Ed 602 - Lesson 4 - Graphing Frequency Distributions

Lesson 4 will consist of the following topics

• Text Assignment for Lesson 4

• Graphical Representation of Data

• Histogram

• Bar Graph

• Creating a Bar Graph with the Excel Spreadsheet Program

• Frequency Polygon

• Creating a Frequency Polygon with the Excel Spreadsheet Program

• Lesson 4 Assignment

• Lesson 4 Quiz

Text Assignment for Lesson 4

For lesson 4, read pages 47-60 in Practical Statistics for Educators, Third Edition by Ruth Ravid (2005, University Press of America)
or read pages 84-94 in Basic Statistics for Behavioral Science Research 2nd ed by Mary B. Harris (1998, Allyn and Bacon)
or read pages 70-90 in Practical Statistics for Educators, 2nd Edition by Ruth Ravid (2000, University Press of America)
or read pages 37-58 in Practical Statistics for Educators by Ruth Ravid (1994, University Press of America).

Graphical Representation of Data

In our last lesson we considered the tabular representation of data (descriptive statistics) as we created frequency distributions from data.

In this lesson we will make graphs from these frequency distributions as we explore the graphical representation of data. We will learn to create histograms, bar graphs, and frequency polygons. We will also discuss how to create graphs with the Excel spreadsheet program.

The graphs we will be considering in this course, are all two dimensional representations of data that could also be shown in a frequency distribution. The typical graph consists of

1. A horizontal axis or x-axis which represents the variable being presented. This axis is referred to as the abscissa of the graph and sometimes as the catagory axis. This axis of the graph should be named and should show the categories or divisions of the variable being represented.
2. A vertical axis or y-axis which is referred to as the ordinate or the value axis. In the graphs we will be considering the ordinate will show the frequency with which each category of the variable occurs. This axis should be labeled as frequency and also have a scale, the values of the scale being represented by tic marks. By convention the length of the ordinate is three-fourths the length of the abscissa. This is referred to as the three-fourths rule in graph construction.
3. Each graph should also have a title which indicates the contents of the graph.

Some of these features of a graph are illustrated in the figure below.

Histogram

A histogram is similar to the common bar graph but is used to represent data at the interval or ratio level of measurement, while the bar graph is used to represent data at the nominal or ordinal level of measurement. The following frequency distribution shows the ages of children participating in an after school program.

For this frequency distribution the variable, age, is at the ratio level of measurement so it would be appropriate to create a histogram from this data.

To create a histogram from this frequency distribtion we proceed as follows:

1. Arrange the age values along the abscissa (horizonal axis) of the graph, using a tic mark to indicate each category or value of the variable. Arrange the ages with the lowest age on the left and the highest age on the right. Provide a label (Age) for the abscissa.
2. Create a ordinate (vertical axis) that is approximately three fourths the length of the abscissa, to contain the range of scores for the frequencies (0 to 8). Arrange the frequency values along the abscissa with tic marks for each value. Provide a label for the ordinate (Frequency).
3. Create the body of the histogram by drawing a bar or column, the length of which represents the frequency for each age value. Arrange the columns so that they are contingent to one another.
4. Provide a title for the histogram.

If we applied these steps to the ages for children data we would have the following histogram.

Bar Graph

A bar graph is similar to a histogram except that the bars or columns are seperated from one another by a space rather than being contingent to one another. The bar graph is used to represent categorical or discrete data, that is data at the nominal or ordinal level of measurement. The variable levels are not continuous, therefore the bars representing various levels of the variable are distinct from one another. When data is at the interval or ratio level of measurement, variable levels or values are continuous, therefore the bars or columns of the histogram are contingent to one another.

The following frequency distribution represents the majors for students taking Ed 602 during the summer of 1996.

The data for majors is at the nominal level of measurement and therefore it would be appropriate to represent this data with a bar graph. The bar graph for Ed 602 Majors appears below.

Frequency Polygon

A frequency polygon is what you may think of as a curve. A frequency polygon can be created with interval or ratio data. Let's create a frequency polygon with the children's ages data we used earlier in this lesson to create a histogram.

For this frequency distribution the variable, age, is at the ratio level of measurement so it would be appropriate to create a frequency polygon from this data.

To create a frequency polygon from the frequency distribution for ages of children in the after school program we proceed as follows:

1. Arrange the age values along the abscissa (horizonal axis) of the graph, using a tic mark to indicate each category or value of the variable. Arrange the ages with the lowest age on the left and the highest age on the right. Provide a label (Age) for the abscissa. Since we must bring the curve for a frequency polygon down to the baseline at the low and the high end of the curve, we must add one age value (4) below the lowest age value (5) with a frequency of 0 and one age value (12) above the highest age value (11) also with a frequency of 0.
2. Create a ordinate (vertical axis) that is approximately three fourths the length of the abscissa, to contain the range of scores for the frequencies (0 to 8). Arrange the frequency values along the abscissa with tic marks for each value. Provide a label for the ordinate (Frequency).
3. Create the body of the frequency polygon by placing a dot for each age value at a position on the chart that represents the frequency for that age value. Connect each of the dots to the next dot with a straight line.
4. Provide a title for the frequency polygon.

If we applied these steps to the ages for children data we would have the following frequency polygon.

Please send electronic mail to the course instructor if you have any questions about this lesson or other concerns.