An Introduction to the Concept of Distribution

Distribution In descriptive statistics, the notion of the “distribution” of a set of data is simply “how the data are spread out”. Are the data all “clumped together”? Are they really spread out? Are there outliers?

Examples of Different Distributions In a “normal” distribution, the mean, median, and mode of a data set are all exactly THE SAME. If you were to graph the data (where the x-axis is the value and the y-axis is the number of occurrences), you would get a “Bell Curve”. Source: http://en.wikipedia.org/wiki/File:Standard_deviation_diagram.svg

Examples of Skewed Distributions In the Negative Skew, the bulk of the data is to the right, but there are some “serious” negative outliers. In the Positive Skew, the bulk of the data is to the left, but there are some “serious” positive outliers. Image source: http://en.wikipedia.org/wiki/File:Skewness_Statistics.svg

Which is which? Imagine a city with 10 people. 9 of the people are at the poverty line, and one is super- wealthy. Is this normal, negative, or positive skew? Several poor people Positive Skew!!! Note that the “bulk” of the data are negative, but that there are some serious positive outliers. 1 Rich Person

Which is which? Now, imagine the entire United States. If we were looking at IQ, what kind of distribution would you expect? Most people in the middle A few people on the really low end Normal Distribution!!! In fact, the Bell Curve is the classic example of what you should expect for a general population’s distribution of IQ… A few super-smart people

Which is which? What about a really, really easy test that your teacher gave? (Imagine everybody studied, except for one person who was sick during the entire unit.) What would the distribution of the scores look like? Most people did well Negative Skew!!! Most people in the class got a really high grade (it was an easy test), but a small number of people who didn’t get the information scored a really low grade. A few people did poorly