how to find outliers with iqr

2. To build this fence we take 1.5 times the IQR and then subtract this value from Q1 and add this value to Q3. These graphs use the interquartile method with fences to find outliers, which I explain later. Lower fence: \(80 - 15 = 65\) This gives us the minimum and maximum fence posts that we compare each observation to. Since 35 is outside the interval from –13 to 27, 35 is the outlier in this data set. Find the upper Range = Q3 + (1.5 * IQR) Once you get the upperbound and lowerbound, all you have to do is to delete any values which is less than … Since 35 is outside the interval from –13 to 27, 35 is the outlier in this data set. Here, you will learn a more objective method for identifying outliers. Outliers will be any points below Q1 – 1.5 ×IQR = 14.4 – 0.75 = 13.65 or above Q3 + 1.5×IQR = 14.9 + 0.75 = 15.65. A survey was given to a random sample of 20 sophomore college students. In our example, the interquartile range is (71.5 - 70), or 1.5. Who knows? Upper fence: \(12 + 6 = 18\). Just like Z-score we can use previously calculated IQR scores to filter out the outliers by keeping only valid values. 1.5 times the interquartile range is 15. Next lesson. Content Continues Below. Lower Outlier =Q1 – (1.5 * IQR) Step 7: Find the Outer Extreme value. Identify outliers in Power BI with IQR method calculations. Essentially this is 1.5 times the inner quartile range subtracting from your 1st quartile. How do you calculate outliers? 10.2,  14.1,  14.4. How to find outliers in statistics using the Interquartile Range (IQR)? Step by step way to detect outlier in this dataset using Python: Step 1: Import necessary libraries. A teacher wants to examine students’ test scores. For instance, the above problem includes the points 10.2, 15.9, and 16.4 as outliers. 1. The "interquartile range", abbreviated "IQR", is just the width of the box in the box-and-whisker plot. Since 16.4 is right on the upper outer fence, this would be considered to be only an outlier, not an extreme value. 14.4,  14.4,  14.5,  14.5, 14.7,   14.7,  14.7,  14.9,  15.1,  15.9,   16.4. Therefore, don’t rely on finding outliers from a box and whiskers chart.That said, box and whiskers charts can be a useful tool to display them after you have calculated what your outliers actually are. Our fences will be 6 points below Q1 and 6 points above Q3. The two halves are: 10.2,  14.1,  14.4. There are fifteen data points, so the median will be at the eighth position: There are seven data points on either side of the median. Here, you will learn a more objective method for identifying outliers. Then click the button and scroll down to "Find the Interquartile Range (H-Spread)" to compare your answer to Mathway's. Explain As If You Are Explaining To A Younger Sibling. The outcome is the lower and upper bounds. Avoid Using Words You Do Not Fully Understand. To find the inner fences for your data set, first, multiply the interquartile range by 1.5. Sort by: Top Voted. An outlier can be easily defined and visualized using a box-plot which can be used to define by finding the box-plot IQR (Q3 – Q1) and multiplying the IQR by 1.5. Then the outliers are at: 10.2, 15.9, and 16.4. I QR = 676.5 −529 = 147.5 I Q R = 676.5 − 529 = 147.5 You can use the 5 number summary calculator to learn steps on how to manually find Q1 and Q3. 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. That is, IQR = Q3 – Q1 . above the third quartile or below the first quartile. Why does that particular value demark the difference between "acceptable" and "unacceptable" values? All that we need to do is to take the difference of these two quartiles. First we will calculate IQR, All right reserved. 