Mean Absolute Deviation Formula

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Definition: - The mean absolute deviation (MAD) is the average of the absolute values of the deviations around the mean for a set of numbers.
 
Mean Absolute Deviation Formula:-
MAD=∑ l x- µl / N
 
Where,
µ= Mean population
N= Number of values
 
Example: - Suppose a small company started a production line to build computers. During the first five weeks of production, the output is 5, 9, 16, 17, and 18 computers respectively. Compute the mean absolute deviation.
 
Solution:-
Step 1:-At first we will find the population mean µ of the given data.
 
µ=∑x / N
=(5+9+16+17+18)/ 5                      Since there are five values in the data.
                                                          So N= 5
=65/5
=13
Step 2:- Find the deviation from the mean.
Number (x) Deviations from the Mean (x- µ) Absolute deviation lx-µl
5 5-13=-8 8
9 9-13=-4 4
16 16-13=+3 3
17 17-13=+4 4
18 18-13=+5 5
∑x =65 ∑(x- µ)=0 ∑ lx-µl = 24
 
Hence
MAD=∑ l x- µl / N
        =24/ 5
        =4.8
 
Another example: - The following data give the prices of seven textbooks randomly from a university bookstore.
89, 57, 104, 73, 26, 121, and 81.
Calculate the mean absolute deviation.



µ=∑x / N
=551/ 7                                            
=78.71
 
And MAD=∑ l x- µl / N
        =160.29/ 7
        =22.899
 

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