Question

the data set below has 6 values.
find the mean absolute deviation for the data set.
if necessary, round your answer to the nearest hundredth.
17, 4, 6, 15, 15, 15
mean absolute deviation:

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, $n = 6$, $x_1=17,x_2 = 4,x_3=6,x_4 = 15,x_5=15,x_6=15$.
$\bar{x}=\frac{17 + 4+6 + 15+15+15}{6}=\frac{72}{6}=12$.

Step2: Calculate the absolute deviations

The absolute deviation of each data point $x_i$ is $|x_i-\bar{x}|$.
For $x_1 = 17$: $|17 - 12|=5$.
For $x_2 = 4$: $|4 - 12|=8$.
For $x_3 = 6$: $|6 - 12|=6$.
For $x_4 = 15$: $|15 - 12|=3$.
For $x_5 = 15$: $|15 - 12|=3$.
For $x_6 = 15$: $|15 - 12|=3$.

Step3: Calculate the mean absolute deviation (MAD)

The mean absolute deviation $MAD=\frac{\sum_{i = 1}^{n}|x_i-\bar{x}|}{n}$.
$\sum_{i = 1}^{6}|x_i-\bar{x}|=5 + 8+6+3+3+3=28$.
$MAD=\frac{28}{6}\approx4.67$.

Answer:

$4.67$