Intuitively, we can notice that it is possible to determine it as the difference of any value and the average of the information:

*D**i*=*x**i*−*x*¯

We can see that to determine this deviation, when we know the average, we only require the value whose deviation which is about to be determined.

Also, we can state that if we possess one piece of information and its absolute deviation, it is possible to separate the average by using a simple subtraction:

*x*¯=*x**i*−*D**i*

and afterwards we can utilize it to calculate other deviations.

In a math examination Pedro got 9, as the average of the class is actually 6.7. Determine the absolute deviation of Pedro's mark.

Using the formula

*D**i*=*x**i*−*x*¯=9−6.7=2.3

The mean absolute deviation is the very first measure of dispersion. It is actually the average of absolute differences between every value in a set of value and the average of all values of that sets.

The mean deviation is determined either from median or mean, however only median is preferred because if the signs are overlooked, the amount of deviation of the sets obtained from median is minimum.

The Mean Absolute Deviation (MAD) of a set of data is actually the average distance between every data value and the mean.

**The steps to locate
the MAD contain:**

1. find the average (mean)

2. find the difference between every data value and the mean

3. consider the absolute value of each difference

4. find the average (mean) of these differences

The average absolute deviation or just average deviation of a data set is the average of an absolute deviations and is an overview statistic of statistical dispersion or variability. In its basic form, the average employed can be the median, mean, mode or the outcome of another measure of central tendency.

The average absolute deviation through the median is lower than or equivalent to the average absolute deviation through the mean. Actually, the average absolute deviation from the median is always equal or lower than to the average absolute deviation from any other set number.

The average absolute deviation from the mean is equal or less than to the standard deviation; one method of proving this depends on Jensen's inequality.

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