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

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Sum

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

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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?
Chapter 3: Skewness - Miscellaneous Exercise 3 [Page 44]

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