coefficient of variation
Standard deviation divided by the mean; lets you compare spread of metrics on different scales.
The coefficient of variation (CV) is the standard deviation divided by the mean, usually shown as a percentage:
It answers the question "how big is the spread relative to the typical level?" A standard deviation of 8 says little on its own: 8 hours is a lot for a 24-hour delivery and negligible for a 30-day subscription cycle. Dividing by the mean cancels the units, so you can compare the volatility of metrics measured in different units or on very different scales: dollars of ad spend against number of orders, sales of a bestseller against a niche product, revenue in a small market against a big one.
In business analytics the CV works as a quick stability score. A low CV means a predictable metric that is easy to plan around; a high one means a volatile metric that needs bigger buffers (stock, budget, staff) or an investigation into what drives the swings. Rules of thumb such as "under 10% is stable" exist, but what counts as high depends on the metric, so compare CVs of similar things rather than against a universal cut-off. (Labs and clinics use the CV to rate how precise a measurement is; the formula is the same.)
The CV only makes sense for positive values measured from a true zero: money, time, counts. For metrics that can be zero or negative, such as NPS, profit or growth rates, the mean can sit near zero and the CV explodes or flips sign. It also inherits the SD's sensitivity to outliers; on heavily skewed data a robust alternative is the interquartile range divided by the median.
Example
CatChow plans weekly stock for two products, based on the last few months of sales:
Looking only at the SD, dry food seems the less predictable product (40 vs 15). The CV says the opposite: relative to its usual level, treats swing 2.5 times as much ().
That changes the stock plan. A simple buffer of two SDs above the mean means bags of dry food (20% above the mean) but packs of treats (50% above the mean). The next question for the marketing team: what makes treat sales jump? Promotions, newsletters and seasonality are the usual suspects.
Common mistakes
- Comparing raw SDs across metrics of different size. A bigger product almost always has a bigger SD; the CV is what tells you which one is relatively more volatile.
- Using the CV on metrics that can be zero or negative. NPS, profit or week-over-week growth can have a mean near zero, and the CV becomes huge or meaningless.
- Comparing CVs at different time grains. Daily sales are naturally more volatile than weekly totals of the same product, so compare daily with daily and weekly with weekly.
- Letting one freak day set the CV. A single Black Friday or stock-out inflates both the SD and the CV; check for outliers first or use IQR ÷ median.
- Trusting a CV from a handful of points. Five weeks of data give a very rough SD, and the CV is just as rough.
Learn it in the course
- Spread: range, SD and quartiles · Two couriers with the same average delivery time, and why only one keeps the promise: range, variance, standard deviation, quartiles, IQR and the coefficient of variation.