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7.4 Mean Absolute Deviation

Mean Absolute Deviation (M.A.D) is the average of the absolute deviations of values from their arithmetic mean, calculated using the formula M.A.D = (1/n) * ∑ |xi - x̄|. For grouped data, it can be computed using midpoints and frequencies. While M.A.D is easy to calculate and accurately represents data, it is sensitive to outliers and cannot be used with open frequency tables.

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125 views3 pages

7.4 Mean Absolute Deviation

Mean Absolute Deviation (M.A.D) is the average of the absolute deviations of values from their arithmetic mean, calculated using the formula M.A.D = (1/n) * ∑ |xi - x̄|. For grouped data, it can be computed using midpoints and frequencies. While M.A.D is easy to calculate and accurately represents data, it is sensitive to outliers and cannot be used with open frequency tables.

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osama7abx
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7.

4_Mean_Absolute_Deviation
Mean Absolute Deviation

Definition
Deviation :
The Deviation of an observation x is the result of subtracting it from the arithmetic
mean (usually) of the sample S .

Mean Absolute Deviation :


The mean absolute deviation is defined as the average of the absolute deviations
of the values from their arithmetic mean and is denoted by the symbol M . A. D .
If we have a set of observations x 1 , x 2 , . . . , x n whose mean is x̄ , then the mean
deviation is :
n
1
M . A. D = . ∑ |x i − x̄|
n
i=1

Where :

xi : represent the observations .


n : is the number of observations .
x̄ : mean .

For Grouped Data :

In the case of data classified in a frequency table with a number of intervals k :

k
1
M . A. D = . ∑ f i |x i − x̄|
n
i=1

Where :
k
n = ∑ fi
i=1

xi : is midpoint for each interval .


fi : the frequency of each interval .

Important Note :
The median or any other measures can be used instead of the arithmetic mean when
calculating the mean deviation .

Advantages and disadvantages of mean deviation


Advantages :
Easy measure to calculate.
An accurate measure and expresses all the data during its calculation.

Disadvantages :
A measure that is affected by the extreme values (outliers).
It cannot be calculated in the case of open frequency tables.

Examples
Ex 1 :
Ex 2 :

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