Question

Can someone show me how to do Mean absolute deviation

What is the means-to-MAD ratio of the two data sets, expressed as a decimal?
Data set Mean Mean absolute deviation (MAD)
1 10.7 2.4
2 13.7 2.5

Answer 1

To find the mean of a set, add up all of the numbers and divide by how many numbers you have. For the first set:

`\mu=\frac{10.7+2.4}2=\frac{13.1}2=6.55`
For the second set:

`\mu=\frac{13.7+2.5}2=\frac{16.2}2=8.1`

To find the mean absolute deviation, (MAD) find the mean of the distances of each number from the mean.
For the first set:

`MAD=\frac10.7-6.552=\frac{4.15+4.15}2=\frac{8.3}2=4.15`
For the second set:

`MAD=\frac2.5-8.12=\frac{5.6+5.6}2=\frac{11.2}2=5.6`
Note that when you only have two data points the mean is directly between them, which is why the distances are the same.

The means-to-MAD ratio is simply that, divide one by the other and that's it.
For the first set:

`6.55/4.15=1.57831325`
For the second set:

`8.1/5.6=1.44642857`