Pekali Variasi Kalkulator

Input Data

Σ Masukkan Nilai Data

Pisahkan nilai dengan koma, ruang, tab atau baris baru

0 nilai dimasukkan

Masukkan nilai data untuk melihat keputusan

What Is the Coefficient of Variation?

The coefficient of variation (CV) is the standard deviation divided by the mean, usually shown as a percentage. It tells you how large the spread is compared with the typical value. Because the units cancel, you can compare the consistency of things measured in different units, such as heights in centimetres and weights in kilograms, or of things on very different scales. It is sometimes called the coefficient of variance or the relative standard deviation; they all mean the same thing. All the examples on this page use the sample standard deviation; if you use the population version, say so, because the CV will be slightly smaller.

Formula

The CV divides the standard deviation by the mean:

Coefficient of Variation

CV = (s / x̄) × 100%

CVCoefficient of variation, as a percentage
sStandard deviation (sample s or population σ; state which)
x̄Mean (use |x̄| if it could be negative)

How to Calculate the Coefficient of Variation Step by Step

Compute the mean.Add all values and divide by the count.
Compute the standard deviation.Use the sample or population formula as appropriate.
Divide the standard deviation by the mean.This gives a ratio with no units.
Multiply by 100.Express the ratio as a percentage.

Coefficient of Variation Examples

1Comparing Heights and Weights

Data:Heights (cm): 170, 165, 180, 175, 172 | Weights (kg): 68, 72, 80, 75, 70

Solution:Heights — Mean = 172.4, SD ≈ 5.59, CV = 5.59 / 172.4 × 100% ≈ 3.25%. Weights — Mean = 73, SD ≈ 4.69, CV = 4.69 / 73 × 100% ≈ 6.43%.

Answer:Weights (CV ≈ 6.43%) vary more, relative to their mean, than heights (CV ≈ 3.25%)

2Lab Measurement Precision

Data:Instrument A: 5.02, 5.01, 5.03, 5.00, 5.02 | Instrument B: 5.10, 4.90, 5.20, 4.80, 5.00

Solution:Instrument A — Mean = 5.016, SD ≈ 0.0114, CV ≈ 0.23%. Instrument B — Mean = 5.00, SD ≈ 0.158, CV ≈ 3.16%.

Answer:Instrument A (CV ≈ 0.23%) is far more precise than Instrument B (CV ≈ 3.16%)

3Annual Rainfall in Two Cities

Data:City X (mm): 800, 850, 780, 820, 810 | City Y (mm): 200, 350, 150, 280, 220

Solution:City X — Mean = 812, SD ≈ 25.88, CV ≈ 3.19%. City Y — Mean = 240, SD ≈ 77.14, CV ≈ 32.14%.

Answer:City Y's rainfall is much less predictable (CV ≈ 32%) than City X's (CV ≈ 3%)

4Two Production Lines

Data:Line A: 100, 102, 98, 101, 99 | Line B: 500, 480, 520, 510, 490

Solution:Line A — Mean = 100, SD ≈ 1.58, CV ≈ 1.58%. Line B — Mean = 500, SD ≈ 15.81, CV ≈ 3.16%.

Answer:Line B is less consistent relative to its output (3.16% vs 1.58%), even though it produces more

5Sprint Times (seconds)

Data:Runner X: 10.2, 10.3, 10.1, 10.4, 10.2 | Runner Y: 12.5, 11.8, 13.2, 12.0, 12.5

Solution:Runner X — Mean = 10.24, SD ≈ 0.114, CV ≈ 1.11%. Runner Y — Mean = 12.40, SD ≈ 0.543, CV ≈ 4.38%.

Answer:Runner X is about four times as consistent (CV ≈ 1.1% vs 4.4%)

6Investment Returns (%)

Data:Fund A: 8, 10, 7, 9, 11 | Fund B: 15, 5, 20, -2, 12

Solution:Fund A — Mean = 9, SD ≈ 1.58, CV ≈ 17.57%. Fund B — Mean = 10, SD ≈ 8.63, CV ≈ 86.31%.

Answer:Fund B's returns are far more volatile relative to their average (CV ≈ 86% vs 18%)

How to Use This Coefficient of Variation Calculator

The CV is shown in the results for any data you enter:

Enter one data set, separated by commas, spaces or line breaks.
Choose Sample or Population; the CV uses the matching standard deviation.
Read the "Coeff. of Variation" result. To compare two data sets, enter each in turn and note both CVs.
Only compare CVs for data measured on a scale with a true zero (lengths, weights, counts, prices).

What the Calculator Shows You

The CV together with the mean and standard deviation it is built from.
Sample and population versions, so you can report which you used.
The full working for the standard deviation.
Calculations run in your browser; your numbers are not sent anywhere.

Where the Coefficient of Variation Is Used

Laboratory science

Judging the repeatability of an assay or instrument.

Finance

Comparing how volatile different assets are relative to their average return.

Manufacturing

Comparing consistency across machines or lines with different targets.

