Let Ube the upper class boundary of a class in a frequency distribution and Mbe the mid-point of the class. Which one of the following is the lower class boundary of the class?

Options

A. M+`(M+L)/2`
B. L+`M+L/2`
C. `2M-U`
D. M-2L

Answer

To find the lower class boundary (L) of a class in a frequency distribution when given the upper class boundary (U) and the midpoint (M), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between U, L, and M**:
- The midpoint (M) of a class is defined as the average of the upper class boundary (U) and the lower class boundary (L).
- This can be expressed mathematically as:
\[ M = \frac{U + L}{2} \]

2. **Rearrange the equation to find L**:
- To find the lower class boundary (L), we can rearrange the equation:
\[ 2M = U + L \]
- Now, isolate L:
\[ L = 2M - U \]

3. **Conclusion**:
- Therefore, the formula for the lower class boundary (L) is:
\[ L = 2M - U \]