A lot of web references I read say that in a Left skewed graph, the mean and median are always on the left of the mode(less than the mode).Please refer What Is Skewness for one such reference.
But my question is,is this always true ? Isn't it possible that the frequency of the mode is so high that it pulls the mean and median to the right of the mode?
Please have a look at this graph I have drawn to support my question.
In the graph SkewedLeft5,
mean = 1*1 + 2*2 + 3*3 + 4*4 + 5*5 + 6*2 + 7*1 == 84/18 == 4.66 which goes as per the web references since it's less than the mode which is 5
Hoever In the graph SkewedLeft15,
mean = 1*1 + 2*2 + 3*3 + 4*4 + 5*15 + 6*2 + 7*1 == 134/18 == 7.44 which is my question since it's greater than the mode which is 5
If you say plot a graph SkewedLeft1000, then it will be further beyond the mode.
Because of the high frequency, the same happens to the mode as well.