## What is class width?

Class width represents the size of each class in a grouped frequency distribution. It is the distance between the *upper class limit* and the* lower class limit* of a class interval:

**Class Width = Upper Class Limit − Lower Class Limit.**

For example, if a class interval is “118 – 125,”

Class Width = 125 −118 = 7.

In a frequency distribution table, classes must all be the same width, which means that you only have to perform this calculation once per table.

## Alternate definitions

In general, “class width” refers to the difference between the upper and lower boundaries of any class (category). Depending on the author, the term “class width” is also sometimes used more specifically to mean:

- The difference between the
*upper*limits of two consecutive (neighboring) classes [1], or - The difference between the
*lower*limits of two consecutive classes.

Note that these are different than the difference between the upper and lower limits of a class. This can give slightly different results. For example, suppose the first class interval is “118 – 125” and the second is “126 to 133.”

- Definition 1: 133 – 125 =
**7.** - Definition 2: 126 – 118 =
**8.**

In the big scheme of things, a slight difference in class calculations rarely makes any difference in statistical analysis. But it may cause you to lose a point on a test! So make sure you know which definition your instructor is using.

## Calculating Class Width in a Frequency Distribution Table

In a frequency distribution table, classes must all be the same width. This makes it relatively easy to calculate the class width, as you’re only dealing with a single width (as opposed to varying ones). To find the width:

- Calculate the range of the entire data set by subtracting the lowest point from the highest,
- Divide it by the number of classes.
- Round this number up (usually, to the nearest whole number).

## Examples of Calculating Class Width

The number of classes you divide them into is somewhat arbitrary, but there are a couple of things to keep in mind:

- Make few enough categories so that you have more than one item in each category.
- Choose a number that is easy to manipulate; usually, something between five and twenty is a good idea. For example, if you are analyzing a relatively small class of 25 students, you might decide to create a frequency table with five classes.

**Example 1**: Find a reasonable class with for the following set of student scores: 52, 82, 86, 83, 56, 98, 71, 91, 75, 88, 69, 78, 64, 74, 81, 83, 77, 90, 85, 64, 79, 71, 64, and 83.

- Find the range by subtracting the lowest point from the highest: the difference between the highest and lowest score: 98 – 52 = 46.
- Divide it by the number of classes: 46/5, = 9.2.
- Round this number up: 9.2≅ 10.

We can also do this a little more rigorously with Sturge’s rule, which is defined as

**Number of classes = 1 + 3.322 log N, where N is the number of items in the set.**

**Example 2**: Find a class width for the following scores:

52, 52, 56, 64, 64, 69, 71, 71, 74, 75, 77, 78, 81, 82, 83, 83, 83, 85, 86, 88, 90, 91, 98

- Subtract the minimum from the maximum data value.
- 98 – 52 = 46

- Figure out the number of classes/categories. For this example, we have 20 items (N). Using Sturges formula:
- 1 + 3.322 log(20) = 5.3, which rounds to the closet whole number of 5.

- Divide your answer from Step 2 by the number of classes you calculated in Step 1:
- 46 / 5 =
**9.2**

- 46 / 5 =
- Round the number from Step 3 up to the nearest whole number (this gives us the class width): 9.2 rounds up to
**10.**

Note: Some instructors add more rigid rules, such as

“The class width should be an odd number. This will guarantee that the class midpoints are integers instead of decimals” ~ James Jones, Professor of mathematics, Richland Community College [2].