Advertisement Remove all ads

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

Advertisement Remove all ads
Advertisement Remove all ads
Sum

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

Advertisement Remove all ads

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?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×