Agriculture

Comparing yield variability across fields or seasons.

Ecology

Comparing population fluctuations of species with very different abundances.

Interpreting a CV in Different Fields

What counts as a "good" CV depends heavily on what you are measuring. These are rough guides, not rules:

Analytical and laboratory work

Repeat measurements of the same sample are usually expected to agree closely, often within a few percent.

Manufacturing

For a stable process, CVs of a few percent are common. A rising CV is an early sign that something has changed.

Finance

CVs of returns are often large and can exceed 100%, especially when the average return is close to zero.

Biology and ecology

Natural variation is high. CVs of 30% or more are normal for things like animal population counts.

When not to use it

Do not use the CV for data that can be negative or has an arbitrary zero, such as temperatures in °C. A mean near zero makes the CV huge and meaningless.

Alatan Kalkulator Berkaitan

Terokai kalkulator berkaitan lain untuk menganalisis varians, serakan dan taburan statistik.

Peratusan Varians Kalkulator

Kira peratusan varians antara nilai atau nyatakan varians sebagai peratusan min. Dapatkan pekali variasi, varians, …

Sisihan Piawai Kalkulator

Kira sisihan piawai serta-merta dengan penyelesaian langkah demi langkah. Masukkan set data anda dan dapatkan popul…

x̄

Min Kalkulator

Kira min (purata) mana-mana set data serta-merta. Dapatkan min aritmetik, bersama-sama dengan varians, sisihan piaw…

s²

Varians Sampel Kalkulator

Kira varians sampel (s²) serta-merta dengan penyelesaian langkah demi langkah. Menggunakan pembetulan Bessel (n−1) …

Soalan Lazim: Pekali Variasi Kalkulator

Semua yang anda perlu tahu tentang varians.

Apakah pekali variasi (CV)?

pekali variasi (CV) bersamaan dengan (sisihan piawai / min) × 100%. Ia mengukur kebolehubahan relatif — berapa besar penyebaran berbanding purata. CV 10% bermakna sisihan piawai ialah 10% daripada min. CV berguna untuk membandingkan kebolehubahan antara set data yang diukur dalam unit atau skala yang berbeza.

Bagaimanakah anda mengira pekali variasi?

Untuk mengira CV: 1. Kira min (x̄). 2. Kira sisihan piawai (s atau σ). 3. Bahagi: CV = (sisihan piawai / min) × 100%. Contohnya, jika min = 50 dan SD = 5, maka CV = (5/50) × 100% = 10%. Gunakan nilai mutlak min jika ia boleh negatif.

Apakah pekali variasi yang baik?

Secara amnya: CV < 15% menunjukkan kebolehubahan yang rendah (konsistensi yang baik). CV 15–30% menunjukkan kebolehubahan sederhana. CV > 30% menunjukkan kebolehubahan yang tinggi. Walau bagaimanapun, apa yang "baik" bergantung pada bidang. Dalam ujian makmal, CV < 5% dijangka. Dalam kajian ekologi, CV> 30% mungkin normal. Dalam pembuatan, CV yang lebih rendah bermakna output yang lebih konsisten.

Bilakah anda harus menggunakan CV dan bukannya sisihan piawai?

Gunakan pekali variasi apabila: 1. Membandingkan kebolehubahan antara set data dengan unit yang berbeza (cth., tinggi dalam cm lwn berat dalam kg). 2. Membandingkan set data dengan cara yang sangat berbeza. 3. Menilai ketepatan pengukuran merentas skala yang berbeza. Sisihan piawai sahaja boleh mengelirukan apabila cara berbeza dengan ketara — CV menormalkan sebaran berbanding min.

Bolehkah pekali variasi lebih besar daripada 100%?

Ya. CV > 100% bermaksud sisihan piawai melebihi min, menunjukkan kebolehubahan relatif yang sangat tinggi. Ini boleh berlaku dengan data yang sangat condong, data dengan nilai hampir sifar atau set data dengan outlier yang melampau. Sebagai contoh, pengagihan pendapatan dalam sesetengah populasi boleh mempunyai CV > 100%.

Apakah perbezaan antara pekali variasi dan varians?

Variance mengukur sebaran mutlak dalam unit kuasa dua. Pekali variasi mengukur sebaran relatif sebagai peratusan min. Varians bergantung pada skala data anda — menggandakan semua nilai menggandakan varians. CV tidak bergantung pada skala — menggandakan semua nilai menjadikan CV tidak berubah. Ini menjadikan CV sesuai untuk perbandingan merentas set data.

Is "coefficient of variance" the same as coefficient of variation?

Yes. "Coefficient of variation" is the standard statistical term; "coefficient of variance" is a common alternative name for the same thing. Both mean (SD / mean) × 100%, and both are abbreviated CV.

Why is the coefficient of variation used in quality control?

It lets you compare the consistency of processes that run at different levels. Two filling machines might have different target weights; comparing their CVs tells you which is more consistent relative to its own target. Laboratories also use CV to judge the repeatability of an assay.