Repeatability and Type A Uncertainty Calculator
Paste a set of repeated readings taken at the same point. The calculator gives the mean, experimental standard deviation, the Type A standard uncertainty of the mean and the degrees of freedom, as used in uncertainty budgets.
- Mean = Σx ÷ n = 10.0017
- s = √[Σ(x − mean)² ÷ (n − 1)] = 0.001494
- uA = s ÷ √n = 0.0004726
Type A Evaluation (GUM)
s = √[Σ(xi − x̄)² ÷ (n − 1)]
uA = s ÷ √n, ν = n − 1
s is the experimental standard deviation of single readings (repeatability), uA the standard uncertainty of the mean of n readings and ν the degrees of freedom, as defined in the GUM (JCGM 100). Use s itself, not s/√n, if the calibration result is based on a single reading.
Worked example
Ten readings around 10.002 have a mean of 10.0017, s ≈ 0.0015 and a Type A uncertainty of the mean of about 0.00048 with 9 degrees of freedom.
Frequently Asked Questions
What is Type A uncertainty?
Uncertainty evaluated by statistics from repeated observations, as opposed to Type B, which comes from certificates, specifications or experience.
Why divide by n − 1?
It gives an unbiased estimate of the variance from a sample, because the mean was estimated from the same data.
How many readings should I take?
At least 5, often 10. Few readings give a poorly known standard deviation and a larger coverage factor.
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