Peak Height Formula for a Normal Distribution

Conditions

• The distribution is a normal distribution.
• $\sigma > 0$ is the standard deviation.
• $\mu$ is the mean.

Reasoning, step by step

1. Recall the probability density function of a normal distribution.
2. Evaluate the function at the mean $x = \mu$.
3. Simplify the expression to find the maximum value (peak height).
4. Observe that the peak height depends only on the standard deviation $\sigma$.
5. State the formula: $f(\mu)=1/(\sigma\sqrt{2\pi})$.

Example

The video states: 'The editorial peak formula is $f(\mu)=1/(\sigma\sqrt{2\pi})$: the entire product of the standard deviation and the square root of 2π is in the denominator.'

Common misconceptions

• Forgetting the $\sqrt{2\pi}$ factor in the denominator.
• Thinking the peak height depends on the mean $\mu$.

Watch the explanation

Connected concepts

Explore next

• Why can't the peak heights be the same when comparing two normal distributions with different standard deviations?
• How does the magnitude of the standard deviation affect the width and height of the normal distribution curve?
• What does the mean represent in a normal distribution graph?