The following would be the tests of skewness :
(i) The values of Mean, Median and Mode are different.
i.e. X¯ ≠ M ≠ Z.
(ii) The difference between the upper Quartile, and the Median is not equal to the difference between the Median and the lower Quartile, i.e. (Q3 – M) ≠ (M – Q1)
(iii) The extreme values of the Percentiles and Deciles are not equidistant from Median i.e.
(P90 – M) ≠ (M – P10)
(D9 – M) ≠ ( M –D1)
(iv) The sum of the positive deviations from the Median is not equal to the sum of the negative deviations from the Median i.e. ∑(X-M)≠ 0
(v) The frequencies are not equally distributed at the points of equal deviation from Mode.
(vi) B1 (Beta one) is not equal to zero
i.e., B1 = ≠ 0
(Vii) Y1 (gamma one) is not equal to zero
i.e. Y1 ≠ 0
(Viii) B 2 (Beta two) is not equal to 3
i.e. B2 ≠ 3
(ix) The values of the variables when plotted on a graph paper do not give a bell shaped curve.