If a class mark of a class-interval 8.5. The class size is 5,then the class limits of the corresponding class-interval is

Options

A. 6.5-11.5
B. `6-11`
C. `5.5-10.5`
D. `7-12`

Answer

To find the class limits of the class interval given the class mark and class size, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- The **class mark** (or midpoint) of a class interval is calculated as:
\[ \text{Class Mark} = \frac{l + h}{2} \]
where \( l \) is the lower limit and \( h \) is the upper limit of the class interval.
- The **class size** is defined as:
\[ \text{Class Size} = h - l \]

2. **Given Values**:
- Class mark = 8.5
- Class size = 5

3. **Set Up the Equations**:
- From the class mark formula:
\[ \frac{l + h}{2} = 8.5 \]
Multiplying both sides by 2 gives:
\[ l + h = 17 \quad \text{(Equation 1)} \]
- From the class size definition:
\[ h - l = 5 \quad \text{(Equation 2)} \]

4. **Solve the Equations**:
- From Equation 2, we can express \( h \) in terms of \( l \):
\[ h = l + 5 \quad \text{(Substituting into Equation 1)} \]
- Substitute \( h \) into Equation 1:
\[ l + (l + 5) = 17 \]
Simplifying this gives:
\[ 2l + 5 = 17 \]
Subtracting 5 from both sides:
\[ 2l = 12 \]
Dividing by 2:
\[ l = 6 \]

5. **Find the Upper Limit**:
- Now substitute \( l = 6 \) back into the equation for \( h \):
\[ h = l + 5 = 6 + 5 = 11 \]

6. **Conclusion**:
- The class limits of the corresponding class interval are:
\[ \text{Lower Limit} = 6, \quad \text{Upper Limit} = 11 \]
- Therefore, the class interval is \( [6, 11] \).

### Final Answer:
The class limits of the corresponding class interval are 6 and 11.