Cumulative Relative Frequency Distribution

Firs, we need to explain a frequency distribution, which lists sets of scores and their frequency, which is how many times the score occurs. For example, a set of scores you are looking at is 1,1, 2, 2, 2, 3, 4, 4, 4. The frequency of score 1 is 2 because it appears twice in the set. The frequency of score 4 is 3 because it is represented three times in the score set. We also need to explain a cumulative frequency distribution, which is a list of scores, their frequency, and their cumulative frequency. Cumulative frequency is the total of a frequency and all of the frequency scores beneath it. In the previous score set example, the cumulative frequency for the score of 3 would be 6. This is determined by adding to frequencies of scores 1,2, and 3. Their respective frequencies are 2,3, and 1: cumulative frequency would be (2+3+1)=6.

Now, Relative frequency is a proportion of the times a score occurs. It is calculated by dividing the frequency of a score with the total number of scores in the score set. In the example score set the relative frequency of a score of 2 would be 0.33: 3 (frequency of score 2) divided by 9 (total number of scores) = 0.33. The cumulative relative frequency of a score is the total of a relative frequency and the relative frequencies of all of the scores below it. The cumulative relative frequency of a score of 2 would be 0.55: .22 (relative frequency of score 1) + .33 (relative frequency of score 2). The cumulative relative frequency of a score set will always add up to equal 1.