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.
12, 14, 12, 25, 26, 19
mean absolute deviation:

Explanation:

Step1: Calculate the mean

The mean $\bar{x}$ of a data set $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.
Here, $n = 6$, $x_1=12,x_2 = 14,x_3=12,x_4=25,x_5=26,x_6=19$.
$\bar{x}=\frac{12 + 14+12+25+26+19}{6}=\frac{108}{6}=18$.

Step2: Calculate the absolute deviations

The absolute deviation of each data point $x_i$ is $|x_i-\bar{x}|$.
For $x_1 = 12$: $|12 - 18|=6$;
For $x_2 = 14$: $|14 - 18|=4$;
For $x_3 = 12$: $|12 - 18|=6$;
For $x_4 = 25$: $|25 - 18|=7$;
For $x_5 = 26$: $|26 - 18|=8$;
For $x_6 = 19$: $|19 - 18|=1$.

Step3: Calculate the mean absolute deviation (MAD)

The mean absolute deviation $MAD=\frac{\sum_{i = 1}^{n}|x_i-\bar{x}|}{n}$.
$\sum_{i = 1}^{6}|x_i-\bar{x}|=6 + 4+6+7+8+1=32$.
$MAD=\frac{32}{6}\approx5.33$.

Answer:

$5.33$