Statistics / Unit 1: Data and Displays
1.6 Describing Shape, Center and Spread
Notes
To describe a distribution, comment on its shape, center, spread and any unusual features (outliers, gaps, clusters), always in context.
- Symmetric: the left and right sides are roughly mirror images.
- Skewed right: the tail stretches toward larger values. Skewed left: the tail stretches toward smaller values. The skew is named for the tail.
- Unimodal has one peak, bimodal has two peaks and uniform is roughly flat.
- Example: Household incomes are skewed right, since a few very high incomes stretch the right tail.
Practice
A histogram of quiz scores has a long tail stretching to the left. The shape is:
Skew is named for the direction of the tail.
Which variable is most likely skewed right?
A few very large values create a long right tail. The other choices are symmetric, skewed left and uniform.
A histogram of heights of players from both a boys' team and a girls' team shows two separate peaks. This most likely means:
A bimodal shape often signals two groups with different typical values.
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