The Mean Absolute Deviation is calculated in three simple steps.
1) Determine the Mean: Add all numbers and divide by the count
example: the weights of the following three people, denoted by letters are
A - 56 Kgs
B - 78 Kgs
C - 90 Kgs
Mean = (56+78+90)/3
= 74.6
2) Determine deviation of each variable from the Mean
i.e 56-74.6 = -18.67
78-74.6= 3.33
90-74.6 =15.33
3) Make the deviation 'absolute' by squaring and determining the roots i.e eliminate the negative aspect
Thus the Mean Absolute Deviation is (18.67 +3.33+15.33)/3 =12.44
Alternatively , you can use the excel formula =AVEDEV(56,78,90) to obtain the result.
Different Methods
There are different formulas for the calculation of mean absolute deviation. For example mean absolute deviation from mean and mean absolute deviation from median. Similarly the formulas for grouped and ungrouped data are also different. In order to see the calculation of mean absolute deviation from mean and mean absolute deviation from median for both grouped and ungrouped data please visit the link given below.
Let's consider the sample {2, 2, 3, 4, 14}.
First of all you must decide, what am I calculating the mean absolute deviation from? Will it be the mean, the mode or the median? (It could be any measure of what statisticians call 'location' or 'central tendency'.)
For no good reason except that it's familiar to most people let me choose the mean of the sample. It proves to be 5.
Now we need the absolute deviation of each sample element from the mean. Notice that these are the distances between the mean and the sample elements.
|2 - 5| = |-3| = 3
|2 - 5| = |-3| = 3
|3 - 5| = |-2| = 2
|4 - 5| = |-1| = 1
|14 - 5| = |9| = 9
The sum of these is 18; then their average is 18/5 = 3.6. So the mean absolute deviation (from the mean) is 3.6. In other words, the sample points are, on average 3.6 units from the mean.
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* * * * *No it is not.Step 1: Calculate the mean = sum of observations/number of observations.Step 2: For each observation, x, calculate deviation = x - mean.Step 3: Sum together the NON_NEGATIVE values of the above deviations.Step 4: Divide by the number of observations.That is the mean absolute deviation, not the rubbish given below!
The mean absolute deviation for a set of data is a measure of the spread of data. It is calculated as follows:Find the mean (average) value for the set of data. Call it M.For each observation, O, calculate the deviation, which is O - M.The absolute deviation is the absolute value of the deviation. If O - M is positive (or 0), the absolute value is the same. If not, it is M - O. The absolute value of O - M is written as |O - M|.Calculate the average of all the absolute deviations.One reason for using the absolute value is that the sum of the deviations will always be 0 and so will provide no useful information. The mean absolute deviation will be small for compact data sets and large for more spread out data.
(0.6745 * Standard deviation)/ (n^1/2) :)
The mean absolute deviation is 28.5
The mean absolute deviation is 8.22