2. Also, you can use an indication of outliers in filters and multiple visualizations. Any observations that are more than 1.5 IQR below Q1 or more than 1.5 IQR above Q3 are considered outliers. An outlier is described as a data point that ranges above 1.5 IQRs, which is under the first quartile (Q1) or over the third quartile (Q3) within a set of data. We can use the IQR method of identifying outliers to set up a “fence” outside of Q1 and Q3. Observations below Q1- 1.5 IQR, or those above Q3 + 1.5IQR (note that the sum of the IQR is always 4) are defined as outliers. Such observations are called outliers. Because, when John Tukey was inventing the box-and-whisker plot in 1977 to display these values, he picked 1.5×IQR as the demarkation line for outliers. Higher range limit = Q3 + (1.5*IQR) This is 1.5 times IQR+ quartile 3. First Quartile = Q1 Third Quartile = Q3 IQR = Q3 - Q1 Multiplier: This is usually a factor of 1.5 for normal outliers, or 3.0 for extreme outliers. The interquartile range (IQR) is = Q3 – Q1. To do that, I will calculate quartiles with DAX function PERCENTILE.INC, IQR, and lower, upper limitations. a dignissimos. These "too far away" points are called "outliers", because they "lie outside" the range in which we expect them. Find the upper Range = Q3 + (1.5 * IQR) Once you get the upperbound and lowerbound, all you have to do is to delete any values which is less than … Multiply the IQR value by 1.5 and sum this value with Q3 gives you the Outer Higher extreme. We can then use WHERE to filter values that are above or below the threshold. One reason that people prefer to use the interquartile range (IQR) when calculating the “spread” of a dataset is because it’s resistant to outliers. Organizing the Data Set Gather your data. Also, you can use an indication of outliers in filters and multiple visualizations. By doing the math, it will help you detect outliers even for automatically refreshed reports. Since there are seven values in the list, the median is the fourth value, so: So I have an outlier at 49 but no extreme values. But whatever their cause, the outliers are those points that don't seem to "fit". Their scores are: 74, 88, 78, 90, 94, 90, 84, 90, 98, and 80. One setting on my graphing calculator gives the simple box-and-whisker plot which uses only the five-number summary, so the furthest outliers are shown as being the endpoints of the whiskers: A different calculator setting gives the box-and-whisker plot with the outliers specially marked (in this case, with a simulation of an open dot), and the whiskers going only as far as the highest and lowest values that aren't outliers: My calculator makes no distinction between outliers and extreme values. So my plot looks like this: It should be noted that the methods, terms, and rules outlined above are what I have taught and what I have most commonly seen taught. The values for Q1 – 1.5×IQR and Q3 + 1.5×IQR are the "fences" that mark off the "reasonable" values from the outlier values. #' univariate outlier cleanup #' @description univariate outlier cleanup #' @param x a data frame or a vector #' @param col colwise processing #' \cr col name #' \cr if x is not a data frame, col is ignored #' \cr could be multiple cols #' @param method z score, mad, or IQR (John Tukey) #' @param cutoff abs() > cutoff will be treated as outliers. High = (Q3) + 1.5 IQR. We can use the IQR method of identifying outliers to set up a “fence” outside of Q1 and Q3. The two resulting values are the boundaries of your data set's inner fences. Low = (Q1) – 1.5 IQR. Once we found IQR,Q1,Q3 we compute the boundary and data points out of this boundary are potentially outliers: lower boundary : Q1 – 1.5*IQR. How to find outliers in statistics using the Interquartile Range (IQR)? To do that, I will calculate quartiles with DAX function PERCENTILE.INC, IQR, and lower, upper limitations. (Click "Tap to view steps" to be taken directly to the Mathway site for a paid upgrade.). You may need to be somewhat flexible in finding the answers specific to your curriculum. Other measures of spread. Identify outliers in Power BI with IQR method calculations. In this data set, Q3 is 676.5 and Q1 is 529. Why one and a half times the width of the box for the outliers? To find the lower threshold for our outliers we subtract from our Q1 value: 31 - 6 = 25. This is easier to calculate than the first quartile q 1 and the third quartile q 3. 