Symmetric and Skew-symmetric Assignment Help

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Symmetric and Skew-symmetric:

In the symmetrical distribution, Mean, Median, Mode coincides. Here, the frequencies are symmetrically distributed on both the sides of the some central value.

A distribution which is not symmetrical, is called as skew-symmetrical. In the moderately skew symmetric distribution,

Mean - Mode = 3 (Mean - Median)

                                 1614_Symmetric and Skew-symmetric.png

In the positively skew-symmetric distribution, the value of mean is maximum and that of the mode is least, and median lies between the 2.

In the negatively skew-symmetric distribution, value of mode is maximum and that of mean is least, and median lies between the 2.

In the negatively skew symmetric distribution, value of mode is maximum and that of mean is least, and median lies between the 2.

Absolute Measures of skewness are

1819_Symmetric and Skew-symmetric1.png

The Relative Measures of Skewness are

(i) Karl Pearson's coefficient of the skewness.

            1422_Symmetric and Skew-symmetric2.png. It lies between -1 and 1.

(ii) Bowley's coefficient of the skewness

            1382_Symmetric and Skew-symmetric3.png. It lies between -1 and 1.

(iii) Kelley's cofficient of the skewness 1918_Symmetric and Skew-symmetric4.png

 

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