Overview:
Relative frequencies refer to estimates of probabilities taken from actual data. Suppose that a survey of 1000 voters is taken and 213 of them state that they are going to vote in favor of a certain issue. The relative frequency would be 213/1000 or .213.
Difference between Probability and Relative Frequency
Suppose that a major league player has a batting average of about .300. That means that the average probability of hits to times at bat is about .30. That player’s actual ratio of hits to times at bat is 45 hits to 136 times at bat or .331. The batting average of .331 expresses the relative frequency of hits to times at bat.
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Figure 1: The batting average of a baseball player is an example of relative frequency, if it is taken from the actual ratio of hits to times at bat, |
Frequency Distributions
Suppose that a researcher is interested in perception, and shows 25 people a reversible figure. She measures how many seconds they see one pattern before it reverses, and gets the following raw scores: 2, 7, 10, 5, 5, 3, 9, 11, 5, 8, 2, 4, 7, 6, 10, 7, 3, 9, 7, 11, 4, 6, 3, 1, and 8. The raw scores don’t mean very much unless they are arranged in some order. A frequency distribution will show how often particular scores are reached, and how many times. For example, the highest score of 11 was reached twice or 2/25, while the most frequent score of 7 was reached 4/25 times. The actual frequency distribution can take the form of a chart or a graph, showing more than one relative frequency.
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Figure 2: A frequency distribution shows relative frequencies from actual data |
Using Equal Fractions to Generate Relative Frequency
When the data gathered is based upon 25 subjects the fractions that form the relative frequency had 25 in the denominator. The relative frequencies were changed into decimal form, so they would be easier to compare. Any fraction can be changed to an equivalent form to make it easier to use in a pattern.
Grouping Data
Often a researcher will group data, especially if there are many data points, to clarify what the frequency distribution means. In the perception experiment, the frequencies of many of the elements are the same. The only thing that is clear from the graph is that the score of 7 occurs the most times. If the data are grouped so the values are from 1 to 3, from 4 to 6, 7 to 9, and 10 to 12, a clearer pattern emerges, showing that the larger scores on the figure test are less frequent. She will be able to use the data from that frequency distribution to generate more accurate probability estimates.
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Figure 3: Grouping data often shows a clearer pattern of relative frequencies. |
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