Uniform and Skewed Distributions

The uniform distribution has an equal number of occurrences in each category. The gray bars at left represent experimental data from a process expected to yield a uniform distribution. The yellow area shows an exact uniform distribution. The number of times a 1, 2, 3, 4, 5, or 6 is rolled on a fair die is theoretically a uniform distribution. In this experiment the results suggest the expected uniform distribution.

Compare the uniform distribution of individual rolls (above) to the distribution of averages in the die roll example(right).

Skewed distributions
In skewed distributions there are members in categories that tail away from the main group. The example at the left could represent a group of people categorized by age. Most are in the younger ages but a few are much older. Extreme values will pull the group average in their direction. In skewed distributions the average can be substantially different from the median. If the average is above the median (to the right on the graph) then the distribution is said to be skewed right, or toward the higher values. In the example, the median is 25 and the average is 30. 7. The direction of skew is always towards the "tail" of the distribution.

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