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Kurtosis: The extent to which the peak of the unimodal probability distribution or the frequency distribution departs from its shape of the normal distribution, by either being more pointed (like leptokurtic)or flatter ( like platykurtic). Commonly measured for a probability distribution as
where 4 is the fourth central moment of distribution, and 2 is its variance.
(consequent functions of sample moments are used for frequency distributions.)
For the normal distribution this index takes the value three and often index is redefined as the value above minus three so that the normal distribution would contain the value zero.
(Other distributions with the zero kurtosis are known as mesokurtic.) For the distribution which is leptokurtic the index is positive and for the platykurtic curves it is negative. It is shown in the figure
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You have learned that there are 3 major central measures of any data set. Namely: mean, median, and mode. Which of the three, do the outliers affect the most?
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Opreation research phase
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Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 20 to be 115 or more?
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