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?

Jul 25, 2018

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

Explanation:

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

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

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

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

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

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

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