The class mark of a particular class is `17.5` and the class size is 5. The class interval is :

Options

A. `14-19`
B. `15-20`
C. `14.5-19.5`
D. `17.5-22.5`

Answer

To find 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** (also called the midpoint) is the average of the upper limit (U) and lower limit (L) of the class interval.
- The **class size** is the difference between the upper limit and lower limit.

2. **Set Up the Equations**:
- From the problem, we know:
\[ \text{Class Mark} = \frac{U + L}{2} = 17.5 \]
This can be rearranged to:
\[ U + L = 35 \quad \text{(Equation 1)} \]
- The class size is given as 5, which means:
\[ U - L = 5 \quad \text{(Equation 2)} \]

3. **Solve the Equations**:
- Now we have two equations:
1. \( U + L = 35 \)
2. \( U - L = 5 \)

- We can add these two equations to eliminate \( L \):
\[ (U + L) + (U - L) = 35 + 5 \]
This simplifies to:
\[ 2U = 40 \]
Dividing both sides by 2 gives:
\[ U = 20 \]

4. **Find the Lower Limit**:
- Now that we have \( U = 20 \), we can substitute it back into Equation 1 to find \( L \):
\[ 20 + L = 35 \]
Solving for \( L \) gives:
\[ L = 35 - 20 = 15 \]

5. **Determine the Class Interval**:
- The class interval is defined by the lower limit and upper limit:
\[ \text{Class Interval} = [L, U] = [15, 20] \]

### Final Answer:
The class interval is **15 to 20**.

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