For a symmetrical distribution `P_(25)` and `P_(75)` are 30 and 70 respectively. The value of median is

Options

A. 50
B. 30
C. 40
D. none of these

Answer

To find the median for the given symmetrical distribution where \( P_{25} \) (first quartile, \( Q_1 \)) is 30 and \( P_{75} \) (third quartile, \( Q_3 \)) is 70, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Quartiles:**
- We know that \( P_{25} \) (or \( Q_1 \)) is given as 30.
- We know that \( P_{75} \) (or \( Q_3 \)) is given as 70.

2. **Use the Formula for Median:**
- For a symmetrical distribution, the median can be calculated using the formula:
\[ \text{Median} = \frac{Q_1 + Q_3}{2} \]

3. **Substitute the Values:**
- Plug in the values of \( Q_1 \) and \( Q_3 \):
\[ \text{Median} = \frac{30 + 70}{2} \]

4. **Calculate the Sum:**
- Calculate \( 30 + 70 \):
\[ 30 + 70 = 100 \]

5. **Divide by 2:**
- Now, divide the sum by 2:
\[ \text{Median} = \frac{100}{2} = 50 \]

6. **Conclusion:**
- Therefore, the value of the median is 50.

### Final Answer:
The value of the median is **50**.