Question

in the data set below, what is the mean absolute deviation? 3 6 9 4 8 6 6 if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad):

Explanation:

Step1: Calculate the mean

The sum of the data set \(3 + 6+9 + 4+8+6+6=42\). There are \(n = 7\) data - points. The mean \(\bar{x}=\frac{42}{7}=6\).

Step2: Calculate the absolute deviations

\(\vert3 - 6\vert=3\), \(\vert6 - 6\vert=0\), \(\vert9 - 6\vert=3\), \(\vert4 - 6\vert=2\), \(\vert8 - 6\vert=2\), \(\vert6 - 6\vert=0\), \(\vert6 - 6\vert=0\).

Step3: Calculate the mean of the absolute deviations

The sum of the absolute deviations is \(3 + 0+3+2+2+0+0 = 10\). The mean absolute deviation \(MAD=\frac{10}{7}\approx1.4\).

Answer:

1.4