# What is the first quartile of 12, 33, 15, 22, 29, 11, 17, 19, 16, 24, 38?

Jun 11, 2017

${Q}_{1} = 15$

#### Explanation:

If you have a TI-84 calculator in hand:
First put the numbers in order.
Then you press the stat button.
Then $\text{1:Edit}$ and go ahead and enter your values in order
After this press the stat button again and go to $\text{CALC}$
and hit $\text{1:1-Var Stats}$ press calculate.
Then scroll down until you see ${Q}_{1}$.

Jun 12, 2017

${Q}_{1} = 15$

#### Explanation:

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

$11 \textcolor{w h i t e}{x} 12 \textcolor{w h i t e}{x} \textcolor{m a \ge n t a}{15} \textcolor{w h i t e}{x} 16 \textcolor{w h i t e}{x} 17 \textcolor{w h i t e}{x} \textcolor{red}{19} \textcolor{w h i t e}{x} 22 \textcolor{w h i t e}{x} 24 \textcolor{w h i t e}{x} 29 \textcolor{w h i t e}{x} 33 \textcolor{w h i t e}{x} 38$

$\text{the median "color(red)(Q_2)" is the middle value of the}$
$\text{data set in ascending order}$

$\Rightarrow \textcolor{red}{{Q}_{2}} = 19$

$\text{the lower quartile "color(magenta)(Q_1)" is the middle value of the}$
$\text{data set to the left of the median}$

$\Rightarrow \textcolor{m a \ge n t a}{{Q}_{1}} = 15$