By Nathan Jacobson
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Here is that stem-and-leaf display, along with the corresponding frequency distribution. 9 Frequency 4 3 15 26 20 8 Leaf 1 6 1 6 0 5 0 6 1 5 1 8 4 2 3 3 3 4 0 6 1 8 1 5 2 1 8 2 8 2 5 2 1 8 2 8 2 6 4 1 9 2 9 3 7 4 2 4 9 9 9 2 3 4 9 Age Frequency 30–35 35–40 40–45 45–50 50–55 55–60 60–65 65–70 70–75 75–80 80–85 85–90 2 1 6 1 7 8 6 5 7 6 4 1 One variation on a frequency distribution that can be made is called a relative frequency distribution. The frequencies are converted to a percentage of the total.
This Frequency means that two classes may not overlap. Consider the classes in the frequency distribution shown on the left. Several of these classes overlap. Suppose you had a value of 52 in your set of data. That value fits into the first class, 40–55, as well as the second class, 50–65. Where should we count it? It would be wrong to arbitrarily place it in one of these classes, and it would be wrong to count it twice. The best way to handle this is to prevent overlapping classes to begin with.
It does not belong in any of the classes, and this creates a problem. There should be no gaps between your classes. The second rule is that the classes must be mutually exclusive. This Frequency means that two classes may not overlap. Consider the classes in the frequency distribution shown on the left. Several of these classes overlap. Suppose you had a value of 52 in your set of data. That value fits into the first class, 40–55, as well as the second class, 50–65. Where should we count it? It would be wrong to arbitrarily place it in one of these classes, and it would be wrong to count it twice.