Standard Error of Median Calculator

How it is calculated

Values can be separated by commas, semicolons, spaces or line breaks. The tool needs at least 2 numbers; one non-numeric item makes the whole entry invalid rather than being skipped. It sorts the data and finds the median (the middle value, or the average of the two middle values when n is even), then computes the sample standard deviation with the n − 1 divisor:

SD = √( Σ(x − x̄)² ÷ (n − 1) )

The standard error of the median is the large-sample approximation for roughly normal data:

SE(median) = 1.2533 × SD ÷ √n

Results are shown to four decimals together with n. Because the formula assumes near-normal data, it is only a rough guide for small or strongly skewed samples; it is not a bootstrap estimate.

Common mistakes

• Typing decimals with a comma, such as 12,5. The comma is a separator, so this is read as the two values 12 and 5 and changes n and the result. Use a decimal point.
• Leaving a word, unit or symbol among the numbers (for example 14 kg). Any non-numeric item makes the tool return nothing.
• Confusing this with the standard error of the mean. The mean's SE is SD ÷ √n; the median's is 1.2533 times larger, so do not swap them in a report.
• Applying it to very skewed or heavy-tailed data and treating the figure as exact. The 1.2533 factor assumes a roughly normal distribution.
• Using the result with a tiny sample. With n = 2 or 3 the estimate is very unstable, since it rests on a sample SD from only a few points.