# What is the mean, median, mode, and range of the following numbers?: {1,2,3,4,5,6,7,8,9}

Sep 3, 2017

Mean $= 5$ and Median = $5$

There is no mode

Range = $9 - 1 = 8$

#### Explanation:

We have the distribution:

$1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9$

The Range is the difference between the highest and the lowest - an indication of how far the numbers are spread out.

range$= 9 - 1 = 8$

Mode, median and mean are all regarded as different types of average, they give different information.

The Mode is the value with the highest frequency - the one that occurs the most often. There is no mode in this case because each number occurs exactly once.

The median is the number exactly in the middle of a set of numbers arranged in order.

There are $9$ numbers, the middle one is $5$
There are $4$ numbers on each side.

$\textcolor{b l u e}{1 , 2 , 3 , 4 ,} \textcolor{red}{5} , \textcolor{b l u e}{6 , 7 , 8 , 9}$

The mean is what is generally understood as 'average'

Mean = $\text{sum of the values"/"the number of values}$

Mean $= \frac{1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9}{9}$

$= \frac{45}{9} = 5$