When quantitative data is used in statistics, a histogram is a great way to provide a useful visual display. But when the data is qualitative, other types of graphs must be used. These graphs may also be used to display quantitative data. The graphs are the bar graph, circle graph, and time-series graph.

**Bar graph**

A bar graph can be horizontal or vertical that are uniformly spaced and have uniform width. The length of each bar show the frequency or percentage of occurrence, depending on what is to be displayed in the data. The lengths of the bars show the variable and the values of the variable being displayed. The graph must be titled with labels for each bar and a scale or precise value for the length of each bar.

For example: Suppose you wish to display the population of Chicago for years 1982, 1992, 2002, and 2012. The population is on the vertical axis and the years are on the horizontal axis. The length of the bars represent the population for each year. The title of the graph might be “Population For Chicago”.

Suppose you wish to break down the population into male and female. This type of graph is known as a clustered bar graph because there are two bars for each year the population is measured. One bar will be for male population, and one bar for female population.

A type of bar graph in which the height of each bar represents frequency is known as a Pareto chart. A distinguishing feature of this bar graph is that the bars are arranged from left to right in decreasing order of frequency. Therefore, the graph will have the highest bar at the far left and lowest bar at the far right.

**Circle graph**

In a circle graph, also known as a “pie chart”, wedges of a circle represent a percent of a population which have a common trait.

For example, suppose you want to know how much time Americans aged 25 to 50 watch television after 7 pm on a weeknight. Suppose in a sample of 200, 25 people watch up to 1 hour of television, 50 people watch between 1 and 2 hours of television, 100 watch between 2 and 3 hours of television, and 25 people watch over 3 hours of television.

That means there are 4 wedges of the pie, 12.5% represent up to 1 hour of television, 12.5% represent 3 or more hours, 25% represent 1 to 2 hours, and 50 percent represent 2 to 3 hours.

Draw the circle and make appropriate sized wedges to show the various percentages, and notice that the total percentages is 100. Label each piece and mark each piece of the chart with the designated numbers of degrees.

**Time-series graph**

When you want to track a change over time, the best type of graph to use is a time-series graph. For example, suppose you start exercising and you ride a bike for 45 minutes. You want to monitor your progress over a month period of time to see how much farther you can bike at the end of the month compared to the beginning of the month.

The time-series graph shows data measurements in chronological order. Time is placed on the horizontal axis, and the variable of interest is placed on the vertical axis. The basic time-series graph is made by connecting the data points by lines.

This article should give students a solid foundation for understanding graphs that can used to display qualitative data, as well as quantitative data.