Question

in preparation for a move across town, todd packed 5 boxes weighing: 20 pounds 85 pounds 55 pounds 40 pounds 18 pounds. what was the mean absolute deviation of the weights of the boxes? if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad): pounds

Explanation:

Step1: Calculate the mean

The mean $\bar{x}$ of a set of data $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here, $n = 5$, $x_1=20$, $x_2 = 85$, $x_3=55$, $x_4 = 40$, $x_5=18$.
$\bar{x}=\frac{20 + 85+55 + 40+18}{5}=\frac{218}{5}=43.6$

Step2: Calculate the absolute - deviations

The absolute - deviation of each data point $x_i$ from the mean $\bar{x}$ is $|x_i-\bar{x}|$.
$|20 - 43.6|=23.6$, $|85 - 43.6| = 41.4$, $|55 - 43.6|=11.4$, $|40 - 43.6| = 3.6$, $|18 - 43.6|=25.6$

Step3: Calculate the mean of the absolute - deviations

The mean absolute deviation (MAD) is $\text{MAD}=\frac{\sum_{i = 1}^{n}|x_i-\bar{x}|}{n}$.
$\text{MAD}=\frac{23.6+41.4 + 11.4+3.6+25.6}{5}=\frac{105.6}{5}=21.12\approx21.1$

Answer:

$21.1$