Answer:
[tex]M.A.D= 4.9[/tex]
Step-by-step explanation:
Given
12.7, 22, 23.5, 24, 11, 22
Required
Determine the M.A.D
Start by calculating the Mean
[tex]Mean = \frac{\sum x}{n}[/tex]
In this case, n = 6
So:
[tex]Mean = \frac{12.7 + 22 + 23.5 + 24 + 11 + 22}{6}[/tex]
[tex]Mean = \frac{115.2}{6}[/tex]
[tex]Mean = 19.2[/tex]
Subtract the mean from each element
[tex]12.7 - 19.2 = -6.5[/tex]
[tex]22 - 19.2 = 2.8[/tex]
[tex]23.5 - 19.2 = 4.3[/tex]
[tex]24 - 19.2 = 4.8[/tex]
[tex]11 - 19.2 = -8.2[/tex]
[tex]22 - 19.2 = 2.8[/tex]
Take absolute value of the results above
[tex]|-6.5| = 6.5[/tex]
[tex]|2.8| = 2.8[/tex]
[tex]|4.3| = 4.3[/tex]
[tex]|4.8| = 4.8[/tex]
[tex]|-8.2| = 8.2[/tex]
[tex]|2.8| = 2.8[/tex]
The mean of the above gives the MAD
[tex]M.A.D= \frac{\sum |x - u|}{n}[/tex]
[tex]M.A.D= \frac{6.5 + 2.8 + 4.3 + 4.8 + 8.2 + 2.8}{6}[/tex]
[tex]M.A.D= \frac{29.4}{6}[/tex]
[tex]M.A.D= 4.9[/tex]
