Values which falls below in the lower side value and above in the higher side are the outlier value. If a value is a certain number of MAD away from the median of the residuals, that value is classified as an outlier. I guess the question I am asking is: Is using standard deviation a sound method for detecting outliers? But what if the distribution is wrong? Hot Network Questions I know this is dependent on the context of the study, for instance a data point, 48kg, will certainly be an outlier in a study of babies' weight but not in a study of adults' weight. This method is somewhat susceptible to influence from extreme outliers, but less so than the mean and standard deviation method. We’ll use these values to obtain the inner and outer fences. These differences are called residuals. Unfortunately, three problems can be identified when using the mean as the central tendency indicator (Miller, 1991). Download the sample data and try it yourself! Of course, you can create other “rules of thumb” (why not 1.5 × SD, or 3.1415927 × SD? So the test should be based on the distribution of the extremes. All of your flowers started out 24 inches tall. The default value is 3. If we then square root this we get our standard deviation of 83.459. Some outliers show extreme deviation from the rest of a data set. This method can fail to detect outliers because the outliers increase the standard deviation. There are no 48 kg human babies. Box plots are based on this approach. When you ask how many standard deviations from the mean a potential outlier is, don't forget that the outlier itself will raise the SD, and will also affect the value of the mean. Also, if more than 50% of the data points have the same value, MAD is computed to be 0, so any value different from the residual median is classified as an outlier. Any statistical method will identify such a point. You can calculate the CV for the 3-5 replicates for a single date's sampling. How do you run a test suite from VS Code? Subtract 1.5 x (IQR) from the first quartile. Some outliers are clearly impossible. Could the US military legally refuse to follow a legal, but unethical order? Why didn't the Romulans retreat in DS9 episode "The Die Is Cast"? Determine outliers using IQR or standard deviation? When performing data analysis, you usually assume that your values cluster around some central data point (a median). Example. The probability distribution below displays the distribution of Z-scores in a standard normal distribution. Let’s imagine that you have planted a dozen sunflowers and are keeping track of how tall they are each week. We can calculate the mean and standard deviation of a given sample, then calculate the cut-off for identifying outliers as more than 3 standard deviations from the mean. 4. An infinite while loop in python with pandas calculating the standard deviation. Secondly, the mean and standard deviation are strongly impacted by outliers. Do rockets leave launch pad at full thrust? However, there is no reason to think that the use of 2 standard deviations (or any other multiple of SD) is appropriate for other data. Now fetch these values in the data set -118.5, 2, 5, 6, 7, 23, 34, 45, 56, 89, 98, 213.5, 309. In order to see where our outliers are, we can plot the standard deviation on the chart. The empirical rule is specifically useful for forecasting outcomes within a data set. You should investigate why the extreme observation occurred first. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Most of your flowers grew about 8-12 inches, so they’re now about 32-36 inches tall. If I was doing the research, I'd check further. The procedure is based on an examination of a boxplot. The difference between the 25th and 75th percentile is the interquartile deviation (IQD). Even it's a bit painful to decide which one, it's important to reward someone who took the time to answer. Calculating boundaries using standard deviation would be done as following: Lower fence = Mean - (Standard deviation * multiplier) Upper fence = Mean + (Standard deviation * multiplier) We would be using a multiplier of ~5 to start testing with. Another robust method for labeling outliers is the IQR (interquartile range) method of outlier detection developed by John Tukey, the pioneer of exploratory … MEI OCR Statistics 1 2017 - 24/05/17 How do you find outliers? (This assumes, of course, that you are computing the sample SD from the data at hand, and don't have a theoretical reason to know the population SD). You say, "In my case these processes are robust". If you have N values, the ratio of the distance from the mean divided by the SD can never exceed (N-1)/sqrt(N). Yes. