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PertengahanKonsep·8 min

Pekali Variasi (CV) Dijelaskan

Pelajari tentang pekali variasi (CV), juga dikenali sebagai sisihan piawai relatif. Fahami bila menggunakan CV vs SD untuk membandingkan kebolehubahan merentasi set data.

Apakah Pekali Variasi?

Pekali Variasi (CV), juga dikenali sebagai Sisihan Piawai Relatif (RSD), ialah ukuran serakan yang distandardkan. Ia menyatakan sisihan piawai sebagai peratusan min, menjadikannya berguna untuk membandingkan kebolehubahan merentasi set data dengan unit atau skala yang berbeza.

Set Data A: Ketinggian

Min: 170 cm, SD: 10 cm CV = 5.9%

Set Data B: Berat

Min: 70 kg, SD: 10 kg CV = 14.3%

SD yang sama (10), tetapi CV mendedahkan bahawa berat secara relatifnya lebih bervariasi

Formula CV

Pekali Variasi

CV = (σ / μ) × 100%

Di mana σ ialah sisihan piawai dan μ ialah min. Untuk data sampel, gunakan s dan x̄ masing-masing.

Contoh Pengiraan

Set Data: 12, 15, 14, 18, 11 - Min (x̄) = 14 - Sisihan Piawai (s) = 2.74 - CV = (2.74 / 14) × 100% = 19.6%

Bila Menggunakan CV

Gunakan CV Apabila:

- Membandingkan set data dengan unit yang berbeza - Membandingkan set data dengan min yang sangat berbeza - Data berskala nisbah (titik sifar sebenar) - Menilai ketekalan dalam pengukuran makmal - Analisis kewangan (membandingkan volatiliti)

Gunakan SD Apabila:

- Set data mempunyai unit yang sama dan min yang serupa - Data berskala selang (seperti suhu) - Min ialah sifar atau hampir sifar - Anda memerlukan maklumat sebaran mutlak

Contoh Praktikal

Kawalan Kualiti Makmal

Dalam kimia analitik, CV di bawah 10% sering dianggap boleh diterima untuk ketepatan. Kaedah yang sangat tepat boleh mencapai CV < 5%.
SahamPulanganSDCV
Saham A8%4%50%
Saham B12%9%75%

Saham A mempunyai CV yang lebih rendah = lebih banyak pulangan per unit risiko

Batasan CV

Batasan Penting

- Tidak tertakrif apabila min = 0: Pembahagian dengan sifar menjadikan CV tidak bermakna - Bermasalah dengan nilai negatif: Boleh menghasilkan keputusan yang mengelirukan - Tidak untuk skala selang: Suhu dalam Celsius/Fahrenheit mempunyai titik sifar sewenang-wenangnya

Further Reading

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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 goalWhat to focus onCommon mistake
DefinitionWhat the metric is and what quantity it summarizesTreating the formula as self-explanatory
Formula choiceSample versus population assumptions and notationUsing n when n-1 is required or vice versa
InterpretationWhether the result indicates concentration, spread, or riskCalling 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.