Average Absolute Deviation?

What is the coding in matlab to find the AAD?

Answer 1

[John D'Errico]

1. Compute the deviation. (You have not said what the deviation is from, so I cannot answer that.)

2. Compute the absolute value of the deviations. abs will suffice.

help abs

3. Use mean to compute the average.

help mean

[Delany MacDonald]

If its standard deviation would it be y= std(x) then absy = abs(y) then meany = mean(absy)?

Answer 2

[Walter Roberson]

mean( abs(x - mean(x)) )

Answer 3

[Image Analyst]

We usually find the median absolute deviation is a better measure https://en.wikipedia.org/wiki/Median_absolute_deviation because the measure itself is less affected by outliers.

On a global basis you can do

mad = median(abs(array(:) - median(array(:))))

We often use it to find outliers in the data.

Answer 4

[Meg Noah]

The Average Absolute Deviation (AAD) is the mean of deviations from a central point (central tendency).

If the central point is the mean of the data set, then the AAD is also referred to as the Mean Absolute Deviation (MAD).

If the central point is the median of the data set, then the AAD is also referred to as the Median Absolute Deviation, which can also be abbreviated as MAD.

If the central point is the mode of the data set, then the AAD is the Mode Absolute Deviation.

The central point can be determined other ways as well.

To add to the confusion of this, the Median Absolute Deviation can also be mathematically defined as:

Example:

rng default
X = randi([1 10],1,20)

X = 1×20

9 10 2 10 7 1 3 6 10 10 2 10 10 5 9 2 5 10 8 10

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

meanAbsoluteDeviation = mean(abs(X-mean(X)))

meanAbsoluteDeviation = 2.9600

medianAbsoluteDeviation = mean(abs(X-median(X)))

medianAbsoluteDeviation = 2.8500

medianAbsoluteDeviation2 = median(abs(X-median(X)))

medianAbsoluteDeviation2 = 1.5000

modeAbsoluteDeviation = mean(abs(X-mode(X)))

modeAbsoluteDeviation = 3.0500