Question

in the data set below, what is the mean absolute deviation?
8 7 4 6 7 4 6
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, $n = 7$, and $\sum_{i=1}^{7}x_i=8 + 7+4 + 6+7 + 4+6=42$.
So, $\bar{x}=\frac{42}{7}=6$.

Step2: Calculate the absolute deviations

The absolute deviation of each data point $x_i$ from the mean $\bar{x}$ is $|x_i-\bar{x}|$.
For $x_1 = 8$: $|8 - 6|=2$.
For $x_2 = 7$: $|7 - 6|=1$.
For $x_3 = 4$: $|4 - 6|=2$.
For $x_4 = 6$: $|6 - 6|=0$.
For $x_5 = 7$: $|7 - 6|=1$.
For $x_6 = 4$: $|4 - 6|=2$.
For $x_7 = 6$: $|6 - 6|=0$.

Step3: Calculate the mean absolute deviation (MAD)

The MAD is the mean of the absolute deviations.
The sum of the absolute deviations is $2+1+2+0+1+2+0 = 8$.
MAD $=\frac{8}{7}\approx1.1$

Answer:

$1.1$