?
Solved

Detect outliers in a series of numbers

Posted on 2011-03-04
6
Medium Priority
?
2,244 Views
Last Modified: 2012-05-11
Suppose I have a series of numbers like this

-0.0289436618082665
-0.0322635297824615
0.0473380547993016
-0.0483053616147235
0.0561386651052217
-0.0546202231192121
3912478746624.73
-0.0570958411471398
-0.0406567550991673
-0.0191101260081410
-0.0178598058749180
5912378756654.12
-0.00649518615382946
-0.0569007033673227
0.00634860933789683

So you most are within a certain range, say +/- 1.0, but there a couple numbers way out of this range.
Is there an algorithm to determine which numbers are these outliers?
I was thinking if I could detect these, then I could calculate the mean of the non-outliers and replace the outliers with that.
0
Comment
Question by:allelopath
6 Comments
 
LVL 18

Accepted Solution

by:
deighton earned 336 total points
ID: 35038303
yes you calculate the mean and standard deviation of the numbers.

then for each number you calculate the number of standard deviations from the mean

if the number is more than 4 standard deviations from the mean, it can be considred an outsider.

I see your out-lying values are extremely outside the range of the others.
0
 
LVL 37

Assisted Solution

by:TommySzalapski
TommySzalapski earned 668 total points
ID: 35038618
if the number is more than 4 standard deviations from the mean, it can be considred an outsider.

This threshold for what makes it an outlier is really application dependent. In fact, for the data you posted, one of the obvious outliers is less than 3 standard deviations from the mean. Many applications would throw out the top and bottom 5-10% of the data before doing any caclulations. If you do that, then your outliers will be over a billion standard deviations from the mean and would be outliers by almost any standard.
0
 
LVL 27

Assisted Solution

by:aburr
aburr earned 332 total points
ID: 35039179
All this outliers business is very fraught with danger.
Physics is full of stories about people ignoring outliers and missing Nobel prizes.
Nevertheless people find it useful to establish algorithms to spot outliers. There is no standard algorithm to which objections cannot be raised.
Several popular ones have been given above.
Obviously if you run your data through whatever algorithm you choose enough times you will end up with one data point. You should not discard any data point without a non-statistical cause. Nevertheless often the problem is not important enough to spend a lot of time on it so one of the algorithms mentioned above will be usually an improvement in the decision making process.
0
Never miss a deadline with monday.com

The revolutionary project management tool is here!   Plan visually with a single glance and make sure your projects get done.

 
LVL 33

Assisted Solution

by:phoffric
phoffric earned 664 total points
ID: 35041453
I just wanted to remind you that the mean and standard deviation includes the outliers and depending upon the quantity and magnitude of these outliers, these values could be adversely skewed. Depending on your model, the mean and standard deviation may be just what you need.

You may also want to consider determining the median instead. And if you can define from your model what an outlier is, then you might consider a % threshold error (or an absolute threshold error value - depends on your model), so that if the absolute value of the difference between the median and the data point exceeds the threshold, then that point will be considered an outlier.

As others have already alluded, you need to understand your model in order to define what an outlier is.
0
 
LVL 33

Assisted Solution

by:phoffric
phoffric earned 664 total points
ID: 35041472
Here are some EE discussions on outliers. Again, make sure that the question in the OP fits your model before applying any points made:

     http://rdsrc.us/GyvkW7

     http://rdsrc.us/U4sDl9

     http://rdsrc.us/VrQc4e
     
0
 
LVL 37

Assisted Solution

by:TommySzalapski
TommySzalapski earned 668 total points
ID: 35044851
Another common thing to do in outlier detection is to consider the mean and standard deviation (sd) of all points but the one in question. This tends to avoid the problem of one massive outlier messing up the statistics.
The best way to do that is to get the mean and sd for the whole set and 'remove' the one in question.
If you have N data points and want to remove x then you just do newmean = (mean*n-x)/(n-1) and that gives you the mean without considering x.
For the sd, remember that the mean of the x^2 minus the mean^2 gives the sd, so if you keep track of the mean of the squares, you can do the same thing for sd.
0

Featured Post

Free Tool: Site Down Detector

Helpful to verify reports of your own downtime, or to double check a downed website you are trying to access.

One of a set of tools we are providing to everyone as a way of saying thank you for being a part of the community.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

This article will show how Aten was able to supply easy management and control for Artear's video walls and wide range display configurations of their newsroom.
There's never been a better time to become a computer scientist. Employment growth in the field is expected to reach 22% overall by 2020, and if you want to get in on the action, it’s a good idea to think about at least minoring in computer science …
With the power of JIRA, there's an unlimited number of ways you can customize it, use it and benefit from it. With that in mind, there's bound to be things that I wasn't able to cover in this course. With this summary we'll look at some places to go…
Introduction to Processes

601 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question