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Mean Absolute Deviation Calculator

MAD Formula

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what's imply Absolute Deviation (MAD) formulation?

The imply deviation or absolute deviation is calculated via the summation of the distinction of every fee from imply. The system used by the calculations of MAD is as follows:

$$ MAD = Σ|xi - m| / n $$

wherein,

xi are the person values

m is the mean of numbers

n is the whole wide variety

MAD facts:

  • The statistics distribution may be determined by way of the usual deviation of the numbers. each are comparable in idea, but the widespread deviation offers the deep know-how of information set with variance and so on.
  • MAD represents the suggest absolute deviation or median absolute deviation. They each aren't the identical, median is calculated from central point & mean is calculated from the numbers in the imply absolute deviation & median absolute deviation respectively.

How to locate MAD Manually (Step-by using-Step):

The system for the calculation is discussed earlier, here we have an instance:

Instance:

Calculate the suggest absolute deviation for the facts set: 4, 16, 8, 9, 14, 5?

Answer:

Step No. 1:

The formula is:

$$ MAD = Σ|xi - m| / n $$

Here,

  • x1 = 4
  • x2 = 16
  • x3 = 8
  • x4 = 9
  • x5 = 14
  • x6 = 5

Step No. 2:

Find the mean:

\(m = 4 + 16 + 8 + 9 + 14 + 5 / 6 \)

\(m = 56 / 6 \)

\(m = 9.33 \)

Step No. 3:

find deviation from the mean:

\(4 – 9.33 = -5.33 \)

\(16 – 9.33 = 6.67\)

\(8 – 9.33 = -1.33 \)

\(9 – 9.33 = -0.33 \)

\(14 – 9.33 = 4.67\)

\(5 – 9.33 = -4.33 \)

Step No. 4:

determine the mode of each cost:

\(|-5.33| = 5.33\)

\( |6.67| = 6.67 \)

\(|-1.33|= 1.33\)

\(|-0.33| = 0.33\)

\(|4.67| = 4.67\)

\( |-4.33| = 4.33 \)

Step No. 5:

decide the mean of absolute values:

\( m = 5.33 + 6.67 + 1.33 + 0.33 + 4.67 + 4.33 / 6 \)

\( m = 22.66 / 6 \)

\( m = 3.8 \)

additionally, our suggest deviation calculator makes use of this components for the calculation of the MAD. For ease, you could additionally attempt our on line mean mode median calculator that lets you calculate the mean, mode & median of your given information set.