Wikimore

Summary

Description	English: Plot of uncertainty vs. number of measurements of normal distributed measurement values. Measurement uncertainty calculated with $s_{\overline {x}}={\frac {1}{\sqrt {N}}}\cdot s$ , with $N$ the number of measurements and $s$ the corrected sample standard deviation ${\displaystyle s={\sqrt {{\frac {1}{N-1}}\sum _{i=1}^{N}\left(x_{i}-{\bar {x}}\right)^{2}}}.}$
Date	6 March 2022
Source	Own work
Author	MikeRun
SVG development InfoField	created on a Raspberry Pi 18px. The SVG code is valid. This diagram was created with Mathematica. Category:Valid SVG created with Mathematica code#Plot-uncertainty-num-of-measurements-200.svg
Source code InfoField	Mathematica code mean = 1.65; stdDev = 0.1; maxSampleSize = 200; data = RandomVariate[NormalDistribution[mean, stdDev], maxSampleSize]; stdDevList = Table[StandardDeviation[data[[1 ;; i]]], {i, 2, maxSampleSize}]; uncertaintyList = Table[1/Sqrt[i]*StandardDeviation[data[[1 ;; i]]], {i, 2, maxSampleSize}]; uncertaintyListPlot = ListPlot[uncertaintyList, PlotRange -> {{0, maxSampleSize}, {0, Max[uncertaintyList]}}, AxesLabel -> {N, Subscript[u, x]}]

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