In: Statistics and Probability
Suppose that the following data represents ages of all tenured faculty members in a certain academic department, and we want to numerically describe the age distribution for this department only:
42, 39, 44, 50, 45, 42, 36, 47, 39, 42, 43, 47
What is the 3rd quartile?
Solution:
Arranging Observations in the ascending order, We get :
36,39,39,42,42,42,43,44,45,47,47,50
Here, n=12
Q3=(3(n+1)4)th value of the observation
=((3⋅13 ) / 4)th value of the observation
=(9.75)th value of the observation
=9th observation +0.75[10th-9th]
=45+0.75[47-45]
=45+0.75(2)
=45+1.5
=46.5
Q3= 46.5
3rd quartile = 46.5