outliers in statistics

Most Prominent Methods of How to Find Outliers in Statistics

Outliers in statistics are considered as the data values which differ considerably from the bulk of a given data set. These data values lie outside the overall trend, which already lies in the data. Outliers are extremely low or extremely high stragglers in a given set of the data that can create an error in your stats. For instance, if one measured the length of children’s nose, their common value might lie if Pinocchio implied in the given class of data values.

There is a necessity to examine the set of given data to study the outliers in statistics, and how to find outliers in statistics that might cause some challenges. Although this might be easy to recognize with the help of a stemplot in which a few values vary from the given data values. So, how much variation does the value has as an outlier? We will study at a particular analysis that provides an external standard about what develops an outlier in the data.

Outliers in statistics have a significant difference as compared to the other data. There are several individuals who have confusion with the noise and outliers. But there is a significant difference between both. Noise is considered a random error, whereas outliers are the portion of the data. 

Several parametric statistics, just as correction, mean, and other statistics parameters, depend on the outliers’ value. But it has been seen that the outliers might cause a problem with the analysis like ANOVA and linear regression. Therefore, it is necessary that we must be consider them correctly and effectively.

Below I have mentioned all the necessary details regarding the outliers in statistics. Moreover, I have given some examples also for your better understanding. Scroll down the page to know all these details.

What are outliers in statistics?

A definition of outliers in statistics can be considered a section of data used to represent an extraordinary range from a point to another point. Or we can say that it is the data that remains outside of the other given values with a set of data. If one had Pinocchio within a class of teenagers, his nose’s length would be considered an outlier than the other children.

Examples of outliers in statistics:

In the given set of random values, 5 and 199 are outliers:

5, 94, 95, 96, 99, 104, 105, 199

“5” is studied as an extremely low value, whereas “199” is recognized as an extremely high value. But, outliers are not always taken as these simple values. Let’s assume one accepted the given paychecks in the last month:

$220, $245, $20, $230.

Your average paycheck is considered as $130. But the smaller paycheck ($20) can be because that person went on holiday; that is why an average weekly paycheck is $130, which is not an actual representation of their earned. Their average is more like $232 if one accepts the outlier ($20) from the given set of data. That is why seeking outliers might not be that simple as it seems. The given data set might resemble as:

60, 9, 31, 18, 21, 28, 35, 13, 48, 2.

One might guess that 2 is an outlier and possibly 60. But one predicts it as 60 is the outlier in the set of data.

Whiskers and box chart often represent outliers:

However, one might not have a passage to the whiskers and box chart. And if one does, the few box plots might not explain outliers. For instance, the chart has whiskers that stand out to incorporate outliers as:

That is why you do not believe in obtaining outliers in statistics from the whiskers and a box chart. It said that whiskers and box charts could be a valuable device to present after one will determine what their outliers are—the efficient method to obtain all outliers with the help of the interquartile range (IQR). These IQR includes the average amount of the data; therefore, outliers could quickly be determined once one understands the IQR.

Key point

Why are the outliers not affected by IQR?

The IQR (Interquartile Range) is not affected by the outliers. One of the most significant reasons is that people mostly prefer to use the IQR while measuring the “spread” of the given data. As the IQR considers the range of the middle that is 50% of the given data value, it does not affect the value of outliers.

How to classify the outliers?

The outliers can be classified into two different categories, that is univariate and multivariate. Let’s check both of these with the relevant example.

Univariate outliers

It usually represents a single variable. Or we can say that the outliers represent within a single column. Let’s check an example of it.

In the above salary column, the value 5000 is the outlier. This outlier is represented in the single (that is, salary) column. Therefore, it is the univariate outlier.

Multivariate Outliers

It is the outlier, which occurs in the joint combinations of two or more variables. Let’s take an example of it:

The above shows a scatter plot between the age and salary variables. Here, the bivariate outliers are represented. You might notice that the single variable data does not have the outliers in some cases. But when it gets associated with another data, the possibility of occurring the outliers increases. These are known as multivariate outliers.

How to find outliers in statistics using the Interquartile Range (IQR)?

An outlier is described as a data point that ranges above 1.5 IQRs under the first quartile (Q1). Moreover, it lies over the third quartile (Q3) within a set of data.

Low = (Q1) – 1.5 IQR

High = (Q3) + 1.5 IQR

Sample Problem: Find all of the outliers in statistics of the given data set: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

Step 1: Get the Interquartile Range, Q1(25th percentile) and Q3(75th percentile).

IQR = 50

Q1 (25th percentile) = 30

Q2 (50th percentile) = 55

Q3 (75th percentile)= 80

How to calculate IQR of the above data set value

Put all the data values in order and mark a line between the values to find Q1(25th percentile) and Q3(75th percentile). [Q1:(10,20,30,40,50) | Q2: (60,70,80,90,100)]Find the median of Q1 and Q2, which is 30 and 80.Subtract Q1 from Q2. [80-30 = 50]IQR = 50.

Also Read

A key point to remember

Why is the median of the data not affected by the outliers?

