In a frequency distribution, the mid values of a class is `10` and width of the class is `6`. The lower limit of the class is

Options

A. `6.5`
B. `7`
C. `8.5`
D. `12`

Answer

To find the lower limit of a class in a frequency distribution when given the mid value and the width of the class, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Mid value of the class (M) = 10
- Width of the class (W) = 6

2. **Use the Formula for Mid Value**:
The mid value (M) of a class can be calculated using the formula:
\[ M = \frac{\text{Lower Limit} + \text{Upper Limit}}{2} \]
The width of the class (W) is given by:
\[ W = \text{Upper Limit} - \text{Lower Limit} \]

3. **Express Upper Limit in Terms of Lower Limit**:
Let the lower limit be \( L \). Then, the upper limit can be expressed as:
\[ \text{Upper Limit} = L + W = L + 6 \]

4. **Substitute into the Mid Value Formula**:
Substitute the expression for the upper limit into the mid value formula:
\[ 10 = \frac{L + (L + 6)}{2} \]

5. **Simplify the Equation**:
Simplifying the equation gives:
\[ 10 = \frac{2L + 6}{2} \]
Multiply both sides by 2:
\[ 20 = 2L + 6 \]
Now, subtract 6 from both sides:
\[ 14 = 2L \]

6. **Solve for Lower Limit**:
Divide both sides by 2:
\[ L = 7 \]

7. **Conclusion**:
Therefore, the lower limit of the class is \( \boxed{7} \).