Each of the four astronomers measures the distance 100 times, and they put their data together in the same dataset: Imagine that four astronomers are all trying to measure the distance between the Earth and Nu2 Draconis A, a blue star that’s part of the Draco constellation. Like platykurtosis, this is a misnomer because it defines kurtosis in terms of “peakedness” instead of tailedness.Ī trick to remember the meaning of “leptokurtic” is to think of a leaping kangaroo with a fat tail. NoteThe “lepto” in “leptokurtosis” comes from the Greek word leptós, which means narrow. Leptokurtosis is sometimes called positive kurtosis, since the excess kurtosis is positive. Leptokurtic distributions are more kurtotic than a normal distribution. This is what is meant by “thin tails.” What is a leptokurtic distribution?Ī leptokurtic distribution is fat-tailed, meaning that there are a lot of outliers. NoteIn the graph above, notice that on the far left and right sides of the distribution-the tails-the space below the uniform distribution curve (purple) is thinner than the space below the normal distribution curve (green). There are no students younger than 14 or older than 18 years. Uniform distributions, like the distribution of students’ ages, are the extreme cases of platykurtic distributions because outliers are so rare that they’re completely absent. Platykurtic distributions have a low frequency of outliers. He concludes that the distribution is platykurtic. The sociologist calculates that the kurtosis of the sample is 1.78 and its excess kurtosis is −1.22. Instead, it approximately follows a uniform distribution (shown by the purple curve). The frequency distribution (shown by the gray bars) doesn’t follow a normal distribution (shown by the dotted green curve). There are 400 students at the school, ranging in age from 14 to 18 years old: Platykurtic distribution exampleĪ sociologist is studying the social media use of students at a small high school. Statisticians now understand that kurtosis is a measure of tailedness, not “peakedness.”Ī trick to remember the meaning of “platykurtic” is to think of a platypus with a thin tail. Although many platykurtic distributions have a flattened peak, some platykurtic distributions have a pointy peak. NoteThe “platy” in “platykurtosis” comes from the Greek word platús, which means flat. Platykurtosis is sometimes called negative kurtosis, since the excess kurtosis is negative. In other words, platykurtic distributions have: Platykurtic distributions have less kurtosis than a normal distribution. Occasionally, a female baby elephant will be born weighing less than 180 or more than 240 lbs.ĭiscover proofreading & editing What is a platykurtic distribution?Ī platykurtic distribution is thin-tailed, meaning that outliers are infrequent. Mesokurtic distributions have outliers that are neither highly frequent, nor highly infrequent, and this is true of the elephant birth weights. If a sample has a kurtosis of approximately 3, you can assume it’s drawn from a mesokurtic population. NoteAlthough a population’s probability distribution can have a kurtosis of exactly 3, real data is almost always at least slightly platykurtic or leptokurtic. She finds that the kurtosis is 3.09 and the excess kurtosis is 0.09, and she concludes that the distribution is mesokurtic. The zoologist calculates the kurtosis of the sample. She collects birth weight data for 400 female baby elephants:įrom the graph, we can see that the frequency distribution (shown by the gray bars) approximately follows a normal distribution (shown by the green curve). Suppose that a zoologist is interested in the distribution of elephant birth weights, so she contacts zoos and sanctuaries around the world and asks them to share their data. On average, a female baby elephant weighs an impressive 210 lbs at birth. Normal distributions have an excess kurtosis of 0, so any distribution with an excess kurtosis of approximately 0 is mesokurtic.Since normal distributions have a kurtosis of 3, excess kurtosis makes comparing a distribution’s kurtosis to a normal distribution even easier: Often, kurtosis is described in terms of excess kurtosis, which is kurtosis − 3. Normal distributions have a kurtosis of 3, so any distribution with a kurtosis of approximately 3 is mesokurtic.Kurtosis is measured in comparison to normal distributions. Frequently asked questions about kurtosisĭistributions can be categorized into three groups based on their kurtosis:Ī mesokurtic distribution is medium-tailed, so outliers are neither highly frequent, nor highly infrequent.
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