# Frequency Distributions

A frequency distribution is used to organize and summarize data.  Remember that frequency means the number of times something happens, and its symbol is f.  The symbol N, the number of subjects, is also used to stand for frequency.

A frequency distribution is simply a table that tells us how many things were observed in a particular category.  The most common way to present a frequency distribution is to have the scores (or categories) listed in order from highest to lowest in the first column, and the number of cases listed in the second column.  Many researchers also include the percentage of cases associated with each score.

Frequency distributions fall under the heading of descriptive statistics.  Recall that the purpose of descriptive statistics is to organize and summarize data.  Constructing a frequency distribution does both.  Because all of the possible values of a variable are collapsed into categories with the number of scores that fell into that category, the frequency distribution has the potential to reduce a very large, incomprehensible matrix of data into something that can be seen and interpreted at a glance.

It is common to present frequency distributions as both tables and graphs.  Either way, two things are presented to the reader.  The first is a list of the categories that the variable has been divided into.  Also, the table or graph presents the number of people that fell into each of the categories.  A very simple frequency distribution may involve the variable gender.  A table would provide a column with male and female in it, and another column that has the number of males and the number of females.  A histogram would have a bar showing the number of males, and another bar showing the number of males.

Since the scores (or categories) are ordered, a frequency distribution shows how scores are distributed on a scale; that’s where the name comes from.  It is a matter of custom that the scores be listed from highest to lowest.  Most computer programs, such as Microsoft’s Excel, will sort data from least to greatest (ascending), or greatest to least (descending).

When presented with a frequency distribution table, you can determine several other descriptive statistics.  To determine the number of participants in the entire study, add up the frequency for every category (Σf = N).  To determine the sum of the scores, take each X (score category) value and multiply it by its frequency, then sum those products (note that this does not work for categories that are a range of scores).

### Proportions and Percentages

You can easily obtain the proportion or percentage of study participants that fall into a particular category in a frequency distribution.  To obtain the proportion, divide the frequency of the category you are interested in by the total number of people in the study (proportion = f/N).  The proportion associated with each category is called its relative frequency. Recall that while proportions can be expressed as fractions, it is more common to see them expressed in decimal form.  To determine the percentage of participants that fall into a particular category, compute the proportion of people that fall into the category you are interested in and multiply that by 100.  These percentages are often shown in frequency distributions by adding a column headed with the percent sign (%).

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