PRB-34

SE of the mean

Sampling SE.

Reading speed

GoverningSE of the mean

Governing equation

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

$n \in \left[2, 400\right]$

where

sig: sig (—)
n: n (—)
se: SE of the mean (—)

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}

$n \in \left[2, 400\right]$

$n = 2$ $se = 2.828$

Along the curve

②

Domain of the variable — blue

n_{\min} = 2,\quad n_{\max} = 400

$n \in \left[2, 400\right]$

$n = 2$ $n = 2$

Along the curve

③

Response curve — green

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

$n \in \left[2, 400\right]$

$n = 2$ $se = 2.828$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}se}{\mathrm{d}n}

$n \in \left[2, 400\right]$

$n = 4.503$ $se^{\prime} = -0.263$

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-34 — SE of the mean) is the form associated with SE of the mean. Working symbols: $sig$ , $n$ $\rightarrow$ $se$ . Sampling SE. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

se

from

sig

n

in Probability & statistics via

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

Sampling SE. 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

sig = 4.000\,\mathrm{—}

n = 25.000\,\mathrm{—}

, the governing relation

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

yields

se = 0.800\,\mathrm{—}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

sig sig4 —n n25 —

Outputs

SE of the mean se0.800 —

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Sampling SE. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube