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 value or group of values in a set of scores. Using the set of scores below, you would construct a table to organize these data by setting up a column including the highest and lowest scores, as well as the possible values in between. In this case, the highest score is 94 and the lowest is 80. You would then count the frequency of each value and list it in a separate column. The total number of the frequencies in the sample distribution is symbolized by the letter n. Table 1 contains the frequency distribution that results from these data.
20 scores from a 100-point psychology exam
80, 90, 94, 82, 83, 84, 88, 90, 89, 92, 82, 83, 83, 84, 85, 85, 85, 87, 85,
84
Table 1.
|
X |
f |
|
94 |
1 |
|
93 |
0 |
|
92 |
1 |
|
91 |
0 |
|
90 |
2 |
|
89 |
1 |
|
88 |
1 |
|
87 |
1 |
|
86 |
0 |
|
85 |
4 |
|
84 |
3 |
|
83 |
3 |
|
82 |
2 |
|
81 |
0 |
|
80 |
1 |
| n = 20 |
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 1), there are few extreme positive scores (not that many people did exceptionally well on the exam) and there are many scores between the values of 82 and 85. 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 values 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 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.