# Math Median Tutorial

## Arithmetic Median

##### Arithmetic Median Definition:

Median is the middle value of the given numbers or distribution in their ascending order.Median is the average value of the two middle elements when the size of the distribution is even.

##### Example 1:

To find the median of 4,5,7,2,1 [ODD].

###### Step 1:

Count the total numbers given. There are 5 elements or numbers in the distribution.

###### Step 2:

Arrange the numbers in ascending order. 1,2,4,5,7

###### Step 3:

The total elements in the distribution (5) is odd. The middle position can be calculated using the formula. (n+1)/2 So the middle position is (5+1)/2 = 6/2 = 3 The number at 3rd position is = Median = 4

##### Example 2:

To find the median of 4,5,7,2,1,8 [Even]

###### Step 1:

Count the total numbers given. There are 6 elements or numbers in the distribution.

###### Step 2:

Arrange the numbers in ascending order. 1,2,4,5,7,8

###### Step 3:

The total elements in the distribution (6) is even. As the total is even, we have to take average of number at n/2 and (n/2)+1 So the position are n/2= 6/2 = 3 and 4 The number at 3rd and 4th position are 4,5

###### Step 4:

Find the median. The average is (4+5)/2 = Median = 4.5

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