` Median , then value of k is ?

Answer

To solve the problem, we need to understand the relationships between percentiles, deciles, and quartiles.

### Step-by-Step Solution:

1. **Understanding the Terms**:
- \( P_{50} \) is the 50th percentile, which is also known as the median of the dataset.
- \( D_5 \) is the 5th decile, which represents the value below which 50% of the data falls.
- \( Q_K \) is the Kth quartile, where quartiles divide the data into four equal parts.

2. **Equating the Values**:
- The problem states that \( P_{50} = D_5 = Q_K \). Since all these values are equal to the median, we can express this as:
\[ P_{50} = D_5 = Q_K = \text{Median} \]

3. **Relating Quartiles to the Median**:
- The median is also the second quartile, denoted as \( Q_2 \).
- Therefore, we can write:
\[ Q_K = Q_2 \]

4. **Finding the Value of K**:
- Since we have established that \( Q_K = Q_2 \), it follows that:
\[ K = 2 \]

5. **Conclusion**:
- Thus, the value of \( K \) is \( 2 \).

### Final Answer:
The value of \( K \) is \( 2 \).