Question

Calculate the first, second, and third quartiles of the following sample. 5 8 2 9 5 3 7 4 2 7 4 10 4 3 5

Answer 1

Answer:

3 ; 4.5 ; 7.25

Step-by-step explanation:

Given the sample :

8 2 9 5 3 7 4 2 7 4 10 4 3 5

Calculate, the first, second, and third quartiles

Arranging the data in ascending order :

2, 2, 3, 3, 4, 4, 4, 5, 5, 7, 7, 8, 9, 10

First quartile :

Q1 = [(n + 1) /4]th value

n = 14

Q1 = [(14 + 1) /4]th = (15/4)th = 3.75 value

Taking the average of the 3rs and 4th observation:

(3 +3) / 2 = 3

Second quartile :

Q2 = [2(n + 1) /4]th value

Q2 = 2(15)/4 = (30/4)th value

Q2 = 7.5 ; taking the 7th and 8th value

Q2 = (4 +5) /2 = 9/2 = 4.5

Q3 = [3(n + 1) /4]th value

Q2 = 3(15)/4 = (45/4)th value

Q2 = 11.25 ; taking the 11th

Q2 = 7 + 0.25 = 7.25