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Median Formula in Statistics
Finding the Mode

On this Page:
 1. Median Examples
 2. The Mode Value

When you have a set of values in Math, the “median” value is the value that is the middle of the set.

How it works is that if the total amount of numbers in a set is  ODD,  then the Median value is the exact middle number.

If the total amount of numbers in a set is  EVEN,  then the Median value is the two most middle numbers added together, divided by  2.

This page will show how to approach calculating the median.




Median Formula in Statistics Examples


(1.1) 

3 , 3 , 4 , 5 , 6 , 6 , 8 , 10 , 10

This is a list of  9  numbers, so a list total that is ODD.

To establish the middle position, we just add  1  to the total amount of values, and then divide by  2.

\bf{\frac{9 \space + \space 1}{2}}  =  \bf{\frac{10}{2}}  =  5

The  5th  value is the median position of the list.

3 , 3 , 4 , 5 ,  6  , 6 , 8 , 10 , 10

Median  =  6




(1.2) 

9 , 11 , 12 , 12 , 14 , 17 , 17 , 18

Here we have a list of  8  numbers, an  EVEN  total.

\bf{\frac{8 \space + \space 1}{2}}  =  \bf{\frac{9}{2}}  =  4.5


What this means is that the Median value is positioned between the  4th  and  5th  value.

What we do is add the values in these places together, and again divide by  2,   this will give the Median of the list.

9 , 11 , 12 , 12  |  14 , 17 , 17 , 18

The  4th  and  5th  values in the list are  12  and  14.

\bf{\frac{12 \space + \space 14}{2}}  =  \bf{\frac{26}{2}}  =  13

Median  =  13





Mode Value in Statistics


The “mode” value, Sometimes called the “modal value”, is the value in a data set that occurs the most times.



Examples    


(2.1) 

Here is a random set of numbers.

7 , 5 , 8 , 2 , 5 , 6 , 5 , 9 , 1 , 5 , 7 , 8 , 6

Often before attempting to work out what the the mode value is, it is helpful to place a set of values in ascending numerical order.

1 , 2 , 5 , 5 , 5 , 5 , 6 , 7 , 7 , 7 , 8 , 8 , 9


This approach should make it a bit easier to see the mode in a list of numbers.
We can now more easily see that  5  is the mode.

It’s the value that appears the most times,  4  times in total.




(2.2) 

It’s also the case that a set of numbers could have more than one mode value.

14 , 14 , 19 , 26 , 26 , 27 , 29

In the set of numbers above,  14  and  26  are both modal values.

When it is the case that a data set has  2  modes, it is called a “bimodal” data set.




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