Question

In a data distribution, the first quartile, the median and the means are 30.8, 48.5 and 42.0 respectively. If the coefficient skewness is - 0.38

What is the appropriate value of the third quartile

Answer 1

56.45

Explanation:

Coefficient skewness=(Third quartile+ first quartile)-n*Median/Third quartile-first quartile

Third quartile is the unknown?

First quartile is 30.8

n is the number of steps taken from first quartile to reach third quartile which is 2 steps.

coefficient skewness is -0.38

let p represent third quartile

-0.38=(p+30.8)-2(48.5)/p-30.8

by cross multiplication

-0.38(p-30.8)=(p+30.8)-97

-0.38p+ 11.704 =p+30.8-97

-0.38p-p=30.8-97-11.704

-1.38p=-77.904

p=-77.904 /-1.38= 56.45