Frequency Distribution Tables
After collecting data for an experiment, a researcher would first want to organize the data in such a way that it is possible to get a general feel for the results. Descriptive statistical techniques are ideal for this purpose, and all the techniques for displaying data in graphs and tables are examples of such techniques.
To get a sense of the data, a researcher may first want to generate a frequency distribution of the data. A frequency distribution is an organized tabulation showing exactly how many individuals (or units of measurement if the measure does not concern individuals) are located in each category on the scale of measurement. A frequency distribution contains the entire set of scores, and allows one to compare each score in the set to the rest of the set of scores.
A frequency distribution table is a table that displays all the scores in the set of scores, and their frequency (how often they occurred). Such a table consists of at least two columns, one listing the categories on the scale of measurement (X) and another listing their respective frequencies (f). In the X column, values are listed from highest to lowest without skipping any. In the frequency column, counts for each X are displayed. For example, if one of the scores in the set is X = 5, and three people had a score of 5, then the value f = 3 would go in the frequency column. The sum of the values in the frequency column should always equal the total number of scores in the entire set of scores (N). A third column can be included that displays the proportion (p), the value for f in the frequency column divided by the total number of values N. Thus, p = f/N. Proportions are always between 0 and 1. The sum of the p column should always equal 1. A fourth column could be included to show the percentage for each value of X. You calculate the percentage for each value of X by multiplying the proportion p by 100. The sum of the percentage column is always 100%, with the percentage for each X being between 0% and 100%.
Example 1:
A developmental psychologist is interested in determining how many minutes it takes children to complete reading a booklet. To do so, she asks ten children to read the booklet, and records the following scores:
1, 3, 1, 1, 2, 1, 2, 1, 1, 2
The following regular frequency distribution table displays these scores.
X |
f |
p = f/N |
Percentage = p x 100 |
1 |
6 |
0.6 |
60% |
2 |
3 |
0.3 |
30% |
3 |
1 |
0.1 |
10% |
In this example, N = 10, the sum of p is 1.0, and the sum of the percentages is 100%. Each square with a number in this table is called a cell.
If there are too many values for X to display them all separately, a grouped frequency table is used. In this table, the X column lists groups of scores, called class intervals. These intervals all have the same width. Each interval begins with a value that is a multiple of the interval width. The interval width should be selected in such a way that the resulting table has no more than approximately ten intervals, and no less than four.