# Calculating the MedianFinding the Mode

Median Examples
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.

### Calculating the Median Examples

(1.1)&nbsp

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

This is a list of &nbsp9&nbsp numbers, so a list total that is ODD.

To establish the middle position, we just add &nbsp1&nbsp to the total amount of values, and then divide by &nbsp2.

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

The &nbsp5th&nbsp value is the median position of the list.

3 , 3 , 4 , 5 , &nbsp6&nbsp , 6 , 8 , 10 , 10

Median &nbsp=&nbsp 6

(1.2)&nbsp

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

Here we have a list of &nbsp8&nbsp numbers, an &nbspEVEN&nbsp total.

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

What this means is that the Median value is positioned between the &nbsp4th&nbsp and &nbsp5th&nbsp value.

What we do is add the values in these places together, and again divide by &nbsp2, &nbsp this will give the Median of the list.

The &nbsp4th&nbsp and &nbsp5th&nbsp values in the list are &nbsp12&nbsp and &nbsp14.

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

Median &nbsp=&nbsp 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 &nbsp &nbsp

(2.1)&nbsp

Here is a random set of numbers.

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

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 &nbsp5&nbsp is the mode.

It’s the value that appears the most times, &nbsp4&nbsp times in total.

(2.2)&nbsp

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,&nbsp 14&nbsp and &nbsp26&nbsp are both modal values.

When it is the case that a data set has &nbsp2&nbsp modes, it is called a “bimodal” data set.

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