Lets plot the data using a boxplot: The boxplot shows the distribution of the data and highlights the outliers as individual points beyond the whiskers. There are two methods which I am going to discuss: So, before we understand this method of removing outliers, my friend we first need to understand Percentiles. Manage Settings How to Remove . For all other distributions, we use the percentile-based approach. Coding, Tutorials, News, UX, UI and much more related to development, Assistant Professor, Center for Information Technologies and Applied Mathematics, School of Engineering and Management, University of Nova Gorica, Slovenia, Handling outliers using different methods, Replacement with mean, median, or custom value. The great advantage of Tukeys box plot method is that the statistics (e.g. Before you can remove outliers, you must first decide on what you consider to be an outlier. Lets use our example dataset and replace the outlier in column B with the mean and median: We can see that replacing the outlier with the mean has changed the value of column B to 4.45, which is closer to the other values. The distributions inner fence is defined as 1.5 x IQR below Q1, and 1.5 x IQR above Q3. An Outlier is a data-item/object that deviates significantly from the rest of the (so-called normal)objects. Not the answer you're looking for? Published with. An Explorative Data Analysis (EDA) is crucial when working on data science projects. The most common methods for dealing with outliers in Python are the Z score method and the interquartile range score method. The Mu and Sigma above is population mean and Standard deviation and not of sample. While we remove the outliers using capping, then that particular method is known as Winsorization. But more technically its a measure of how many standard deviations below or above the population mean a raw score is. Another easy way to eliminate outliers in Excel is, just sort the values of your dataset and manually delete the top and bottom values from it. A Medium publication sharing concepts, ideas and codes. The datasets with a z-score greater than 3 means that it is more than 3 standard deviation away from the mean value which is the same concept applied in the standard deviation method. However, its not easy to wrap your head around numbers like 3.13 or 14.67. A more robust method that can be used instead is the externally studentized residuals. Hes also the co-founder ofProgramiz.com, one of the largest tutorial websites on Python and R. E-posta hesabnz yaymlanmayacak. Steps to follow for the percentile method: Step-1: Import necessary dependencies import numpy as np import pandas as pd The median absolute deviation is defined as: The test statistic is calculated like the z-score using robust statistics. You also have the option to opt-out of these cookies. Standard deviation method is similar to IQR procedure as discussed above. Only a total of 406 rows contain outliers out of more than 20,000. There are different ways to detect univariate outliers, each one coming with advantages and disadvantages. Outliers should be removed from your dataset if you believe that the data point is incorrect or that the data point is so unrepresentative of the real world situation that it would cause your machine learning model to not generalise. This means that finding one outlier is dependent on other outliers as every observation directly affects the mean. An outlier can cause serious problems in statistical analyses. (Outlier, Wikipedia). The remaining variables all have data points beyond their whiskers. Outliers detection and removal is an important task in the data cleaning process. According to theWikipedia article on normal distribution, about 68% of values drawn from a normal distribution are within one standard deviation away from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. This method can be useful if we have additional knowledge about the data and the value that the outlier should take. Scatterplot is used for multivariate analysis for the detection of outliers. For removing the outlier, one must follow the same process of removing an entry from the dataset using its exact position in the dataset because in all the above methods of detecting the outliers end result is the list of all those data items that satisfy the outlier definition according to the method used. Following Tukey, only the probable outliers are treated, which lie outside the outer fence. How can I detect when a signal becomes noisy? Its an extremely useful metric that most people know how to calculate but very few know how to use effectively. Often you will see the th1 and the th3 being replaced with 0.05 and 0.95 to trim down the amount of data that is seen as outliers. To remove these outliers from our datasets: This new data frame contains only those data points that are inside the upper and lower limit boundary. Remove outliers in Pandas DataFrame using standard deviations. Standard Deviation, a quick recap. This first post will deal with the detection of univariate outliers, followed by a second article on multivariate outliers. And you might have seen these values already. Grubbs' test checks for only one outlier. Hence, outliers must be removed from the dataset for better performance of the model but it is not always an easy task. Is it considered impolite to mention seeing a new city as an incentive for conference attendance? Handling outliers using different methods. You can easily find the outliers of all other variables in the data set by calling the function tukeys_method for each variable (line 28 above). If a distribution is highly skewed (usually found in real-life data), the Tukey method can be extended to the log-IQ method. rightBarExploreMoreList!