Question

find the mean absolute deviation of the following data set. the data set: {24, 30, 36, 42, 48, 54}. 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, $n = 6$, $x_1=24,x_2 = 30,x_3=36,x_4 = 42,x_5=48,x_6=54$. Then $\sum_{i=1}^{6}x_i=24 + 30+36+42+48+54=234$, and $\bar{x}=\frac{234}{6}=39$.

Step2: Calculate the absolute deviations

The absolute deviation of each data - point $x_i$ from the mean $\bar{x}$ is $|x_i-\bar{x}|$.
$|24 - 39|=15$, $|30 - 39|=9$, $|36 - 39|=3$, $|42 - 39|=3$, $|48 - 39|=9$, $|54 - 39|=15$.

Step3: Calculate the mean absolute deviation

The mean absolute deviation (MAD) is $\text{MAD}=\frac{\sum_{i = 1}^{n}|x_i-\bar{x}|}{n}$.
$\sum_{i=1}^{6}|x_i - \bar{x}|=15 + 9+3+3+9+15=54$.
So, $\text{MAD}=\frac{54}{6}=9$.

Answer:

9