# Median, Mode, Mean and Range

Finding the median, mode, mean and range of a series of numbers are some of the easiest tasks in mathematics. Although, students quickly learn and understand how to find the median, mode, mean and range, some students will soon forget which method goes with which ‘M’, because three of these terms start with the letter ‘M’.

So, before starting to learn how to find the median, mode, mean and range, I will teach you something quick to remember two of these three ‘M s’. Then the remaining ‘M’ can also be remembered.

## Definitions of Median Mode Mean and Range

Median

The number which is in the middle or the middle value of a list of numbers. (‘med’ in median sounds like ‘mid’. So, remember it as the number in the middle.)

Mode

The number that appears the most in a list of numbers. (Remember ‘mo’ in mode as ‘most’.)

So, now the remaining term starting with the letter ‘m’ is mean.

Mean

The total of the numbers divided by how many numbers there are in a list of numbers. You can also remember this as the ‘average’. Remember the way you find your average marks?

Range

The difference between the largest and the smallest number in a list of numbers.

Now, let’s learn how to find each of these in a series of numbers.

## Median

(‘median’ => ‘med’ => ‘mid’ => middle)

### What is median?

Median is the number that appears in the middle of a series of numbers, also called the middle value.

### How to find the median?

A number series with an odd number of numbers;

It is easy to find the middle value in a number series with an odd number of numbers.

Look at the following series of numbers.

11 7 11 18 9 7 6 23 7

How many numbers are there? 9

Step 1:

Order the numbers in ascending order (from smallest to largest).

6 7 7 7 9 11 11 18 23

Step 2:

Now, find the number which is in the middle.

6 7 7 7 9 11 11 18 23

Therefore, the median of this series of numbers is 9.

***Remember – median’ => ‘med’ => ‘mid’ => middle

A number series with an even number of numbers;

Let’s assume you’ve got a number series with an even number of numbers.

7 11 18 9 7 6 23 7

How many numbers are there? 8

Step 1:

Order the numbers in ascending order (from smallest to largest).

6 7 7 7 9 11 18 23

Step 2:

Now, find the number which is in the middle.

Here comes the problem! There’s no number in the middle.

6 7 7 7 9 11 18 23

Instead, let’s find the two numbers in the middle.

6 7 7 7 9 11 18 23

The two numbers in the middle are 7 and 9

Step 3:

Next, find the halfway of the two middle values.

7 + 9 = 16

16 / 2 = 8

Therefore, the median of this series of numbers is 8.

***Remember this might always not be a whole number.

I hope now you will remember what the median of a series of numbers means and how to find the median.

Our next task is to find the mode.

## Mode

(‘mode’ => ‘mo‘ => ‘most’)

### What is mode?

Mode is the number that appears most in a series of numbers.

### How to find the mode?

Look at the following series of numbers.

11 7 11 18 9 7 6 23 7

Step 1:

Order the numbers in ascending order (from smallest to largest).

6 7 7 7 9 11 11 18 23

Step 2:

Now, see which number appears the most.

6 7 7 7 9 11 11 18 23

Therefore, the mode of this series of numbers is 7.

***Remember – ‘mode’ => ‘mo‘ => ‘most’

I hope now you will remember what the mode of a series of numbers means and how to find the mode.

Next, let’s learn how to find the mean.

## Mean

### What is mean?

The mean is the total of the numbers divided by how many numbers there are. We also call this average.

When you need to find the average of your marks, what do you do?

You first find the total of all the marks you’ve scored.

Example:

Maths – 97%

English – 83%

Science – 85%

Geography – 75%

History – 62%

ICT – 90%

Total marks        = 97 + 83 + 85 + 75 + 62 + 90 = 492

No. of subjects    = 6

Average            = 492 / 6 = 82

Finding the mean is also the same.

### How to find the mean?

Look at the following series of numbers.

11 7 11 18 9 7 6 23 7

Step 1:

Add all the numbers in the series.

11 + 7 + 11 + 18 + 9 + 7 + 6 + 23 + 7 = 99

Step 2:

Now, divide the total by the number of numbers.

Total                    = 99

No. of numbers  = 9

Mean                   = 99 / 9 = 11

Therefore, the mean of this series of numbers is 11.

***Remember the mean is not always a whole number.

I hope now you will remember what the mean of a series of numbers means and how to find the mean.

Last but not least! Let’s learn to find the range of a series of numbers.

## Range

### What is range?

The range is the difference between the largest and the smallest number in a series of numbers.

### How to find the range?

Look at the following series of numbers.

11 7 11 18 9 7 6 23 7

Step 1:

Find the smallest number. It is 6.

Find the largest number. It is 23.

Step 2:

Now, find the difference between the largest and the smallest number.

23 – 6 = 17

Therefore, the range of this series of numbers is 17.

I hope now you will remember what the range of a series of numbers means and how to find the range.