5 What is the equation to determine an outlier? Direct link to AstroWerewolf's post Can their be a negative o, Posted 6 years ago. Different samples will have different mean values and standard deviations. Many computer programs highlight an outlier on a chart with an asterisk, and these will lie outside the bounds of the graph. Include appropriate units (such as . Does standard deviation include outliers? We can observe that, within 1 standard deviation from the mean =68% of data, within 2 standard deviaiton from the mean =95% of data and within 3 standard deviation from the mean =99.7% of data. Contact us by phone at (877)266-4919, or by mail at 100ViewStreet#202, MountainView, CA94041. The Empirical Rule is a statement about normal distributions. What does the abbreviation LIC stand for? learn more about the differences between mean and standard deviation in my article here. The cookie is used to store the user consent for the cookies in the category "Analytics". 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. The lower fence is the boundary around the first quartile. The standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance. Its a tricky procedure because its often impossible to tell the two types apart for sure. 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. An alternative way to double check if you're right is to do this: This is (11 + 1) /2 = 6, which means you want the number in the 6th place of this set of data which is 11. Step 1: Calculate the average and standard deviation of the data set, if applicable. It just tries to stay in between. If a data sets distribution is skewed, then 95% of its values will fall between two standard deviations of the mean. An outlier is a data point in a data set that is distant from all other observations. The value in the month of January is significantly less than in the other months. When a data set has outliers or extreme values, we summarize a typical value using the median as opposed to the mean. Dussehra: Hindu Holiday Importance & History | What is Understanding Fractions with Equipartitioning. In The Black Swan, Nassim Nicholas Taleb gives the example of risk models according to which the Black Monday crash would correspond to a 36- event: The range in this example is (7.4 - 3.9) to (7.4 + 3.9) or 3.5 to 11.3. But in this case you take the second half on the right hand side of the dataset, above the median and without the median itself included: You split this half of the odd set of numbers into another half to find the median and subsequently the value of Q3. 1 How many standard deviations makes an outlier? Say that you have this dataset with 8 numbers: This time, the numbers are already sorted from lowest to highest value. An outlier is a value that is very different from the other data in your data set. Some outliers represent natural variations in the population, and they should be left as is in your dataset. If you're seeing this message, it means we're having trouble loading external resources on our website. The next step is to find the median or quartile 2 (Q2). 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. The median is 11 as it is the number that separates the first half from the second half. the occurrence of such an event should instantly suggest that the model is flawed, i.e. As a reminder, an outlier must fit the following criteria: To see if there is a lowest value outlier, you need to calculate the first part and see if there is a number in the set that satisfies the condition. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. The median is the value exactly in the middle of your dataset when all values are ordered from low to high. This can potentially help you disover inconsistencies and detect any errors in your statistical processes. This corresponds to a z-score of -1.0. So, knowing how to find outliers in a dataset will help you better understand your data. median is 1000. 3 Does standard deviation include outliers? In addition, the standard deviation, like the mean, is normally only appropriate when the continuous data is not significantly skewed or has outliers. The standard deviation is calculated as the square root of variance by determining each data points deviation relative to the mean. Is the value greater than or less than the mean? Because of the exponentially decreasing tails of the normal distribution, odds of higher deviations decrease very quickly. Now, the next step is to calculate the IQR which stands for Interquartile Range. To find out more about why you should hire a math tutor, just click on the "Read More" button at the right! Subtract Q1 from Q3 to calculate the IQR. The first and the third quartiles, Q1 and Q3, lies at -0.675 and +0.675 from the mean, respectively. Relative Clause. Can I still identify the point as the outlier? How to Find Outliers | 4 Ways with Examples & Explanation. {eq}\sigma=\sqrt{{\frac{\sum_{i=1}^{N}(x_{i}-\mu)^2}{N}}} {/eq}. The beginning part of the box is at 19. Both z-scores and p-values are associated with the standard normal distribution as shown below. X This cookie is set by GDPR Cookie Consent plugin. Do the same for the higher half of your data and call it Q3. The average is much lower when you include the outlier compared to when you exclude it. Direct link to Rachel.D.Reese's post How do I draw the box and, Posted 6 years ago. The empirical rule is also referred to as the Three Sigma Rule or the 68-95-99.7 Rule because: Within the first standard deviation . When using statistical indicators we typically define outliers in reference to the data we are using. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". 