PermulaanKonsep·6 min

Peraturan Empirikal 68-95-99.7 Dijelaskan

Kuasai peraturan empirikal (peraturan 68-95-99.7) untuk taburan normal. Pelajari cara menganggarkan kebarangkalian dengan cepat dan mengenal pasti pencilan menggunakan sisihan piawai.

Apakah Peraturan Empirikal?

Peraturan empirikal (juga dipanggil peraturan 68-95-99.7 atau peraturan tiga-sigma) ialah kaedah ringkas untuk mengingati peratusan nilai dalam taburan normal yang jatuh dalam 1, 2, dan 3 sisihan piawai daripada min.

68%

dalam ±1σ

95%

dalam ±2σ

99.7%

dalam ±3σ

Pecahan Visual

The Classic Bell Curve

Julat	Peratusan
μ ± 1σ	68.27%
μ ± 2σ	95.45%
μ ± 3σ	99.73%

Aplikasi Praktikal

Anggaran Kebarangkalian Pantas:Tanpa pengiraan yang rumit, anda boleh menganggarkan bahawa kira-kira 95% data jatuh dalam 2 sisihan piawai daripada min.
Pengesanan Pencilan:Titik data melebihi 3σ berlaku kurang daripada 0.3% daripada masa, menjadikannya pencilan statistik yang patut disiasat.
Kawalan Kualiti:Metodologi Six Sigma menggunakan peraturan ini untuk menetapkan ambang kualiti dan mengenal pasti variasi proses.

Contoh Penyelesaian

Contoh: Markah SAT

Markah SAT bertaburan normal dengan μ = 1050 dan σ = 200. - 68% markah jatuh antara 850 dan 1250 (±1σ) - 95% markah jatuh antara 650 dan 1450 (±2σ) - 99.7% markah jatuh antara 450 dan 1650 (±3σ) Markah 1450+ meletakkan pelajar dalam 2.5% teratas pengambil ujian.

Batasan

Hanya Berkesan untuk Taburan Normal

Peraturan empirikal HANYA terpakai untuk data yang mengikuti taburan normal (Gaussian). Untuk data yang pencong atau bukan normal, peratusan ini tidak terpakai. Sentiasa semak sama ada data anda bertaburan normal sebelum menggunakan peraturan 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.