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Skill Builder 5: Visual Displays for Continuous Variables

Evaluate Visual Displays of Data for Continuous Variables

Visual Displays

A researcher conducted a study in which she observed students’ scores on an examination. One of the first steps in analyzing a sample of data is to examine the distribution of values for variables in the data set. The distribution of the data tells her about the frequency with which various values are observed. Distributions can be examined in visual displays such as tables and graphs. A good graph or table is informative and allows researchers to identify and communicate the important characteristics of the data. Different approaches are taken for visually displaying categorical and continuous variables.

Identifying Continuous Variables

There are a number of ways of classifying variables.  This Skill Builder focuses on continuous variables. Formally, a continuous variable is one that reflects an interval or ratio level of measurement. In addition, between any two values for the variable, there is another possible value. For example, consider scores of 1.0 and 1.01 on a continuous variable. Between 1.0 and 1.1, 1.01 is a possible value. Then between 1.00 and 1.001, 1.0001 is a possible value. Note that by using more and more decimal places, you can always find a value between any two values. The number of possible values is infinite. Physical characteristics like height and weight are good examples of constructs that can be measured using continuous variables.

Some variables are not continuous according to the formal definition but are amenable to the visual display methods that are typically used for continuous variables. For example, the number of children in a family is not a continuous variable because only whole numbers (e.g., 1, 2, 3) are used to count children. It makes sense, however, to visually display the data for the number of children the same way that you would typically display data for continuous variables. Review the definitions for the following terms to see subtle differences in kinds of variables: Continuous, discrete, quantitative, qualitative, and categorical.

Histograms, Line Graphs, and Frequency Distributions

Histograms, Line Graphs, and Frequency Distributions

To illustrate how you can visually display data for continuous variables, return to the example of students’ exam scores and examine the process of creating a histogram for a set of data.

The following are the exam grades of 15 students

You first need to break the range of values into intervals (also called "bins" or "classes").  In this case, since the data-set consists of exam scores, it will make sense to choose intervals that typically correspond to the range of a letter grade, 10 points wide: 40-50, 50-60, ... 90-100. By counting how many of the 15 observations fall in each of the intervals, you get the table below