Mean Deviation about Median:

The mean deviation about median is the mean of the absolute deviations of a set of data about the median of the data.

For Ungrouped data:

• Ungrouped data is the raw data we gather from an experiment or study initially. 
• The data is raw — that is, it's not sorted into categories, classified, or otherwise grouped. 
• An ungrouped set of data is basically a list of numbers.

Let n observations be x₁, x₂, x₃, ...,x_n. 

Steps to calculate mean deviation about median for ungrouped data: 

Step 1: 

Calculate the measure of central tendency about which we are to find the mean deviation. Let it be 'a'. 

Step 2: 

Find the deviation of each xi from a, i.e., x₁-a, x₂-a, x₃-a, ...,x_n-a.

Step 3: 

Find the absolute values of the deviations, i.e., drop the minus sign (-), if it is there, i.e., |x₁-a|, |x₂-a|, |x₃-a|, ...,|x_n-a| 

Step 4: 

Find the median of the absolute values of the deviations. This median is the mean deviation about a.

=Σ^|x_n-a|/_n

Mean Deviation about median =Σ^|x_n-M|/_n

Example 1 
Find the mean deviation about the median for the following data:
6, 7, 10, 12, 13, 4, 8, 12

Solution:
We proceed step-wise and get the following:

Step 1:
Median of the given data is:= 4,6,7,8, 10, 12, 12, 13

Median(for odd Numbers)=^nth/₂ term

Median(for even Numbers)= ^{{nth+(n+1)th}}/₂ term

Median=⁽⁸⁺¹⁰⁾/₂

             =9

Step 2: 
The deviations of the respective observations from the median M, i.e.,x_i-M are

6–9,7-9, 10-9, 12-9, 13–9,4–9,8–9, 12-9

or -3, -2, 1, 3, 4, -5, -1,3

Step 3: 

The absolute values of the deviations, i.e., (xi-M| are
3,2,1,3,4,5,1,3

Step 4: 
The required mean deviation about the median is = Σ^|x_i-M|/_n

=^{(3+2+1+3+4+5+1+3)}/₈ 

=2.75