Question

The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 13,14,15,6,17,16,3

Answer 1

Given:

The data set is 13, 14, 15, 6, 17, 16, 3.

To find:

The mean absolute deviation for the data set.

Solution:

We have,

13, 14, 15, 6, 17, 16, 3

Mean of the data set is:

`\text{Mean}=\frac{\text{Sum of all observations}}{\text{Number of observations}}`

`\overline{x}=(13+14+15+6+17+16+3)/(7)`

`\overline{x}=(84)/(7)`

`\overline{x}=12`

The formula for mean absolute deviation is:

`MAD=\frac{\sum_(i=1)^n|x_i-\overline{x}|}{n}`

Using this formula, the mean absolute deviation for the data set is:

`MAD=(|13-12|+|14-12|+|15-12|+|6-12|+|17-12|+|16-12|+|3-12|)/(7)`

`MAD=(1+2+3+6+5+4+9)/(7)`

`MAD=(30)/(7)`

`MAD\approx 4.29`

Therefore, the mean absolute deviation for the data set is about 4.29.