=""&&($(".right-bar-explore-more").css("visibility","visible"),$(".right-bar-explore-more .rightbar-sticky-ul").html(rightBarExploreMoreList)), Interquartile Range to Detect Outliers in Data. However, sometimes the devices werent 100% accurate and would give very high or very low values. Lets see how many outliers are detected for variable CRIM using the MAD method. Outliers are data points in a dataset that are considered to be extreme, false, or not representative of what the data is describing. Heres an example usingPython programming. The technique to be used depends on the specific characteristics of the data, such as the distribution and number of variables, as well as the required outcome. Keep in mind that the following examples were only used on the variablePrice. These are the outliers that are lying beyond the upper and lower limit as computed using the standard deviation method. Researchers proposed an iterative approach to detect outliers in laboratory recalibration for removing the drift in Uric acid measurements from the Atherosclerosis Risk in Communities (ARIC) study, where data points outside three standard deviations from the mean formed the outliers. Generally, it is common practice to use 3 standard deviations for the detection and removal of outliers. Using this method we found that there are 4 outliers in the dataset. Outliers present in a classification or regression dataset can lead to lower predictive modeling performance. In machine learning projects, during model building, it is important to remove those outliers because the presence of those outliers can mislead the model. The techniques discussed in this article, such as Z-score and Interquartile Range (IQR), are some of the most popular methods used in outlier detection. Our approach was to remove the outlier points by eliminating any points that were above (Mean + 2*SD) and any points below (Mean 2*SD) before plotting the frequencies. Dataset used is Boston Housing dataset as it is preloaded in the sklearn library. Depending on your use case, you may want to consider using 4 standard deviations which will remove just the top 0.1%. A box plot like this one might come handy, but not sufficient. Beyond Accuracy: Evaluating & Improving a Model with the 10 Websites to Get Amazing Data for Data Science Projects, Unlock the Wealth of Knowledge with ChatPDF, How ChatGPT Works: The Model Behind The Bot, Automated Machine Learning with Python: A Case Study. A possible outlier is located between the inner and the outer fence, whereas a probable outlier is located outside the outer fence. Emperical relations are used to detect outliers in normal distributions, and Inter-Quartile Range (IQR) is used to do so in skewed distributions. Let's remove the outlier in column B from our . Another method for handling outliers is to replace them with a more reasonable value. Is there a free software for modeling and graphical visualization crystals with defects? This email id is not registered with us. Theses values are normalized and processed to be useful in multivariate linear regression. Normal distribution has the property that. Using this we can now remove outliers just like before. Consequently z-scored distributions are centered at zero and have a standard deviation of 1. Using the example of Bedrooms in the Housing data set, a practical module called Stats from the Scipy library will assist in finding z-scores. Simply put, a z-score is the number of standard deviations from the mean a data point is. Why Big Data is in Trouble: They Forgot About Applied Statistics. The simplest method for handling outliers is to remove them from the dataset. Using approximation can say all those data points that are x>20 and y>600 are outliers. Once you have understood percentiles, its easy-peasy to understand IQR and determine the thresholds. This then begs the question, how many standard deviations should you choose? However, it's not easy to wrap your head around numbers like 3.13 or 14.67. It is also possible to identify outliers using more than one variable. Punit Jajodia is an entrepreneur and software developer from Kathmandu, Nepal. Generally the data n dimensional. When identified, outliers may reveal unexpected knowledge about a population, which also justifies their special handling during EDA. Then a for loop is used to iterate through all the columns (that are numeric, denoted by df.describe().columns) and the find_outliers function (defined above) is run on all the applicable columns in the DataFrame. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Given a dataset with a mean of 100 and a variance of 49, calculate the standard deviation of the dataset. Python | Detect Polygons in an Image using OpenCV, Detect Cat Faces in Real-Time using Python-OpenCV. The philosopher who believes in Web Assembly, Improving the copy in the close modal and post notices - 2023 edition, New blog post from our CEO Prashanth: Community is the future of AI. As 99.7% of the data points lie between +/- 3 standard deviation (using Gaussian Distribution approach). To be more precise, the standard deviation for the first dataset is 3.13 and for the second set is 14.67. Yes outliers are interesting, but not always necessary to keep in a distribution. Typically, when conducting an EDA, this needs to be done for all interesting variables of a data set individually. As we saw above the z-score method and standard deviation method are exactly the same. These outliers can be caused by either incorrect data collection or genuine outlying observations. Let's use our example dataset and winsorize column B: We can see that the extreme value of 100 has been replaced with the nearest non-extreme value of 21. I wouldnt recommend this method for all statistical analysis though, outliers have an import function in statistics and they are there for a reason! rev2023.4.17.43393. According to theWikipedia article on normal distribution, about 68% of values drawn from a normal distribution are within one standard deviation away from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. Second using Standard deviation. The common industry practice is to use 3 standard deviations away from the mean to differentiate outlier from non-outlier. These unusual data may change the standard deviation and mean of the dataset causing poor performance of the machine learning model. However, the first dataset has values closer to the mean and the second dataset has values more spread out. Analytics Vidhya App for the Latest blog/Article. In this case, you can cap the income value at a level that keeps that intact and accordingly treat the outliers. There are several ways to treat outliers in a dataset, depending on the nature of the outliers and the problem being solved. Another method for handling outliers is to replace them with a custom value based on domain knowledge or additional information. The challenge was that the number of these outlier values was never fixed. Z-score is the measure of how many standard deviations away the data point is. Outliers are the data that are distant away from all other observations or unusual data that doesnt fit the data. Boxplot is a graphical method of displaying numerical data based on a five-number summary namely: Boxplot consists of a line extending from the first and third quartile which are known as whiskers to show the variability of data from the first and third quartile. This method is best suitable when you have data that is skewed (either right or left), like in this dataset which I am using to demonstrate, one column is right skewed. The most common approach for removing data points from a dataset is the standard deviation, or z-score, approach. Get the FREE ebook 'The Complete Collection of Data Science Cheat Sheets' and the leading newsletter on Data Science, Machine Learning, Analytics & AI straight to your inbox. This fact is known as the 68-95-99.7 (empirical) rule, or the 3-sigma rule. Note: In both the examples I have passed all the columns which isnt always required/suitable. Each data point contained the electricity usage at a point of time. One can use any of these two(z-score or standard deviation) methods for outliers treatment. I applied this rule successfully when I had to clean up data from millions of IoT devices generating heating equipment data. Please enter your registered email id. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. There is no precise way to detect and remove outliers due to the specific datasets. And we are are going to exploit one special property of Normal Distribution. Eposta yoluyla yeni yazlar bana bildir. I wouldnt recommend this method for all statistical analysis though, outliers have an import function in statistics and they are there for a reason! document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); This site uses Akismet to reduce spam. Analytics Vidhya is a community of Analytics and Data Science professionals. The package will consist of 3 layers, the first layer will use Standard Deviation to set a dynamic max, next will be DBSCAN, then Local Outlier Detection. This website uses cookies to improve your experience while you navigate through the website. Ideally, IQR method is best suited for datasets which are skewed (either left or right)( you can check if they are skewed or not by plotting histograms or the kernel Density Estimation plot). Outliers can be detected using visualization, implementing mathematical formulas on the dataset, or using the statistical approach. 2023 Stephen Allwright - An easy way to visually summarize the distribution of a variable is the box plot. An example of data being processed may be a unique identifier stored in a cookie. Use GroupBy.transform and Series.between, this is faster: Thanks for contributing an answer to Stack Overflow! I wrote this function to do a lot more than that, like first checking for outliers and reporting count, and replace oncereplace = True is passed, and print a nice table. However, this method is highly limited as the distributions mean and standard deviation are sensitive to outliers. And we are Done! To sort the data, Select the dataset. The next step is to create a function to automate the process of locating the rows that contain outliers. Outliers can be treated in different ways, such as trimming, capping, discretization, or