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Standard Error of Median Calculator

Paste your data values to compute the standard error of the median.

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.

Worked example

Data: 12, 15, 11, 18, 14, 16, 13, 20. Sorted: 11, 12, 13, 14, 15, 16, 18, 20, so n = 8 and the median is (14 + 15) ÷ 2 = 14.5. The mean is 119 ÷ 8 = 14.875. The squared deviations add up to 64.875, so the variance is 64.875 ÷ 7 = 9.268 and SD = 3.044. Standard error: 1.2533 × 3.044 ÷ √8 = 1.2533 × 3.044 ÷ 2.828 = 1.3490. The median is therefore reported as 14.5 with an SE of about 1.35.

Try this example →

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.

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.

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  • Editorial team

    A quick sanity check: for roughly normal data the standard error of the median is about 25 percent larger than the standard error of the mean, because the tool multiplies by 1.2533. So the median is the less precise summary when nothing is skewed, and its advantage is robustness to outliers, not precision. Very small samples make the approximation shaky. Do you usually report median with this SE, or compare it with a bootstrap?

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