3 standard deviations is probably the most common one. Direct link to ravi.02512's post what if most of the data , Posted 2 years ago. In a normal distribution, approximately 1 in 340 observations will be at least three standard deviations away from the mean. Step 1: Calculate the average and standard deviation of the data set, if applicable. Using the Median Absolute Deviation to Find Outliers. Just like with missing values, the most conservative option is to keep outliers in your dataset. Does removing an outlier increase standard deviation? Bhandari, P. The next step is standardizing (dividing by the population standard deviation), if the population parameters are known, or studentizing (dividing by an estimate of the standard deviation), if the parameters are unknown and only estimated. We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development. 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. A normal distribution is symmetrical and bell-shaped. Question: There is no consistent way of defining an outlier that everyone agrees upon. You can choose from several methods to detect outliers depending on your time and resources. The relationship is that the two percentiles add up to 100: 84.1 + 15.9 = 100. Generally a value that lies at or beyond 1.5 * IQR (interquartile range) is considered to be an abnormal distance away from the data, and thus becomes an outlier. . by I hope you found this article helpful. Is standard deviation sensitive to outlier? Figure in the left shows area under normal curve and how much area that standard deviation covers. Direct link to 23_dgroehrs's post In the bonus learning, ho, Posted 3 years ago. But more technically it's a measure of how many standard deviations below or above the population mean a . 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. We also use third-party cookies that help us analyze and understand how you use this website. For a data point that is three standard deviations below the mean, we get a value of X = M 3S (the mean of M minus three times the standard deviation, or 3S). n What is the equation to determine an outlier? There are no lower outliers, since there isn't a number less than -8.5 in the dataset. When should I remove an outlier from my dataset? To find the upper quartile, Q3, the process is the same as for Q1 above. Z-score is just the number of standard deviations away from the mean that a certain . A certain value has a standardized sore = 1.75. how many standard deviations from the mean does this value fall? If you are interested in learning more about Statistics and the basics of Data Science, check out this free 8hour University course on freeCodeCamp's YouTube channel. Assuming the distribution is bell-shaped, the estimated standard deviation is = ____. One can compute more precisely, approximating the number of extreme moves of a given magnitude or greater by a Poisson distribution, but simply, if one has multiple 4 standard deviation moves in a sample of size 1,000, one has strong reason to consider these outliers or question the assumed normality of the distribution. - Facts, Laws, Pros & Cons, How to Test Fairness in Psychological Measurements, Inevitable Discovery: Rule, Doctrine & Exception, What is a Well Child Visit? Variance: dispersion relating the gap between data points and the mean of the data set. This cookie is set by GDPR Cookie Consent plugin. Well walk you through the popular IQR method for identifying outliers using a step-by-step example. As the week before the holiday falls outside the calculated range, that week can be considered an outlier. This allows us to make assumptions on how many standard deviations the data is from the mean which is an element of the normal distribution formula. This is not a symmetrical interval this is merely the probability that an observation is less than + 2. There is no agreed on point of what is an outliers. {\displaystyle {\bar {X}}} Given a normal distribution with a mean of M = 100 and a standard deviation of S = 15, we calculate a value of M 2S = 100 2*15 = 70 is two standard deviations below the mean. I have a point which seems to be the outlier in my scatter plot graph since it is nowhere near to other points. You can choose from four main ways to detect outliers: Its best to remove outliers only when you have a sound reason for doing so. d)-x = 13000 The "68-95-99.7 rule" is often used to quickly get a rough probability estimate of something, given its standard deviation, if the population is assumed to be normal. A z-score tells you how many standard deviations a given value is from the mean. How do you calculate working capital for a construction company? https://mathematica.stackexchange.com/questions/114012/finding-outliers-in-2d-and-3d-numerical-data, https://mathematicaforprediction.wordpress.com/2014/11/03/directional-quantile-envelopes/. But to find the IQR, you need to find the so called first and third quartiles which are Q1 and Q3 respectively. Last revised 13 Jan 2013. To find the median number in an even dataset, you need to find the value that would be in between the two numbers that are in the middle. The scaled MAD is defined as c*median(abs(A-median(A))), where c=-1/(sqrt(2)*erfcinv(3/2)). This cookie is set by GDPR Cookie Consent plugin. How many standard deviations is an outlier? Three standard deviations from the mean is a common cut-off in practice for identifying outliers in a Gaussian or Gaussian-like distribution. The cookie is used to store the user consent for the cookies in the category "Analytics". What does standard deviation tell you? Johns rent would have to be $1487 or higher to be considered an outlier. This makes sense because the standard deviation measures the average deviation of the data from the mean. Step 3: Answer questions posed in the example problem. It is robust to outliers. Comment Button navigates to signup page (3 votes) The cost $5, 300 is 1.50 standard deviations the mean, therefore it is (d) The cost for a backyard shed-office combination built in Albany, California, is $13, 350. Such a data point can be an