Introduction - Probability and Probability
d. Measures of Skewness
Def.-It is the chance of occurrence of an
The value of probability ranges between 0
The probability of the occurrence of the
outcomes deduced mathematically forms a
Probability distribution may be-
1. Discrete probability distribution
2. Continuous probability distribution
5. NORMAL DISTRIBUTION
Def.-It represents the
, whose frequencies
closely around the
center and gradually
fall towards the two
Def.-Measure of extent of deviation from the
The data may be skewed to the left or right.
Features of skewed distribution
Curve is not bell shaped.
Mean , median and mode do not coincide.
In skewed distribution curve , the first and the
third quartiles of frequency are not equidistant
from median i.e. Q3 – Me ≠ Me –Q1
9. Measure of Skewness
Skewness can be measured in the terms
of differences between Mean and Mode.
The various measures of skewness are:-
1. Absolute skewness
2. Relative skewness
3. Standardised skewness
4. Karl Pearson’s coefficient of skewness
5. Bowley’s coefficient of skewness
10. 1. Absolute Skewness
It is the difference between Mean and
Also called coefficient of skewness.
It is expression of skewness in relative
Relative skewness= Mean-Mode
11. 3.Standardised Skewness
•In a distribution , the average of the
powers of deviation from arithmetic mean is
called Moment of distribution(m).
Ex. m1 =Ʃ(X-X)1
•These powers determine the sign of
Ex.m2 =Ʃ(X-X)2 ; m3 =Ʃ(X-X)3
12. 4.Karl Pearson’s coefficient of
5.Bowley’s coefficient of skewness
•Based on Quartiles.
0-2 2-4 4-6 6-8 8-10 10-12 12-14
1 2 4 9 4 3 2
Find Relative skewness.
Ans. S= Mean-Mode