Answer:
[tex]m =13[/tex]
Step-by-step explanation:
Given
The attached dataset
Required
The mean absolute deviation
First, calculate the mean
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{42+40+39+76+71+55+68+65}{8}[/tex]
[tex]\bar x = \frac{456}{8}[/tex]
[tex]\bar x = 57[/tex]
The mean absolute deviation (m) is:
[tex]m =\frac{1}{n} \sum|x - \bar x|[/tex]
So, we have:
[tex]m =\frac{1}{8} (|42 - 57| + |40 - 57| + |39 - 57| + |76 - 57| + |71 - 57| + |55 - 57| + |68 - 57| + |65 - 57|)[/tex]
Using a calculator, we have:
[tex]m =\frac{1}{8} (|-15| + |-17| + |-18| + |19| + |14| + |-2| + |11| + |8|)[/tex]
Remove absolute bracket
[tex]m =\frac{1}{8} (15 + 17 + 18 + 19 + 14 + 2 + 11 + 8)[/tex]
[tex]m =\frac{1}{8} *104[/tex]
[tex]m =13[/tex]
The mean absolute deviation is 13
