Calculating the mean for a set of numbers while neglecting outliers

Question

First of all this is more of a math question than it is a coding one, so please be patient. I am trying to figure out an algorithm to calculate the mean for a set of numbers. However I need to neglect any numbers that are not close to the majority of the results. Here is an example of what I am trying to do:

Lets say I have a set of numbers that are similar to the following:

{ 90, 91, 92, 95, 2, 3, 99, 92, 92, 91, 300, 91, 92, 99, 400 }

it is clear for the set above that the majority of numbers lies between 90 and 99, however I have some outliers like { 300, 400, 2, 3 }. I need to calculate the mean of those numbers while neglecting the outliers. I do remember reading about something like that in a statistics class but I cant remember what was it or how to approach the solution.

Will appreciate any help..

Thanks

Answer 1

What you could do is:

1. estimate the percentage of outliers in your data: about 25% (4/15) of the provided dataset,
2. compute the adequate quantiles: 8-quantiles for your dataset, so as to exclude the outliers,
3. estimate the mean between the first and the last quantile.

PS: Outliers constituting 25% of your dataset is a lot!

PPS: For the second step, we assumed outliers are "symmetrically distributed". See the graph below, where we use 4-quantiles and 1.5 times the interquartile range (IQR) from Q1 and Q3: