You need not do this rather complicated calculation for x and s by hand. The "Online Statistics" in all instruments of the Surfix® family automatically calculates these values and displays them updated after each measurement.

However, the measurement result M is not yet complete. It must still be complemented by the measurement uncertainty u of the measurement instrument described in the following Point 2.

To 2. The statistical measurement uncertainty u, specified by the manufacturer of the measurement instrument, overlaps the measurement result determined under Point 1, i.e. the standard deviation s and the measurement uncertainty u are added geometrically and not arithmetically:

Depending of the type of calibration, there are three different measurement uncertainties specified for the various Surfix® instrument families:
e.g.

u1 = ± 3μm/0.12mils or ± 3% of the measurement value (works calibration)
u2 = ± (1μm/0.04mils + 2% of the measurement value) (single-point calibration)
u3 = ± (1μm/0.04mils + 1% of the measurement value) (two-point calibration)

Also refer to the measurement uncertainties stated in technical specifications for the instrument.

The corresponding measurement uncertainty u is to be calculated and applied.

Example (in μm; after a two point calibration):

Example (in μm; after a two point calibration):