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Statistics and uncertainty

Combined uncertainty - formula in LaTeX

Combines statistical scatter with the accuracy of the instrument. The components are added in quadrature because they are independent. A subscript and a power on the same symbol are written together, in either order: u_A^2.

uc=uA2+uB2u_c = \sqrt{u_A^2 + u_B^2}

LaTeX code

Open in editor 
$$
u_c = \sqrt{u_A^2 + u_B^2}
$$

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What the symbols mean

ucu_c
combined uncertainty
uAu_A
type A uncertainty (statistical)
uBu_B
type B uncertainty (from the instrument)

A statistics and uncertainty formula - a required part of the data analysis in every lab report.

Worked example

Timing a pendulum: the scatter of results gives u_A = 0.03 s, and you estimate the stopwatch reaction time as u_B = 0.04 s. The root sign adjusts its height to the contents by itself, so it needs no \left or \right.

uc=(0.03 s)2+(0.04 s)2=0.05 su_c = \sqrt{(0.03\,\mathrm{s})^2 + (0.04\,\mathrm{s})^2} = 0.05\,\mathrm{s}

LaTeX commands in this formula

x_{0}
subscript; wrap several characters in braces
\sqrt
square root
x^{2}
superscript (power); wrap several characters in braces

How to use this formula in LaTeX?

  1. Copy the code with the button above - $$…$$ is centered display math.
  2. Paste it into the CamteX editor, Overleaf or any LaTeX document.
  3. Inside a sentence, use single $…$ instead of double.
  4. The formula works without extra packages.

Related formulas - Statistics and uncertainty

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