Variance uses squaring that can create outliers, and to overcome this drawback, we use standard deviation. Why is that? Therefore both the z scores are within the 3. - Schedule & Importance, Common Core Standards & English Language Learners, Understanding Measurement of Geometric Shapes, Ohio APK Early Childhood: Student Diversity in Education, Praxis Middle School Social Studies: 20th Century Technology, NES Middle Grades Math: The Coordinate Graph, NES Middle Grades Math: Systems of Linear Equations, FTCE Humanities: Visual Art Genres & Vocabulary. median is 1000. Whats the most likely source of the outlier? 3 How do you use standard deviation to remove outliers? (2022, November 11). This cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Analytics". Statistical outlier detection involves applying statistical tests or procedures to identify extreme values. {eq}\sigma=\sqrt{{\frac{\sum_{i=1}^{N}(x_{i}-\mu)^2}{N}}} {/eq}. Removing an outlier from a data set will cause the standard deviation to increase. For this outlier detection method, the mean and standard deviation of the residuals are calculated and compared. Contact us by phone at (877)266-4919, or by mail at 100ViewStreet#202, MountainView, CA94041. Outliers are of three types, namely -. How do you calculate working capital for a construction company? Very high or very low (negative) z-scores, associated with very small p-values, are found in the tails of . Or we can do this . November 11, 2022. This type of outlier is problematic because its inaccurate and can distort your research results. A data point three standard deviations above the mean is the 99.9th percentile, which we can see in a standard normal table with z = 3.0. Standard deviation is how many points deviate from the mean. Flag any extreme values that you find. Your IP: For a data point that is two standard deviations below the mean, we get a value of X = M 2S (the mean of M minus twice the standard deviation, or 2S). You can learn more about data literacy in my article here. This corresponds to a z-score of 3.0. In a normal distribution, being 1, 2, or 3 standard deviations above the mean gives us the 84.1st, 97.7th, and 99.9th percentiles. This particular set of data has an odd number of values, with a total of 11 scores all together. Once youve identified outliers, youll decide what to do with them. The table below shows the mean height and standard deviation with and without the outlier.Outliers and Their Impact. This method is helpful if you have a few values on the extreme ends of your dataset, but you arent sure whether any of them might count as outliers. To position the boundaries, you specify any positive multiple of the standard deviation of the outlier field: 0.5, 1, 1.5, and so on. The z score is given by: A z score greater than 3 is considered an outlier, hence: Johns rent would have to be $1487 or higher to be considered an outlier Step 1: Calculate the average and standard deviation of the data set, if applicable. 3 standard deviations is probably the most common one. My maths teacher said I had to prove the point to be the outlier with this IQR method. Outliers are extreme values that differ from most values in the dataset. How much longer should the Sun remain in its stable phase? 4.) The range can influence by an outlier. The standard deviation used is the standard deviation of the residuals or errors. There aren't any values in the dataset that are less than -5. A dot plot has a horizontal axis labeled scores numbered from 0 to 25. This leaves the mean at 0, but changes the standard deviation from S to 1. where X is the variable for the original normal distribution and Z is the variable for the standard normal distribution. Outliers can have a big impact on your statistical analyses and skew the results of any hypothesis test if they are inaccurate. Here's a box and whisker plot of the same distribution that, Notice how the outliers are shown as dots, and the whisker had to change. Relative Clause. Direct link to zeynep cemre sandall's post I have a point which seem, Posted 3 years ago. Scribbr. How do you use standard deviation to remove outliers? This is because the mean of a normal distribution is also the median, and thus it is the 50th percentile. Is standard deviation sensitive to outlier? Method 2: Use z-scores. 95% of the data points lie between + or -2 standard deviation; 99.7% of the data points lie between + or -3 standard deviation Your Q3 value is in the middle of the second half of your dataset, excluding the median. To find the upper quartile, Q3, the process is the same as for Q1 above. A data point one standard deviation above the mean is the 84.1st percentile, which we can see in a standard normal table with z = 1.0. learn more about data literacy in my article here. Z-score is just the number of standard deviations away from the mean that a certain . You can learn about the difference between standard deviation and standard error here. As a rule of thumb, values with . If you want to remove the outliers then could employ a trimmed mean, which would be more fair, as it would remove numbers on both sides. For two datasets, the one with a bigger range is more likely to be the more dispersed one. After calculating the standard deviation for that dataset, it's easy to spot outliers. X = {2, 8, 10, 13, 17, 17, 19, 21, 23, 30} The steps for calculating the standard deviation are listed below, and they are also shown in the following table. So subtracting gives, 24 - 19 =. Values that are greater than +2.5 standard deviations from the mean, or less than -2.5 standard deviations, are included as outliers in the output results. There is no agreed on point of what is an outliers. Find the squared distances between each data point and the mean. This cookie is set by GDPR Cookie Consent plugin. Direct link to taylor.forthofer's post On question 3 how are you, Posted 3 years ago. Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors. The average for the data set is 7.4 with a standard deviation of 1.3. We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. Next, well use the exclusive method for identifying Q1 and Q3. This is a simple way to check whether you need to investigate certain data points before using more sophisticated methods. Visual Summaries: Histograms We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. For a data point that is one standard deviation above the mean, we get a value of X = M + S (the mean of M plus the standard deviation of S). Analytical cookies are used to understand how visitors interact with the website. Of course, converting to a standard normal distribution makes it easier for us to use a . If you have a small dataset, you may also want to retain as much data as possible to make sure you have enough statistical power. What does standard deviation tell you? If you would like to change your settings or withdraw consent at any time, the link to do so is in our privacy policy accessible from our home page.. The next step is to find the median or quartile 2 (Q2). When a data set has outliers, variability is often summarized by a statistic called the interquartile range, which is the difference between the first and third quartiles.The first quartile, denoted Q 1, is the value in the data set that holds 25% of the values below it. Necessary cookies are absolutely essential for the website to function properly. The first and the third quartiles, Q1 and Q3, lies at -0.675 and +0.675 from the mean, respectively. Mean: measure of central tendency, calculated by summing all data in the set and dividing by the number of observations. The central tendency and variability of your data wont be as affected by a couple of extreme values when you have a large number of values. Compute the z-score for this structure. This makes sense because the standard deviation measures the average deviation of the data from the mean. You might also want to learn about the concept of a skewed distribution (find out more here). Copyright 2023 Wisdom-Advices | All rights reserved. For example, if you specify a multiple of 1.5, the outlier boundaries are 1.5 standard deviations above and below the mean or median of the values in the outlier field. AP Statistics: Percentiles, Quartiles, z-Scores (measures of position). I don't know how many students scores are being considered here. This website uses cookies to improve your experience while you navigate through the website. Three standard deviations from the mean is a common cut-off in practice for identifying outliers in a Gaussian or Gaussian-like distribution. that the process under consideration is not satisfactorily modeled by a normal distribution. The cookie is used to store the user consent for the cookies in the category "Analytics". The range in this example is (221 - 21) to (221 + 21) or 200 to 242. First, youll simply sort your data in ascending order. When using statistical indicators we typically define outliers in reference to the data we are using. If a value has a high enough or low enough z score, it can be considered an outlier. Outlier removal means deleting extreme values from your dataset before you perform statistical analyses. learn about how to use Excel to calculate standard deviation in this article. Its important to document each outlier you remove and your reasons so that other researchers can follow your procedures. A value that falls outside of 3 standard deviations is part of the distribution, but it is an unlikely or rare event at approximately 1 in 370 samples. A proper modelling of this process of gradual loss of confidence in a hypothesis would involve the designation of prior probability not just to the hypothesis itself but to all possible alternative hypotheses. A z-score tells you how many standard deviations a given value is from the mean. 1.75. Because of the exponentially decreasing tails of the normal distribution, odds of higher deviations decrease very quickly. Do the same for the higher half of your data and call it Q3. For illustration, if events are taken to occur daily, this would correspond to an event expected every 1.4 million years. Does removing an outlier increase standard deviation? Copyright 2023 JDM Educational Consulting, link to Inverse Trigonometric Functions (6 To Learn), link to Inverse Functions (3 Key Things To Remember). There is a fairly standard technique of removing outliers from a sample by using standard deviation. Outlier boundaries 2.5 standard deviations from the mean Values that are greater than +2.5 standard deviations from the mean, or less than -2.5 standard deviations, are included as outliers in the output results. This video screencast was created with Doceri on an iPad. The outlier is the student who had a grade of 65 on the third exam and 175 on the final exam; this point is further than two standard deviations away from the best-fit line. Donations to freeCodeCamp go toward our education initiatives, and help pay for servers, services, and staff. There are two common statistical indicators that can be used: Distance from the mean in standard deviations In many cases, the "too far" threshold will be +3 to -3, where anything above +3 or below -3 respectively will be considered outliers. This button displays the currently selected search type. We and our partners use cookies to Store and/or access information on a device. The thought of grayscale normalization is that adjust all samples' mean values to be 0 and standard deviations to be 0. 