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# Mean Deviation Calculator

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Mean deviation is the difference between average of each data set value about the mean of the data set. Mean deviation is also known as a mean absolute deviation. Plug in the set of data into this online mean deviation calculator to find the mean and the mean deviation.

## Steps

Step 1 : Note the given data set and find the mean of the given data set.

Step 2 : Calculate the difference between each set of data value and the mean.

Step 3 : Determine the mean of these differences by using the formula given below,

Mean deviation = $\frac{1}{n}\sum_{i \to 1}^{n}|x_i - \bar{x}|$

where,
$x_i$ = each observation
$\bar{x}$ = mean
n = total number of observations

## Problems

Given below are some of the problems based on mean deviation.

### Solved Examples

Question 1: Determine the mean deviation of 6, 6, 3, 8, 7, 11, 15, 16.
Solution:

Step 1 : Given observations : 6, 6, 3, 8, 7, 11, 15, 16

$Mean \ \bar{x}$ = $\frac{6+6+3+8+7+11+15+16}{8}$ = $\frac{72}{8}$ = 9

Step 2 : $\sum_{i \to 1}^{n}|x_i - \bar{x}|$ = |6-9| + |6-9| + |3-9| + |8-9| + |7-9| + |11-9| + |15-9| + |16-9|

$\sum_{i \to 1}^{n}|x_i - \bar{x}|$
= 3 + 3 + 6 + 1 + 2 + 2 + 6 + 7 = 30

Step 3 : $\frac{1}{n}\sum_{i \to 1}^{n}|x_i - \bar{x}|$ = $\frac{30}{8}$ = 3.75

Question 2: Determine the mean deviation of 20, 20, 10, 20, 30.
Solution:

Step 1 : Given observations : 20, 20, 10, 20, 30

$Mean \ \bar{x}$ = $\frac{20+20+10+20+30}{5}$ = $\frac{100}{5}$ = 20

Step 2 : $\sum_{i \to 1}^{n}|x_i - \bar{x}|$ = |20-20| + |20-20| + |10-20| + |20-20| + |30-20|

$\sum_{i \to 1}^{n}|x_i - \bar{x}|$
= 0 + 0 + 0 + 10 + 10 = 20

Step 3 : $\frac{1}{n}\sum_{i \to 1}^{n}|x_i - \bar{x}|$ = $\frac{20}{5}$ = 4