Spread

In the last several sections we learned that one way to summarize a dataset is to describe its center. Now we'll look at a second way to summarize a dataset, which is the spread.

Dispersion, variability and scatter are synonyms for spread.

Intuitively, spread refers to how spread out the data elements are from one another. A dataset with high spread has its elements highly separated from one another, and a dataset with low spread has its elements close together.

Let's see a couple examples.

Example: Test scores for a reasonably challenging chemistry test

Students taking a chemistry test received the following scores (scale is 0-100):

83, 87, 61, 92, 38, 78, 73, 55, 98, 74, 86, 69, 40, 83

Since the scores are spread out over a fairly large part of the range of possible scores, we'd say that the scores have a reasonably high spread.

Note that judgments of "high" and "low" are subjective when we're talking about spread in an intuitive way. You might point out that there are no scores below 38 and so the spread could be even higher. That's true. But that's exactly why we want to be able to quantify the spread as we do in the following sections: we want to replace subjective judgments with objective measurements.

Example: Test scores for an easy math test

Students taking an easy math test received the following scores (scale is 0-100):

100, 100, 93, 92, 95, 98, 100, 100, 100, 95, 94, 88, 92

Here the spread is low, as everybody received a score in the narrow range 88-100. After the test the student who received an 88 admitted that she didn't know there was a test, and didn't study for it at all.

As with central tendency, there are multiple ways to measure spread, each with its own characteristics. We'll look at several approaches in the following sections.

Exercises

Exercise 1. At target practice, a skilled archer shoots ten arrows with the following result. How would you describe the spread?

Target

Exercise 2. A beginning archer shoots ten arrows with the following result. How would you describe the spread?

Target

Exercise 3. An archer shoots ten arrows with the following result. How would you describe the spread?

Target