PemulaKonsep·6 min

Aturan Empiris 68-95-99,7 Dijelaskan

Kuasai aturan empiris (aturan 68-95-99,7) untuk distribusi normal. Pelajari cara mengestimasi probabilitas dan mengidentifikasi pencilan menggunakan simpangan baku.

Apa itu Aturan Empiris?

Aturan empiris (juga disebut aturan 68-95-99,7 atau aturan tiga sigma) adalah cara ringkas untuk mengingat persentase nilai dalam distribusi normal yang berada dalam 1, 2, dan 3 simpangan baku dari rata-rata.

68%

dalam ±1σ

95%

dalam ±2σ

99,7%

dalam ±3σ

Penjelasan Visual

The Classic Bell Curve

Rentang	Persentase
μ ± 1σ	68,27%
μ ± 2σ	95,45%
μ ± 3σ	99,73%

Aplikasi Praktis

Estimasi Probabilitas Cepat:Tanpa perhitungan rumit, Anda dapat mengestimasi bahwa sekitar 95% data berada dalam 2 simpangan baku dari rata-rata.
Deteksi Pencilan:Titik data di luar 3σ terjadi kurang dari 0,3% dari waktu, menjadikannya pencilan statistik yang layak diselidiki.
Pengendalian Mutu:Metodologi Six Sigma menggunakan aturan ini untuk menetapkan ambang batas mutu dan mengidentifikasi variasi proses.

Contoh Perhitungan

Contoh: Skor SAT

Skor SAT berdistribusi normal dengan μ = 1050 dan σ = 200. - 68% skor berada antara 850 dan 1250 (±1σ) - 95% skor berada antara 650 dan 1450 (±2σ) - 99,7% skor berada antara 450 dan 1650 (±3σ) Skor 1450+ menempatkan siswa di 2,5% teratas dari peserta ujian.

Keterbatasan

Hanya Berlaku untuk Distribusi Normal

Aturan empiris HANYA berlaku untuk data yang mengikuti distribusi normal (Gaussian). Untuk data yang menceng atau non-normal, persentase ini tidak berlaku. Selalu periksa apakah data Anda berdistribusi normal sebelum menggunakan aturan ini.

How to Read This Article

A statistics tutorial is a practical interpretation guide, not just a formula dump. It refers to the assumptions, notation, and reporting language that analysts need when they explain a result to a teacher, manager, client, or reviewer. The article body covers the specific topic, while the sections below create a common interpretation frame that readers can reuse across related metrics.

Reading goal	What to focus on	Common mistake
Definition	What the metric is and what quantity it summarizes	Treating the formula as self-explanatory
Formula choice	Sample versus population assumptions and notation	Using n when n-1 is required or vice versa
Interpretation	Whether the result indicates concentration, spread, or risk	Calling a large value good or bad without context

Frequently Asked Questions

How should I interpret a high standard deviation?

A high standard deviation means the observations are spread farther from the mean on average. Whether that spread is acceptable depends on the context: wide dispersion might signal risk in finance, instability in manufacturing, or genuine natural variation in scientific data.

Why do some articles mention n while others mention n-1?

The denominator reflects the difference between population and sample formulas. Population variance and population standard deviation use N because the full dataset is known. Sample variance and sample standard deviation often use n-1 because Bessel’s correction reduces bias when estimating population spread from a sample.

What is a statistical interpretation guide?

A statistical interpretation guide is a page that moves beyond arithmetic and explains meaning. It tells you what a metric is, when the formula applies, and how to describe the result in plain English without overstating certainty.

Can I cite this article in a report?

You should cite the underlying authoritative reference for formal work whenever possible. This page is best used as an explanatory bridge that helps you understand the concept before quoting the original standard or handbook.

Why include direct citations on every article page?

Direct citations give readers a route to verify the definition, notation, and assumptions. That improves trust and reduces the chance that a simplified explanation is mistaken for the entire technical standard.

Authoritative References

These sources define the concepts referenced most often across our articles. Bessel's correction is a sample adjustment, variance is a squared measure of spread, and standard deviation is the square root of variance expressed in the same units as the data.