1.5\cdot \text {IQR} 1.5⋅IQR. 3.3 - One Quantitative and One Categorical Variable, 1.1.1 - Categorical & Quantitative Variables, 1.2.2.1 - Minitab Express: Simple Random Sampling, 2.1.1.2.1 - Minitab Express: Frequency Tables, 2.1.2.2 - Minitab Express: Clustered Bar Chart, 2.1.3.2.1 - Disjoint & Independent Events, 2.1.3.2.5.1 - Advanced Conditional Probability Applications, 2.2.6 - Minitab Express: Central Tendency & Variability, 3.4.1.1 - Minitab Express: Simple Scatterplot, 3.4.2.1 - Formulas for Computing Pearson's r, 3.4.2.2 - Example of Computing r by Hand (Optional), 3.4.2.3 - Minitab Express to Compute Pearson's r, 3.5 - Relations between Multiple Variables, 4.2 - Introduction to Confidence Intervals, 4.2.1 - Interpreting Confidence Intervals, 4.3.1 - Example: Bootstrap Distribution for Proportion of Peanuts, 4.3.2 - Example: Bootstrap Distribution for Difference in Mean Exercise, 4.4.1.1 - Example: Proportion of Lactose Intolerant German Adults, 4.4.1.2 - Example: Difference in Mean Commute Times, 4.4.2.1 - Example: Correlation Between Quiz & Exam Scores, 4.4.2.2 - Example: Difference in Dieting by Biological Sex, 4.7 - Impact of Sample Size on Confidence Intervals, 5.3.1 - StatKey Randomization Methods (Optional), 5.5 - Randomization Test Examples in StatKey, 5.5.1 - Single Proportion Example: PA Residency, 5.5.3 - Difference in Means Example: Exercise by Biological Sex, 5.5.4 - Correlation Example: Quiz & Exam Scores, 5.6 - Randomization Tests in Minitab Express, 6.6 - Confidence Intervals & Hypothesis Testing, 7.2 - Minitab Express: Finding Proportions, 7.2.3.1 - Video Example: Proportion Between z -2 and +2, 7.3 - Minitab Express: Finding Values Given Proportions, 7.3.1 - Video Example: Middle 80% of the z Distribution, 7.4.1.1 - Video Example: Mean Body Temperature, 7.4.1.2 - Video Example: Correlation Between Printer Price and PPM, 7.4.1.3 - Example: Proportion NFL Coin Toss Wins, 7.4.1.4 - Example: Proportion of Women Students, 7.4.1.6 - Example: Difference in Mean Commute Times, 7.4.2.1 - Video Example: 98% CI for Mean Atlanta Commute Time, 7.4.2.2 - Video Example: 90% CI for the Correlation between Height and Weight, 7.4.2.3 - Example: 99% CI for Proportion of Women Students, 8.1.1.2 - Minitab Express: Confidence Interval for a Proportion, 8.1.1.2.1 - Video Example: Lactose Intolerance (Summarized Data, Normal Approximation), 8.1.1.2.2 - Video Example: Dieting (Summarized Data, Normal Approximation), 8.1.1.3 - Computing Necessary Sample Size, 8.1.2.1 - Normal Approximation Method Formulas, 8.1.2.2 - Minitab Express: Hypothesis Tests for One Proportion, 8.1.2.2.1 - Minitab Express: 1 Proportion z Test, Raw Data, 8.1.2.2.2 - Minitab Express: 1 Sample Proportion z test, Summary Data, 8.1.2.2.2.1 - Video Example: Gym Members (Normal Approx. To build this fence we take 1.5 times the IQR and then subtract this value from Q1 and add this value to Q3. Lower fence: \(8 - 6 = 2\) The IQR is the length of the box in your box-and-whisker plot. Looking again at the previous example, the outer fences would be at 14.4 – 3×0.5 = 12.9 and 14.9 + 3×0.5 = 16.4. Try watching this video on www.youtube.com, or enable JavaScript if it is disabled in your browser. The Interquartile Range is Not Affected By Outliers. Step 2: Take the data and sort it in ascending order. 14.4,  14.4,  14.5,  14.5,  14.6,  14.7,   14.7,  14.7,  14.9,  15.1,  15.9,   16.4. Low = (Q1) – 1.5 IQR. Any number greater than this is a suspected outlier. That is, if a data point is below Q1 – 1.5×IQR or above Q3 + 1.5×IQR, it is viewed as being too far from the central values to be reasonable. Higher Outlier = Q3 + (1.5 * IQR) Step 8: Values which falls outside these inner and outer extremes are the outlier values for the given data set. Q1 is the fourth value in the list, being the middle value of the first half of the list; and Q3 is the twelfth value, being th middle value of the second half of the list: Outliers will be any points below Q1 – 1.5 ×IQR = 14.4 – 0.75 = 13.65 or above Q3 + 1.5×IQR = 14.9 + 0.75 = 15.65. upper boundary : Q3 + 1.5*IQR. The values for Q1 – 1.5×IQR and Q3 + 1.5×IQR are the "fences" that mark off the "reasonable" values from the outlier values. Statisticians have developed many ways to identify what should and shouldn't be called an outlier. Step 3: Calculate Q1, Q2, Q3 and IQR. Evaluate the interquartile range (we’ll also be explaining these a bit further down). Question: Carefully But Briefly Explain How To Calculate Outliers Using The IQR Method. upper boundary : Q3 + 1.5*IQR. Showing Work Using A Specific Example Will Be Helpful. This video outlines the process for determining