Standard Error of Median Calculator

About this calculator

The standard error of the sample median is estimated with the classic asymptotic formula SE(median) ≈ 1.2533 × SD ÷ √n, where the constant 1.2533 is √(π/2) and comes from the relationship between the normal distribution's density at its center and the median's sampling variability. It's larger than the standard error of the mean (SD ÷ √n) by that same factor, reflecting that the median is a less statistically efficient estimator than the mean under normality.

Statisticians and researchers use this when reporting a median alongside a confidence interval or margin of error in a paper — especially for skewed data where the median is the preferred central-tendency measure — and biostatisticians use it when summarizing lab values or survival-type data that don't follow a normal distribution.