# What is the interquartile range of 86, 72, 85, 89, 86, 92, 73, 71, 91, 82?

May 29, 2017

$I Q R = 16$

#### Explanation:

$\text{arrange the data set in ascending order}$

$71 \textcolor{w h i t e}{x} 72 \textcolor{w h i t e}{x} \textcolor{m a \ge n t a}{73} \textcolor{w h i t e}{x} 82 \textcolor{w h i t e}{x} 85 \textcolor{red}{\uparrow} \textcolor{w h i t e}{x} 86 \textcolor{w h i t e}{x} 86 \textcolor{w h i t e}{x} \textcolor{m a \ge n t a}{89} \textcolor{w h i t e}{x} 91 \textcolor{w h i t e}{x} 92$

$\text{the quartiles split the data into 4 groups}$

$\text{the median } \textcolor{red}{{Q}_{2}} = \frac{85 + 86}{2} = 85.5$

$\text{the lower quartile } \textcolor{m a \ge n t a}{{Q}_{1}} = \textcolor{m a \ge n t a}{73}$

$\text{the upper quartile } \textcolor{m a \ge n t a}{{Q}_{3}} = \textcolor{m a \ge n t a}{89}$

$\text{the interquartile range } \left(I Q R\right) = {Q}_{3} - {Q}_{1}$

$\textcolor{w h i t e}{t h e \int e r q u a r t i \le r a n \ge \times \times x} = 89 - 73$
$\textcolor{w h i t e}{t h e \int e r q u a r t i \le r a n \ge \times \times x} = 16$