Quantitative Aptitude · Measures of Central Tendency and Dispersion

Coefficient of Variation and Comparing Dispersion

Updated 1 October 2026 · Fact-checked

The coefficient of variation (CV) is the standard deviation divided by the mean, multiplied by 100. It is a relative measure, so it compares variability across data sets with different units or averages. The series with the smaller CV is more consistent. The series with the larger CV is more variable.

Understand Coefficient of Variation and Comparing Dispersion

Standard deviation tells you how spread out data is. But it is an absolute measure. It carries the unit of the data and depends on the size of the values.

Suppose one shop has daily sales with mean ₹10,000 and SD ₹500. Another has mean ₹1,00,000 and SD ₹2,000. The second SD is larger. Does that mean the second shop is less steady? Not really. Compared with its average, the spread is tiny.

The coefficient of variation fixes this. It expresses SD as a percentage of the mean. That removes the unit and the scale, so you can compare any two series fairly.

The rule is simple. Lower CV means more consistent, more stable, more uniform. Higher CV means more variable. Questions use words like consistency, stability, uniformity, variability and risk. All of them point to CV.

Use CV when the means differ, or when the units differ (for example kg and cm). If both series have the same mean and unit, comparing SD directly gives the same answer.

Key formulas to remember

Coefficient of variation: CV = (σ ÷ x̄) × 100; σ is the standard deviation, x̄ is the arithmetic mean. The result is a percentage. Use the mean as a positive value.
Variance to SD: σ = √Variance; If a question gives variance, take the square root before computing CV.
Consistency rule: Smaller CV ⇒ more consistent; larger CV ⇒ more variable; Compare CVs of the two series only. Do not compare SDs when means differ.
Finding SD from CV: σ = CV × x̄ ÷ 100; Use this when CV and mean are given and SD is asked.
Effect of change of origin and scale: For y = a + bx: ȳ = a + b·x̄ and σy = |b|·σx; Adding a constant does not change SD, but it changes the mean, so CV changes.

How to solve Coefficient of Variation and Comparing Dispersion questions

This method works for any question that asks which series is more consistent, or asks for CV itself.

1Read what is asked: CV value, the more consistent series, or a missing mean or SD.
2Write down the mean and SD of each series. If variance is given, take its square root.
3If the mean or SD is not given, compute it from the data first.
4Apply CV = (σ ÷ x̄) × 100 for each series.
5Compare the two CVs. The smaller one is more consistent.
6Check the wording. If it asks for 'more variable', pick the larger CV.
7Match your answer to the options and state the series name, not just the number.

Quickest way: Compare ratios without full division

When to use it: Use this when two series are given with their means and SDs and you only need to decide which is more consistent.

Do not multiply by 100. It is common to both series, so skip it.
Compare the fractions σ₁/x̄₁ and σ₂/x̄₂ by cross-multiplying: compare σ₁ × x̄₂ with σ₂ × x̄₁.
The series with the smaller fraction is more consistent.
Round only if the options are far apart. If two CVs are close, compute to one decimal place.
If the means are equal, the smaller SD wins directly. If the SDs are equal, the larger mean wins.
Skip questions that need a long SD calculation from raw data unless the numbers are small. Come back if time remains.

Common mistakes in Coefficient of Variation and Comparing Dispersion

Choosing the series with the larger CV as more consistent.
Students associate a bigger number with better.
Fix: Remember that CV measures variation. Less variation means more consistency, so pick the smaller CV.
Comparing standard deviations instead of CVs when the means differ.
SD is the first number given, so it feels like the answer.
Fix: Whenever the means are different, compute CV. Only use SD alone if the means and units are the same.
Using variance in place of SD in the formula.
The question gives variance and the student forgets the square root.
Fix: Check the label. If it says variance or σ², take the square root first.
Writing CV without the percentage or forgetting the ×100 when the option is a value.
Students rush and stop at σ ÷ x̄.
Fix: Multiply by 100 whenever the answer must be a CV value. You may skip it only when comparing.
Assuming CV stays the same when a constant is added to every item.
SD does not change when a constant is added, so students assume CV does not change either.
Fix: The mean changes when you add a constant, so CV changes. Recompute the mean and then the CV.

Worked examples

Example 1

Series A has mean 50 and SD 10. Series B has mean 80 and SD 12. Which statement is correct? (a) A is more consistent, CV 20% (b) B is more consistent, CV 15% (c) A is more consistent, CV 15% (d) B is more consistent, CV 20%

Show the solution

CV of A = (10 ÷ 50) × 100 = 20%.
CV of B = (12 ÷ 80) × 100 = 15%.
B has the smaller CV, so B is more consistent.
The correct option states B with CV 15%.

Answer: (b) B is more consistent, CV 15%

Example 2

A firm's workers in Plant X earn a mean wage of ₹600 with variance 144. Plant Y has mean ₹500 and SD ₹15. Which is correct? (a) X has CV 2% and is more consistent (b) X has CV 2% and is less consistent (c) Y has CV 3% and is more consistent (d) Y has CV 12% and is more consistent

Show the solution

For X, SD = √144 = 12.
CV of X = (12 ÷ 600) × 100 = 2%.
CV of Y = (15 ÷ 500) × 100 = 3%.
X has the smaller CV (2% against 3%), so X is more consistent.
Option (a) states X with CV 2% and more consistent. Options (b), (c) and (d) each contradict these results.

Answer: (a) X has CV 2% and is more consistent

Example 3

For a series, the mean is 40 and the CV is 25%. What is the variance? (a) 10 (b) 25 (c) 100 (d) 1,000

Show the solution

σ = CV × x̄ ÷ 100 = 25 × 40 ÷ 100 = 10.
Variance = σ² = 10² = 100.
Option (a) 10 is the SD, not the variance. That is the trap.

Answer: (c) 100

Exam tips

Read the last line first. It tells you whether to pick the more consistent or the more variable series.
Check whether the question gives SD or variance. Many wrong answers come from this one slip.
Under time pressure, compare σ ÷ x̄ by cross-multiplying and skip the ×100 step.
Questions that give CV and mean and ask for variance are common. Find SD first, then square it.
With negative marking of 0.25, skip a long raw-data SD question if you are unsure. Attempt the quick comparison questions first.

Practice questions from Measures of Central Tendency and Dispersion

Coefficient of Variation and Comparing Dispersion: frequently asked questions

What is the formula for coefficient of variation?

CV = (standard deviation ÷ mean) × 100. It is expressed as a percentage. It is used to compare the relative spread of different data sets.

Which series is more consistent, the one with higher or lower CV?

The series with the lower CV is more consistent. A lower CV means the spread is small compared with the average. A higher CV means greater variability.

Why can't I just compare standard deviations?

Standard deviation is an absolute measure and depends on the size and unit of the data. If the means differ, a larger SD does not necessarily mean more variation. CV removes this problem by relating SD to the mean.

Is CV the same as variance?

No. Variance is the square of the standard deviation and carries squared units. CV is a unit-free percentage that compares relative variability.