Download Skewness

Skewness
The coefficient of Skewness is a measure for the degree of symmetry in the variable distribution.
Negatively skewed distribution
or Skewed to the left
Skewness <0
Normal distribution
Symmetrical
Skewness = 0
Positively skewed distribution
or Skewed to the right
Skewness > 0
Skewness is important because it affects the measure of central tendency we use to describe the data in the distribution. Consider these points:
•In a negatively skewed distribution, the mean is less than the median- in certain circumstances, the median is a more appropriate description of the
central tendency of the sample than the mean.
•In a positively skewed distribution, the mean is greater than the median- in certain circumstances, the median is a more appropriate appropriate
description of the central tendency of the sample than the mean.
•In a normal distribution, the mean, median, and mode are all the same- while this can be convenient for describing the central tendency of the sample,
it RARELY happens and so we can dismiss this is a relatively rare occurrence.
Skewness and Measures of Central Tendency
In a symmetrical
distribution, the
mean, median,
and mode are
all the same
number.
In a negatively skewed
distribution, the mean
is the smallest number;
the mode is the largest
number; the median is
between the mean and
mode.
In a positively skewed
distribution, the mean
is the largest number;
the mode is the
smallest number; the
median is between the
mean and mode.
Kurtosis
The coefficient of Kurtosis is a measure for the degree of peakedness/flatness in the variable distribution.
Platykurtic distribution
Low degree of peakedness
Kurtosis <0
Normal distribution
Mesokurtic distribution
Kurtosis = 0
Leptokurtic distribution
High degree of peakedness
Kurtosis > 0
Kurtosis is important because it affects the measure of dispersion we use to describe the data in the distribution. It does not directly affect the measure of
dispersion we use, but we should note that:
•In a platykurtic or flat distribution, the variance and standard deviation will be greater than in a normal or leptokurtic distribution; this means that there
is more dispersion or variability in a platykurtic distribution than in either of the other shapes.
•In a leptokurtic distribution or peaked distribution, the variance and standard deviation will be less than in a normal or platykurtic distribution; this means
that there is less dispersion or variability in a leptokurtic distribution than in either of the other shapes.
•In a normal distribution, the variance and standard deviation will be between those figures for a platykurtic or leptokurtic distribution;l such a
distribution RARELY happens and so we can dismiss this is a relatively rare occurrence.
Kurtosis and Measures of Dispersion
|
|
|
|
|
|
|
|
3
2
1
Mean
1
Most peaked curve
Smallest dispersion
Symmetrical curve
Standard dispersion
Flattest curve
Widest dispersion
2
3