Kurtosis Explained: Basics of Kurtosis Interpretation on Graphs

Kurtosis is a statistical measure referring to the number of standard deviations from the mean you can see in the tails of a uniform distribution. This is why some statisticians refer to kurtosis as “tailedness”—it has to do with how light-tailed or fat-tailed a standard normal distribution is when you plot the data points on a graph. In mathematical equations, you might see kurtosis statistics abbreviated as “Kurt.”

Kurtosis shows up in how fat or slim the tails are in statistical measures. As you compare these tails to the peak of the diagram—often represented by a bell curve—you get a general idea of what the kurtosis is for any specific set of data. You can also see kurtosis in different types of diagrams like Pearson or exponential distributions.

These distribution tails indicate how often outliers occur in statistical data. High kurtosis (and heavy tails) mean there are more extreme values than you’d expect in a normal probability distribution. Low kurtosis (and light tails) mean there are fewer outliers than is normally the case. If the tails of the distribution include the usual amount of outliers, you likely have a kurtosis of zero (the normal amount) as opposed to an excess of positive or negative kurtosis.

In descriptive statistics, kurtosis can help you gain a better understanding of the data you are reviewing. Here are three key elements to familiarize yourself with if you want to expand your definition of kurtosis:

1. 1. Additional variables: The accurate characterization of kurtosis requires you to look at other aspects of statistical data. Mathematicians call kurtosis the fourth moment of a distribution, implying there are three others you must also take into account. These first three moments are—in order from first to third—mean (the average of all the data in your sample size), variance (the spread between data points), and skewness (the deviation from a normal symmetric distribution).
2. 2. Peaks: Kurtosis has just as much to do with the peak of a histogram as it does with its tails. For instance, while statisticians primarily define leptokurtosis in terms of its fat tails, it can also manifest in a higher peak. The peakedness of a frequency distribution helps you understand how many data points fall among the average as opposed to existing as outliers. Comparing averages against outliers is one of the primary ways to determine kurtosis.
3. 3. Tails: As you look at the tails of your dataset, you get to the core of kurtosis. If these tails are full of random variables and outliers (and have fatter tails as a result), you have an excess of positive kurtosis on your hands. The same goes in reverse—fewer outliers means less kurtosis. The closer your tails are to mimicking the pattern of a standard deviation, the more likely you are to have a regular amount of kurtosis.

Kurtosis can break down in a variety of different ways depending on the data you use. Consider these prominent types of kurtosis measures:

• Leptokurtic distributions: The term “leptokurtic” derives from the Greek words “lepto” (meaning “narrow”) and “kurtos” (meaning “bulging”). In other words, the positive excess kurtosis in a leptokurtic distribution manifests itself in a greater degree of heaviness in your distribution tails. The Laplace distribution is a standard example of a leptokurtic distribution, in contrast to the more typical Gaussian one.
• Mesokurtic distributions: In this measure of kurtosis, your expected value is close to the norm in a standard distribution. The lack of excess kurtosis values in either a positive or negative direction translates to a diagram within normal parameters. “Meso” means “middle,” so it should come as no surprise mesokurtic distributions have the moderate or typical amount of outliers you would expect in a normal representation of data.
• Platykurtic distributions: If your distribution has plenty of negative values for outliers, you likely have a platykurtic diagram with negative excess kurtosis. “Platy” derives from the Greek “platus,” meaning “broad.” Although some might expect platykurtic diagrams to appear flat-topped, this is actually a misconception. While this can happen, it’s not necessary for it to in order for a distribution to be platykurtic.

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