Lecture 7/ Finite Sample Space with Equally Points/2018- 2019 /

SKEWNESS AND KURTOSIS
The average and measure of dispersion can describe the distribution but they are not
sufficient to describe the nature of the distribution. For this purpose we use other
concepts known as Skewness and Kurtosis.
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.
Skewness
The first thing you usually notice about a distribution’s shape is whether it has
one mode (peak) or more than one. If it’s unimodal (has just one peak), like
most data sets, the next thing you notice is whether it’s symmetric or
skewed to one side. If the bulk of the data is at the left and the right tail is
longer, we say that the distribution is skewed right or positively skewed;
if the peak is toward the right and the left tail is longer, we say that the
distribution is skewed left or negatively skewed.
Look at the two graphs below. They both have ? = 0.6923 and ? = 0.1685,
but their shapes are different.