Log-normal Distribution Median Calculator

Log‑normal Distribution Median Calculator

For a log‑normal distribution where \(\ln(X) \sim N(\mu, \sigma^2)\), the median is: $$ \text{Median} = \exp(\mu). $$

* Enter the location parameter \(\mu\) (in practice, \(\mu\) is the mean of \(\ln(X)\)).

Step 1: Enter Parameter

e.g., 0

How It Works

The log‑normal distribution describes a random variable whose logarithm is normally distributed.

If \(\ln(X) \sim N(\mu, \sigma^2)\), the median of \(X\) is the 50th percentile, which for the underlying normal distribution is \(\mu\).

Therefore, the median of \(X\) is given by: $$ \text{Median} = \exp(\mu). $$

Formula: \( \text{Median} = \exp(\mu) \)

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