Question

Mark as Review
The standard deviation of a symmetrical distribution is 4. What must be the value of the fourth
moment in order that the distribution be Platykurtic?​

Answer 1

Summary:You’ve learned numerical measures of center, spread, and outliers, but what about measures of shape? The histogram can give you a general idea of the shape, but two numerical measures of shape give a more precise evaluation: skewness tells you the amount and direction of skew (departure from horizontal symmetry), and kurtosis tells you how tall and sharp the central peak is, relative to a standard bell curve.

Why do we care? One application is testing for normality: many statistics inferences require that a distribution be normal or nearly normal. A normal distribution has skewness and excess kurtosis of 0, so if your distribution is close to those values then it is probably close to normal.