# What is the interquartile range for this set of data? 11, 19, 35, 42, 60, 72, 80, 85, 88

Jun 30, 2017

See a solution process below:

#### Explanation:

This data set is already sorted. So, first, we need to find the median:

$11 , 19 , 35 , 42 , \textcolor{red}{60} , 72 , 80 , 85 , 88$

Next we put parenthesis around the upper and lower half of the data set:

$\left(11 , 19 , 35 , 42\right) , \textcolor{red}{60} , \left(72 , 80 , 85 , 88\right)$

Next, we find Q1 and Q3, or in other words, the median of the upper half and lower half of the data set:

$\left(11 , 19 , \textcolor{red}{|} 35 , 42\right) , \textcolor{red}{60} , \left(72 , 80 , \textcolor{red}{|} 85 , 88\right)$

$Q 1 = \frac{35 + 19}{2} = \frac{54}{2} = 27$

$Q 3 = \frac{80 + 85}{2} = \frac{165}{2} = 82.5$

Now, we subtract $Q 1$ from $Q 3$ to find the interquartile range:

$82.5 - 27 = 55.5$