What is the formula for the standard deviation of a continuous uniform distribution?

Conditions

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

Reasoning, step by step

1. Identify the lower bound a and the upper bound b of the distribution.
2. Subtract the lower bound from the upper bound to find the interval width.
3. Divide the interval width by the square root of 12 to calculate the standard deviation.

Example

For the bus waiting time uniformly distributed on [0, 60], the standard deviation is calculated as $\sigma = \frac{60 - 0}{\sqrt{12}} \approx 17.321$ minutes.

Common misconceptions

• Assuming the standard deviation indicates a clustering of outcomes around the mean, which is false for a uniform distribution.
• Forgetting to take the square root of 12 in the denominator.

Watch the explanation

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