Class Limits, Boundaries and Intervals

Class Limits

Class limits are the smallest and largest observations (data, events etc) in each class. Therefore, each class has two limits: a lower and upper.

Example:

Class Frequency
200 – 299 12
300 – 399 19
400 – 499 6
500 – 599 2
600 – 699 11
700 – 799 7
800 – 899 3
Total Frequency 60

Using the frequency table above, what are the lower and upper class limits for the first three classes?

For the first class, 200 – 299

The lower class limit is 200

The upper class limit is 299

For the second class, 300 – 399

The lower class limit is 300

The upper class limit is 399

For the third class, 400 – 499

The lower class limit is 400

The upper class limit is 499

Class Boundaries

Class Boundaries are the midpoints between the upper class limit of a class and the lower class limit of the next class in the sequence. Therefore, each class has an upper and lower class boundary.

Example:

Class Frequency
200 – 299 12
300 – 399 19
400 – 499 6
500 – 599 2
600 – 699 11
700 – 799 7
800 – 899 3
Total Frequency 60

Using the frequency table above, determine the class boundaries of the first three classes.

For the first class, 200 – 299

The lower class boundary is the midpoint between 199 and 200, that is 199.5

The upper class boundary is the midpoint between 299 and 300, that is 299.5

For the second class, 300 – 399

The lower class boundary is the midpoint between 299 and 300, that is 299.5

The upper class boundary is the midpoint between 399 and 400, that is 399.5

For the third class, 400 – 499

The lower class boundary is the midpoint between 399 and 400, that is 399.5

The upper class boundary is the midpoint between 499 and 500, that is 499.5

Class Intervals

Class interval is the difference between the upper and lower class boundaries of any class.

Example:

Class Frequency
200 – 299 12
300 – 399 19
400 – 499 6
500 – 599 2
600 – 699 11
700 – 799 7
800 – 899 3
Total Frequency 60

Using the table above, determine the class intervals for the first class.

For the first class, 200 – 299

The class interval = Upper class boundary – lower class boundary

Upper class boundary = 299.5

Lower class boundary = 199.5

Therefore, the class interval = 299.5 – 199.5

= 100

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