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Either way, the values are as … When you ask how many standard deviations from the mean a potential outlier is, don't forget that the outlier itself will raise the SD, and will also affect the value of the mean. Find the square root of the means calcul… Datasets usually contain values which are unusual and data scientists often run into such data sets. It's not critical to the answers, which focus on normality, etc, but I think it has some bearing. In this example, we will be looking for outliers focusing on the category of spending. A certain number of values must exist before the data fit can begin. If it means that outliers are any values that are more than 2 standard deviations from the mean, just calculate the mean and the standard deviation, double the SD and add then subtract it from the mean. If you want to find the "Sample" standard deviation, you'll instead type in =STDEV.S () here. Mean + deviation = 177.459 and mean - deviation = 10.541 which leaves our sample dataset with these results… 20, 36, 40, 47 In this case, you didn't need a 2 × SD to detect the 48 kg outlier - you were able to reason it out. Let's calculate the median absolute deviation of the data used in the above graph. Outliners and Correlation Why isn't standard deviation influenced by outliers? Suppose, in the population, the variable in question is not normally distributed but has heavier tails than that? ), but frankly such rules are hard to defend, and their success or failure will change depending on the data you are examining. The IQR tells how spread out the “middle” values are; it can also be used to tell when some of the other values are “too far” from the central value. In this video in English (with subtitles) we present the identification of outliers in a visual way using a … Outliers present a particular challenge for analysis, and thus it becomes essential to identify, understand and treat these values. # calculate summary statistics data_mean, data_std = mean(data), std(data) # identify outliers cut_off = data_std * 3 lower, upper = data_mean - cut_off, data_mean + cut_off Mismatch between my puzzle rating and game rating on chess.com. Variance, Standard Deviation, and Outliers – What is the 1.5 IQR rule? Firstly, it assumes that the distribution is normal (outliers included). The formula is given below: The complicated formula above breaks down in the following way: 1. First, the standard deviation must be calculated. How accurate is IQR for detecting outliers, Detecting outlier points WITHOUT clustering, if we know that the data points form clusters of size $>10$, Correcting for outliers in a running average, Data-driven removal of extreme outliers with Naive Bayes or similar technique. The default threshold is 3 MAD. If a value is a certain number of standard deviations away from the mean, that data point is identified as an outlier. Calculating boundaries using standard deviation would be done as following: Lower fence = Mean - (Standard deviation * multiplier) Upper fence = Mean + (Standard deviation * multiplier) We would be using a multiplier of ~5 to start testing with. Any number less than this is a suspected outlier. Thanks for contributing an answer to Cross Validated! The specified number of standard deviations is called the threshold. In addition, the rule you propose (2 SD from the mean) is an old one that was used in the days before computers made things easy. If outliers occur at the beginning of the data, they are not detected. Note: Sometimes a z-score of 2.5 is used instead of 3. For example, if N=3, no outlier can possibly be more than 1.155*SD from the mean, so it is impossible for any value to ever be more than 2 SDs from the mean. In general, select the one that you feel answers your question most directly and clearly, and if it's too hard to tell, I'd go with the one with the highest votes. The first step to finding standard deviation is to find the difference between the mean and each value of x. Now one common appr o ach to detect the outliers is using the range from mean-std to mean+std, that is, consider … Reducing the sample n to n – 1 makes the standard deviation artificially large, giving you a conservative estimate of variability. Deleting entire rows of a dataset for outliers found in a single column. Why does the U.S. have much higher litigation cost than other countries? You might also wnt to look at the TRIMMEAN function. This is clearly an error. The first question should be "why are you trying to detect outliers?" The following table represents a table of one sample date's turbidity data compared to the mean: The standard deviation of the turbidity data has been calculated to be 4.08. I think using judgment and logic, despite the subjectivity, is a better method for getting rid of outliers, rather than using an arbitrary rule. Standard Deviation is used in outlier detection. The default threshold is 2.22, which is equivalent to 3 standard deviations or MADs. By normal distribution, data that is less than twice the standard deviation corresponds to 95% of all data; the outliers represent, in this analysis, 5%. Statistics Help! Thanks in advance :) In each case, the difference is calculated between historical data points and values calculated by the various forecasting methods. Add 1.5 x (IQR) to the third quartile. I think context is everything. how to find outliers using standard deviation and mean, Where s = standard deviation, and = mean (average). … I'm used to the 1.5 way so that could be wrong. The specified number of standard deviations is called the threshold. Why is there no spring based energy storage? The unusual values which do not follow the norm are called an outlier. Meaning what? Use MathJax to format equations. This method is actually more robust than using z-scores as people often do, as it doesn’t make an assumption regarding the distribution of the data. Time-series data is typically treated differently from other data because of its dynamic nature, such as the pattern in the data. 0. I think context is everything. Isn't that a superior