Page 11 - Azerbaijan State University of Economics

Yadulla Hasanli, Nazim Hajiyev, Gunay Rahimli:Distribution and Analysis of Admission
Scores (In the Case of Azerbaijan

Defining the level of asymmetry
Asymmetry means that the variable is not symmetrically distributed. To assess the
level of asymmetry, the moment and structural asymmetry coefficients are used
(Anderson D., Sweeney D., Williams T., Camm J., Cochran J., 2016).

The moment coefficient of the asymmetry is calculated by the following formula:

m
a = 3
3
 3

3
Where, m is the third central moment,  - average cubic deviation (that is, it
3
represents the third level of deviation from the average of a sequence).

 x ( i − x) 3 n i
m = i
3
n

3
Where  = (m 2 )
3

 x ( i − x) 2 n i

m is the second central moment and m = i
2
2
n
The sign of the moment coefficient of the asymmetry determines the direction of the
asymmetry. If,
a 3 = 0 then the sequence is symmetric;

a 3  0 then it is asymmetric to right;
a 3  0then it is asymmetric to left.

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