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13.5 - Shapes of distributions

Histograms and box plots can be quite useful in suggesting the shape of a probability distribution. Here, we'll concern ourselves with three possible shapes: symmetric, skewed left, or skewed right.

Skewed Left For a distribution that is skewed left, the bulk of the data values (including the median) lie to the right of the mean, and there is a long tail on the left side.

Skewed Right For a distribution that is skewed right, the bulk of the data values (including the median) lie to the left of the mean, and there is a long tail on the right side.

For a distribution that is symmetric, approximately half of the data values lie to the left of the mean, and approximately half of the data values lie to the right of the mean.

The following examples probably illustrate symmetry and skewness of distributions better than any formal definitions can.

Example 13-5 Section

Consider a random sample of weights (in pounds) of 40 female college students:

Do these data suggest that the distribution of female weights is symmetric, skewed right, or skewed left?