Let x be the class mark & y be the upper limit of a class-interval in a continuous frequency-distribution.
The lower limit of the class is:

Options

A. 2x+y
B. 2x-y
C. x-y
D. x+y

Answer

To find the lower limit of a class interval in a continuous frequency distribution, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- Let \( x \) be the class mark.
- Let \( y \) be the upper limit of the class interval.
- We need to find the lower limit, which we will denote as \( L \).

2. **Class Mark Formula**:
- The formula for the class mark \( x \) is given by:
\[ x = \frac{L + y}{2} \]
- This formula states that the class mark is the average of the lower limit \( L \) and the upper limit \( y \).

3. **Rearranging the Formula**:
- To find \( L \), we can rearrange the formula:
\[ L + y = 2x \]
- This means that the sum of the lower limit and the upper limit equals twice the class mark.

4. **Isolating the Lower Limit**:
- Now, we isolate \( L \) by subtracting \( y \) from both sides:
\[ L = 2x - y \]

5. **Final Expression**:
- Thus, the lower limit \( L \) of the class interval is given by:
\[ L = 2x - y \]

### Conclusion:
The lower limit of the class interval is \( 2x - y \).

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