Question

In a data distribution the first quartile, median and mean are 30.8,48.5,42.0 respectively. If the coefficient skewness is - 0.38,
1.Find the appropriate value of the third quartile
2.Find the appropriate value of the variance

Answer 1

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

To find : value for the third quartile?

Solution:

Q1  =  30.8

Median Q2 =  48.5

Mean  = 42

Mean < median hence -ve  coefficient skewness

coefficient skewness  =  (Q1   + Q3  - 2Q2)/(Q3 - Q1)

-0.38  = (30.8 + Q3  - 2(48.5) )/(Q3 - 30.8)

=> -0.38Q3  + 11.704  = 30.8 + Q3  - 97

=> 1.38Q3  =  77.904

=> Q3 = 56.45

value for the third quartile = 56.45

3IQR  = 4SD

IQR = 56.45 - 30.8  = 25.65

SD = 3(25.65)/4 = 19.24

Variance = SD² = 370

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