# How can we detect the existence of outliers using mean and median?

How can we detect the existence of outliers using mean and median?

Is it really possible to detect the existence of outliers in a set of data from their feature-wise mean and median?

Suppose, I have a data set with eight features in my hand.

I have juxtaposed their means and medians row by row.

            f1       f2        f3        f4        f5        f6        f7        f8
mean      2.5000    0.1868    0.0148    0.2105    0.2088   79.6583    1.0604    0.0091
median    2.5000    0.1826    0.0001    0.0002    0.0000   -0.0000    0.0000   -0.0000


Can we tell anything about the existence of outliers from these information?

Edit:

How are the data distributed?

Data set is considered to be normally distributed.

Do they all have the same mean and variance?

I don't know.

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.

• Data set is considered to be normally distributed.
– user9232
Nov 26 '16 at 9:40
• My answer still applies, obviously, since you don't have any idea of the mean and sd of those normal distributions. Or do they all have the same mean and variance? Can you edit your question with all relevant information so nobody else wastes their time working with partial information? Nov 26 '16 at 9:42