Question

Find the interquartile range for the following data set:7,9,13,4,18,3,9,10,15,8,2,6,9A. 9B. 6.5C. 5D. 7.5E. 11.5

Answer 1

Consider that the interquartile range is given by the following expression:

I = Q3 - Q1

where Q1 and Q3 are the first and third quartiles of the given data.

To find Q1 and Q3, use the following formulas:

$\begin{gathered} Q_1=\frac{n+1}{4}=\frac{13+1}{4}=\frac{14}{4}=3.5 \\ Q_3=\frac{3(n+1)}{4}=\frac{3(14)}{4}=10.5 \end{gathered}$

The previous results indicates the position of the elements in the order list, in the following way:

ordered list:

2, 3, 4, 6, 7, 8, 9, 9, 9, 10, 13, 15, 18

then, the first quartile is:

4 + 0.25(6-4) = 4.5

the third quartile:

10 + 0.75(13 -10) = 12.25

Hence, the interquartile range is:

I = 12.25 - 4.5

I = 7.75

Then, by approximating the previous result, the answer is:

I = 7.5