For a symmetrical distribution lower quartile is 20 and upper quartile is 40. The value of 50th percentile is

Options

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

Answer

To find the value of the 50th percentile (which is also known as the median) for a symmetrical distribution, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Quartiles**:
- We are given the lower quartile (Q1) which is 20.
- We are also given the upper quartile (Q3) which is 40.

2. **Understand the Relationship**:
- In a symmetrical distribution, the median (which is the 50th percentile) can be calculated using the formula:
\[ \text{Median} = \frac{Q1 + Q3}{2} \]

3. **Substitute the Values**:
- Substitute the values of Q1 and Q3 into the formula:
\[ \text{Median} = \frac{20 + 40}{2} \]

4. **Calculate the Sum**:
- Calculate the sum of Q1 and Q3:
\[ 20 + 40 = 60 \]

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

6. **Final Answer**:
- Therefore, the value of the 50th percentile (median) is 30.

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