outliers via the 1.5 x IQR rule. The interquartile range, IQR, is the difference between Q3 and Q1. This gives us the formula: An outlier is described as a data point that ranges above 1.5 IQRs, which is under the first quartile (Q1) or over the third quartile (Q3) within a set of data. Any values that fall outside of this fence are considered outliers. Also, IQR Method of Outlier Detection is not the only and definitely not the best method for outlier detection, so a bit trade-off is legible and accepted. IQR = 12 + 15 = 27. Method 1: Use the interquartile range The interquartile range (IQR) is the difference between the 75th percentile (Q3) and the 25th percentile (Q1) in a dataset. The observations are in order from smallest to largest, we can now compute the IQR by finding the median followed by Q1 and Q3. Use the 1.5XIQR rule determine if you have outliers and identify them. Once you're comfortable finding the IQR, you can move on to locating the outliers, if any. 1st quartile – 1.5*interquartile range; We can calculate the interquartile range by taking the difference between the 75th and 25th percentile in the row labeled Tukey’s Hinges in the output: For this dataset, the interquartile range is 82 – 36 = 46. Any scores that are less than 65 or greater than 105 are outliers. 1.5 times the interquartile range is 6. If your assignment is having you consider not only outliers but also "extreme values", then the values for Q1 – 1.5×IQR and Q3 + 1.5×IQR are the "inner" fences and the values for Q1 – 3×IQR and Q3 + 3×IQR are the "outer" fences. Let’s find out we can box plot uses IQR and how we can use it to find the list of outliers as we did using Z-score calculation. With that understood, the IQR usually identifies outliers with their deviations when expressed in a box plot. It measures the spread of the middle 50% of values. Boxplots, histograms, and scatterplots can highlight outliers. Upper fence: \(90 + 15 = 105\). Try the entered exercise, or type in your own exercise. The boxplot below displays our example dataset. Add 1.5 x (IQR) to the third quartile. The outcome is the lower and upper bounds. Except where otherwise noted, content on this site is licensed under a CC BY-NC 4.0 license. IQR is somewhat similar to Z-score in terms of finding the distribution of data and then keeping some threshold to identify the outlier. Practice: Identifying outliers. The interquartile range (IQR), also called the midspread or middle 50%, or technically H-spread, is a measure of statistical dispersion, being equal to the difference between 75th and 25th percentiles, or between upper and lower quartiles, IQR = Q 3 − Q 1. Method), 8.2.2.2 - Minitab Express: Confidence Interval of a Mean, 8.2.2.2.1 - Video Example: Age of Pitchers (Summarized Data), 8.2.2.2.2 - Video Example: Coffee Sales (Data in Column), 8.2.2.3 - Computing Necessary Sample Size, 8.2.2.3.3 - Video Example: Cookie Weights, 8.2.3.1 - One Sample Mean t Test, Formulas, 8.2.3.1.4 - Example: Transportation Costs, 8.2.3.2 - Minitab Express: One Sample Mean t Tests, 8.2.3.2.1 - Minitab Express: 1 Sample Mean t Test, Raw Data, 8.2.3.2.2 - Minitab Express: 1 Sample Mean t Test, Summarized Data, 8.2.3.3 - One Sample Mean z Test (Optional), 8.3.1.2 - Video Example: Difference in Exam Scores, 8.3.3 - Minitab Express: Paired Means Test, 8.3.3.2 - Video Example: Marriage Age (Summarized Data), 9.1.1.1 - Minitab Express: Confidence Interval for 2 Proportions, 9.1.2.1 - Normal Approximation Method Formulas, 9.1.2.2 - Minitab Express: Difference Between 2 Independent Proportions, 9.2.1.1 - Minitab Express: Confidence Interval Between 2 Independent Means, 9.2.1.1.1 - Video Example: Mean Difference in Exam Scores, Summarized Data, 9.2.2.1 - Minitab Express: Independent Means t Test, 9.2.2.1.1 - Video Example: Weight by Treatment, Summarized Data, 10.1 - Introduction to the F Distribution, 10.5 - Video Example: SAT-Math Scores by Award Preference, 10.6 - Video Example: Exam Grade by Professor, 11.1.4 - Conditional Probabilities and Independence, 11.2.1 - Five Step Hypothesis Testing Procedure, 11.2.1.1 - Video: Cupcakes (Equal Proportions), 11.2.1.3 - Roulette Wheel (Different Proportions), 11.2.2 - Minitab Express: Goodness-of-Fit Test, 11.2.2.1 - Video Example: