# Is it untypical or atypical? ## How to identify outliers

When examining outlier data, it is not necessary to group the records. You may be interested in finding outliers in an entire table rather than just in specific groups.

The standard deviation is a measure of the dispersion of a data set; that is, how spread out the values are. The outlier calculation uses the population standard deviation.

If you calculate the standard deviation for a set of normally distributed values, 68% of the values fall within one standard deviation of the mean (±) and 99.7% of the values fall within three standard deviations of the mean (±). Only a very few values exceed three standard deviations from the mean.

In the outlier field, the number of standard deviations between the mean or median and the upper and lower outlier limits. You can specify a positive decimal or integer (0.5; 1; 1.5; 1.5; 2 . . . . )For example, specifying 2 sets the following for each key field group or for the field as a whole:All values in the outlier field that exceed an upper limit or are less than a lower limit are included in the output results as outliers.NoteFor the same data set, as you increase the number of standard deviations, you reduce the number of outliers in the output results.

## How to determine if a point is atypical or not?

An outlier is an oddly large or small observation. Outliers can have a disproportionate effect on statistical results, such as the mean, which can lead to misleading interpretations. For example, a data set includes the values: 1, 2, 3, and 34.

## What do you do with atypical data?

Substitute outliers and extremes with the nearest value that would not be considered extreme. For example, if an outlier is defined as anything above or below three standard deviations, all outliers would be replaced by the largest or smallest value in this range.

### Outliers

In statistics, an outlier is a data that is significantly different from the other data in the sample. Often, outliers in a data set can alert statisticians to experimental abnormalities or errors in the measurements taken, and because of this they may discard them from the data set. If outliers in the set are ignored, there may be important changes in the conclusions drawn from the study. Therefore, knowing how to calculate and evaluate outliers is important to ensure proper understanding of the statistical data.

### How to eliminate an outlier?

Outliers are sometimes a subjective matter, and there are numerous methods for classifying them. The method most widely used academically for its simplicity and results is the Tukey test, which takes as a reference the difference between the first quartile (Q1) and the third quartile (Q3), or interquartile range.

### What is an atypical observation?

Value that differs so widely from the rest of the data as to suspect that a serious error has been made.

### How to identify outliers in R?

In the case of R, it can be verified that the option boxplot. stats(x)\$out allows to identify the values considered as outliers and the values used to represent the boxplot.

### Outlier example

We all know the advantages of Tableau to visualize and make decisions very quickly with our data in a visual way, but what if I want to eliminate certain values that can be considered outliers? Let’s see how we can do it with a couple of calculations and in a totally dynamic way in Tableau.

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And we already have our box plot, which shows us the median, the values between quartile 1 and quartile 3 and the famous “whiskers” that indicate how far the data with values 1.5 times higher or lower than the interquartile range (IQR) reach.

All data beyond that vertical line would be mild outliers. Of course I could select those marks and exclude them from my visualization but what if you want it to be filtered dynamically?

And we could in the same way identify that value above which, if the discount is greater than that value, it would be an outlier. Recall that by definition these are those with a value 1.5 times higher than Q3 or Q1. If we wanted to identify only the cases that are outliers above, i.e., with an atypically high discount we would need to calculate the values greater than Q3 + 1.5 * IQR. That is:

### When is a value atypical?

In statistics, such as stratified samples, an outlier is an observation that is numerically distant from the rest of the data. Statistics derived from data sets that include outliers will often be misleading.

### To what extent are you influenced by outliers?

Outliers “outweigh more” than data close to the mean. Not considering an extreme data has greater consequences on the estimation of the mean than eliminating a data from the region with the highest density. A single value is enough to greatly influence the mean of the data set!

### How to identify outliers in R?

The boxplot() function detects outliers as any value that is beyond the whiskers. The whiskers are the lines that are determined as the third quartile + 1.5 times the interquartile range (Third quartile minus the first quartile) and the first quartile -1.5 times the interquartile range. It shows us three outliers.

### W

This example indicates that the robustness (what a word!) of the estimator is important when we have outliers and also when we do not want one data to have more influence than the others in the calculations.

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If we calculate the median (the central value of an ordered sample) for the second data set we have a value of 14 (the same as for the first data set). We see that this centrality statistic has not been disturbed by the presence of an extreme value, so it is more robust.

The trimmed mean (trimming) “discards” the extreme values. That is, it removes a fraction of the extreme data (e.g. 20%) from the analysis and calculates the mean of the new data set. The trimmed mean for our case would be 13.67.

The winsorized mean progressively replaces a percentage of the extreme values (e.g. 20%) with less extreme ones. In our case, the winsorized mean of the second sample would be the same 13.62.

Yuen’s robust test, which uses the trimmed means, is able to detect significant differences between the two groups, differences that the other tests were not able to detect! (Table 2). #### By Rachel Robison

Rachel Robison is a blogger who collects information on court filings and notices.