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For K-12 Students · Law of Large Numbers

Law of Large Numbers for a confidence interval

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a confidence interval live below — adjust the inputs and watch it respond, right in your browser.

Law of Large NumbersLive

chance averages out

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True P(heads)

Flip a coin a few times and the proportion of heads jumps around wildly; flip it thousands of times and it settles onto the true probability. That is the law of large numbers — averages converge even though individual flips stay random. Crucially, it does not mean a run of tails is "due" to reverse; that belief is the gambler's fallacy.

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Data Inspector

Flips0

Observed p0.0000

Deviation-50.00%

Governing equation

\overset{x}{ˉ}_{n} \to μ = 0.5 as n \to \infty (n = 0, ∣ \overset{x}{ˉ}_{n} - μ ∣ = 0.5000)

Reading this result: With a near-fair coin the running proportion wanders wildly at first, but the law pulls it toward 0.50 as flips pile up — and a streak of tails never makes heads “due.”

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Law of Large Numbers for a confidence interval" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.