Question

Third quartile is at a distance of 12.8 from the median in a frequency distribution and its first
quartile is at a distance of 11.2 from the medium. Find the skewness and its coefficient.​

Answer 1

Given : Third quartile is at a distance of 12.8 from the median in a frequency distribution and

first quartile is at a distance of 11.2 from the medium.

To Find : the skewness and its coefficient.​

 Solution:

  Third quartile is at a distance of 12.8 from the median  

 =>  Q₃  - Q₂  = 12.8

first quartile is at a distance of 11.2 from the medium.

=>  Q₂ - Q₁  = 11.2

as 11.2 < 12.8

 Q₂ - Q₁     <   Q₃  - Q₂ hence longer tail on right side

Hence Positive skewness ,  Right Skewed

Coefficient of skewness =  ((Q₃  - Q₂ ) - (Q₂ - Q₁) )/(Q₃ - Q₁)

= ( 12.8 - 11.4)/(Q₂+ 12.8 -(Q₂- 11.4))

=  1.4/ (24.2)

= 14/242

= 7/121

 

positive skewness ,  Right  Skewed  , coefficient = 7/121

Mean < median  -ve  coefficient skewness

 Mean > Median + ve coefficient skewness

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