Skip to main content

Rolling Median (MEDIAN)

Summary

The middle order statistic of the trailing window: the central value when optInTimePeriod is odd, the mean of the two central values when it is even. A robust measure of central tendency — unlike SMA, a single spike moves it by at most one rank however large the spike is, which is what makes it useful as a filter rather than as a level.

Not to be confused with MEDPRICE, which is (High + Low) / 2 of one bar and is not an order statistic.

Formula

With W the window sorted ascending and W[1] its smallest value:

n odd :   MEDIAN = W[(n+1)/2]
n even:   MEDIAN = ( W[n/2] + W[n/2 + 1] ) / 2

Notes

  • This is not PERCENTILE at 50. PERCENTILE reports the nearest rank, which at even n selects the lower of the two central values: on a 4-bar window of 1, 2, 3, 4 this function returns 2.5 and PERCENTILE returns 2. At odd n the two agree bit for bit.
  • At even n the output can therefore be a value the series never traded at, which is the deliberate opposite of PERCENTILE's design property.
  • optInTimePeriod is not restricted to odd values: TA-Lib has no odd-only range mechanism, and it would surprise any caller reaching for a 20-bar median.
  • Every input value must be finite. A NaN makes every comparison against it false, which breaks the order the window is kept in, and the output can stay wrong long after the NaN has left the window.

Inputs

  • inReal — The series to take the median of

Outputs

  • outReal — Median of the trailing window

Parameters

ParameterTypeDefaultAccepted valuesDescription
optInTimePeriodinteger302–10000Number of trailing values in the window

Properties

Numerical Stability: Start-Independent

✅ Overlap Input i
☐ Independent Y-Axis
☐ Candlestick
☐ Can Output NaN or ±Inf
☐ Identity at Period 1

Implementation

TA-Lib Definition: median.c · median.yaml

NativeFile
Cta_MEDIAN.c
Rustmedian.rs
JavaCore_MEDIAN.java
C#Core_MEDIAN.cs

TA-Lib is also available for Python, R and more using a wrapper.

Aliases

Rolling Median, Moving Median, Running Median

See Also

PERCENTILE · SMA · MEDPRICE

References

  • NumPy numpy.median, R stats::median, scipy, Excel MEDIAN — four independent implementations of one unambiguous definition.
Last Updated: