Question

in the data set below, what is the mean absolute deviation? -76.1 -84.6 -37.8 18.1 86.5 -69.8 -29.7 -83.4 0 65.8 if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad):

Explanation:

Step1: Calculate the mean

The data set is $-76.1,-84.6,-37.8,18.1,86.5,-69.8,-29.7,-83.4,0,65.8$.
The sum of the data is $-76.1-84.6 - 37.8+18.1+86.5-69.8-29.7-83.4 + 0+65.8=-110$.
There are $n = 10$ data - points.
The mean $\bar{x}=\frac{-110}{10}=-11$.

Step2: Calculate the absolute deviations

For $x_1=-76.1$, the absolute deviation is $| - 76.1-(-11)|=| - 76.1 + 11| = 65.1$.
For $x_2=-84.6$, the absolute deviation is $| - 84.6-(-11)|=| - 84.6 + 11| = 73.6$.
For $x_3=-37.8$, the absolute deviation is $| - 37.8-(-11)|=| - 37.8 + 11| = 26.8$.
For $x_4 = 18.1$, the absolute deviation is $|18.1-(-11)|=|18.1 + 11| = 29.1$.
For $x_5 = 86.5$, the absolute deviation is $|86.5-(-11)|=|86.5 + 11| = 97.5$.
For $x_6=-69.8$, the absolute deviation is $| - 69.8-(-11)|=| - 69.8 + 11| = 58.8$.
For $x_7=-29.7$, the absolute deviation is $| - 29.7-(-11)|=| - 29.7 + 11| = 18.7$.
For $x_8=-83.4$, the absolute deviation is $| - 83.4-(-11)|=| - 83.4 + 11| = 72.4$.
For $x_9 = 0$, the absolute deviation is $|0-(-11)|=11$.
For $x_{10}=65.8$, the absolute deviation is $|65.8-(-11)|=|65.8 + 11| = 76.8$.

Step3: Calculate the mean of the absolute deviations

The sum of the absolute deviations is $65.1+73.6+26.8+29.1+97.5+58.8+18.7+72.4+11+76.8 = 459.8$.
The mean absolute deviation $MAD=\frac{459.8}{10}=45.98\approx46.0$.

Answer:

$46.0$