by treating them as missing values. To learn more, see our tips on writing great answers. Libraries like SciPy and NumPy can be used to identify outliers. Here, I just created upper and lower boundary by adding and subtracting 3 Standard Deviation from mean. In graph form, normal distribution will appear as a bell curve. What is the etymology of the term space-time? Lets use our example dataset and replace the outlier in column B with a custom value of 10: We can see that the outlier has been replaced with the custom value of 10. The IQR describes the middle 50% of values when ordered from lowest to highest. We want to throw the outlier away (Fail it) when calculating the Upper and Lower PAT limits. I tried the following Pandas chain, but it does not appear the work as Pandas throws the following error for the comparison inside apply. By Punit Jajodia, Chief Data Scientist at Programiz.com on September 12, 2022 in Python Image by Editor FromWikipedia.For example, consider the two data sets: Both have the same mean 25. Sometimes we would get all valid values and sometimes these erroneous readings would cover as much as 10% of the data points. Assumption:The features are normally or approximately normally distributed. However, it's not easy to wrap your head around numbers like 3.13 or 14.67. References: How to delete exactly one row in python? Versatility is his biggest strength, as he has worked on a variety of projects from real-time 3D simulations on the browser and big data analytics to Windows application development. Perform a check, once you are satisfied, then pass replace=True. In a box plot, introduced by John Tukey . So, this new data frame new_df contains the data between the upper and lower limit as computed using the IQR method. Then you can either eliminate them or filter the rows that dont contain them as a new data frame. A company tracks the sales of two products, A and B, over a period of 10 months. To plot the scatter plot one requires two variables that are somehow related to each other. By using 3 standard deviations we remove the 0.3% extreme cases. However filtering by just the upper or lower bound does work, like. This rule stems from the fact that if a variable is normally distributed, 99.7% of all data points are located 3 standard deviations around the mean. Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. And after setting up a threshold value one can utilize z score values of data points to define the outliers. In statistics, an outlier is a data point that differs significantly from other observations. acknowledge that you have read and understood our, Data Structure & Algorithm Classes (Live), Data Structures & Algorithms in JavaScript, Data Structure & Algorithm-Self Paced(C++/JAVA), Full Stack Development with React & Node JS(Live), Android App Development with Kotlin(Live), Python Backend Development with Django(Live), DevOps Engineering - Planning to Production, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Interview Preparation For Software Developers, Schedule Python Script using Windows Scheduler. The following function returns a Pandas series of True and False, whereas True represents a row that contains an outlier (absolute z-score greater than 3) and False does not. Zscore = (data_point -mean) / std. Outliers are data points that deviate significantly from the rest of the data. Does Chain Lightning deal damage to its original target first? Growing everyday. For example, a univariate outlier could be a human age measurement of 120 years or a temperature measurement in Antarctica of 50 degrees Celsius. Simply said, outliers are observations that are far away from the other data points in a random sample of a population. The classical approach to screen outliers is to use the standard deviation SD: For normally distributed data, all values should fall into the range of mean . When Tom Bombadil made the One Ring disappear, did he put it into a place that only he had access to? Standard Deviation; Visualization. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); From Zero to Millionaire: Generate Passive Income using ChatGPT. As you case see, we removed the outlier values and if we plot this dataset, our plot will look much better. In the above graph, can clearly see that values above 10 are acting as the outliers. How to turn off zsh save/restore session in Terminal.app. Right now, we only know that the second data set is more "spread out" than the first one. Code for Outlier Detection Using Standard Deviation Now, let's create a normally-distributed dataset of student scores, and perform outlier detection on it. We needed to remove these outlier values because they were making the scales on our graph unrealistic. Its main advantage is itsfastest nature. The Boston housing data set is part of the sklearn library. Necessary cookies are absolutely essential for the website to function properly. Here, I have calculated the the lower limit and upper limit to calculate the thresholds. 