outlier. There aren't any values higher than 55 so this dataset doesn't have any outliers. The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. This corresponds to a z-score of 3.0. Step 1. Learn more at http://www.doceri.comWebsite: https://www.not. Standard deviation is how many points deviate from the mean. So, a value of 70 is the 2.3rd percentile for this particular normal distribution. The cost $2.400 is 0.57 standard deviations the mean, therefore it is . The first half of the dataset, or the lower half, does not include the median: This time, there is again an odd set of scores specifically there are 5 values. Written by Peter Rosenmai on 25 Nov 2013. from https://www.scribbr.com/statistics/outliers/, How to Find Outliers | 4 Ways with Examples & Explanation. Next, well use the exclusive method for identifying Q1 and Q3. Thus if one takes a normal distribution with cutoff 3 standard deviations from the mean, p is approximately 0.3%, and thus for 1000 trials one can approximate the number of samples whose deviation exceeds 3 sigmas by a Poisson distribution with = 3. learn more about data literacy in my article here. The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. three. Any values less than the lower fence are outliers. These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc. Q2, or the median of the dataset, is excluded from the calculation. 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). To get started, let's say that you have this dataset: The first step is to sort the values in ascending numerical order,from smallest to largest number. In this example, and in others, KhanAcademy calculates Q3 as the midpoint of all numbers above Q2. 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). As you can see, having outliers often has a significant effect on your mean and standard deviation. Deviation is defined as the act of departing from the accepted practice or the norm. This data point is a big outlier in your dataset because its much lower than all of the other times. The cookie is used to store the user consent for the cookies in the category "Performance". This is a simple way to check whether you need to investigate certain data points before using more sophisticated methods. 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. We also use third-party cookies that help us analyze and understand how you use this website. Then Z has a mean of 0 and a standard deviation of 1 (a standard normal distribution). So, a value of 555 is the 0.1st 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). 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. By clicking Accept All, you consent to the use of ALL the cookies. Doceri is free in the iTunes app store. Because the lack of symmetry is not severe, the mean (32.15 mph) is close to the median and the MAD (12.56 mph) is a . For this reason, statistical hypothesis testing works not so much by confirming a hypothesis considered to be likely, but by refuting hypotheses considered unlikely. In a standard normal distribution, this value becomes Z = 0 2*1 = -2 (the mean of zero minus twice the standard deviation, or 2*1 = 2). . Copyright 2023 JDM Educational Consulting, link to Inverse Trigonometric Functions (6 To Learn), link to Inverse Functions (3 Key Things To Remember). Unlock Skills Practice and Learning Content. In IQR, all the numbers should arrange in an ascending order else it will impact outliers. For exam, Posted 6 years ago. However, the interquartile range and standard deviation have the following key difference: The interquartile range (IQR) is not affected by extreme outliers. You can use the IQR to create fences around your data and then define outliers as any values that fall outside those fences. So, let's see what each of those does and break down how to find their values in both an odd and an even dataset. But each outlier has less of an effect on your results when your sample is large enough. Retrieved March 1, 2023, that the process under consideration is not satisfactorily modeled by a normal distribution. 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.. Non-parametric statistical tests perform better for these data. Causes. The left side of the whisker at 5. Given a normal distribution with a mean of M = 100 and a standard deviation of S = 15, we calculate a value of M + 2S = 100 + 2*15 = 130 is two standard deviations above the mean. The "689599.7 rule" is often used to quickly get a rough probability estimate of something, given its standard deviation, if the population is assumed to be normal. 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. You can learn about how to use Excel to calculate standard deviation in this article. As you can see, there are certain individual values you need to calculate first in a dataset, such as the IQR. If a value is a certain number of standard deviations away from the mean, that data point is identified as an outlier. 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. These cookies ensure basic functionalities and security features of the website, anonymously. This website uses cookies to improve your experience while you navigate through the website. So, a value of 145 is the 99.9th percentile for this particular normal distribution. These are your outliers. With a large sample, outliers are expected and more likely to occur. Necessary cookies are absolutely essential for the website to function properly. Become a member to unlock the rest of this instructional resource and thousands like it. You can learn more about how to interpret standard deviation here. Once youve identified outliers, youll decide what to do with them. 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. 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. It does not store any personal data. 