Question

What is the mean absolute deviation (MAD) of the data set?

Answer 1

Answer:

$\frac{16}{5}$

Step-by-step explanation:

The formula for MAD is  attached in the pic below.

X_i are all the x values

x bar is the mean (sum of all the numbers divided by the number of numbers)

n is the number of numbers

Basically, we subtract the mean (x bar) from each of the values and take the absolute value of it and SUM all of them. Then we divide by the number of numbers.

Thus, mean = $\frac{2+6+8+12+12}{5}=\frac{40}{5}=8$

Now, $\frac{|2-8|+|6-8|+|8-8|+|12-8|+|12-8|}{5}\\=\frac{6+2+0+4+4}{5}\\=\frac{16}{5}$

The MAD is  $\frac{16}{5}$