Question

in the data set below, what is the mean absolute deviation? 5 5 6 4 1 1 6 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 \(5,5,6,4,1,1,6\). The sum of the data is \(5 + 5+6 + 4+1+1+6=28\). There are \(n = 7\) data - points. The mean \(\bar{x}=\frac{28}{7}=4\).

Step2: Calculate the absolute deviations

For \(x_1 = 5\), \(\vert x_1-\bar{x}\vert=\vert5 - 4\vert = 1\); for \(x_2 = 5\), \(\vert x_2-\bar{x}\vert=\vert5 - 4\vert = 1\); for \(x_3 = 6\), \(\vert x_3-\bar{x}\vert=\vert6 - 4\vert = 2\); for \(x_4 = 4\), \(\vert x_4-\bar{x}\vert=\vert4 - 4\vert = 0\); for \(x_5 = 1\), \(\vert x_5-\bar{x}\vert=\vert1 - 4\vert = 3\); for \(x_6 = 1\), \(\vert x_6-\bar{x}\vert=\vert1 - 4\vert = 3\); for \(x_7 = 6\), \(\vert x_7-\bar{x}\vert=\vert6 - 4\vert = 2\).

Step3: Calculate the mean of the absolute deviations

The sum of the absolute deviations is \(1+1 + 2+0+3+3+2=12\). The mean absolute deviation \(MAD=\frac{12}{7}\approx1.7\).

Answer:

\(1.7\)