How can we detect the existence of outliers using mean and median?
No. Unless you have some other idea of the scale and spread and distribution of the feature values. You can construct data sets that have any given mean and median with no outliers or with one massive outlier.

For example, f2 looks like a well-balanced set of numbers with a very close mean and median, maybe all those values are from a N(0.184,3) distribution. Scale that up by a linear transformation to an N(X,Y) and you'll get a mean and median much like f6. Exercise: find X and Y.