# Dynamic analysis on outliers

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### Introduction

Outliers are the extreme values that a variable has, depending on the model or requirement, it could be necessary to treat them, either transforming or deleting.

### Variable “Income” distribution

This is going to be our main variable in this example, which represents customer's income in $. We can observe how there are a few cases with very high values, while on the other hand, there are lots of cases with low/mid values.

#### If we choose to delete them…

A common question is: “How many cases do we have to leave out?”, we can choose to leave out highest 1%, so we will obtain:

Now the distribution looks very similar to last one, except now it reaches $300.000 instead of $500.000.

If we do this process **iteratively** -deleting highest 1%, and then to that result, we delete again highest 1%, and so on, repeating this process 10 times- we're analyzing different cut-off values in order to leave out extreme values. We obtain a curious result, **silhouette remains always similar to**:

#### Animating the example

The following animation shows in action this iterative deleting process:

As we leave out the highest 1%, silhouette keeps a similar aspect to:

In other words, there are *always* lots of people with low/mid income, and just a few number of cases with high income -because of distribution nature-.

Axis values change within each iteration.

If we change the histogram plot, by a **density** one, the result is more similar to *zoom* on the data left side:

**When we delete the lowest or highest values of any variable, what we are doing is a “zoom” to the area where most cases are.**

#### Final thoughts

In this particular case, we could choose to leave out highest 0.5 or 1% of data. However it is not always recommended to delete all outliers, sometimes they represent valuable information such as fraud or a machine failure, or any other event which deserves further inspection.

#### Contact

*Made by Pablo C. from Data Science Heroes.*

R code and data available on github

Outliers issues and data treatment are topics of the **e-learning course: Data Science with R** (just email for a free demo:[email protected])

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