Frequency Distributions for Quantitative Data

Frequency and relative frequency distributions for quantitative data are just like for qualitative data, except that the data are divided into ranges of values, called classes, rather than categories.

Definitions

The lower class limit of a class is the smallest value that can appear in that class.

The upper class limit is the largest value that can appear in that class.

The class width is the difference between consecutive lower class limits.

Note: The class width is the difference between the lower limit of one class and the lower limit of the next class. It is NOT the difference between the upper and lower class limit of a single class!

Requirements for Choosing Classes

  • Every observation must fall into one of the classes.
  • The classes must not overlap.
  • The classes must be of equal width.
  • There must be no gap between classes. Even if there are no observations in a class, it must be included in the frequency distribution.

Class limits should be expressed with the same number of decimal places as the data. Also, there is not one "correct" number of classes to create given a set of data. In general, you usually want somewhere between 5 and 20 classes for many data sets, so that you have enough classes to see a pattern, but few enough classes that the frequency distribution summarizes your data and gives you multiple values in at least most of the classes that have data in them. Another rule of thumb that some people use for determining a potential number of classes is to choose a number of classes approximately equal to the square root of the sample size, and then let the class width be the range of the data values divided by this number of classes. (Don't be confused that these two methods don't always agree, as statisticians don't always agree on many things!) For very large data sets, a larger number of classes may be appropriate.

Procedure for Constructing a Frequency or a Relative Frequency Distribution for Quantitative Data

  1. Choose a class width. 
  2. Choose a lower class limit for the first class. This should be a convenient number that is slightly less than the minimum data value.
  3. Compute the lower class limit for the second class by adding the class width to the lower class limit of the first class:   Lower class limit for the second class = Lower class limit for the fist class + Class width.
  4. Compute the lower class limits for each of the remaining classes by adding the class width to the lower class limit of the preceding class. Stop when the largest data value in included in the class.
  5. Count the number of observations in each class, and construct the frequency distribution.
  6. For a relative frequency distribution, take each of the frequency values from step 5, and divide it by the sample size. (The sample size is the total number of values in your data set.)

Example

Please follow along in this video to watch how a set of data can be used to create a frequency distribution.