The class marks of a frequency distribution are 15, 20, 25, 30, ..... The class corresponding to the class mark 25 is

Options

A. 12.5-17.5
B. 20.5-29.5
C. 18.5-21.5
D. 22.5-27.5

Answer

To find the class corresponding to the class mark 25, we can follow these steps:

### Step 1: Understand the concept of class marks
The class mark (or mid-point) of a class interval is calculated using the formula:
\[ \text{Class Mark} = \frac{a + b}{2} \]
where \(a\) is the lower limit and \(b\) is the upper limit of the class interval.

### Step 2: Set up the equation
Given that the class mark is 25, we can set up the equation:
\[ \frac{a + b}{2} = 25 \]
Multiplying both sides by 2 gives:
\[ a + b = 50 \quad \text{(Equation 1)} \]

### Step 3: Determine the class size
From the provided class marks (15, 20, 25, 30), we can see that the difference between consecutive class marks is consistent.
For example:
- \(20 - 15 = 5\)
- \(25 - 20 = 5\)
- \(30 - 25 = 5\)

Thus, the class size (or width) is:
\[ b - a = 5 \quad \text{(Equation 2)} \]

### Step 4: Solve the equations
Now we have two equations:
1. \(a + b = 50\)
2. \(b - a = 5\)

We can solve these equations simultaneously.

First, let's add both equations:
\[ (a + b) + (b - a) = 50 + 5 \]
This simplifies to:
\[ 2b = 55 \]
Dividing by 2 gives:
\[ b = 27.5 \]

### Step 5: Find the value of \(a\)
Now, substitute the value of \(b\) back into Equation 1:
\[ a + 27.5 = 50 \]
Subtracting 27.5 from both sides gives:
\[ a = 50 - 27.5 = 22.5 \]

### Step 6: Write the class interval
Now that we have both \(a\) and \(b\):
- Lower limit \(a = 22.5\)
- Upper limit \(b = 27.5\)

Thus, the class corresponding to the class mark 25 is:
\[ \text{Class Interval} = [22.5, 27.5] \]

### Final Answer
The class corresponding to the class mark 25 is \([22.5, 27.5]\).

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