PRB-05

Standard error

Mean of n.

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ProbabilitySEM

Governing equation

\\mathrm{SE}=\\sigma/\\sqrt{n}

$n \in \left[2, 1000\right]$

where

\sigma: σ (—)
n: n (—)
SE: SE (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\\mathrm{SE}=\\sigma/\\sqrt{n}

$n \in \left[2, 1000\right]$

$n = 2$ $SE = 7.071$

Along the curve

②

Domain of the variable — blue

n_{\min} = 2,\quad n_{\max} = 1000

$n \in \left[2, 1000\right]$

$n = 2$ $n = 2$

Along the curve

③

Response curve — green

\\mathrm{SE}=\\sigma/\\sqrt{n}

$n \in \left[2, 1000\right]$

$n = 2$ $SE = 7.071$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}SE}{\mathrm{d}n}

$n \in \left[2, 1000\right]$

$n = 8.277$ $SE^{\prime} = -0.354$

Along the curve

Lecture brief

Historical brief

Bernoulli trials, Poisson, Gauss, Bayes and Shannon entropy turned chance into a calculus of belief and noise. The lab computes likelihood, interval and information in SI-free counts. This sheet (PRB-05 — Standard error) is the form associated with SEM. Working symbols: $\sigma$ , $n$ $\rightarrow$ $SE$ . Mean of n.

Purpose

Purpose: compute

SE

from

\sigma

n

in Probability & statistics via

\\mathrm{SE}=\\sigma/\\sqrt{n}

Mean of n. Use it when a real probability & statistics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\sigma = 10.000\,\mathrm{—}

n = 25.000\,\mathrm{—}

, the governing relation

\\mathrm{SE}=\\sigma/\\sqrt{n}

yields

SE = 2.0000\,\mathrm{—}

. Mean of n. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

σ \sigma10 —n n25 —

Outputs

SE SE2.0000 —

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Narration of this film

Mean of n.

Reading speed

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