These are presented in more detail below. Skewness and kurtosis involve the tails of the distribution. Though you will still see this as part of the definition in many places, this is a misconception. Kurtosis originally was thought to measure the peakedness of a distribution.
This makes the normal distribution kurtosis equal 0. Kurtosis is sometimes reported as “excess kurtosis.” Excess kurtosis is determined by subtracting 3 form the kurtosis. If the kurtosis is less than 3, then the dataset has lighter tails than a normal distribution (less in the tails). If the kurtosis is greater than 3, then the dataset has heavier tails than a normal distribution (more in the tails). The value is often compared to the kurtosis of the normal distribution, which is equal to 3. It measures the amount of probability in the tails. Kurtosis is a measure of the combined sizes of the two tails. Skewness essentially measures the relative size of the two tails. So, a normal distribution will have a skewness of 0. A symmetrical dataset will have a skewness equal to 0. Skewness is a measure of the symmetry in a distribution. Many books say that these two statistics give you insights into the shape of the distribution. Skewness and kurtosis are two commonly listed values when you run a software’s descriptive statistics function. You may also leave a comment at the end of the publication. You may also download an Excel workbook containing the impact of sample size on skewness and kurtosis at the end of this publication. You may download a pdf copy of this publication at this link. What do the skewness and kurtosis really represent? And do they help you understand your process any better? Are they useful statistics? Let’s take a look These two statistics are called "shape" statistics, i.e., they describe the shape of the distribution. This month's publication covers the skewness and kurtosis statistics. What do these two statistics tell you about your sample? You spy two numbers: the skewness and kurtosis. You get a lot of numbers – the sample size, average, standard deviation, range, maximum, minimum and a host of other numbers. You enter the data into your software package and run the descriptive statistics. And your software package has a feature that will generate the descriptive statistics for these data. Now you are armed with data you can analyze. Maybe you took 15 samples from a batch of finished product and measured those samples for density. New information on both skewness and kurtosis has also been added. This article has been revised to correct that misconception. Kurtosis is a measure of the combined weight of the tails relative to the rest of the distribution. This is technically not correct (see below). The original article indicated that kurtosis was a measure of the flatness of the distribution – or peakedness. Note: This article was originally published in April 2008 and was updated in February 2016.
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