Let us look at a list of observations 1 to n of variable Y:
Responses to Epsom salt synergist 
List item ( i = ) 
1 
2 
3 
4 
5 
6 
. . . 
n 
% Original bodyweight ( Y = ) 
9.4 
11.2 
13.5 
10.1 
14.7 
13.2 
. . . 
12.0 
This list is represented algebraically as:
Y_{(i=1)} + Y_{(i=2)} + Y_{(i=3)} + ... Y_{(i=n)}
The mean, written out completely, is:
_{i=n} 
Σ Y_{i} / n 
^{i=1} 
If we represent the deviation of each observation from its mean as y_{i}
Then y_{i} = Y_{i} 
Or more briefly as y = Y 
In which case :
the square of each deviation is y^{2}
their sum is Σy^{2}
which makes their mean Σy^{2} / n
Which is the variance.
Incidentally, the Mean Absolute Deviation (MAD), could be written like this :
MAD = 
Σ y 

n 
Where y is the 'absolute' value of y
(In other words all the negative deviations from the mean are rendered positive)