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4.1 – Range

Range is the simplest measure of spread. Range measures the distance between the highest score (Xmaximum) and the lowest score (Xminimum) in a distribution.

Range

[latex]\text{Range}=X_{max}-X_{min}[/latex]

Take, for example, the following distribution of scores:

2, 5, 8, 3, 5, 7, 4, 2, 8, 3

Our first step is to put the scores in numerical order so that we can find the highest and lowest scores:

2, 2, 3, 3, 4, 5, 5, 7, 8, 8

Now we can see that the lowest score is 2, and the highest score is 8. Now we can calculate the range:

[latex]\text{Range}=X_{max}-X_{min}=8-2=6[/latex]

Thus, the range for this group of scores is 6. In other words, the group of scores vary from highest to lowest by 6 points.

While the range is relatively easy to calculate, it does not provide us with a lot of information. It is only based upon two scores in the distribution (the highest and the lowest), and ignores the others. For instance, take the following scores:

2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 8

Again, we can see that the lowest score is 2, and the highest score is 8. Now we can calculate the range:

[latex]\text{Range}=X_{max}-X_{min}=8-2=6[/latex]

These scores would also have a range = 6. However, all but one of the scores are bunched between 2 and 3. In other words, the scores in the group don’t vary that much (they are mostly either 2 or 3). Yet, because the range ignores most of the scores, and only is calculated based on the highest and lowest scores, it is really only useful for providing a very rough estimate of the spread in the scores.

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Introduction to Statistics and Statistical Thinking Copyright © 2022 by Eric Haas is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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