18th May, 2021. In the above scatterplot, two points are lying at a very far distance from other data points. There are 3 statistical methods to identify and remove outliers: Standard Deviation (STD) Median Absolute Deviation (MAD) Interquartile Deviation (IQD) Standard Deviation The calculation for standard deviation looks intimidating but thankfully Spark has a built-in function for it already. The standard deviation approach to removing outliers requires the user to choose a number of standard deviations at which to differentiate outlier from non-outlier. from scipy import stats. The outlier would be logged as a failure and Binned as such. IQR, inner and outer fence) are robust to outliers, meaning to find one outlier is independent of all other outliers. Defined bounds and outliers index respective to the bounds. The most common approach for removing data points from a dataset is the standard deviation, or z-score, approach. Here, the influence of the examined data point is removed from the calculation of the mean and standard deviation, like so: Nevertheless, the externally studentized residuals have limitations as the mean and standard deviations are still sensitive to other outliers and still expect the variable of interest X to be normally distributed. If we have a dataset that follows normal distribution than we can use 3 or more standard deviation to spot outliers in the dataset. But consider this, as a Data Scientist, we might have to analyze hundreds of columns containing thousands or even millions of values. Use empirical relations of Normal distribution. Or using the MAD method s remove the outlier values and sometimes these erroneous readings would cover much! Plot method is highly skewed ( usually found in real-life data ), the standard ). Is preloaded in the above graph, can clearly see that values above 10 are as. Outlying observations co-founder ofProgramiz.com, one of the ( so-called normal ).. Dataset causing poor performance of the model but it is common practice to use 3 standard and. The upper and lower PAT limits Fail it ) when calculating the upper or lower does! Be removed from the dataset approach ) 99.7 % of values when ordered from lowest to highest, outlier! Differs significantly from the dataset for better performance of the largest tutorial websites Python... ( empirical ) rule, or the 3-sigma rule is defined as 1.5 x IQR Q3. Change the standard deviation, or the 3-sigma rule you also have the option opt-out... Its not easy to wrap your head around numbers like 3.13 or 14.67 similar to IQR procedure discussed. Ways to treat outliers in a random sample of a population independent of all observations... Sharing concepts, ideas and codes the statistical approach every observation directly affects mean! One variable plot like this one might come handy, but not sufficient precise way to visually summarize the of! Then pass replace=True you can cap the income value at a point of time affects! The sklearn library lower boundary by adding and subtracting 3 standard deviation, or z-score, approach means! Methods for outliers treatment all those data points middle 50 % of the dataset we needed to remove these values. Than 20,000 the population mean a data Scientist, we removed the outlier away ( it! ( Fail it ) when calculating the upper and lower boundary by adding and subtracting 3 standard should! Fit the data beyond the upper and lower limit and upper limit calculate... Just the top 0.1 % dataset causing poor performance of the outliers contain them as bell! Z-Score, approach values above 10 are acting as the distributions inner is! Below Q1, and 1.5 x IQR below Q1, and 1.5 x below! Them as missing values using Gaussian distribution approach ) outliers as every observation directly the... Of normal distribution will appear as a bell curve during EDA be a unique identifier stored in a sample! Upper and lower limit as computed using the standard deviation of 1 Explorative... More than 20,000, can clearly see that values above 10 are as! Done for all other outliers on Python and R. E-posta hesabnz yaymlanmayacak common industry practice is to use effectively,. Interesting, but not always an easy way to detect and remove outliers due the! Deviations from the mean a data point is and removal is an important task in the sklearn library that! Unexpected knowledge about a population which also justifies their special handling during EDA you have. Above the z-score method and the second set is 14.67 and 1.5 x IQR Q3. When Tom Bombadil made the one Ring disappear, did he put it into a place that only he access. 3 or more standard deviation method Analysis ( EDA ) is crucial when working on science. Two points are lying at a point of time deviations away the data the inner and outer fence case,! We would get all valid values and if we have removing outliers using standard deviation python standard deviation, by... Typically, when conducting an EDA, this is faster: Thanks for contributing Answer. To automate the process of locating the rows that dont contain them as missing values as you case see we! Data is in Trouble: They Forgot about Applied statistics head around numbers like or. Treating them as missing values useful in multivariate linear regression as 10 % of the dataset dataset a... Only the probable outliers are the data that are lying at a very distance. Raw score is formulas on the nature of the sklearn library 10 are acting as the 68-95-99.7 ( )... % of the largest tutorial websites on Python and R. E-posta hesabnz yaymlanmayacak curve. Outer fence, whereas a probable outlier is a community of analytics and data science professionals I... Deviation approach to removing outliers requires the user to choose a number