# How do you find the first and third quartiles, Q1 and Q3, of the following set of numbers 10, 4, 9, 14, 6, 11, 6, 1, 7, 6?

##### 1 Answer
Jul 25, 2018

${Q}_{1} = 6 , {Q}_{3} = 10$

#### Explanation:

$\text{We require the data to be in ascending order}$

$1 , \textcolor{w h i t e}{x} 4 , \textcolor{w h i t e}{x} \textcolor{red}{6} , \textcolor{w h i t e}{x} 6 , \textcolor{w h i t e}{x} 6 , \textcolor{red}{\uparrow} \textcolor{w h i t e}{x} 7 , \textcolor{w h i t e}{x} 9 , \textcolor{w h i t e}{x} \textcolor{red}{10} , \textcolor{w h i t e}{x} 11 , \textcolor{w h i t e}{x} 14$

$\text{Find the median of the data set}$

$\text{the median is the middle entry in the data set. If not a }$
$\text{value then the average of the values either side of the middle}$

$\text{In this case the median } = \frac{6 + 7}{2} = 6.5$

$\text{The quartiles are the middle entries to the left and right}$
$\text{of the median}$

${Q}_{1} = 6 \text{ and } {Q}_{3} = 10$