What is the formula for the mean of a continuous uniform distribution?

Conditions

• The distribution is continuous and uniform on the interval [a, b].
• a is the lower bound and b is the upper bound.

Reasoning, step by step

1. Identify the lower bound a and the upper bound b of the distribution.
2. Add the lower bound and the upper bound together.
3. Divide the sum by 2 to find the mean.

Example

For the bus waiting time uniformly distributed on [0, 60], the mean is calculated as $\mu = \frac{0 + 60}{2} = 30$ minutes.

Common misconceptions

• Assuming the mean predicts the most likely specific outcome, whereas in a uniform distribution all outcomes are equally likely.
• Confusing the mean with the median, although they are identical in a continuous uniform distribution.

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Explore next

• What is the formula for the standard deviation of a continuous uniform distribution?
• Why do the mean and standard deviation have no predictive power for a uniform distribution?
• How do you calculate the probability of an event occurring in a subinterval for a continuous uniform distribution?