Bookdown
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13.5 Identifying outliers | Scientific Research and Methodology
This suggests a rule for identifying outliers in approximately bell-shaped distributions: any observation more than 3 standard deviations away from the mean is unusual, so may be considered an outlier.
Reddit
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r/APStatistics on Reddit: Outliers using Standard Deviation
September 13, 2024 -
I was doing some review and was wondering which way outliers are found using the standard deviation rule. Some methods say any value 2 SD above or below the mean is an outlier while other methods say 3 SD above or below the mean.
Top answer 1 of 3
7
On the exam, it will be 1.5 IQR beyond Q1 and Q3. But there is no definitive rule about when values become extreme-this is all based on context. Without context, start with 2SD but make your analysis make sense based on the case study
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ive seen this on the ap recently and they used the 2sd rule. it isnt really a hard case so be careful. iirc they mentioned using the 2sd rule so kids wont use the iqr rule
Videos
shorthand used in statistics
Wikipedia
en.wikipedia.org βΊ wiki βΊ 68β95β99.7_rule
68β95β99.7 rule - Wikipedia
1 week ago - In statistics, the 68β95β99.7 rule, also known as the empirical rule or 68β95β99.7 rule for a normal distribution and sometimes abbreviated 3SR or 3 Ο, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately ...
Study.com
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Determining Outliers Using Standard Deviation | Statistics and Probability | Study.com
Step 2: Determine if any results are greater than +/- 3 times the standard deviation. 3 sigma is equal to 3.9, therefore the any data outside 7.4 +/-3.9 would be considered an outlier.
Top answer 1 of 4
30
Some outliers are clearly impossible. You mention 48 kg for baby weight. This is clearly an error. That's not a statistical issue, it's a substantive one. There are no 48 kg human babies. Any statistical method will identify such a point.
Personally, rather than rely on any test (even appropriate ones, as recommended by @Michael) I would graph the data. 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.
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 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.
But what if the distribution is wrong? Suppose, in the population, the variable in question is not normally distributed but has heavier tails than that?
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Yes. It is a bad way to "detect" oultiers. For normally distributed data, such a method would call 5% of the perfectly good (yet slightly extreme) observations "outliers". 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. The maximum and minimum of a normally distributed sample is not normally distributed. So the test should be based on the distribution of the extremes. That is what Grubbs' test and Dixon's ratio test do as I have mention several times before. Even when you use an appropriate test for outliers an observation should not be rejected just because it is unusually extreme. You should investigate why the extreme observation occurred first.
Statistics LibreTexts
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12.7: Outliers - Statistics LibreTexts
April 2, 2023 - However, we would like some guideline as to how far away a point needs to be in order to be considered an outlier. As a rough rule of thumb, we can flag any point that is located further than two standard deviations above or below the best-fit line ...
Highbond
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Identifying outliers
In Number of times of S.dev, specify a multiple of the standard deviation to use for the outlier boundaries. You can specify any positive integer or decimal numeral (0.5, 1, 1.5, 2 .
Netlify
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13.5 Identifying outliers | Scientific Research Methods
This suggests a rule for identifying outliers in approximately bell-shaped distributions: any observation more than 3 standard deviations away from the mean is unusual, so may be considered an outlier.
KDnuggets
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Removing Outliers Using Standard Deviation in Python - KDnuggets
According to the Wikipedia article on normal distribution, about 68% of values drawn from a normal distribution are within one standard deviation Ο away from the mean; about 95% of the values lie within two standard deviations; and about 99.7% ...
Brainly
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{14, 22, 9, 15, 20, 17, 12, 11}
[FREE] Use the standard deviation to identify any outliers in the given data set. {14, 22, 9, 15, 20, 17, 12, 11} - brainly.com
Standard deviation β β17.5 β 4.18 (rounded to two decimal places) Identify potential outliers. Using the rule of thumb, any data point that is more than 2 standard deviations away from the mean can be considered an outlier.
YouTube
youtube.com βΊ watch
Identifying univariate outliers using the 2 standard deviation method in SPSS - YouTube
Identifying univariate outliers using the 2 standard deviation method in SPSS
Published Β June 12, 2017
ScienceDirect
sciencedirect.com βΊ science βΊ article βΊ abs βΊ pii βΊ S0022103113000668
Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median - ScienceDirect
March 27, 2013 - Given the results of our survey of two journals, emphasizing a poor management of outliers, we showed that the method conventionally used (βThe mean plus or minus three standard deviationsβ rule) is problematic and we argued in favor of a robust alternative. We have finally explained that, whatever the method selected, the decision-making concerning the exclusion criteria of outliers (a deviation of 3, 2.5 or 2 units) is necessarily subjective.
YouTube
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Using the mean and standard deviation to identify outliers - YouTube
This video screencast was created with Doceri on an iPad. Doceri is free in the iTunes app store. Learn more at http://www.doceri.comWebsite: https://www.not...
Published Β January 22, 2022
Statistics By Jim
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5 Ways to Find Outliers in Your Data - Statistics By Jim
September 30, 2025 - For example, a Z-score of 2 indicates that an observation is two standard deviations above the average while a Z-score of -2 signifies it is two standard deviations below the mean.
Towards Data Science
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Outlier Detection (Part 1) | Towards Data Science
March 5, 2025 - This is because 2 times stdev implies a stricter limit set and majority of the probable extreme points are already removed by the procedure. Only few are remaining after the removal and those are still considered outlier when a new boxplot is ...
Wikipedia
en.wikipedia.org βΊ wiki βΊ Outlier
Outlier - Wikipedia
1 month ago - In a sample of 1000 observations, the presence of up to five observations deviating from the mean by more than three times the standard deviation is within the range of what can be expected, being less than twice the expected number and hence within 1 standard deviation of the expected number β see Poisson distribution β and not indicate an anomaly. If the sample size is only 100, however, just three such outliers are already reason for concern, being more than 11 times the expected number.
Quora
quora.com βΊ What-is-the-two-standard-deviation-rule
What is the two standard deviation rule? - Quora
Answer (1 of 5): If your data is ... then approximately 95% of the observations will fall between the values the mean minus two times the standard deviation and the mean plus two times the standard deviations....
PubMed Central
pmc.ncbi.nlm.nih.gov βΊ articles βΊ PMC8801745
Multiple Desirable Methods in Outlier Detection of Univariate Data With R Source Codes - PMC
As a result, 56 papers (about half ... the method βthe conventional methodβ in this article. In this method, outliers are the values which do not fall within the mean Β± x times standard deviation (x = 2 or 2.5 are common; Leys et al., 2013; Yang et al., 2019)....
Quora
quora.com βΊ What-is-the-standard-deviation-Can-it-be-used-to-find-outliers-in-any-type-of-data-not-just-normally-distributed
What is the standard deviation? Can it be used to find outliers in any type of data (not just normally distributed)? - Quora
Answer (1 of 2): TL;DR: Yes, the standard deviation can be used to find outliers in any type of distribution, but it might not be used, depending on the method used to identify outliers. Standard deviation, Ο, is one means of measuring the βspreadβ, or variation, in a set of data.
Medium
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Detecting and Removing Outliers in Data: A Comprehensive Guideππ | by Lomash Bhuva | Medium
February 9, 2025 - According to this rule: About 68% of data points fall within one standard deviation of the mean. About 95% fall within two standard deviations. Roughly 99.7% are found within three standard deviations.