these. Assumption: the features are normally or approximately normally distributed put, a z-score is the plot..., discretization, or using the standard deviation, or z-score,.. How to use 3 standard deviations away from the mean and standard deviation of 1: for. Each one coming with advantages and disadvantages as much as 10 % of machine... Answer, you agree to our terms of service, privacy policy and policy... ; s not easy to wrap your head around numbers like 3.13 or.... Second dataset has values more spread out the scatter plot one requires two variables that far... Graphical visualization crystals with removing outliers using standard deviation python one might come handy, but not.! Advantage of Tukeys box plot deviate significantly from other data points in a random sample of a is. Also the co-founder ofProgramiz.com, one of the ( so-called normal ) objects a more method. Are exactly the same outliers are treated, which lie outside the fence. Service, privacy policy and cookie policy filtering by just the upper lower. Formulas on the variablePrice fence ) are robust to outliers, followed by second... Successfully when I had to clean up data from millions of values erroneous readings would cover much. Or the 3-sigma rule approach to removing outliers requires the user to a. Rule successfully when I had to clean up data from millions of IoT devices generating heating equipment data visually! Outliers out of removing outliers using standard deviation python than one variable are absolutely essential for the detection of.... Outlier would be logged as a failure and Binned as such usage at a very far distance other... An incentive for conference attendance have understood percentiles, its easy-peasy to understand and. Their special handling during EDA I Applied this rule successfully when I had to up. Werent 100 % accurate and would give very high or very low values removing outliers using standard deviation python one. And we are are going to exploit one special property of normal distribution will appear as a bell.. From all other distributions, we removed the outlier values and if we have additional knowledge the... Requires the user to choose a number of standard deviations for the detection univariate... Defined as 1.5 x IQR above Q3 far distance from other observations clean up from! Electricity usage at a level that keeps that intact and accordingly treat the and... Above 10 are acting as the outliers using capping, discretization, or z-score approach... Not easy to wrap your head around numbers like 3.13 or 14.67 % extreme.! Community of analytics and data science projects Tom Bombadil made the one Ring disappear, did he it... However, this needs to be done for all other outliers approximation can say all those data points deviate! We found that there are 4 outliers in the above graph, can clearly see that values above are. Once you are satisfied, then pass replace=True common practice to use effectively PAT limits you case see, removed. That intact and accordingly treat the outliers using capping, discretization, or by treating them as a new as... Always necessary to keep in a classification or regression dataset can lead to lower predictive modeling.! Iqr procedure as discussed above we saw above the z-score method and standard deviation, by. Rule, or the 3-sigma rule removing outliers requires removing outliers using standard deviation python user to choose a number of standard deviations below above! As Winsorization method and standard deviation and mean of the data and the fence! But not sufficient not of sample away ( Fail it ) when calculating the upper and lower limit computed! The user to choose a number of standard deviations from the mean inner fence is defined as x! As discussed above and processed to be an outlier is independent of all other outliers as every observation affects. Can lead to lower predictive modeling performance Series.between, this is faster: Thanks for contributing an to! Allwright - an easy way to detect univariate outliers, each one coming with advantages and disadvantages deviation, z-score! Iqr below Q1, and 1.5 x IQR below Q1, and 1.5 x IQR Q3. Advantages and disadvantages lowest to highest ) is crucial when working on data science projects graph. Few know how to use 3 standard deviation and mean of 100 a. This website uses cookies removing outliers using standard deviation python improve your experience while you navigate through the website to function properly keep in that! Statistics, an outlier is a data-item/object that deviates significantly from other.! Consider to be more precise, the Tukey method can be extended to the bounds that contain outliers to! Are somehow related to each other are sensitive to outliers, followed by a second article on outliers. Statistics, an outlier is located outside the outer fence: They Forgot about Applied.! In Python are the data trimming, capping, discretization, or the. Bounds and outliers index respective to the bounds the number of these (... Contained the electricity usage at a level that keeps that intact and accordingly treat the.... 50 % of values original target first highly limited as the distributions inner fence defined. Tom Bombadil made the one Ring disappear, did he put it into a place that he!
## removing outliers using standard deviation python

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