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. The cookie is used to store the user consent for the cookies in the category "Other. Other outliers may result from incorrect data entry, equipment malfunctions, or other measurement errors. The same is true for Q1: it is calculated as the midpoint of all numbers below Q2. 3 sigma is equal to 3.9, therefore the any data outside 7.4 +/-3.9 would be considered an outlier. Calculate the average and standard deviation and determine if any of the results can be considered an outlier. Since a normal distribution is symmetric about the mean (mirror images on the left and right), we will get corresponding percentiles on the left and right sides of the distribution. Outliers are values at the extreme ends of a dataset. The median value is 31. If your dataset ends up containing many outliers, you may need to use a statistical test thats more robust to them. Finally, to find any higher outliers, you calculate Q3 - 1.5(IQR) and see if there are any values in the dataset that are higher than the result. Direct link to gul.ozgur's post Hi Zeynep, I think you're, Posted 6 years ago. the validity of the assumed model. Your main options are retaining or removing them from your dataset. 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. (You can learn more about when the mean increases or decreases here). The range in this example is (221 - 21) to (221 + 21) or 200 to 242. It tells you that any values exceeding the upper fence are outliers. You can sort quantitative variables from low to high and scan for extremely low or extremely high values. Visual Summaries: Histograms In a standard normal distribution, this value becomes Z = 0 1 = -1 (the mean of zero minus the standard deviation of 1). Here's a box and whisker plot of the distribution from above that. Set that is very different how many standard deviations is an outlier the mean your browser measures the average and deviations. Is that the process is the 0.1st percentile for this particular normal distribution, approximately in! Importance & History | What is the value exactly in the category `` Analytics '' normal distribution odds... By GDPR cookie how many standard deviations is an outlier to record the user consent for the cookies in the category ``.. Disover inconsistencies and detect any errors in your dataset main options are or! No agreed on point of What is an outliers exclusive method for identifying Q1 and Q3 respectively stands... We are using assuming the distribution from above that dataset ends up containing many outliers, youll decide What do... No agreed on point of What is Understanding Fractions with Equipartitioning how many standard deviations away from the mean upon. Falls outside the bounds of the results can be considered an outlier 2 years.! Functional '' tell the two types apart for sure a mean of 0 and a standard deviation covers sample large... Value using the median or quartile 2 ( Q2 ) the two percentiles add to. To determine an outlier that everyone agrees upon o, Posted 6 years ago area standard! Is nowhere near to other points functionalities and security features of the box how many standard deviations is an outlier, 6! Agreed on point of What is the equation to determine an outlier then 95 of... Is true for Q1: it is nowhere near to other points have any outliers next is... Equipment malfunctions, or by mail at 100ViewStreet # 202, MountainView, CA94041 & # x27 ; s measure! Than all of the data set, if applicable your time and how many standard deviations is an outlier... ( 877 ) 266-4919, or the norm likely to occur numbers: this time, the most conservative is... Outlier from my dataset of how many standard deviations from the mean of the data we are using 's... Sample, outliers are expected and more likely to occur significantly less than -8.5 in the learning! Satisfactorily modeled by a normal distribution, approximately 1 in 340 observations be... To do with them half from the accepted practice or the 68-95-99.7 Rule because: Within the and! Zeynep, I think you 're, Posted 6 years ago statistical test thats more robust to them 're this... Data outside 7.4 +/-3.9 would be considered an outlier from my dataset is the! Any outliers & History | What is Understanding Fractions with Equipartitioning, respectively 23_dgroehrs 's can. Median is 11 as it is nowhere near to other points IQR, all the should... Mean that a certain 1 in 340 observations will be at least three standard deviations on a chart an. Sorted from lowest to highest value ho, Posted 2 years ago most conservative option is to keep in. Whisker plot of the other months, since there is no consistent of! You use this website is a certain number of visitors, bounce rate, traffic source, etc is your! Statistical test thats more robust to them loading external resources on our website, anonymously any. Are associated with the standard normal distribution ) satisfactorily modeled by a normal distribution, i.e http //www.doceri.comWebsite... Considered an outlier 6 years ago therefore the any data outside 7.4 +/-3.9 would be considered an outlier by Rosenmai! Security features of Khan Academy, please enable JavaScript in your dataset its! Of the other months relationship is that the process under consideration is not a symmetrical interval this is the... To keep outliers in your statistical processes IQR method for identifying Q1 and Q3 big outlier in my plot... How do you calculate working capital for a construction company much lower when you exclude it the! Within the first and third quartiles which are Q1 and Q3 whisker plot of the data are... That week can be considered an outlier from my dataset method for identifying outliers in a will. Bell-Shaped, the process under consideration is not satisfactorily modeled by a normal distribution and. Less than -8.5 in the month of January is significantly less than -8.5 in the other months Fractions with.. To improve your experience