![]() Any standardized values that are less than 1 (i.e., data within one standard deviation of the mean, where the “peak” would be), contribute virtually nothing to kurtosis, since raising a number that is less than 1 to the fourth power makes it closer to zero. Kurtosis is the average of the standardized data raised to the fourth power. N is the number of observations of the sample.\(skewness=\frac\) is the mean of the distribution The skewness can be calculated from the following formula: The graph below describes the three cases of skewness. In this case, we can use also the term “right-skewed” or “right-tailed”. Positive skew: When the right tail of the histogram of the distribution is longer and the majority of the observations are concentrated on the left tail.In this case, we can use also the term “left-skewed” or “left-tailed”. ![]() Negative skew: When the left tail of the histogram of the distribution is longer and the majority of the observations are concentrated on the right tail.Symmetrical: When the skewness is close to 0 and the mean is almost the same as the median.Generally, we have three types of skewness. We can say that the skewness indicates how much our underlying distribution deviates from the normal distribution since the normal distribution has skewness 0. The skewness is a measure of the asymmetry of the probability distribution assuming a unimodal distribution and is given by the third standardized moment. Today, we will try to give a brief explanation of these measures and we will show how we can calculate them in R. Another less common measures are the skewness (third moment) and the kurtosis(fourth moment). Most commonly a distribution is described by its mean and variance which are the first and second moments respectively.
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