The Shape of Distributions Chapter 2 The Shape of Distributions

“Shape” of Distributions Symmetric/Normal Data is symmetric if the left half of its histogram is roughly a mirror image of its right half. Skewed Left or Right Data is skewed if it is not symmetric and if it extends more to one side than the other. Uniform Data is uniform if it is equally distributed (on a histogram, all the bars are the same height or approximately the same height).

Symmetric A distribution is symmetric if the left side of the graph is roughly a mirror image of the right side.

Skewed right A distribution is skewed to the right when the right side of the graph is more spread out than the left side.

Skewed left A distribution is skewed to the left when the left side of the graph is more spread out than the right side.

Uniform A distribution is uniform when the heights of the bars are all about the same.

Unimodal A distribution is unimodal when it shows one distinct peak Unimodal A distribution is unimodal when it shows one distinct peak. Note: the previous three graphs can also be considered unimodal.

Bimodal A distribution is bimodal if it has two distinct peaks Bimodal A distribution is bimodal if it has two distinct peaks. This graph has a peak at 0 and a peak at 0.8.

Caution: Unimodal vs Bimodal A common error is calling a distribution bimodal when it is really unimodal. To call a distribution bimodal, the peaks need to be clearly distinct. Sometimes a peak occurs because of our choice in boundaries. A good rule of thumb is that if moving one or two observations would eliminate a peak, then there is a good chance that the peak is only there because of our choice in boundaries.

Caution: Unimodal vs Bimodal Here are two histograms that use the exact same data, but different class widths. The first looks like it has two peaks, but the second seems clearly unimodal.

The Shape of Distributions Symmetric/Normal Uniform Bimodal Skewed left Skewed Right

Practice Identify the Shape of the Distribution

Answers to Worksheet Questions

Practice Normal Curve (Symmetric)

Skewed Left

Skewed Right

Bimodal

Skewed Left

Uniform

Matching i) (e) ii) (f) iii) (d) iv) (a) v) (b) vi) (c)

Guess the distribution Larson/Farber 4th ed.

Click to-Conversion Time

Adult Ganglion Cell Number