Average Deviation Formula with Problem Solution & Solved Example

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The average deviation is generally used by statisticians to calculate the dispersion among measures in a given population. For example, if you are given a complete set of scores then it could be calculated by computing mean and check their specific distance between each score an don’t forget to consider the Mean either the score is above or below the mean. The other name for the same concept is average absolute deviation. The formula to calculate the average deviation in mathematics is given below –

\[\LARGE Average\:Deviation=\sum_{i=1}^{n}\left | x-\overline{x} \right |\]

x, represents the observation.
$bar{x}$, represents the mean.
n, represents the number of observation.

If you wanted to get the complete understanding of the average deviation concept then you should know the term absolute deviation first. This is the distance between each value in the data set and their mean or median calculations.

Absolute deviation usage is not so common with standard deviation but it is highly similar and used to measure the spread. There are particular situations when two different data sets with variable spreads produce the exactly same absolute deviation. However, this is possible standard deviation is also the same for different data sets.

If you will consider real-life scenarios then absolute deviations are always more accurate and suitable to use as compared to the standard deviations. Not only they are accurate in real-life situations but simpler to calculate as well.

You must be wondering how can you calculate the average deviation in mathematic. For this purpose, you just have to replace the mean value with the median values. That’s all for the day! Don’t forget to share the experience how did you calculate the average deviations in your case.