Question

Find the mean absolute deviation of the set of data 9 12 3 5 8

Answer 1

`\bar X =(9 + 12 + 3 + 5 + 8)/(5) =7.4`

`MAD= |1.6| + |4.6| + |4.4| + |2.4| + |0.6| = 13.6`

Explanation:

For this case we have the following data given: 9,12,3,5,8

1 step

The mean for this case can be calculated with this formula:

`\bar X= (\sum_(i=1)^n X_i)/(n)`

And replacing we got:

`\bar X =(9 + 12 + 3 + 5 + 8)/(5) =7.4`

2 Step

We can calculate the deviation for each value from the mean like this:

9 - 7.4 = 1.6

12 - 7.4 = 4.6

3 - 7.4 = - 4.4

5 - 7.4 = - 2.4

8 - 7.4 = 0.6

And in order to calculate the mean absolute deviation we just need the following formula:

`MAD= \sum_(i=1)^n |X_i -\bar X|`

And replacing we got:

`MAD= |1.6| + |4.6| + |4.4| + |2.4| + |0.6| = 13.6`

Answer 2

Explanation:

The formula for determining the mean of a data is

Mean = sum of items/number of items

Looking at the given data, sum of the items is

9 + 12 + 3 + 5 + 8 = 37

Number of items = 5

Mean = 37/5 = 7.4

Deviation of each item from the mean is

9 - 7.4 = 1.6

12 - 7.4 = 4.6

3 - 7.4 = - 4.4

5 - 7.4 = - 2.4

8 - 7.4 = 0.6

The sum of the absolute values are

1.6 + 4.6 + 4.4 + 2.4 + 0.6 = 13.6

The mean absolute deviation is

13.6/5 = 2.72