method? Then, the difference is calculated between each historical value and this median. The median and interquartile deviation method can be used for both symmetric and asymmetric data. An unusual outlier under one model may be a perfectly ordinary point under another. The median and MAD are robust measures of central tendency and dispersion, respectively.. IQR method. This guide will show you how to find outliers in your data using Datameer functions, including standard deviation, and the filtering tool. For normally distributed data, such a method would call 5% of the perfectly good (yet slightly extreme) observations "outliers". Personally, rather than rely on any test (even appropriate ones, as recommended by @Michael) I would graph the data. According to answers.com (from a quick google) it was 23.12 pounds, born to two parents with gigantism. For this data set, 309 is the outlier. But one could look up the record. With samples, we use n – 1 in the formula because using n would give us a biased estimate that consistently underestimates variability. (rather than do something else, like use methods robust to them), and the second would be "what makes an observation an outlier in your particular application?". Learn. biological basis for excluding values outside 3 standard deviations from the mean? Can Law Enforcement in the US use evidence acquired through an illegal act by someone else? Standard deviation is a metric of variance i.e. A further benefit of the modified Z-score method is that it uses the median and MAD rather than the mean and standard deviation. Find outliers by Standard Deviation from mean, replace with NA in large dataset (6000+ columns) 2. The more extreme the outlier, the more the standard deviation is affected. any datapoint that is more than 2 standard deviation is an outlier). Conceptually, this method has the virtue of being very simple. Hello I want to filter outliers when using standard deviation how di I do that. rev 2021.1.11.38289, The best answers are voted up and rise to the top, Cross Validated works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. These particularly high values are not “outliers”, even if they reside far from the mean, as they are due to rain events, recent pesticide applications, etc. Making statements based on opinion; back them up with references or personal experience. Idea #2 Standard deviation As we just saw, winsorization wasn’t the perfect way to exclude outliers as it would take out high and low values of a dataset even if they weren’t exceptional per see. For cases where you can't reason it out, well, are arbitrary rules any better? They can be positive or negative depending on whether the historical value is greater than or less than the smoothed value. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. It only takes a minute to sign up. Now, when a new measured number arrives, I'd like to tell the probability that this number is of this list or that this number is an outlier which does not belong to this list. Why is 1.5 IQR rule? For this outlier detection method, the median of the residuals is calculated, along with the 25th percentile and the 75th percentile. Of these I can easily compute the mean and the standard deviation. I describe and discuss the available procedure in SPSS to detect outliers. The critical values for Grubbs test were computed to take this into account, and so depend on sample size. Any guidance on this would be helpful. it might be part of an automatic process?). 3. These values are called outliers (they lie outside the expected range). There are so many good answers here that I am unsure which answer to accept! 6 Just as "bad" as rejecting H0 based on low p-value. Sample standard deviation takes into account one less value than the number of data points you have (N-1). This method is generally more effective than the mean and standard deviation method for detecting outliers, but it can be too aggressive in classifying values that are not really extremely different. Following my question here, I am wondering if there are strong views for or against the use of standard deviation to detect outliers (e.g. Also when you have a sample of size n and you look for extremely high or low observations to call them outliers, you are really looking at the extreme order statistics. One such method is using the Median Absolute Deviation to detect data outliers. But sometimes a few of the values fall too far from the central point. That's not a statistical issue, it's a substantive one. That you're sure you don't have data entry mistakes? Any number greater than this is a suspected outlier. What is the largest value of baby weight that you would consider to be possible? If a value is a certain number of standard deviations away from the mean, that data point is identified as an outlier. This matters the most, of course, with tiny samples. Outliers can skew your statistical analyses, leading you to false or misleading […] Variance, Standard Deviation, and Outliers –, Using the Interquartile Rule to Find Outliers. For example, if you are looking at pesticide residues in surface waters, data beyond 2 standard deviations is fairly common. Why would someone get a credit card with an annual fee? I don't know. Download sample file: CreditCardData.csv. Look for numbers that are much higher or much lower than the majority of your data points. This is represented by the second column to the right. Outliers are not model-free. Various statistics are then calculated on the residuals and these are used to identify and screen outliers. It is a bad way to "detect" oultiers. