Representation of Data
Because a list of raw data may be difficult to interpret, psychologists prefer to represent their data in an organized way. Two of the most common ways are frequency distributions and graphs.
Frequency Distributions
Suppose that you had a set of 20 scores from a 100-point psychology exam. You might arrange them in a frequency distribution, listing the frequency of each score or group of scores in a set of scores. Using the set of scores in Table B.1, you would set up a column including the highest and lowest scores, as well as the possible scores in between. In this case, the highest score is 94 and the lowest is 80. You would then count the frequency of each score and list it in a separate column. The total of the frequencies in the distribution is symbolized by the letter N.
The frequency distribution might show a pattern in the set of scores that is not apparent when simply examining the individual scores. In this example (presented in Table B.1), the exam scores do not bunch up toward the lower, middle, or upper portions of the distribution. In some cases, typically when the difference between the highest score and the lowest score is greater than 15, you might prefer to use a grouped frequency distribution. The scores are grouped into intervals, and the frequency of scores in each interval is listed in a separate column. The intervals can be of any size, but, for ease of construction, a grouped frequency distribution should end up with no more than about 10 groups. A grouped frequency distribution provides less precise information than does an ungrouped one, because the individual scores are lost. However, the benefit of a grouped frequency distribution is that one can understand any trends in the data at a quick glance.
Learning Check #1: Suppose we ask 23 students how many music CDs that they own. Present the following data in a frequency distribution: 43, 15, 52, 24, 84, 36, 75, 70, 98, 44, 56, 60, 48, 41, 38, 7, 62, 49, 32, 71, 25, 46, 58.
Graphs
If a picture is worth a thousand words, then a graph is worth several paragraphs in a research report. Because it provides a pictorial representation of the distribution of scores, a graph can be an even more effective representation of research data than a frequency distribution. Among the most common kinds of graphs are pie graphs, frequency histograms, frequency polygons, and line graphs.
Pie Graph
A simple, but visually effective, way of representing data is the pie graph. It represents data as percentages of a pie-shaped graph. The total of the slices of the pie must add up to 100 percent.
Learning Check #2: Suppose in a class of 150 students there are 13 First-year students, 68 Sophomores, 50 Juniors, and 19 Seniors. Construct a pie chart to illustrate this data.
Frequency Histogram
Another approach to representing frequency data is the frequency histogram, which graphs frequencies as bars. This type of graph may also be called a bar graph. In general, the scores are plotted on the abscissa (the horizontal axis) and the frequencies on the ordinate (the vertical axis). The width of the bars represents the intervals, and the height of the bars represents the frequency of scores in each interval. Figure B.1 is a frequency histogram of the exam scores in the ungrouped frequency distribution presented in Table B.1.
Frequency Polygon
A frequency polygon serves the same purpose as a frequency histogram. As shown in Figure B.2, the frequency polygon is drawn by connecting the points, representing frequencies, located above the scores. Note that the polygon is completed by extending it to the abscissa one score below the lowest score and one score above the highest score in the distribution.
An advantage of the frequency polygon over the frequency histogram is that it permits the plotting of more than one distribution on the same set of axes. Plotting more than one frequency histogram on a set of axes would create a confusing graph. If more than one frequency polygon is plotted on a set of axes, they should be distinguished from one another. This can be done by drawing a different kind of line for each polygon (perhaps a solid line for one and a broken line for the other), drawing the lines in different colors (perhaps red for one polygon and blue for the other), or representing the points above the scores with geometric shapes (perhaps a circle for one polygon and a triangle for the other).
There are a few shapes that a frequency polygon can take that are particularly interesting to psychologists. A graph in which scores bunch up toward either end of the abscissa (as shown in Figure B.3) is said to be skewed. The skewness of a graph is in the direction of its “tail.” If the scores bunch up toward the high end, the graph has a negative skew. If the scores bunch up toward the low end, the graph has a positive skew. A distribution is said to be normal (or bell-shaped) if the scores bunch up in the middle and then taper off fairly equally on each side. Finally, a distribution is called a rectangular distribution if the scores are fairly evenly distributed throughout the graph.
Learning Check #3: Remember the 23 students who reported the number of music CDs that they own? Present the following data in a frequency polygon: 43, 15, 52, 24, 84, 36, 75, 70, 98, 44, 56, 60, 48, 41, 38, 7, 62, 49, 32, 71, 25, 46, 58.
Learning Check #4: What shape is the distribution graphed in Learning Check #3? What would have made the distribution take on a positive skew? A negative skew? A rectangular shape?
Line Graph
Whereas pie graphs, frequency histograms, and frequency polygons are useful for plotting frequency data, a line graph is useful for plotting data generated by experiments. It uses lines to represent the relationship between independent variables and dependent variables. If you skim through your introductory psychology textbook, you will see several examples of line graphs. The graph shown in Figure B.4 represents the data from an experiment on exercise and weight loss. Note in this figure that one line represents a group of people who agree to exercise regularly and the other line represents a group of people who do not engage in exercise. In all other ways these two groups are equal. They are weighed one week after agreeing to participate in the study and again two weeks after agreeing to participate. Note that this graph allows the reader to note quickly the benefits of exercise on weight loss.
As the range of scores is greater than 15, a grouped frequency distribution is most appropriate. Although your table may look slightly different, you should make sure to have about 10 intervals.
Score Frequency
| 90-99 | 1 |
| 80-89 | 1 |
| 70-79 | 3 |
| 60-69 | 2 |
| 50-59 | 3 |
| 40-49 | 6 |
| 30-39 | 3 |
| 20-29 | 2 |
| 10-19 | 1 |
| 0-9 | 1 |
A pie chart lists the percentage of each category. The categories must add up to 100 percent. To get the percentages of each category simply divide the number in that category by the total number in the entire group (here the total is 150) and then multiply that number by 100%: First-year students = 9%; Sophomores = 45%; Juniors = 33%; and Seniors = 13%.
The shape is a normal (or bell) shaped distribution. If many of the participants had stated that they owned 70 - 90 compact disks and very few reported owning in the 0 - 20 range, then the distribution would have been negatively skewed. If many had reported owning between 0 and 20 compact disks and only a few reported owning between 70 and 90 compact discs, then the distribution would have had a positive skew. To get a rectangular distribution, there would have to be roughly equal number of compact disks reported for each interval.
