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 data that can create an error in your stats. For instance, if one measured the length of a child’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 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 been confused about the noise and outliers. But there is a significant difference between both. On the other hand, Noise is considered a random error, whereas outliers are the portion of the data.
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?
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A definition of outliers in statistics can be considered a section of data used to represent an extraordinary range from one 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:
| 5 | 94 | 95 | 96 | 99 | 104 | 105 | 199 |
In the given set of random values, 5 and 199 are outliers. “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, and $230.
Your average paycheck is considered $130. But the smaller paycheck is $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 as 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 as 60 is the outlier in the set of data.
Whiskers and box charts 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.
What Is An Outlier In Statistics?
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.
1. Univariate outliers
It usually represents a single variable. Or we can say that the outliers represent 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.
2. 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 outliers in some cases. But when it gets associated with other data, the possibility of occurring outliers increases. These are known as multivariate outliers.
Read, More:
How To Find An Outlier 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 | Q3 (75th percentile)= 80 |
| Q2 (50th percentile) = 55 | Q3 (75th percentile)= 80 |
| How to calculate the 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. |
How To Deal With The Outliers?
There are 4 different approaches to dealing with the outliers. And these are as follows:
1. 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.
2. Cap the outlier’s data
One of the other approaches to handling 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.
3. 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.
4. 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 with 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 conditions when you need to drop the idea of outliers. And these are:
- If the outliers are caused because of incorrectly measured or entered data, then drop the idea of the outliers.
- If the outliers do not affect the result and assumptions, then you must drop the idea of outliers.
- 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
Q1. How do you determine an outlier in statistics?
The data point is an outlier if it is over 1.5 times the IQR below the first quartile or 1.5 times the IQR above the third quartile. This is the general rule for using it.
On the other hand, if you want to calculate the IQR, then you need to know the percentile of the first and the third quartile.
Q2. What is outliers with example?
An outlier is a value that lies outside most of the other values in a set of data. For example, in this value 33,12,45,77,12,4,45,44, both the 4 and 77 are “outliers”.
