Algorithm A calculator

Robust mean, robust SD and u(xpt) from a list of results. Free, no sign-up. Everything runs in your browser; nothing you enter is sent or stored.

Try Algorithm A

Edit the results. The robust and plain statistics update as you type. Decimal commas work too.

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Results, p12

Median5.2150

Robust mean x*5.2160

Robust SD s*0.0531

Plain mean5.2350

Plain SD0.2700

u(x_pt) = 1.25 s*/√p0.0192

Iterations30

Solid line: robust mean. Dashed: plain mean. Shaded: x* ± 1.5 s*. Orange dots were clipped.

How it works

Algorithm A (ISO 13528) finds a mean and standard deviation that ordinary outliers cannot drag around. It starts from the median and 1.483 × MAD, pulls any result further than 1.5 s* from x* in to that limit, recomputes the mean and 1.134 × the SD of the adjusted values, and repeats until the numbers stop changing.

When the robust mean is used as the assigned value, its standard uncertainty is about 1.25 × s* / √p for p results. If that is more than 0.3 σ_pt, consider z′ instead of z.

Robust statistics need enough results: with fewer than about a dozen, or with two groups of results (two methods), treat the output with care.

For learning and for checking your own arithmetic. Your scheme's report and rules are what count.