Question

The number of showtimes for one movie over several days is shown. What is the mean absolute deviation (MAD)? 9, 6, 8, 9, 7, 4, 3, 5, 2, 4 *

Answer 1

Given:

The data set is:

9, 6, 8, 9, 7, 4, 3, 5, 2, 4

To find:

The mean absolute deviation (MAD) of the given data.

Solution:

We have,

9, 6, 8, 9, 7, 4, 3, 5, 2, 4

The mean of the given data set is:

$\overline{x}=\dfrac{1}{n}\sum x_i$

$\overline{x}=\dfrac{1}{10}(9+6+8+9+7+4+3+5+2+4)$

$\overline{x}=\dfrac{1}{10}(57)$

$\overline{x}=5.7$

So, the mean of the given data set is 5.7.

The mean absolute deviation (MAD) is:

$MAD=\dfrac{1}{n}\sum |x-\overline{x}|$

The mean absolute deviation (MAD) of the given data is:

$MAD=\dfrac{1}{10}(3.3+0.3+2.3+3.3+1.3+1.7+2.7+0.7+3.7+1.7)$

$MAD=\dfrac{1}{10}(21)$

$MAD=2.1$

Therefore, the mean absolute deviation (MAD) of the given data set is 2.1.