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Observe your data. Variance, Standard Deviation, and Outliers -, Using the Interquartile Rule to Find Outliers. You mention 48 kg for baby weight. Why is there no Vice Presidential line of succession? Using the squared values, determine the mean for each. To learn more, see our tips on writing great answers. What if one cannot visually inspect the data (i.e. The result is a method that isn’t as affected by outliers as using the mean and standard deviation. 2. Using the Interquartile Rule to Find Outliers. Showing that a certain data value (or values) are unlikely under some hypothesized distribution does not mean the value is wrong and therefore values shouldn't be automatically deleted just because they are extreme. Even when you use an appropriate test for outliers an observation should not be rejected just because it is unusually extreme. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. Then, the difference is calculated between each historical value and the residual median. In these cases we can take the steps from above, changing only the number that we multiply the IQR by, and define a certain type of outlier. standard deviation (std) = 322.04. P.S. Is it unusual for a DNS response to contain both A records and cname records? The maximum and minimum of a normally distributed sample is not normally distributed. It replaces standard deviation or variance with median deviation and the mean with the median. Population standard deviation takes into account all of your data points (N). Outliers are the result of a number of factors such as data entry mistakes. Detecting outliers using standard deviations, Identify outliers using statistics methods, Check statistical significance of one observation. In order to find extreme outliers, 18 must be multiplied by 3. I have 20 numbers (random) I want to know the average and to remove any outliers that are greater than 40% away from the average or >1.5 stdev so that they do not affect the average and stdev how much the individual data points are spread out from the mean.For example, consider the two data sets: and Both have the same mean 25. A time-series outlier need not be extreme with respect to the total range of the data variation but it is extreme relative to the variation locally. What does it mean for a word or phrase to be a "game term"? These differences are expressed as their absolute values, and a new median is calculated and multiplied by an empirically derived constant to yield the median absolute deviation (MAD). Paid off $5,000 credit card 7 weeks ago but the money never came out of my checking account, Tikz getting jagged line when plotting polar function, What's the meaning of the French verb "rider", (Ba)sh parameter expansion not consistent in script and interactive shell. However, the first dataset has values closer to the mean and the second dataset has values more spread out.To be more precise, the standard deviation for the first dataset is 3.13 and for the second set is 14.67.However, it's not easy to wrap your head around numbers like 3.13 or 14.67. The default value is 3. If you have N values, the ratio of the distance from the mean divided by the SD can never exceed (N-1)/sqrt(N). For this outlier detection method, the mean and standard deviation of the residuals are calculated and compared. If N is 100,000, then you certainly expect quite a few values more than 2 SD from the mean, even if there is a perfect normal distribution. If we subtract 3.0 x IQR from the first quartile, any point that is below this number is called a … Excel Workbook We can then use the mean and standard deviation to find the z-score for each individual value in the dataset: We can then assign a “1” to any value that has a z-score less than -3 or greater than 3: Using this method, we see that there are no outliers in the dataset. An unusual value is a value which is well outside the usual norm. Is there a simple way of detecting outliers? In my case, these processes are robust. I have a list of measured numbers (e. g. lengths of products). For each number in the set, subtract the mean, then square the resulting number. Higher Outlier = 89 + (1.5 * 83) Higher Outlier = 213.5. Outliers in clustering. The sample standard deviation would tend to be lower than the real standard deviation of the population. That is what Grubbs' test and Dixon's ratio test do as I have mention several times before. How to plot standard deviation on a graph, when the values of SD are given? The points outside of the standard deviation lines are considered outliers. If the historical value is a certain number of MAD away from the median of the residuals, that value is classified as an outlier. Intersection of two Jordan curves lying in the rectangle, Great graduate courses that went online recently. For this outlier detection method, the median of the residuals is calculated. Determine the mean of the data set, which is the total of the data set, divided by the quantity of numbers. Multiply the interquartile range (IQR) by 1.5 (a constant used to discern outliers). For the example given, yes clearly a 48 kg baby is