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Mean, median, mode and range

Mean, median, mode and range

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Summary

Mean, median, mode and range

​​In a nutshell

The mean, median, mode and range are used to compare and analyse data. They tell you information about a set of data such as the average or how big it is. 



What are the mean, median, mode and range?

Sometimes the mean, median, mode and range are referred to as averages but each one has their own definition.


​​Definitions

Mean

The average: the total of all the items added up ÷\div the total number of items.

Median

The middle value. The position can be found by using n+12\frac{n+1}{2}  where n is the number of values.  (Note: The values MUST be in order from smallest to largest).

Mode

The most common value.

Range

The difference between the biggest and smallest 


Example

What is the mean, median, mode and range of the following set of numbers? 

1,4,6,2,3,8,1,2,1,31,4,6,2,3,8,1,2,1,3


Mean: 

all the values added upthe number of values=1+4+6+2+3+8+1+2+1+310=3110=3.1\frac{\text{all the values added up}}{\text{the number of values}} = \frac{1+4+6+2+3+8+1+2+1+3}{10}=\frac{31}{10}=\underline{3.1}


Median: 

First, reorder the values.

1,1,1,2,2,3,3,4,6,8 1,1,1,2,2,3,3,4,6,8


Find the position of the median.

n+12=112=5.5\frac{n+1}{2} = \frac{11}{2} = 5.5

Note: Since the position of the median is 5.55.5, this means it sits in the middle of the fifth and sixth value. Add them together and divide by two to find the mean.

(2+3)÷2=2.5(2+3)\div2=\underline{2.5}


Mode:

The most common number in the sequence.

1\underline1


Note: Sometimes there could be multiple modes if two values share the same frequency or no mode where all values are repeated the same number of times!


Range:

Take the smallest number away from the biggest number.

81=78-1=\underline7​​


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