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Average Deviation Calculator
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Average deviation is something which gives idea about how much the any value deviates from its average value among the given group of data.
Average deviation calculator calculates the mean as well as the average deviation for the given data instantly when you enter the data.

## Steps for Average Deviation Calculator

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Step 1 :

Enter the given data say x1, x2, x3,....xn. Find the number of values given which is represented as n

Step 2 :

Find the mean of the given values which is given as
$\bar{x}$ = $\frac{x_{1} + x_{2} + x_{3} + .... + x_{n}}{n}$

Step 3 :

Now find the deviation of each value by calculating the difference between it and the mean value. Represent all the given values in the table if needed.

Then add the deviation of all the values and divide it by given number of data (n) to get the average deviation. It is given by formula
$D_{\bar{x}}$ = $\frac{\sum_{i=1}^{n} x - \bar{x}}{n}$.

## Problems on Average Deviation Calculator

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1. ### Calculate the average deviation for the given data: 3,5,7,9,11

Step 1 :

Given data is 3,5,7,9,11.

Hence the no of values = n = 5

Step 2 :

The mean of given values are given by the formula
$\bar{x}$ = $\frac{x_{1} + x_{2} + x_{3} + .... + x_{n}}{n}$
= $\frac{3 + 5 + 7 + 9 +11}{5}$
=7.

Step 3 :

The deviation for values 3,5,7,9,11 are

For xi = 3, |xi - $\bar{x}$| = |3 - 7| = 4

For xi = 5, |xi - $\bar{x}$| = |5 - 7| = 2

For xi = 7, |xi - $\bar{x}$| = |7 - 7| = 0

For xi = 9, |xi - $\bar{x}$| = |9 - 7| = 2

For xi = 11, |xi - $\bar{x}$| = |11 - 7| = 4

The Average deviation is given by
$D_{\bar{x}}$ = $\frac{\sum_{i=1}^{n} x - \bar{x}}{n}$

= $\frac{4 + 2 + 0 + 2+ 4}{5}$

= $\frac{12}{5}$

= 2.4.

Answer  :

The average deviation for 3, 5, 7, 9, 11 is 2.4.

2. ### Find average deviation for following data: 32, 34, 36, 38 40.

Step 1 :

Given data is 32, 34, 36, 38, 40, 42.

Hence the no of values = n = 6

Step 2 :

The mean of given values are given by the formula
$\bar{x}$ = $\frac{x_{1} + x_{2} + x_{3} + .... + x_{n}}{n}$
= $\frac{32 + 34 + 36 + 38 + 40 + 42}{6}$
= 37.

Step 3 :

The deviation for values  are

For xi = 32, |xi - $\bar{x}$| = |32 - 37| = 5

For xi = 34, |xi - $\bar{x}$| = |34 - 37| = 3

For xi = 36, |xi - $\bar{x}$| = |36 - 37| = 1

For xi = 38, |xi - $\bar{x}$| = |36 - 37| = 1

For xi = 40, |xi - $\bar{x}$| = |40 - 37| = 3

For xi = 42, |xi - $\bar{x}$| = |42 - 37| = 5

The Average deviation is given by
$D_{\bar{x}}$ = $\frac{\sum_{i=1}^{n} x - \bar{x}}{n}$

= $\frac{5 + 3 + 1 + 1 + 3 +5}{6}$

= $\frac{18}{6}$

= 3.

Answer  :

The average deviation for 32, 34, 36, 38, 40 and 42 is 3.

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