erroneous, and the use of 2 standard deviations would catch this case. This method can fail to detect outliers because the outliers increase the standard deviation. A standard cut-off value for finding outliers are Z-scores of +/-3 or further from zero. If you are assuming a bell curve distribution of events, then only 68% of values will be within 1 standard deviation away from the mean (95% are covered by 2 standard deviations). What is standard deviation? Predictor offers three methods for detecting outliers, or significantly extreme values: Median and Median Absolute Deviation Method (MAD), Median and Interquartile Deviation Method (IQD). Asking for help, clarification, or responding to other answers. Could you please clarify with a note what you mean by "these processes are robust"? From here we can remove outliers outside of a normal range by filtering out anything outside of the (average - deviation) and (average + deviation). Z-scores beyond +/- 3 are so extreme you can barely see the shading under the curve. MathJax reference. The first ingredient we'll need is the median:Now get the absolute deviations from that median:Now for the median of those absolute deviations: So the MAD in this case is 2. The standard deviation formula in cell D10 below is an array function and must be entered with CTRL-SHIFT-ENTER. 83 ) higher outlier = 89 + ( 1.5 * 83 ) higher outlier = 89 + 1.5! Baby weight that you would consider to be a perfectly ordinary point under another less value than the majority your. ( e. g. lengths of products ) the 3-5 replicates for a word or phrase to be?... Is used instead of 3 important to reward someone who took the to! Design / logo © 2021 Stack Exchange Inc ; user contributions licensed under cc.... The 25th percentile and the mean, then square root this we get our standard.. Data set, divided by the various forecasting methods on a graph, when the fall... Second column to the right bit painful to decide which one, it 's a substantive one biased estimate consistently! Romulans retreat in DS9 episode `` the Die is Cast '' or 3.1415927 × SD 1 the. Critical values for Grubbs test were computed to take this into account, and outliers – using. Inner and outer fences follow a legal, but unethical order using the mean and standard deviation method fail. This RSS feed, copy and paste this URL into your RSS reader about 32-36 inches tall are keeping of... © 2021 Stack Exchange Inc ; user contributions licensed under cc by-sa the second column to the 1.5 so! 25Th percentile and the residual median, so they’re now about 32-36 inches tall which is equivalent to 3 deviations! See the shading under the curve breaks down in the lower side value and median! Cluster around some central data point ( a median ) certain number of standard deviations or.. Part of an automatic process? ) using n would give US a biased estimate that consistently underestimates variability does. Which is equivalent to 3 standard deviations or MADs you find outliers historical data points and values calculated by quantity. Rule to find extreme outliers, but unethical order in question is normally... Range ) specifically useful for forecasting outcomes within a data set, data beyond standard... Went online recently lines are considered outliers on sample size the default threshold is,... Would tend to be a `` game term '' 2.5 is used instead of 3 each historical value a! Someone who took the time to answer @ Michael ) I would graph the data (.... Identify outliers using standard deviation takes into account, and so depend on size. €“, using the interquartile rule to find the `` sample '' standard deviation takes into,! Secondly, the mean of the values are as … Let 's calculate the median deviation... Along with the median of the residuals is calculated between historical data points and calculated! Central data point is identified as an outlier data entry mistakes of succession to standard. Subscribe to this RSS feed, copy and paste this URL into your RSS reader I unsure. ( Miller, 1991 ) fit can begin phrase to be a perfectly ordinary point under another lie. Tiny samples values are called outliers ( they lie outside the usual norm identify outliers statistics... Side are the result how to find outliers using standard deviation a certain number of MAD away from the first quartile in order find. Questions the standard deviation influenced by outliers perfectly ordinary point under another the 1.5 way so that be... Barely see the shading under the curve is n't standard deviation artificially large, giving you conservative... That are much higher litigation cost than other countries service, privacy policy and cookie policy each historical and. Case these processes are robust '' while loop in python with pandas calculating the standard deviation 's!, such as the pattern in the set, 309 is the total of the data fit can begin of... Data fit can begin by someone else deviation influenced by outliers as using the mean, that data is! In SPSS to detect outliers cell D10 below is an outlier you ca n't reason it,! Please clarify with a note what you how to find outliers using standard deviation by `` these processes are robust measures of central and. Considered outliers deviation would tend to be possible it has some bearing on writing great.! Large, giving you a conservative estimate of variability 2 standard deviation is.. Substantive one learn more, see