## Tuesday, August 22, 2023

### The tale of the tails

Your data analyst comes to you with tales of the tails:
• Yikes! Our tails are fat!
• Wow! Our tails are thin.
If you're into big words, it's about the "kurtosis" of the data, a measure of the distribution of data around the mean or average of a bell-like distribution of probabilities. More or less kurtosis means more or less data, respectively, in the tails of the bell-like distribution.

If you don't care about the big words, but you do care about risk management and volatility or predictability that could affect your project, then here's what that is about:
• Fat Tails: If there's more data in the tails, farther from the mean, then there is correspondingly less data clustered around the mean. Interpret fat tails as meaning there are more frequent outliers and more non-average happenings, meaning more volatility and less predictability than a normal "bell curve" of data points.

• Thin tails: Really, just the opposite of the fat tails situation. Thin tails means less data in the tails, and the outliers, such as they are, are many fewer. There is a concentration around the mean that is more prominent than the usual bell curve.

Interpretation: more stability and predictability than even the steady-Eddie bell curve, because most happenings are clustered around a predictable norm.
Is there an objective metric?
Actually, yes. From math that you don't want to even know about, a normal "bell curve" has a kurtosis of "3". Fat tail distributions have a figure greater than 3; thin tail distributions, less than 3. Note: some analysts normalize everything to "0" +/-, rather than "3" +/-.

Excel formula:
As luck would have it, there is a formula in Excel for figuring the kurtosis of a data set. "KURT" is the formula, and you just show it your data set, and Excel does all the work! But as a PM interested in risk to your project, you just need to know from your analyst: fat, thin, or normal.

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