For a symmetrical distribution `Q_(1) =20 and Q_(3) =40. ` The value of `50^(th)` percentile, is

Options

A. 20
B. 30
C. 40
D. none of these

Explanation

To find the value of the 50th percentile (P50) for a symmetrical distribution where the first quartile (Q1) is 20 and the third quartile (Q3) is 40, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Quartiles**:
- We are given that \( Q_1 = 20 \) and \( Q_3 = 40 \).

2. **Understand the Relationship**:
- In a symmetrical distribution, the median (which is the 50th percentile, P50) can be calculated using the formula:
\[ P_{50} = \frac{Q_1 + Q_3}{2} \]

3. **Substitute the Values**:
- Substitute the values of \( Q_1 \) and \( Q_3 \) into the formula:
\[ P_{50} = \frac{20 + 40}{2} \]

4. **Calculate the Sum**:
- Calculate the sum of \( Q_1 \) and \( Q_3 \):
\[ 20 + 40 = 60 \]

5. **Divide by 2**:
- Now divide the sum by 2 to find the median:
\[ P_{50} = \frac{60}{2} = 30 \]

6. **Conclusion**:
- Therefore, the value of the 50th percentile (P50) is 30.

### Final Answer:
The value of the 50th percentile is **30**.