Lognormal Distribution Calculator

Find the mean, median and variance of a lognormal distribution.

Mean 3.08

Median 2.718

Variance 2.695

Formula: mean = e^(μ+σ²/2); median = e^μ

Step-by-step with your numbers:

1. Values used:

2. μ (mean of ln X) = 1

3. σ (SD of ln X) = 0.5

5. Mean = 3.08

6. Median = 2.718

7. Variance = 2.695

Did we solve your problem today?

If a variable's logarithm is normal, the variable itself is lognormal — common for incomes and sizes.

The math behind it

mean = e^(μ+σ²/2), median = e^μ. The mean exceeds the median, giving a right skew.

μ 1, σ 0.5 → mean ≈ 3.08, median ≈ 2.72.

Why is it skewed?

Exponentiating a symmetric normal stretches the upper tail.