Question

93, 95 , 102, 91, 104, 93, 95, 98, 97, 92 , 102 , 96, 92, 104 , 100, 98,

Find the MEAN is this data set ?
And the ABSOLUTE DEVIATION ?

Answer 1

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

`93+95+102+91+104+93+95+98+97+92+102+96+92+104+100+98=1552`

And there are 16 elements, so the mean is

`\mu = (1552)/(16)=97`

The absolute deviation is computed as follows:

• For each term in the dataset, we consider its distance from the mean. In formulas, we compute
  `|x_i-\mu|` for every element
  `x_i`

• We take the average of all these terms:
  `(1)/(n)\sum|x_i-\mu|`

So, following the first point, the new dataset is

`\{4, 2, 5, 6, 7, 4, 2, 1, 0, 5, 5, 1, 5, 7, 3, 1\}`

And the average of this dataset is

`(4+2+5+6+7+4+2+1+0+5+5+1+5+7+3+1)/(16) = (58)/(16)=3.625`