Question

in the data set below, what is the mean absolute deviation?
2 3 9 4 4 5
if the answer is a decimal, round it to the nearest tenth.
mean absolute deviation (mad):

Explanation:

Step1: Calculate the mean

The mean $\bar{x}$ of a data set $x_1,x_2,\cdots,x_n$ is given by $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.
Here, $n = 6$, and $\sum_{i=1}^{6}x_i=2 + 3+9+4+4+5=27$.
So, $\bar{x}=\frac{27}{6}=4.5$.

Step2: Calculate the absolute deviations

The absolute deviations are $|x_1-\bar{x}|,|x_2-\bar{x}|,\cdots,|x_n-\bar{x}|$.
For $x_1 = 2$: $|2 - 4.5|=2.5$; for $x_2 = 3$: $|3 - 4.5| = 1.5$; for $x_3=9$: $|9 - 4.5|=4.5$; for $x_4 = 4$: $|4 - 4.5|=0.5$; for $x_5 = 4$: $|4 - 4.5|=0.5$; for $x_6 = 5$: $|5 - 4.5|=0.5$.

Step3: Calculate the mean absolute deviation (MAD)

The MAD is $\frac{\sum_{i = 1}^{n}|x_i-\bar{x}|}{n}$.
$\sum_{i=1}^{6}|x_i-\bar{x}|=2.5+1.5 + 4.5+0.5+0.5+0.5=10$.
So, $MAD=\frac{10}{6}\approx1.7$.

Answer:

$1.7$