The mean of a dataset is the sum of the elements divided by how many elements are present in the data set.
The sum of the elements in this dataset is
[tex]93+95+102+91+104+93+95+98+97+92+102+96+92+104+100+98=1552[/tex]
And there are 16 elements, so the mean is
[tex]\mu = \dfrac{1552}{16}=97[/tex]
The absolute deviation is computed as follows:
- For each term in the dataset, we consider its distance from the mean. In formulas, we compute [tex]|x_i-\mu|[/tex] for every element [tex]x_i[/tex]
- We take the average of all these terms: [tex]\frac{1}{n}\sum|x_i-\mu|[/tex]
So, following the first point, the new dataset is
[tex]\{4, 2, 5, 6, 7, 4, 2, 1, 0, 5, 5, 1, 5, 7, 3, 1\}[/tex]
And the average of this dataset is
[tex]\dfrac{4+2+5+6+7+4+2+1+0+5+5+1+5+7+3+1}{16} = \dfrac{58}{16}=3.625[/tex]