Most of you do not know that the median and the mode of the data do not affect the outliers. Doesn’t it make sense? Actually, it does!! You all might know that the median relies on the order of the data. On the other hand, the outliers decrease the average value by which the measurement can easily represent. That is why we can conclude that the median is not affected by the outliers.

Step 2: Multiply the calculated IQR with 1.5 that has been obtained in Step 1:

IQR * 1.5 = 50* 1.5 = 75.

Step 3: Add the number of Step 2 to Q3 [calculated in Step 1]:

75+ 80= 155.

It is considered as an upper limit. Keep this number away for a specific moment.

Step 4: Subtract the number which one has found in Step 2 from Q1 from Step 1:

30 – 50= -20.

It is the lower limit. Put the number aside for a moment.

Step 5: Keep the values from the data set in order:

10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

Step 6: Include these low and high values to the given data set in order:

-20, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 155.

Step 7: Highlight a value above or below the values that one has put in Step 6:

-20, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 155.

Here is the method for how to find outliers in statistics, and for this example, it will be 100.

How to find the outliers in statistics using the Tukey method?

The Tukey method to discover the outliers in statistics applies the Interquartile Range to separate very small or very large numbers. It is the equivalent of the above method, but one might examine the formulas (like standard deviation, mean, and more). These are composed slightly differently, and the specification is slightly different. For instance, the Tukey method utilizes the idea of “fences.”

The specifications are:

High outliers = Q3 + 1.5(Q3 – Q1) = Q3 + 1.5(IQR)

Low outliers = Q1 – 1.5(Q3 – Q1) = Q1 – 1.5(IQR)

Where:

Q1 = first quartile

Q2 = middle quartile

Q3 = third quartile

IQR = Interquartile range

The above equations provide two values. One can study a fence that can highlight the outliers from the values included in the amount of the data. Now, let’s check how to find potential outliers in statistics.

Sample Problem: Use Tukey’s method to get the value of outliers of the following data: 3,4,6,8,9,11,14,17,20,21,42.

Step 1: Calculate the Interquartile range [follow the same procedure shown in the table as mentioned above], which give the value as

Q1 = 6

Q3 = 20

IQR = 14

Step 2: Measure the value of 1.5 * IQR:

1.5 * IQR = 1.5 * 14= 21

Step 3: Subtract the value of Q1 to obtain the lower fence:

6 – 21 = -15

Step 4: Sum the value to Q3 to obtain the upper fence:

20+ 21 = 41.

Step 5: Add these fences to the given data to get the value of outliers:

-15, 3, 4, 6, 8, 9, 11, 14, 17, 20, 21, 41, 42.

Anything which is outside the fences is considered to be the outliers. For the given data set, 42 is considered as the only outlier.

How to deal with the outliers?

There are 4 different approaches to deal with the outliers. And these are:

Drop the outlier records

In some cases, it is always better to remove or eliminate the records from the dataset. It helps to keep the events or person from skewing the statistical analysis.

Cap the outliers data

One of the other approaches to handle the outlier is to cap it. For instance, in the salary variable, you notice that the salary above the particular value behaves the same as that of the lower salary. In such cases, you cap the salary value to keep it the same throughout the analysis. 

Provide the new value

If you find an outlier that is chosen by mistake, you can assign the new value to it. A common method for this includes a regression model that can predict the missing value.

Try to modify the value

Sometimes, it is better to transform the data instead of using the data itself. For instance, try to change the value to the percentage. This makes your data more reliable, as well as you can deal with it more easily.

Now here a question arises: Where did the outliers in statistics come from?
It is quite important to note that it might take domain expertise and in-depth analysis. Moreover, it is difficult to say where the outliers in statistics come from or arise from. But you always try to consider various opportunities as it always helps to proceed in a better way.
Therefore, we can say that it is always beneficial to understand your data and then proceed to the research. Try different approaches to see the theoretical sense and to get suitable answers to your outliers’ problems.

When to drop the outliers in statistics?

There are some of the conditions when you need to drop the idea of outliers. And these are:

  1. If the outliers are caused because of incorrectly measured or entered data, then drop the idea of the outliers.
  2. If the outliers do not affect the result and assumptions, then you must drop the idea of outliers.
  3. When the outliers affect the assumptions and result, then run the analysis of the data without or with the outliers’ value.

Conclusion

Several students face difficulty regarding how to find outliers in statistics; that is why we have mentioned two different methods to calculate them. Besides this, there are other advanced methods too to get the value of outliers. Such as Dixon’s Q Test, Generalized ESD, and much more. Use the above-mentioned IQR and Tukey method to solve the problems of outlier values.

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Frequently Asked Questions

Why are outliers bad?

Outliers are often considered not a problem. Instead, they are taken as a help portion of statistics data. An outlier plays a significant role in changing the results, such as dragging the average value in a particular direction and can help draw useful conclusions.

How do outliers affect data?

Outlier is an extreme value of higher or lower data compared to another number. Outliers are responsible for the average value of the data. It is also important to note that they have little effect on that particular dataset’s mode and median value.

Which statistics are not affected by outliers?

It has been seen that median and mode are two statistics that do not affect the value of outliers.