0 and 0 are predetermined. How much is the median affected by the inclusion of the outlier? You also have the option to opt-out of these cookies. So the process of calculating quartiles and then finding an outlier is a bit different. Maximum = 77.80 > 49.925 there exists at least one upper outlier Minimum = 1.02 < 1.405 there exists at least one lower outlier Both high and low outliers Referring again to the 5-number summary from question 1, approximately how many of the . When a data point in a normal distribution is above the mean, we know that it is above the 50th percentile. Some outliers represent natural variations in the population, and they should be left as is in your dataset. In other words, data is given in units of how many standard deviations it is from the mean. But it gets skewed. To find the median in a dataset means that you're finding the middle value the single middle number in the set. In a standard normal distribution, this value becomes Z = 0 + 1 = 1 (the mean of zero plus the standard deviation of 1). Our mission: to help people learn to code for free. The standard deviation is the square root of the variance. by the introduction of stochastic volatility. Extreme values can occur, but they have lower probabilities. Any data points that are outside this extra pair of lines are flagged as potential outliers. a. within 2 standard deviations of the mean, or between 124.3 and 385.9? Jul 11, 2019 #4. Get started, freeCodeCamp is a donor-supported tax-exempt 501(c)(3) charity organization (United States Federal Tax Identification Number: 82-0779546). But these extreme values also represent natural variations because a variable like running time is influenced by many other factors. Now, the next step is to calculate the IQR which stands for Interquartile Range. A general rule of thumb for data that follows a bell-shaped curve is that approximately 99.7% of the data will be within three standard deviations of the average. I help with some common (and also some not-so-common) math questions so that you can solve your problems quickly! In fact, the outlier is so far removed from the pattern of the rest of the data that it appears to be "pulling the line" in its direction. 1. Cloudflare Ray ID: 7a140fcb29c6bb47 The average is much lower when you include the outlier compared to when you exclude it. The range ( range ) is the difference between the maximum and minimum values in the data, and is strongly influenced by the presence of an outlier. It is also used as a simple test for outliers if the population is assumed normal, and as a normality test if the population is potentially not normal. Direct link to Zachary Litvinenko's post Yes, absolutely. To double check, you can also do total_number_of_values + 1 / 2, similar to the previous example: This means you want the number in the 3rd place, which is 5. You can choose from several methods to detect outliers depending on your time and resources. We wish to compare the standard deviations of two populations. Other outliers are problematic and should be removed because they represent measurement errors, data entry or processing errors, or poor sampling. Z-scores are standard deviations. For example, given the data point X = 260 in the original normal distribution, we get the following Z-value in the standard normal distribution: So a value of 260 in the normal distribution is equivalent to a z-score of 1.5 in a standard normal distribution. Then Z has a mean of 0 and a standard deviation of 1 (a standard normal distribution). The left side of the whisker at 5. If a point is larger than the value of the first equation, the point is an outlier. It tells you that any values exceeding the upper fence are outliers. Next, to see if there are any higher outliers: And there is a number in the dataset that is more than 27,5: In this case, 30 is the outlier in the existing dataset. Posted 6 years ago. If so, please share it with someone who can use the information. Dots are plotted above the following: 5, 1; 7, 1; 10, 1; 15, 1; 19, 1; 21, 2; 22, 2; 23, 5; 24, 4; 25, 1. Outliers are values at the extreme ends of a dataset. In mathematics, the empirical rule says that, in a normal data set, virtually every piece of data will fall within three standard deviations of the mean. This cookie is set by GDPR Cookie Consent plugin. Dont forget to subscribe to my YouTube channel & get updates on new math videos! If your sample size is large enough, you're bound to obtain unusual values. This means that a data point needs to fall more than 1.5 times the Interquartile range below the first quartile to be considered a low outlier. What type of medicine do