Skip to main content icon/video/no-internet
icon backReturn to Entries

Frequency Distribution

A frequency distribution shows all the possible scores a variable has taken in a particular set of data, together with the frequency of occurrence of each score in the respective set. This means that a frequency distribution describes how many times a score occurs in the data set.

Frequency distributions are one of the most common methods of displaying the pattern of observations for a given variable. They offer the possibility of viewing each score and its corresponding frequency in an organized manner within the full range of observed scores. Along with providing a sense of the most likely observed score, they also show, for each score, how common or uncommon it is within the analyzed data set.

Both discrete and continuous variables can be described using frequency distributions. Frequency distributions of a particular variable may be displayed using stem-and-leaf plots, frequency tables, and frequency graphs (typically bar charts or histograms, and polygons). This entry discusses each of these types of displays, along with its shape and modality, and the advantages and drawbacks of using frequency distributions.

Stem-and-Leaf Plots

Stem-and-leaf plots were developed by John Tukey in the 1970s. To create a stem-and-leaf plot for a set of data, the raw data first must be arranged in an array (in ascending or descending order). Then, each number must be separated into a stem and a leaf. The stem consists of the first digit or digits, and the leaf consists of the last digit. Whereas the stem can have any number of digits, the leaf will always have only one. Table 1 shows a stem-and-leaf plot of the ages of the participants at a city hall meeting.

The plot shows that 20 people have participated at the city hall meeting, five in their 30s, none in his or her 40s, eight in their 50s, five in their 60s, and two in their 70s.

Stem-and-leaf plots have the advantage of being easily constructed from the raw data. Whereas the construction of cumulative frequency distributions and histograms often requires the use of computers, stem-and-leaf plots are a simple paper-and-pencil method for analyzing data sets. Moreover, no information is lost in the process of building up stem-and-leaf plots, as is the case in, for example, grouped frequency distributions.

Frequency Tables

A table that shows the distribution of the frequency of occurrence of the scores a variable may take in a data set is called a frequency table. Frequency tables are generally univariate, because it is more difficult to build up multivariate tables. They can be drawn for both ungrouped and grouped scores. Frequency tables with ungrouped scores are typically used for discrete variables and when the number of different scores the variable may take is relatively low. When the variable to be analyzed is continuous and/or the number of scores it may take is high, the scores are usually grouped into classes.

Two steps must be followed to build a frequency table out of a set of data. First, the scores or classes are arranged in an array (in an ascending or descending order). Then, the number of observations corresponding to each score or falling within each class is counted. Table 2 presents a frequency distribution table for the age of the participants at the city hall meeting from the earlier example.

...

  • Loading...
locked icon

Sign in to access this content

Get a 30 day FREE TRIAL

  • Watch videos from a variety of sources bringing classroom topics to life
  • Read modern, diverse business cases
  • Explore hundreds of books and reference titles

Read next

More like this

Sage Recommends

We found other relevant content for you on other Sage platforms.

close

Have you created a personal profile? Login or create a profile so that you can save clips, playlists and searches

close
close
close Signed In to profile You are signed in as:
close
Logged in Institution Institution