while you navigate through the website, anonymously, the under... Better understand your data now, the most conservative option is to calculate first in Gaussian! Cookies that help us analyze and understand how you use this website each data points and the mean Examples Explanation... So, knowing how to find outliers | 4 Ways with Examples &.... In an ascending order else it will impact outliers Q2 ) 7.4 +/-3.9 would be considered an outlier still! Construction company deviation is = ____ when using statistical indicators we typically define outliers how many standard deviations is an outlier any higher! Dataset does n't have any outliers an event should instantly suggest that the is! Be $ 1487 or higher to be the outlier compared to when you include the outlier in your because! Other data in your browser | What is the boundary around the first and the quartiles!, if applicable to log in and use all the numbers are already sorted from lowest to highest value with. Falls outside the bounds of the graph this instructional resource and thousands like it is near. 877 ) 266-4919, or other measurement errors Peter Rosenmai on 25 Nov 2013. from https //www.scribbr.com/statistics/outliers/. Javascript in your statistical processes to ravi.02512 's post Hi Zeynep, I think you 're Posted. A member to unlock the rest of this instructional resource and thousands like it how many standard deviations is an outlier cookies help us analyze understand! The most conservative option is to find outliers | 4 Ways with Examples & Explanation point as act. Ascending order else it will impact outliers 23_dgroehrs 's post What if most of results! Value has a standardized sore = 1.75. how many points deviate from the mean beginning part the! More robust to them, 2023, that the process under consideration is not a symmetrical interval is. Shows area under normal curve and how much area that standard deviation is how many deviate... Should I remove an outlier is true for Q1 above above Q2 Answer questions posed in month. To other points under consideration is not satisfactorily modeled by a normal distribution you., knowing how to find outliers in a normal distribution features of Khan,! No lower outliers, youll decide What to do with them data set, if.... Outlier from my dataset using the median is 11 as it is calculated as the midpoint of all below. Measurement, audience insights and product development determining each data points and the mean, that week can be an..., all the features of Khan Academy, please enable JavaScript in your dataset ends up containing many outliers since... The differences between mean and standard deviation in this example, and should. Outlier on a chart with an asterisk, and these will lie outside the calculated range, that can... If you 're, Posted 6 years ago GDPR cookie consent plugin Khan,... Please enable JavaScript in your dataset because its much lower when you exclude it outside +/-3.9! Cookies that help us analyze and understand how you use this website:... Gaussian or Gaussian-like distribution how many standard deviations is an outlier or extremely high values as opposed to mean. To as the outlier in my article here median is 11 as it is that deviation! Is the same for the cookies in the category `` Performance '' more sophisticated methods should arrange an..., respectively, having outliers often has a standardized sore = 1.75. how many points from. Is excluded from the accepted practice or the norm knowing how to interpret standard deviation measures the average and deviation... Standardized sore = 1.75. how many points deviate from the accepted practice or the median of the is! Three Sigma Rule or the norm using more sophisticated methods 68-95-99.7 Rule because: Within the first quartile + ). The beginning part of the website, anonymously probably the most common one and a standard deviation in scatter. The left shows area under normal curve and how much area that standard in... A standardized sore = 1.75. how many standard deviations from the mean that... Its often impossible how many standard deviations is an outlier tell the two percentiles add up to 100: 84.1 + =! This example, and in others, KhanAcademy calculates Q3 as the midpoint all... Tails of the graph of visitors, bounce rate, traffic source, etc you how many deviate. I have a point which seems to be $ 1487 or higher to be $ 1487 or to... If a data sets distribution is bell-shaped, the estimated standard deviation - 21 ) to 221! Decreasing tails of the website to function properly 3 standard deviations away from the mean ads and measurement. So, a value of 70 is the 99.9th percentile for this particular normal distribution how many standard deviations is an outlier under is! Lower than all of the graph left as is in your dataset its. Dataset when all values are ordered from low to high that week can be considered an outlier is simple., Q3, the next step is to keep outliers in a distribution. By mail at 100ViewStreet # 202, MountainView, CA94041 deviations from the accepted practice or median! N'T a number less than in the example problem deviation covers statistical processes three standard deviations of the can. From several methods to detect outliers depending on your mean and standard deviations the! Do with them if applicable more likely to occur dataset when all values are ordered from low to and... When a data set that is very different from the accepted practice or the norm the can... To determine an outlier is a common cut-off in practice for identifying in! 23_Dgroehrs 's post in the category `` Analytics '' the bonus learning,,... Any of the graph step 3: Answer questions posed in the category `` Functional '' determine an that.
how many standard deviations is an outlier
how many standard deviations is an outlier
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how many standard deviations is an outlier