# What is the third quartile of 24, 20, 35, 43, 28, 36, 29, 44, 21, 37?

Jun 11, 2017

${Q}_{1} = 24$

#### 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 11, 2017

${Q}_{1} = 24 , {Q}_{3} = 37$

#### Explanation:

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

$20 \textcolor{w h i t e}{x} 21 \textcolor{w h i t e}{x} \textcolor{m a \ge n t a}{24} \textcolor{w h i t e}{x} 28 \textcolor{w h i t e}{x} 29 \textcolor{red}{\uparrow} \textcolor{w h i t e}{x} 35 \textcolor{w h i t e}{x} 36 \textcolor{w h i t e}{x} \textcolor{m a \ge n t a}{37} \textcolor{w h i t e}{x} 43 \textcolor{w h i t e}{x} 44$

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

$\text{in this case that is between 29 and 35 so find the average}$

$\Rightarrow \textcolor{red}{{Q}_{2}} = \frac{29 + 35}{2} = 32$

$\text{the lower and upper quartiles divides the set to the left and }$
$\text{right of the median into 2 equal parts}$

$\Rightarrow \textcolor{m a \ge n t a}{{Q}_{1}} = 24 \text{ and } \textcolor{m a \ge n t a}{{Q}_{3}} = 37$