The class marks of a frequency distribution are given as follows 15,20, 25,……….. The class corresponding to the class mark 20 is

Options

A. `12.5-17.5`
B. `16.5-21.5`
C. `17.5-22.5`
D. `19.5-20.5`

Answer

To find the class corresponding to the class mark of 20, we can follow these steps:

### Step 1: Identify the Class Marks
The class marks given are 15, 20, 25, and so on. These are the midpoints of the classes.

### Step 2: Determine the Class Size
To find the class size, we can calculate the difference between consecutive class marks.

- Class mark 1: 15
- Class mark 2: 20

Class Size = Class Mark 2 - Class Mark 1 = 20 - 15 = 5

### Step 3: Calculate the Upper Limit of the Class for Class Mark 20
We can use the formula for the upper limit of the class:

\[ \text{Upper Limit} = \text{Class Mark} + \frac{\text{Class Size}}{2} \]

Substituting the values:

\[ \text{Upper Limit} = 20 + \frac{5}{2} = 20 + 2.5 = 22.5 \]

### Step 4: Calculate the Lower Limit of the Class for Class Mark 20
Using the formula for the lower limit of the class:

\[ \text{Lower Limit} = \text{Class Mark} - \frac{\text{Class Size}}{2} \]

Substituting the values:

\[ \text{Lower Limit} = 20 - \frac{5}{2} = 20 - 2.5 = 17.5 \]

### Step 5: Determine the Class Interval
Now that we have both the lower and upper limits, we can state the class interval corresponding to the class mark of 20:

The class corresponding to the class mark 20 is from 17.5 to 22.5.

### Final Answer
The class corresponding to the class mark 20 is (17.5, 22.5).

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