Answer to Question #120436 in Statistics and Probability for Elmo

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 , use the information to answer questions 1 and 2
1. What is the approximate value of the third quartile, correct to 2 decimal places?
2. What is the approximate value of the variance, correct to the nearest whole number?

Answer 1

approximate value of the third quartile:

z value for Q1(25%)=-0.67

-0.67=(Q1-μ)/σ=-11.2/σ

σ=-11.2/-0.67=16.7

3*IQR = 4*σ

IQR =4*σ/3=22.2

IQR =Q3-Q1, so Q3=IQR+Q1=22.2+30.8=53.0

approximate value of the variance

VAR=σ²=279