How to calculate lower limit and upper limit in statistics

In a frequency distribution, class limits represent the smallest and largest data values that can belong to each class.

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Each class in a frequency distribution has a lower class limit and an upper class limit:

The following examples show how to find class limits for different frequency distributions.

Suppose we have the following frequency distribution that represents the number of wins by different basketball teams:

The lower class limit is simply the smallest possible value in each class:

Conversely, the upper class limit is the largest possible value in each class:

Suppose we have the following frequency distribution:

The lower class limit is the smallest possible value in each class:

And the upper class limit is the largest possible value in each class:

How to Find Class Boundaries (With Examples)
How to Find Class Midpoints (With Examples)
How to Find Class Intervals (With Examples)

In a frequency distribution, class boundaries are the values that separate the classes.

We use the following steps to calculate the class boundaries in a frequency distribution:

1. Subtract the upper class limit for the first class from the lower class limit for the second class.

2. Divide the result by two.

3. Subtract the result from the lower class limit and add the result to the the upper class limit for each class.

The following examples show how to use these steps in practice to calculate class boundaries in a frequency distribution.

Suppose we have the following frequency distribution that represents the number of wins by various basketball teams:

Use the following steps to calculate the class boundaries:

1. Subtract the upper class limit for the first class from the lower class limit for the second class.

The upper class limit for the first class is 30 and the lower class limit for the second class is 31. Thus, we get: 31 – 30 = 1.

2. Divide the result by two.

Next, we divide the result by 2. So, we get 1/2 = 0.5.

3. Subtract the result from the lower class limit and add the result to the the upper class limit for each class.

Lastly, we subtract 0.5 from the lower class limit and add 0.5 to the upper class limit for each class:

We interpret the results as follows:

The first class has a lower class boundary of 25.5 and an upper class boundary of 30.5.
The second class has a lower class boundary of 30.5 and an upper class boundary of 35.5.
The third class has a lower class boundary of 35.5 and an upper class boundary of 40.5.

And so on.

Suppose we have the following frequency distribution:

Use the following steps to calculate the class boundaries:

1. Subtract the upper class limit for the first class from the lower class limit for the second class.

The upper class limit for the first class is 60.9 and the lower class limit for the second class is 61. Thus, we get: 61 – 60.9 = 0.1.

2. Divide the result by two.

Next, we divide the result by 2. So, we get 0.1/2 = 0.05.

3. Subtract the result from the lower class limit and add the result to the the upper class limit for each class.

Lastly, we subtract 0.05 from the lower class limit and add 0.05 to the upper class limit for each class:

We interpret the results as follows:

The first class has a lower class boundary of 55.95 and an upper class boundary of 60.95.
The second class has a lower class boundary of 60.95 and an upper class boundary of 65.95.
The third class has a lower class boundary of 65.95 and an upper class boundary of 70.95.

And so on.