What Is the Coefficient of Variation?

The coefficient of variation (CV) measures how spread out a data set is relative to its own mean. It is the standard deviation divided by the mean, expressed as a percentage: CV = (σ / μ) × 100. Because it is unit-free, the CV lets you compare variability between data sets that use completely different scales — a lab measurement in milligrams versus a stock return in dollars, for example.

How This Calculator Works

Paste or type your data values separated by commas, spaces, or new lines, choose between sample and population standard deviation, and click Calculate. The calculator computes the mean, variance, standard deviation, and coefficient of variation, then visualizes each data point against the mean so you can see which values fall within one standard deviation of the center.

With the default data set (10, 12, 23, 23, 16, 23, 21, 16), the mean is 18 and the sample standard deviation is about 5.24, giving a CV of roughly 29.1% — moderate variability. Switching to population mode changes the standard deviation to about 4.90 and the CV to 27.2%, since the variance then divides by n instead of n − 1.

Sample vs Population Standard Deviation

Use population when your data covers every member of the group (all students in a class, every batch a factory produced). Use sample when your data is a subset drawn from a larger group — the typical case in research. The sample formula divides by n − 1, a correction that prevents the variance from being systematically underestimated on average.

Interpreting Your Result

A CV below 15% indicates low relative variability, meaning values cluster tightly around the mean — desirable in quality control and measurement. A CV of 15–30% is moderate. Above 30%, the data is highly variable relative to its center. In investing, the CV is used as a risk-adjusted return measure: a lower CV means more consistent returns per unit of average return.

When the CV Should Be Avoided

The CV is only meaningful when the mean is a sensible reference point. If the mean is at or near zero, the ratio becomes extreme or undefined. If values can be negative (like temperature in Celsius or profit margins), the mean may not represent a meaningful center, and the CV can mislead. In those cases, report the standard deviation directly instead.