Logics of M3

M3 -  1) Mean 2) Median 3) Mode

1. Mean -   The mean is just the average of the numbers.

It is easy to calculate: add up all the numbers, then divide by how many numbers there are.

 In other words it is the sum divided by the count.


Positive numbers -
 Example 1: What is the Mean of these numbers?
      6, 11, 7
 Add the numbers: 6 + 11 + 7 = 24
 Divide by how many numbers (there are 3 numbers): 24 / 3 = 8
 The Mean is 8


Why Does This Work?
It is because 6, 11 and 7 added together is the same as 3 lots of 8:

Negative Numbers

How do you handle negative numbers? Adding a negative number is the same as subtracting the number (without the negative). For example 3 + (-2) = 3-2 = 1.

Knowing this, let us try an example:

Example 3: Find the mean of these numbers:

3, -7, 5, 13, -2

The sum of these numbers is 3 - 7 + 5 + 13 - 2 = 12

There are 5 numbers.

The mean is equal to 12 ÷ 5 = 2.4

The mean of the above numbers is 2.4 .

2. Median -  The middle number (in a sorted list of numbers). 

To find the Median, place the numbers you are given in value order and find the middle number.

Example: find the Median of {13, 23, 11, 16, 15, 10, 26}. 

Put them in order: {10, 11, 13, 15, 16, 23, 26}

The middle number is 15, so the median is 15. 

Try from urself -

 17 , 26 , 13, 24 , 02

Put them in order & try to find the median 

3. Mode -

To find the mode, or modal value, first put the numbers in order, then count how many of each number.

Example:

3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29

In order these numbers are:

3, 5, 7, 12, 13, 14, 20, 23, 23, 23, 23, 29, 39, 40, 56

This makes it easy to see which numbers appear most often.

In this case the mode is 23.

More Than One Mode -

You can have more than one mode.

Example: {1, 3, 3, 3, 4, 4, 6, 6, 6, 9}

3 appears three times, as does 6.

So there are two modes: at 3 and 6

Having two modes is called "bimodal".

Having more than two modes is called "multimodal".

Grouping -

When all values appear the same number of times the idea of a mode is not useful. But you could group them to see if one group has more than the others. 

Example: {4, 7, 11, 16, 20, 22, 25, 26, 33}

Each value occurs once, so let us try to group them.

We can try groups of 10:

0-9: 2 values (4 and 7)

10-19: 2 values (11 and 16)

20-29: 4 values (20, 22, 25 and 26)

30-39: 1 value (33)

In groups of 10, the "20s" appear most often, so we could choose 25 as the mode.

You could use different groupings and get a different answer!