GRAPHING FREQUENCY DISTRIBUTIONS

With interval or ratio scales two types of graphs may be used: Histograms or Polygons.

STEPS IN CONSTRUCTING HISTOGRAMS AND POLYGONS

FREQUENCY HISTOGRAM

1. Mark off the abscissa (horizontal axis, or x axis) with values corresponding to the midpoints of the class intervals and mark off the ordinate (vertical axis, or y axis) in frequencies.  Label the axes appropriately.

2. Construct each bar of the histogram over its class interval so that the bar’s width covers the class interval (or individual score) from its lower to its upper real limits, and its height corresponds to the frequency of scores in the interval.  There should be no space between bars.

Example:

For grouped data:

FREQUENCY POLYGON

1.        Mark off and label axes as for a frequency histogram, but add one interval below the lowest and one above the highest class interval and assign them 0 frequencies.

2.        Place points corresponding to the frequencies of each interval (including the two 0-frequency intervals) directly over the midpoints of each class interval (or over each score).  Connect all adjacent points (including the 0s) with straight lines.

For grouped data

RELATIVE FREQUENCY HISTOGRAM OR POLYGON

1.        These are plotted in the same way as above, but the labels on the ordinate (and the height of the bars or points) show relative frequency, not frequency.

 CUMULATIVE FREQUENCY HISTOGRAM OR POLYGON

1.       Follow the steps for constructing a frequency histogram or polygon, except:

a.       Mark off and label the ordinate for cumulative frequency rather than frequency.

b.       In drawing a cumulative frequency polygon, the points are placed over the upper real limit of each class interval, including the lowest interval of 0 accumulated frequencies (there is no upper 0-frequency interval).

CUMULATIVE RELATIVE FREQUENCY HISTOGRAM OR POLYGON

These are plotted in the same way as above, except that the labels on the ordinate (and the height of the bars or points) show cumulative relative frequency.

With nominal or ordinal scales: Bar graphs                             

In a Bar graph, the height of the bar corresponds to the frequency of each X-value.

            Spaces separate the bars. Category names are used for each X-value.

Figure 2-7  (p. 47)
A bar graph showing the distribution of personality types in a sample of college students. Because personality type is a discrete variable measured on a nominal scale, the graph is drawn with space between the bars.