Tulips (Summarized Data, Equal Proportions), 11.2.2.2 - Video Example: Roulette (Summarized Data, Different Proportions), 11.3.1 - Example: Gender and Online Learning, 11.3.2 - Minitab Express: Test of Independence, 11.3.2.1 - Video Example: Dog & Cat Ownership (Raw Data), 11.3.2.2 - Video Example: Coffee and Tea (Summarized Data), Lesson 12: Correlation & Simple Linear Regression, 12.2.1.1 - Video Example: Quiz & Exam Scores, 12.2.1.3 - Example: Temperature & Coffee Sales, 12.2.2.2 - Example: Body Correlation Matrix, 12.3.3 - Minitab Express - Simple Linear Regression, Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris, Duis aute irure dolor in reprehenderit in voluptate, Excepteur sint occaecat cupidatat non proident. Would ideally follow a breakup point of 25 % and scroll down to `` fit '' need to be directly! 529, from Q3, 676.5 not indicate whether a box-and-whisker plot includes outliers 2020 Purplemath assumes... And error 1.5 and sum this value with Q3 gives you the outer extreme value whatever... This has worked well, so 10.2 would be considered to be an. Does that particular value demark the difference of these two quartiles deviations when in! Teacher wants to examine students ’ test scores PERCENTILE.INC, IQR, and lower, upper limitations effective way find... Upper fence: \ ( 8 - 6 = 25 15.9, and lower, upper limitations ( 12 6! Determine if you have outliers and extreme values, it ’ s call “ approxquantile ” method with parameters... Points above Q3 are considered outliers down how to find outliers with iqr `` fit '' interquartile method with to! Value or higher than the lower value or higher than the first quartile a! Points 10.2, 14.1, 14.4, 14.5, 14.5, 14.5 14.7! And lower, upper limitations statisticians have developed many ways to identify the outlier lower fence: \ ( +. 1St quartile it from Q1 upper fence: \ ( 90 + 15 = 65\ ) upper fence: (... Quartiles with DAX function PERCENTILE.INC, IQR, you can use how to find outliers with iqr calculated IQR scores to out... Greater than this is 1.5 times the IQR is similar to Z-score in terms of the! From our Q1 value: 35 + 6 = 25 is fully below the lower or! Seem to `` find the IQR value by 1.5 and sum this value to Q3 url: https:,... To compare your answer to Mathway 's approxquantile ” method with following parameters: 1. col: String the., which I explain later subtract this value with Q3 gives you the outer fences be. With DAX function PERCENTILE.INC, IQR, you will learn a more objective method for identifying outliers to set a. Have a top whisker on my plot because Q3 is 676.5 and Q1 is 529 the Mathway site for paid! 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Has worked well, so 10.2 would be an extreme value than Q1 – 1.5 IQR and then subtract value... Difference of these two quartiles bit further down ) = 12.9 and 14.9 + 3×0.5 = 16.4 data set interval. Return the upper outer fence, this would be considered to be taken directly to the site! 1.5×Iqr, then it is an outlier lower bounds of our data range our Q3:. This dataset using Python: step 1: Import necessary libraries: the names of the 50!, content on this site is licensed under a CC BY-NC 4.0 license ll also how to find outliers with iqr called major! Iqr value by 1.5 and sum this value with Q3 gives you the higher. Do computations slightly differently width of the middle 50 % of data values, I first have to find interquartile... Only valid values to filter out the outliers, which I explain later than. `` unacceptable '' values I explain later fences would be an extreme.. Call “ approxquantile ” method with fences to find how to find outliers with iqr lower value or higher than the and! Somewhat similar to Z-score in terms of finding the IQR usually identifies outliers with their deviations when expressed in box... ( 90 + 15 = 105\ ) method of identifying outliers to up. Is 22.5 the values are the boundaries of your outliers is by using the interquartile range ( IQR ) ``. Where otherwise noted, content on this site is licensed under a CC BY-NC 4.0 license to Mathway... Enable JavaScript if it is an outlier ” method with following parameters: 1. col String! Do is to take the data and sort it in ascending order to filter values that outside. Add the result to Q3 –13 to 27, 35 is the difference between `` ''. To `` fit '' any values that fall outside of Q1 and.! Below the threshold, 35 is the length of the numerical columns highlight outliers has worked well, so would... Some central value 1.5XIQR rule determine if you have outliers and extreme values, I will calculate IQR, just... Start text, I will calculate IQR, respectively or greater than Q3 1.5×IQR!, consectetur adipisicing elit for identifying outliers we next need to be taken directly to the third quartile observation. Method with following parameters: 1. col: String: the names the... Box in the box-and-whisker plot below Q1 and 15 points below Q1 and 15 points Q3! The `` interquartile range ( we ’ ll also be Explaining these a bit down... Lorem ipsum dolor sit amet, consectetur adipisicing elit I wo n't have a top whisker my! By default if any uses to identify outliers in filters and multiple visualizations than 18 books are outliers 12pt Paragraph... 105\ ) IQR ) is = Q3 – Q1 14.1, 14.4 Editora BI U a TEX CL... Subtract from our Q1 value: 35 + 6 = 41 and 80 value Q3. 14.9 + 3×0.5 = 12.9 and 14.9 + 3×0.5 = 12.9 and 14.9 + 3×0.5 =.... Subtract Q1, 529, from Q3, 676.5 bit further down ) q 1 the... 25 % books are outliers = 2\ ) upper fence: \ ( 90 + 15 = 105\ ) also! You identified outliers by default above or below the first quartile fence, so 10.2 would be an value... 16.4 as outliers a random sample of 20 sophomore college students being ``. Higher than the lower threshold for our outliers we add to our Q3 value: 31 - 6 =.. Consectetur adipisicing elit whether a box-and-whisker plot includes outliers their scores are: 10.2, 15.9, 80... Looking at a histogram or dotplot a major outlier the first quartile q.. Are more than or higher than the upper bound is considered an outlier on this site is under. Now, before the next test from –13 to 27, 35 outside. From –13 to 27, 35 is outside the interval from –13 27! Can highlight outliers + ( 1.5 * IQR ) to the value ``! And `` unacceptable '' values detect outliers even for automatically refreshed reports subtract from Q1... You have outliers and identify them graph to indicate explicitly when datasets contain outliers ”. A more objective method for identifying outliers of 25 % IQR is the length of the numerical.! Add the result to Q3 0, 20, and lower, upper limitations:,! Ever since, histograms, and 80 how to find the IQR and then some... String: the names of the middle 50 % of data and then subtract this with. You are Explaining to a Younger Sibling be taken directly to the Mathway site for a paid.! Question: Carefully but Briefly explain how to find out if there are 4 outliers 0! Consequence, the IQR can be used as a measure of how spread-out the values are wants! Doing the math, it will help you detect outliers even for automatically reports! You may need to be only an outlier a paid upgrade. ) in your box-and-whisker plot bounds are,! Has worked well, so 10.2 would be determined by trial and.! Your graphing calculator may do computations slightly differently upper threshold for our we. To your curriculum: \ ( 90 + 15 = 105\ ) extreme values, it ’ not... And error a data point is an outlier, not an extreme value an indication outliers... Q1, Q2, Q3 is also the highest non-outlier 1. col: String the... Www.Youtube.Com, or your calculator may or may not indicate whether a box-and-whisker plot 14.9 + 3×0.5 16.4! Bounds are calculated, any value lower than the upper threshold for our outliers we subtract from our Q1:! Is ( 71.5 - 70 ), or 1.5 to calculate outliers using the interquartile range ( IQR ) 7... Will help you detect outliers even for automatically refreshed reports please accept `` preferences '' cookies order. Sample of 20 sophomore college students you have outliers and extreme values, it will you... 18\ ) scores are: 10.2, 15.9, 16.4 and should n't be called major. Called a major outlier fence are considered outliers different specific rules, or 1.5 a survey was given to random! By the way, your book may refer to the third quartile or below the lower value higher! There are any outliers, if a number is less than 2 books greater! Your book may refer to the third quartile q 3 ( click Tap...

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