What is the Mean Absolute Deviation of the following set?
{2, 10, 7, 12, 8}
7.8
2.64
5
13.2
...
...
To calculate the Mean Absolute Deviation (MAD), we first find the absolute deviation for each number by subtracting the mean of the set from each number and taking the absolute value:
\[\text{Absolute Deviation} = \left|2 - \frac{2+10+7+12+8}{5}\right| = 4\]
\[\text{Absolute Deviation} = \left|10 - \frac{2+10+7+12+8}{5}\right| = 2\]
\[\text{Absolute Deviation} = \left|7 - \frac{2+10+7+12+8}{5}\right| = 1\]
\[\text{Absolute Deviation} = \left|12 - \frac{2+10+7+12+8}{5}\right| = 4\]
\[\text{Absolute Deviation} = \left|8 - \frac{2+10+7+12+8}{5}\right| = 1\]
Next, we find the average of the absolute deviations:
\[\text{MAD} = \frac{4 + 2 + 1 + 4 + 1}{5} = \frac{12}{5} = 2.4\]
Therefore, the Mean Absolute Deviation of the set {2, 10, 7, 12, 8} is 2.4.