Mean Absolute Deviation

In mathematics, mean deviation is also known as mean absolute deviation. By using the mean deviation formula explained by tutor, we can calculate the mean absolute deviation. The dispersion of numbers should be calculated by mean absolute deviation. In this article, tutor explains the mean absolute deviation in step by step.


Explanation to Mean Absolute Deviation Tutor:

 

The general formula used for mean absolute deviation is,

Mean absolute deviation = `(sum|x - barx|)/n`

where,

  • `barx` - mean 
  • n - number of values

 

Example Problems to Mean Absolute Deviation Tutor:

 

Example: 1

Find out mean absolute deviation: 

26, 27, 28, 29, 30

Tutor solution:

Given,

26, 27, 28, 29, 30

Step 1:

n = 5 

Step 2:

Mean absolute deviation = `(sum|x - barx|)/n`

Step 3:

Mean =  `barx` = `(sumx)/n`

  =  `(26 + 27 + 28 + 29 + 30)/5`

  =  `140/5`

   `barx`= 28

Step 4:

x x - `barx` ( `barx = 28` ) `|x - barx|`
26 - 2 2
27 - 1 1
28 0 0
29 1 1
30 2 2


Total = 6

Step 5: 

Mean absolute deviation = `(sum|x - barx|)/n`

`6/5`

= 1.2

Tutor answer: Mean absolute deviation = 1.2


Example: 2

Find out mean absolute deviation: 

9, 10, 11, 12, 13, 14, 15, 16

Tutor solution:

Given: 9, 10, 11, 12, 13, 14, 15, 16

Step 1:

n = 8 

Step 2:

Mean absolute deviation = `(sum|x - barx|)/n`

Step 3: 

Mean = `barx` = `(sumx)/n`

=  `(9 + 10 + 11 + 12 + 13 + 14 + 15 + 16)/8`

=  `100/8`

          `barx` = 12.5

Step 4: 

x x - `barx` ( `barx = 12.5` ) `|x - barx|`
9 - 3.5 3.5
10 - 2.5 2.5
11 - 1.5 1.5
12 - 0.5 0.5
13 0.5 0.5
14 1.5 1.5
15 2.5 2.5
16 3.5 3.5


Total = 16

Step 5: 

Mean absolute deviation =  `(sum|x -barx|)/n`

`16/8`

= 2

Tutor answer: Mean absolute deviation = 2

 

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Practice Problems to the Mean Absolute Deviation Tutor:

 

Problem: 1

Find out mean absolute deviation: 

5, 6, 7

Answer: 0.67

Problem: 2

Find out mean absolute deviation: 

15, 16, 17, 18

Answer: 1

Problem: 3

Find out mean absolute deviation: 

80, 78, 76, 74, 72

Answer: 2.4