Tests of Skewness

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.