Measures of Dispersion and Skewness

Measures of Dispersion and Skewness
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  • 0:01 Our Data
  • 0:55 Variability
  • 1:50 Positive Skew
  • 2:21 Negative Skew
  • 3:02 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn how you can describe your data using two different statistical characteristics. Learn what it means for your graph to have variability and what it means for your graph to be skewed.

Our Data

In statistics, we have various ways of describing how our data is behaving. In this video lesson, we will look at two of these methods. We will look at measures of dispersion, or variability, and skewness. I will define these terms when we get to each. It is important to learn about them because you will come across these terms as you progress in your statistics classes. You will also see these terms describing real-world statistical data. For example, you might come across these terms at a bank when you are discussing money matters and your banker is showing you graphs of how the bank is performing.

To help with our discussion, we will look at this graph:

Example graph
dispersion

This graph shows how often a certain number of donuts are purchased. We see that most people purchase four donuts at a time. Rarely do people purchase a dozen or 11 donuts. We see that the graph has a high point at four donuts and trails off to the right and to the left. Now let's see how we can describe this statistically.

Variability

We begin with variability, or dispersion. This means how much spread out our data is. Looking at our data, we see that our data ranges from 1 donut purchased to 12 donuts purchased. How we note this variability depends on the particular measurement type we choose. There is not enough room in this video lesson to go into the various types of statistical measurements. But all of the measurement types for dispersion or variability do have one thing in common, and that is all of the measurements will be positive.

If the measurement is zero, then that means all the data is exactly the same. In our donut example, a dispersion of zero would mean that everybody buys the same number of donuts. The higher the dispersion amount, the more varied the data is. Data that ranges from 0 to 50 will have a smaller dispersion amount than data that ranges from 0 to 100.

Positive Skew

Let's move on to our next topic, which is skewness. When data is skewed, it means that data leans more to one side than the other. You can see this in our donut example: The tip of our data is not perfectly in the center. We call the data that trails to the left and to the right the tails. So if our right tail is longer than the left, then we call our graph right-tailed. And if our data trails more to the right, then the amount of skew will be positive. In our donut example, we have a positive skew.

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