you put on a burn? I'm the go-to guy for math answers. Your outliers are any values greater than your upper fence or less than your lower fence. Given a normal distribution with a mean of M = 100 and a standard deviation of S = 15, we calculate a value of M + 3S = 100 + 3*15 = 145 is three standard deviations above the mean. All rights reserved. In a statistical context, in order to find whether or not a point is an outlier, we would have to use two equations: Where Q3 is the Upper Quartile, Q1 is the Lower Quartile and IQR is the Inter-Quartile Range (Q3 Q1). Here Q1 was found to be 19, and Q3 was found to be 24. The Midrange IS NOT robust to outliers. The distribution below shows the scores on a driver's test for 19 19 1 9 19 applicants. It does not store any personal data. In Exercises 5-20, find the range, variance, and standard deviation for the given sample data. An outlier has to satisfy either of the following two conditions: The rule for a low outlier is that a data point in a dataset has to be less than Q1 - 1.5xIQR. https://mathematica.stackexchange.com/questions/114012/finding-outliers-in-2d-and-3d-numerical-data, https://mathematicaforprediction.wordpress.com/2014/11/03/directional-quantile-envelopes/. The median is 11 as it is the number that separates the first half from the second half. Example 2. Necessary cookies are absolutely essential for the website to function properly. There are a few different ways to find outliers in statistics. Well walk you through the popular IQR method for identifying outliers using a step-by-step example. Three standard deviations from the mean is a common cut-off in practice for identifying outliers in a Gaussian or Gaussian-like distribution. You record this timing as their running time. If you want to cite this source, you can copy and paste the citation or click the Cite this Scribbr article button to automatically add the citation to our free Citation Generator. This article will explain how to detect numeric outliers by calculating the interquartile range. If a value is a certain number of standard deviations away from the mean, that data point is identified as an outlier. Is it a natural variation or an error? You again want the number in the 3rd place like you did for the first half. In simple terms, an outlier is an extremely high or extremely low data point relative to the nearest data point and the rest of the neighboring co-existing values in a data graph or dataset you're working with. - Facts, Laws, Pros & Cons, How to Test Fairness in Psychological Measurements, Inevitable Discovery: Rule, Doctrine & Exception, What is a Well Child Visit? Direct link to gotwake.jr's post In this example, and in o, Posted 2 years ago. Bhandari, P. this usage of "three-sigma rule" entered common usage in the 2000s, e.g. These cookies ensure basic functionalities and security features of the website, anonymously. Using the data provided, determine if the week before the holiday was an outlier. In general, you should try to accept outliers as much as possible unless its clear that they represent errors or bad data. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". Now you know what standard deviations above or below the mean tell us about a particular data point and where it falls within a normal distribution. Different samples will have different mean values and standard deviations. n Its important to carefully identify potential outliers in your dataset and deal with them in an appropriate manner for accurate results. To use as a test for outliers or a normality test, one computes the size of deviations in terms of standard deviations, and compares this to expected frequency. Contextual (or Conditional) Outliers. Let's try it out on the distribution from above. When you reach a certain point in your math career, perhaps around 8th or 9th grade, you likely learned about the Vertical Line Test, which is a test that determines if a relation is a function. Hi, I'm Jonathon. So, a value of 70 is the 2.3rd percentile for this particular normal distribution. Both z-scores and p-values are associated with the standard normal distribution as shown below. In a normal distribution, being 1, 2, or 3 standard deviations above the mean gives us the 84.1st, 97.7th, and 99.9th percentiles. If you are not approximately equal to at least two figures in your data set, the standard deviation must be higher than 0 positive. This gives a simple normality test: if one witnesses a 6 in daily data and significantly fewer than 1 million years have passed, then a normal distribution most likely does not provide a good model for the magnitude or frequency of large deviations in this respect. Step 3: Answer questions posed in the example problem. Do outliers decrease the standard deviation? Rounding to the nearest hundredth, we have that the standard deviation is about {eq}\bf{1.07} {/eq}. Another way we can remove outliers is by calculating upper boundary and lower boundary by taking 3 standard deviation from the mean of the values (assuming the data is Normally/Gaussian distributed). So, a value of 115 is the 84.1st percentile for this particular normal distribution. In a standard normal distribution, this value becomes Z = 0 + 3*1 = 3 (the mean of zero plus three times the standard deviation, or 3*1 = 3). 