Why do we need coefficient of mean deviation? Mean deviation can give us a sense of how much data is dispersed from one of the average measurements (mean,mode,median). Mean deviation depends on the difference between the data and the average measurement.$MD=1/n∑(x - y)$ where x is the different data values and y is the mean/mode/median.I don't think it really depends on the average. Rather it is completely controlled by the data differences from the average value. What I thought at first is maybe we need the $Coefficient$ $of$ $mean$ $deviation$ to compare two or more data lists. But when we measure the mean deviation we  measure how much the data is dispersed. More difference means greater mean deviation. I don't think there is any effect on this of what the average value is. So we don't really need to come up with a ratio of mean deviation and the average value to see what's actually going on. Finding the mean deviation should be the end of story. So what's the use of coefficient of MD?
 A: (I think you're missing an absolute value in your definition.)
It adjusts for differences in scale, for one thing.  Compute the mean deviation for some data (say, lengths measured in cm); divide all measurements by 100 (say, to convert to m); now compute the new mean deviation.  It's 100 times smaller.  But you only changed the units of measurement.  Is mean deviation really the "end of the story"?
Similarly, say you're interested in whether there is more variation in the sizes of horseflies than in the size of horses.  You measure the masses of 100 horseflies, and of 100 horses.  I'd expect that since the horses are bigger, the mean deviation will also be bigger, perhaps on the order of 100 kg, while the mean deviation for horseflies might be on the order of 1 g, even though some horseflies are twice as large as others.  Again, then, is mean deviation the "end of the story"?
See Le Wik: https://en.wikipedia.org/wiki/Coefficient_of_variation, specifically "advantages" under "comparison to standard deviation".
