Statistics Dictionary

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Uniform Distribution

The meaning of the term "uniform distribution" depends on the context in which it is used.

In the context of probability distributions, uniform distribution refers to a probability distribution for which all of the values that a random variable can take on occur with equal probability. This probability distribution is defined as follows.

Uniform Distribution. Suppose the random variable X can assume k different values. Suppose also that the P(X = xk) is constant. Then,

P(X = xk) = 1/k

Consider the toss of a single die. The outcome of this toss is a random variable that can take on any of six possible values: 1, 2, 3, 4, 5, or 6. Each of these outcomes is equally likely to occur. The probability that any particular outcome will occur is equal to 1/6. Therefore, the outcome from the toss of a single die has a uniform distribution.

The term "uniform distribution" is also used to describe the shape of a graph that plots observed values in a set of data. Graphically, when the observed values in a set of data are equally spread across the range of the data set, the distribution is also called a uniform distribution. Graphically, a uniform distribution has no distinct peaks.

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Uniform distribution
(no peaks)
 Non-uniform distribution
(peaks and valleys)
See also:   Statistics Tutorial: Probability Distributions | AP Statistics Tutorial: Graphical Display of Data