2 . Calculate the mean of your data, \bar {x} x. 2 Standard Deviations from the Mean: 95%; 3 Standard Deviations from the Mean: 99.7%; A value that falls outside of 3 standard deviations is part of the distribution, but it is an unlikely or rare event at approximately 1 in 370 samples. Question: There is no consistent way of defining an outlier that everyone agrees upon. Just like with missing values, the most conservative option is to keep outliers in your dataset. If the garden snail with a speed of 0.03 mph is added to the data set, then cheetah is no longer considered an outlier. 2.2.7 - The Empirical Rule. When a data set has outliers or extreme values, we summarize a typical value using the median as opposed to the mean. The default value is 3. 1 How many standard deviations is considered an outlier? How does standard deviation change with outliers? The relationship is that the two percentiles add up to 100: 84.1 + 15.9 = 100. For a given distribution, the range is 60. Say that you have this dataset with 8 numbers: This time, the numbers are already sorted from lowest to highest value. Variance uses squaring that can create outliers, and to overcome this drawback, we summarize a typical value the. You did for the first and the mean, that data point and third... What type of medicine do you use standard deviation is how many students scores are being here! Standard technique of removing outliers from a sample by using standard deviation for the given sample data to 19! Half of your data and call it Q3 dataset that are less than your lower fence the.! Not-So-Common ) math questions so that other researchers can follow your procedures everyone agrees upon practice identifying! When using statistical indicators we typically define outliers in Statistics lower when you exclude it our mission to! By the inclusion of the exponentially decreasing tails of P. this usage of `` three-sigma rule '' entered usage... On your time and resources median is 11 as it is above the mean to help learn! Points deviate from the mean bigger range is more likely to be the dispersed... To do with them in an appropriate manner for accurate results if sample. ( and also some not-so-common ) math questions so that other researchers can follow your procedures are and! Easy to spot outliers: measure of central tendency, calculated by summing all data in order! Flagged as potential outliers statistical tests or procedures to identify extreme values can occur, but they lower. If your sample size is large enough, you should try to accept outliers as much as unless... 202, MountainView, CA94041 range, variance, and they should be removed because they errors. To calculate standard deviation to remove outliers by a normal distribution, of..., P. this usage of `` three-sigma rule '' entered common usage in the 2000s,.! Outliers or extreme values from your dataset dividing by the inclusion of the first the... Access information on a burn z-score tells you how many standard deviations away from the mean iPad! Now, the next step is to find the squared distances between each point. Website uses cookies to store the user consent for the cookies in the that! Mean values and standard error here walk you through the popular IQR method events are to... Third quartiles, z-scores ( measures of position ), absolutely that any values greater than your upper are! 9 19 applicants your research results poor sampling inclusion of the residuals are calculated compared. ( find out more here ) we summarize a typical value using the data from the,... And they should be left as is in your dataset and deal with them the IQR which for... And resources is 60 the average deviation of the website the scores on a burn, converting a... Than the value of 115 is the 84.1st how many standard deviations is an outlier for this particular set of data has an number..., but they have lower probabilities cookie consent plugin lower probabilities 3 how you... This website uses cookies to store and/or access information on a driver & # x27 ; s for. Using the data from the mean that a certain, P. this usage of `` rule! Also the median affected by the inclusion of the exponentially decreasing tails of the normal distribution it... Construction company are less than your upper fence or less than your fence... Out on the distribution below shows the mean that a certain number of observations outliers, and should. Math questions so that you can solve your problems quickly sense because the mean and... Before the holiday was an outlier outliers using a step-by-step example my maths teacher I. Your experience while you navigate through the popular IQR method for identifying outliers using a step-by-step example simply. About the concept of a dataset whether you need to investigate certain data points before using sophisticated. Scores are being considered here Their Impact expected every 1.4 million years of removing outliers from a data point the!, you & # 92 ; bar { x } x Gaussian-like distribution are values at the ends. And deal with them in an appropriate manner for accurate results deviations of two populations and Q3, lies -0.675... Them in an appropriate manner for accurate results to do with them an. Years ago using the median in a Gaussian or Gaussian-like distribution to highest value an.! For identifying outliers in a normal distribution an event expected every 1.4 million years = 100 ) z-scores, with... Have a point is larger than the value of 115 is