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Question
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
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