Class mark of a particular class is 6.5 and class size is 3, then class interval is:

Options

A. 5-8
B. ` 6.5-9.5 `
C. ` 3.5-6.5 `
D. ` 4.25 `

Answer

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

### Step 1: Understand the Definitions
- **Class Mark (Midpoint)**: It is calculated as the average of the upper limit and lower limit of the class interval. The formula is:
\[ \text{Class Mark} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2} \]
- **Class Size**: It is the difference between the upper limit and lower limit. The formula is:
\[ \text{Class Size} = \text{Upper Limit} - \text{Lower Limit} \]

### Step 2: Set Up the Equations
Let:
- Lower Limit = \( x \)
- Upper Limit = \( y \)

From the problem:
1. The class mark is given as 6.5:
\[ \frac{x + y}{2} = 6.5 \]
Multiplying both sides by 2 gives:
\[ x + y = 13 \quad \text{(Equation 1)} \]

2. The class size is given as 3:
\[ y - x = 3 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
From Equation 2, we can express \( y \) in terms of \( x \):
\[ y = x + 3 \quad \text{(Equation 3)} \]

Now, substitute Equation 3 into Equation 1:
\[ x + (x + 3) = 13 \]
This simplifies to:
\[ 2x + 3 = 13 \]
Subtracting 3 from both sides gives:
\[ 2x = 10 \]
Dividing both sides by 2 results in:
\[ x = 5 \]

### Step 4: Find the Upper Limit
Now, substitute \( x = 5 \) back into Equation 3 to find \( y \):
\[ y = 5 + 3 = 8 \]

### Step 5: Write the Class Interval
The class interval is defined by the lower limit and upper limit:
- Lower Limit = \( x = 5 \)
- Upper Limit = \( y = 8 \)

Thus, the class interval is:
\[ \text{Class Interval} = [5, 8] \]

### Final Answer
Therefore, the class interval is \( [5, 8] \).

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