Answer:
We have been given the data: 47,45,44,41,48
[tex]Mean=\frac{\text{sum of observations}}{\text{number of observations}}[/tex]
On substituting the values in the above formula to find mean:
[tex]Mean=\frac{47+45+44+41+48}{5}[/tex]
[tex]Mean=\frac{225}{5}=45[/tex]
Now, we need to find the absolute deviation that is:
[tex]\text{absolute deviation}=\sum{|x-\bar{x}|}[/tex]
Where [tex]\bar{x}[/tex] is the mean and x is the values given of x which are: 2,0,1,4
[tex]\text{absolute deviation}=|2-45|+|0-45|+|1-45|+|4-45|=43+45+44+41[/tex]
[tex]\Rightarrow \text{absolute deviation}=173[/tex]
Now, to find mean absolute deviation we have a formula:
[tex]\text{mean absolute deviation}=\sum\frac{(x-\bar{x})}{N}[/tex]
[tex]\text{mean absolute deviation}=\frac{|47-45|+|45-45|+|44-45|+|41-45|+|48-45|}{5}[/tex]
[tex]\text{mean absolute deviation}=\frac{2+0+1+4+3}{5}[/tex]
[tex]\text{mean absolute deviation}=2[/tex]
