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Fundamentals of Statistics 1: Basic Concepts :: The Standard Deviation and Coefficient of Variation

Properties of the Standard Deviation

In terms of measuring the variability of spread of data, we've seen that the standard deviation is the preferred and most used measure.


Some additional things to think about the standard deviation:
  1. The standard deviation is the typical or average distance a value is to the mean
  2. If all values are the same, then the standard deviation is 0
  3. The standard deviation is heavily influenced by outliers just like the mean (it uses the mean in its calculation).
  4. The sample standard deviation is denoted with the letter s and the population standard deviation is denoted with the lower case Greek letter sigma σ.
If your data is more spread out (has more variability) then you will have a higher standard deviation. It's often difficult to interpret a standard deviation since it's based on the sample of data. Is a standard deviation of 12 high or is a .20 high? 

Coefficient of Variation (CV)

If you know nothing about the data other than the mean, one way to interpret the relative magnitude of the standard deviation is to divide it by the mean. This is called the coefficient of variation. For example, if the mean is 80 and standard deviation is 12, the cv = 12/80 = .15 or 15%.

If the standard deviation is .20 and the mean is .50, then the cv = .20/.50 = .4 or 40%. So knowing nothing else about the data, the CV helps us see that even a lower standard deviation doesn't mean less variable data.

I've found the CV to be an underused metric considering it is so simple to compute and helps a lot with understanding relative variability.

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