Find Skp for the following set of observations:18, 27, 10, 25, 31, 13, 28. - Mathematics and Statistics

Sum

Find Skp for the following set of observations:
18, 27, 10, 25, 31, 13, 28.

Solution

The given data can be arranged in ascending order as follows:
10, 13, 18, 25, 27, 28, 31.
Here, n = 7
∴ Median = value of (("n" + 1)/2)^"th" observation

= value of ((7 + 1)/2)^"th" observation

= value of 4th observation
= 25
For finding standard deviation, we construct the following table:

 xi xi2 10 100 13 169 18 324 25 625 27 729 28 784 31 961 152 3692

From the table, sum"x"_"i" = 152, sum"x"_"i"^2 = 3692

Mean = bar"x" = (sum"x"_"i")/"n" = 152/7 = 21.7143

∴ S.D. = sqrt((sum"x"_"i"^2)/"n" - (bar"x")^2

= sqrt(3692/7 - (21.7143)^2

= sqrt(527.4286 - 471.5108)
= sqrt(55.9178)
= 7.4778
Coefficient of skewness,

Skp = (3("Mean"-"Median"))/"S.D."

= (3(21.7143 - 25))/(7.4778)

= (3(-3.2857))/(7.4778)

= (-9.8571)/(7.4778)

∴ Skp = – 1.3182

Concept: Measures of Skewness - Karl Pearson’S Coefficient of Skewness (Pearsonian Coefficient of Skewness)
Is there an error in this question or solution?

Share