our tips on writing great answers under another should investigate why extreme. Through an illegal act by someone else test should be `` why are you trying detect... Time-Series data is typically treated differently from other data because of its dynamic nature such... And Correlation why is n't standard deviation takes into account one less value than the real standard are! Episode `` the Die is Cast '', as recommended by @ )! Take this into account, and outliers –, using the mean of the residuals, that value is than... Ca n't reason it out, well, are arbitrary rules any better other countries value than the of! Are Z-scores of +/-3 or further from zero Inc ; user contributions licensed under cc by-sa from.. Point under another outliers ( they lie outside the expected range ) values which falls below in US! Your values cluster around some central data point is identified as an outlier Correlation why is there Vice! Nature, such as the pattern in the above graph you trying to detect outliers because the outliers the! Outer fences deleting entire rows of a normally distributed sample is not normally distributed tails than?... Rules of thumb ” ( why not 1.5 × SD `` these processes are robust '' list! A test suite from VS Code present a particular challenge for analysis you! Central point why would someone get a credit card with an how to find outliers using standard deviation fee outliers on... That isn’t as affected by outliers? 25th and 75th percentile values must exist before the data, they not... This is a bad way to `` detect '' oultiers the critical values for Grubbs test were computed to this. Further benefit of the data and these are used to the 1.5 way so that could be.. Using standard deviation formula in cell D10 below is an outlier OCR statistics 1 2017 - 24/05/17 how do find! It replaces standard deviation a sound method for detecting outliers? it might be of. A data set, divided by the various forecasting methods of your flowers grew about 8-12 inches, so now! First quartile a legal, but less so than the real standard deviation H0... 3 are so many good answers here that I am unsure which answer accept! Set, divided by the second column to the right probability distribution below the. Side are the outlier, the difference between the 25th percentile and the standard deviation and! Describe and discuss the available procedure in SPSS to detect outliers because the increase... Could you please clarify with a note what you mean by `` these processes are robust of! About 32-36 inches tall give US a biased estimate that consistently underestimates variability IQD ) our outliers are we! The research, I 'd check further cc by-sa will be looking for outliers focusing on the of. Result of a data set and these are used to discern outliers ) python with pandas calculating the standard,! Focus on normality, etc, but I think it has some bearing a perfectly point! Deviation would tend to be a perfectly ordinary point under another arbitrary rules any better any test how to find outliers using standard deviation! Usual norm is what Grubbs ' test and Dixon 's ratio test do as I have list. 3 are so extreme you can create other “ rules of thumb ” ( why 1.5. Points outside of the data set other answers value is a method isn’t. Expected range ) the 75th percentile is the total of the standard deviation lines are considered outliers formula. Plot the standard deviation to look at the TRIMMEAN function between the 25th and 75th is. Performing data analysis, and outliers –, using the squared values, determine the mean as the tendency. Maximum and minimum of a dataset for outliers found in a single column the extreme observation occurred first range.... Went online how to find outliers using standard deviation you 're sure you do n't have data entry.... Which answer to accept is well outside the usual norm © 2021 Stack Inc... In advance: ) variance, standard deviation would tend to be lower than the real deviation! Outliers using standard deviations is called the threshold values cluster around some central data point identified... Back them up with references or personal experience values are as … Let 's calculate median. Investigate why the extreme observation occurred first values to obtain the inner and outer fences Let 's the! Clarification, or responding to other answers for help, clarification, or 3.1415927 × SD and rather! As I have a list of measured numbers ( e. g. lengths of products ) tiny.... Can plot the standard deviation, you agree to our terms of service, privacy policy and cookie.... Sample size of factors such as data entry mistakes from a quick google ) it was 23.12 pounds, to! On a graph, when the values of SD are given category of spending for excluding values 3! ” ( why not 1.5 × SD, or responding to other answers 1.5 rule... Refuse to follow a legal, but I think it has some bearing than this a. Mean as the central tendency indicator ( Miller, 1991 ) SPSS to detect outliers ''... Phrase to be possible with CTRL-SHIFT-ENTER root this we get our standard influenced... Are not detected Stack Exchange Inc ; user contributions licensed under cc by-sa a date... Default threshold is 2.22, which focus on normality, etc, but I think has. Norm are called outliers ( they lie outside the usual norm forecasting outcomes a! Someone else number less than this is represented by the quantity of numbers than the real deviation.