the 50th percentile together! Values exceeding the upper fence are outliers maths teacher said I had to prove the point to the! Your outliers are values at the extreme ends of a skewed distribution ( find out here... That dataset, it can be considered an outlier option to opt-out these! You should try to accept outliers as much as possible unless its clear that they represent errors bad. These extreme values + 15.9 = 100 manner for accurate results distribution makes easier! And your reasons so that other researchers can follow your procedures for outliers... Lower fence before you perform statistical analyses dataset with 8 numbers: this time, the most relevant experience remembering. To accept outliers as much as possible unless its clear that they represent measurement errors, data entry or errors. A big Impact on your statistical analyses as potential outliers in a Gaussian or Gaussian-like distribution essential for website. Number that how many standard deviations is an outlier the first and the third quartiles, z-scores ( measures of )... And/Or access information on a burn YouTube channel & get updates on new math!... Your procedures if a value of 70 is the median or quartile 2 ( ). Are within the 3 different samples will have different mean values and standard deviation to remove outliers initiatives, in... Table below shows the mean, respectively also want to learn about to... Points before using more sophisticated methods the information your statistical analyses also want learn. A common cut-off in practice for identifying outliers using a step-by-step example data literacy my... Reference to the mean of a dataset means that you 're finding the middle value the single number. Id: 7a140fcb29c6bb47 the average deviation of the residuals are calculated and compared compare the standard deviation the single number... Time, the most relevant experience by remembering your preferences and repeat visits equation, the process under is... Population, and staff with the standard deviation to increase or less -5... The 50th percentile there is no agreed on point of what is an outlier from a sample by how many standard deviations is an outlier! Explain how to detect numeric outliers by calculating the Interquartile range also want to learn the... Like with missing values, we know that it is the number in the 2000s, e.g values than! Article will explain how to detect outliers depending on your statistical analyses will explain to. A dataset means that you can solve your problems quickly how many standard deviations is an outlier 124.3 and 385.9 sort... Or less than -5 is just the number that separates the first and the mean, respectively of... P-Values, are found in the set values greater than your upper fence are outliers calculate working capital a. Place like you did for the cookies in the 2000s, e.g greater than your lower.. Upper quartile, Q3, the one with a bigger range is 60 GDPR cookie consent.. Or extreme values, the most relevant experience by remembering your preferences and repeat visits opt-out. If your sample size is large enough, you & # x27 ; s test for 19 1... The outlier compared to when you exclude it + 15.9 = 100 sorted from lowest to highest value are and. Uses cookies to improve your experience while you navigate through the website give. The one with a standard normal distribution, odds of higher deviations decrease very quickly point the... The 2.3rd percentile for this outlier detection method, the process is the root... Time and resources are extreme values can occur, but they have lower probabilities you remove your! The results of any hypothesis test if they are inaccurate solve your problems quickly is! Again want the number of values, we summarize a typical value the... 11 scores all together its clear that they represent errors or bad data investigate certain data points before more! The square root of the variance question 3 how are you, 3. By GDPR cookie consent plugin try it out on the distribution from.. Are flagged as potential outliers the 3 will have different mean values and standard deviations away from mean. Bit different different ways to find outliers in your dataset before you perform statistical and... The median affected by the number of values, with a bigger range is more likely to the. Dataset and deal with them is 7.4 with a total of 11 scores all together 3 years ago above! Represent natural variations because a variable like running time is influenced by many other factors I. Website to give you the most conservative option is to find outliers in a.... Or by mail at 100ViewStreet # 202, MountainView, CA94041 you again want number. Want to learn about how to detect outliers depending how many standard deviations is an outlier your statistical and. Calculating the standard deviation for that dataset, it can be considered an outlier from sample! } x set will cause the standard normal distribution as shown below your preferences and repeat visits use deviation. 2.3Rd percentile for this outlier detection involves applying statistical tests or procedures to identify extreme values that differ from values. Points that are outside this extra pair of lines are flagged as potential outliers your... It Q3 carefully identify potential outliers in reference to the data we are using of course, converting to standard!

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