1. AN OVERVIEW OF SKEWNESS AND KURTOSIS

2. INTRODUCTION
Skewness :- In statistics, Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero or negative. Kurtosis :- In statistics, Kurtosis is a measure of the “tailedness” of the probability distribution of a real-valued random variable.

3. GRAPHICAL REPRESENTATION OF SKEWNESS
MEAN<MEDIAN<MODE
MEAN=MEDIAN=MODE
MEAN>MEDIAN>MODE

4. FORMULA OF SKEWNESS Skewness : Σ(x – x̄)3 (n-1).S3 Σf(x – x̄)3
where, x = individual data value of a set x̄ = mean of the data set n = number of observation S = standard deviation f = frequency
Skewness : Σ(x – x̄)3
(n-1).S3
Σf(x – x̄)3
(n-1).S3

5. FORMULA OF KURTOSIS Kurtosis : Σ(x – x̄)4 (n-1).S4 Σf(x – x̄)4
where, x = individual data value of a set x̄ = mean of the data set n = number of observation S = standard deviation f = frequency
Kurtosis : Σ(x – x̄)4
(n-1).S4
Σf(x – x̄)4
(n-1).S4

6. EXAMPLE OF A NUMERICAL DEALING WITH SKEWNESS AND KURTOSIS
Q. Calculate the Skewness and Kurtosis with the help of the table given below:
CLASS
FREQUENCY
2-4 3
4-6 4
6-8 2
8-10 1

7. Σ SOLUTION: CLASS MID VALUE (X) f f.x x-x̄ f.(x-x̄)2 f.(x-x̄)3
2-4 3 9
(3-5.2)
= -2.2
3.(-2.2)2
= 14.52
14.52*(-2.2) =
-31.94*(-2.2)
= 70.27
4-6 5 4 20
(5-5.2)
= -0.2
4.(-0.2)2
= 0.16
0.16*(-0.2) =
-0.032*(-0.2) =
6-8 7 2 14
(7-5.2)
= 1.8
2.(1.8) 2
= 6.48
6.48*1.8
= 11.66
11.66*1.8
= 20.99
8-10 1
(9-5.2)
= 3.8
1.(3.8) 2
= 14.44
14.44*3.8
= 54.87
54.87*3.8 = Σ 10 52
35.6
34.56
299.77
x̄ = Σfx => 52 => 5.2
Σfn

8. 1. S.D : √ Σ(xi – x̄)2
(n-1)
= √ = 1.98
10-1
2. Skewness : Σ(x – x̄)3
(n-1).S3
= = 0.49
9*(1.98)3
= = 2.17
9* (1.98)4
3. Kurtosis : Σ(x – x̄)4
(n-1).S4

9. APPLICATION OF SKEWNESS AND KURTOSIS
Skewness can be used to obtain approximate probabilities of distributions.
With the help of skewness we can know or understand whether deviations from the mean are going to be positive or negative.
It also indicates the direction and relative magnitude of a distribution’s deviation from the normal distribution.
Kurtosis is a useful method to check whether there is a problem with the outliers in a particular dataset.

10. THANK YOU