What common class width was used to construct the frequency distribution?

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Calculating Class Width in a Frequency Distribution Table
Example of Calculating Class Width

Updated March 01, 2020

By Kevin Beck

Reviewed by: Lana Bandoim, B.S.

Data, especially numerical data, is a powerful tool to have if you know what to do with it; graphs are one way to present data or information in an organized manner, provided the kind of data you're working with lends itself to the kind of analysis you need.

Often, statisticians, instructors and others are curious about the distribution of data. For example, if the data is a set of chemistry test results, you might be curious about the difference between the lowest and the highest scores or about the fraction of test-takers occupying the various "slots" between these extremes.

Frequency distributions are a powerful tool for scientists, especially (but not only) when the data tends to cluster around a mean or average smack-dab between the right and left sides of the graph. This is the familiar "bell-shaped curve" of normally distributed data.

A frequency distribution is a table that includes intervals of data points, called classes, and the total number of entries in each class. The frequency f of each class is just the number of data points it has. The limiting points of each class are called the lower class limit and the upper class limit, and the class width is the distance between the lower (or higher) limits of successive classes. It is not the difference between the higher and lower limits of the same class.

The range is the difference between the lowest and highest values in the table or on its corresponding graph.

When creating a grouped frequency distribution, you start with the principle that you will use between five and 20 classes. These classes must have the same width, or span or numerical value, for the distribution to be valid. Once you determine the class width (detailed below), you choose a starting point the same as or less than the lowest value in the whole set.

As noted, choose between five and 20 classes; you would usually use more classes for a larger number of data points, a wider range or both. In addition, follow these guidelines:

The class width should be an odd number. This will assure that the class midpoints are integer numbers rather than decimal numbers.
Every data value must fall into exactly one class. None are ignored, and none can be included in more than one class.
The classes must be continuous, meaning that you have to include even those classes that have no entries. (Exceptions are made at the extremes; if you are left with an empty first or an empty last class class, exclude it).
As stated, the classes must be equal in width. The first and last classes are again exceptions, as these can be, for example, any value below a certain number at the low end or any value above a certain number at the high end,

In a properly constructed frequency distribution, the starting point plus the number of classes times the class width must always be greater than the maximum value.

A professor had students keep track of their social interactions for a week. The number of social interactions over the week is shown in the following grouped frequency distribution. What is the class midpoint for each class?

0–7: 7
8–14: 37
15–21: 32
22–28: 21
29–35: 3
Total 100

The class width was chosen in this instance to be seven. Given a range of 35 and the need for an odd number for class width, you get five classes with a range of seven. The midpoints are 4, 11, 18, 25 and 32.

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A frequency distribution table showing a class width of 7 for IQ scores (e.g. 125-118 = 7)

Class width refers to the difference between the upper and lower boundaries of any class (category). Depending on the author, it’s also sometimes used more specifically to mean:

The difference between the upper limits of two consecutive (neighboring) classes, 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.

Calculating Class Width in a Frequency Distribution Table

Watch the video to find out how to calculate class width:

How to Make a Frequency Distribution Table

Watch this video on YouTube.

Can’t see the video? Click here.

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).

Example of Calculating Class Width

Suppose you are analyzing data from a final exam given at the end of a statistics course. The number of classes you divide them into is somewhat arbitrary, but there are a few 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: 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.

References

Gleaton, James U. Lecture Handout: Organizing and Summarizing Data. Retrieved from http://www.unf.edu/~jgleaton/LectureTransCh2.doc on August 27, 2018.
Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial. Jones, James. Statistics: Frequency Distributions & Graphs. Retrieved from https://people.richland.edu/james/lecture/m170/ch02-def.html on August 27, 2018.

Levine, D. (2014). Even You Can Learn Statistics and Analytics: An Easy to Understand Guide to Statistics and Analytics 3rd Edition. Pearson FT Press

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