Introduction

A continuous frequency distribution is a statistical representation of data that falls into continuous intervals or classes. Each class has a corresponding class mark, which is the average of the upper and lower limits of the class. In this case, the class marks are given as 12, 14, 16, 18, and so on.

Given Class Marks

The given class marks are: 12, 14, 16, 18, ...

Finding the Class Interval for 16

To find the class interval corresponding to the class mark 16, we need to determine the lower and upper limits of the class.

1. Lower Limit:
- The lower limit of a class is found by subtracting half of the class interval from the class mark.
- In this case, since the class marks are increasing by 2, the class interval is 2.
- Therefore, the lower limit is 16 - (2/2) = 16 - 1 = 15.

2. Upper Limit:
- The upper limit of a class is found by adding half of the class interval to the class mark.
- In this case, the class interval is 2.
- Therefore, the upper limit is 16 + (2/2) = 16 + 1 = 17.

Thus, the class interval corresponding to the class mark 16 is 15 - 17.

Finding the Class Interval for 22

To find the class interval corresponding to the class mark 22, we follow the same steps as above.

1. Lower Limit:
- The lower limit is found by subtracting half of the class interval from the class mark.
- Since the class marks are increasing by 2, the class interval is 2.
- Therefore, the lower limit is 22 - (2/2) = 22 - 1 = 21.

2. Upper Limit:
- The upper limit is found by adding half of the class interval to the class mark.
- In this case, the class interval is 2.
- Therefore, the upper limit is 22 + (2/2) = 22 + 1 = 23.

Thus, the class interval corresponding to the class mark 22 is 21 - 23.

Conclusion

In a continuous frequency distribution, the class interval corresponding to a given class mark can be found by subtracting half of the class interval from the class mark to get the lower limit, and adding half of the class interval to the class mark to get the upper limit. In this case, the class intervals corresponding to the class marks 16 and 22 are 15 - 17 and 21 - 23, respectively.