Variationskoefficient Kalkylator

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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

  1. Compute the mean.Add all values and divide by the count.
  2. Compute the standard deviation.Use the sample or population formula as appropriate.
  3. Divide the standard deviation by the mean.This gives a ratio with no units.
  4. 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:

  1. Enter one data set, separated by commas, spaces or line breaks.
  2. Choose Sample or Population; the CV uses the matching standard deviation.
  3. Read the "Coeff. of Variation" result. To compare two data sets, enter each in turn and note both CVs.
  4. 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.

Relaterade kalkylatorverktyg

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Vanliga Frågor: Variationskoefficient Kalkylator

Allt du behöver veta om varians.

Vad är variationskoefficienten (CV)?

variationskoefficienten (CV) är lika med (standardavvikelse/medelvärde) × 100 %. Den mäter relativ variabilitet — hur stor spridningen är i förhållande till genomsnittet. En CV på 10 % betyder att standardavvikelsen är 10 % av medelvärdet. CV är användbart för att jämföra variabilitet mellan datauppsättningar mätta i olika enheter eller skalor.

Hur beräknar man variationskoefficienten?

För att beräkna CV: 1. Beräkna medelvärdet (x̄). 2. Beräkna standardavvikelsen (s eller σ). 3. Divide: CV = (standardavvikelse/medelvärde) × 100 %. Till exempel, om medelvärde = 50 och SD = 5, då CV = (5/50) × 100 % = 10 %. Använd det absoluta värdet av medelvärdet om det kan vara negativt.

Vad är en bra variationskoefficient?

Generellt: CV < 15 % indikerar låg variation (god konsistens). CV 15–30 % indikerar måttlig variation. CV > 30 % indikerar stor variation. Men vad som är "bra" beror på fältet. Vid laboratorietester förväntas CV < 5 %. I ekologiska studier kan CV > 30 % vara normalt. Inom tillverkning betyder lägre CV mer konsekvent produktion.

När ska man använda CV istället för standardavvikelse?

Använd variationskoefficienten när: 1. Jämför variation mellan datauppsättningar med olika enheter (t.ex. höjd i cm kontra vikt i kg). 2. Jämföra datamängder med mycket olika medel. 3. Bedömning av mätprecision över olika skalor. Enbart standardavvikelse kan vara missvisande när medelvärdet skiljer sig markant — CV normaliserar spridningen i förhållande till medelvärdet.

Kan variationskoefficienten vara större än 100%?

Ja. Ett CV > 100 % betyder att standardavvikelsen överstiger medelvärdet, vilket indikerar mycket hög relativ variabilitet. Detta kan hända med mycket skeva data, data med värden nära noll eller datauppsättningar med extrema extremvärden. Till exempel kan inkomstfördelningar i vissa populationer ha CV > 100 %.

Vad är skillnaden mellan variationskoefficient och varians?

Varians mäter absolut spridning i kvadratenheter. Variationskoefficient mäter relativ spridning i procent av medelvärdet. Varians beror på omfattningen av dina data — dubblering av alla värden fyrdubblar variansen. CV är skaloberoende — dubblering av alla värden lämnar CV oförändrat. Detta gör CV idealiskt för jämförelser mellan datauppsättningar.

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.