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The standard deviation helps estimate the spread or variation in a dataset. It can be used to compare two datasets only if they share the same scale or units, such as degrees Celsius, and have similar means.

So, datasets with significantly different means and scales of measurements can instead be compared using the coefficient of variation. The higher the variation in the datasets, the larger the coefficient of variation.

The sample and population coefficient of variation is the ratio of the standard deviation to the mean, expressed as a percentage.

Consider the meteorological reports on the temperature and rainfall, recorded over five months in a year. On computing the coefficient of variation for both these datasets, one observes that fluctuations in temperature are far less than that of rainfall.

Financially, the coefficient of variation allows investors to determine the price volatility in a stock investment or real estate. An investment with a lower coefficient of variation is less volatile and a safer investment.

The coefficient of variation measures the dispersion of the data points or distribution around the mean. Using the coefficient of variation, we can compare two data series with drastically different means or different units of measurement. The coefficient of variation for a sample and a population is expressed as a percentage of the ratio of standard deviation to the mean.

The coefficient of variation is a practical statistical tool in finance. It allows investors to assess the volatility or risk and the returns associated with their investments. An investment with a low coefficient of variation has lower volatility or risk, and hence it is safer than one with a high coefficient of variation.

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4.7 : Coefficient of Variation