# What is the mean, median, mode, and range of 2, 3, 3, 3, 3, 4, 4, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9?

Jun 30, 2017

Range $= 7$
Median = $6$
Modes =$3 , 6 , 8$
Mean = $5.58$

#### Explanation:

$2 , 3 , 3 , 3 , 3 , 4 , 4 , 5 , 6 , 6 , 6 , 6 , 7 , 7 , 8 , 8 , 8 , 8 , 9$

Count the number of values first: There are $19$

Range: Difference between highest and lowest values:
color(blue)(2),3,3,3,3,4,4,5,6,6,6,6,7,7,8,8,8,8, color(blue)(9)

Range =$\textcolor{b l u e}{9 - 2 = 7}$

Median: Value exactly in the middle of a set of data arranged in order. There are $19$ values so this one is easy to find. It will be the $\frac{19 + 1}{2} t h$ value = $10 t h$
$19 = 9 + 1 + 9$

$\textcolor{red}{2 , 3 , 3 , 3 , 3 , 4 , 4 , 5 , 6} , 6 , \textcolor{red}{6 , 6 , 7 , 7 , 8 , 8 , 8 , 8 , 9}$
$\textcolor{w h i t e}{w w w w w w w w w w w w} \uparrow$
$\textcolor{w h i t e}{w w w w w w w w w w w} m e \mathrm{di} a n = 6$

Median: the value with the highest frequency - the one that occurs the MOST often:

$2 , \textcolor{\lim e}{3 , 3 , 3 , 3} , 4 , 4 , 5 , \textcolor{\lim e}{6 , 6 , 6 , 6} , 7 , 7 , \textcolor{\lim e}{8 , 8 , 8 , 8} , 9$

There are three values which each occur $4$ times
This is a tri-modal distribution, the modes are $3 , 6 \mathmr{and} 8$

Mean: what is usually called the average. If all the values were the same, what would it be? Find one value to represent them all.

Mean: add all the values together and divide by $19$

$2 + 3 + 3 + 3 + 3 + 4 + 4 + 5 + 6 + 6 + 6 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 = 106$

$m e a n = \textcolor{m a \ge n t a}{\frac{106}{19} = 5.5789 \ldots \approx 5.58}$