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:

$\text{Mean}=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}$

$\overline{x}=\dfrac{13+14+15+6+17+16+3}{7}$

$\overline{x}=\dfrac{84}{7}$

$\overline{x}=12$

The formula for mean absolute deviation is:

$MAD=\dfrac{\sum_{i=1}^n|x_i-\overline{x}|}{n}$

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

$MAD=\dfrac{|13-12|+|14-12|+|15-12|+|6-12|+|17-12|+|16-12|+|3-12|}{7}$

$MAD=\dfrac{1+2+3+6+5+4+9}{7}$

$MAD=\dfrac{30}{7}$

$MAD\approx 4.29$

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