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     • What Is Outlier Analysis? Outlier analysis is the process of identifying outliers, or abnormal observations, in a dataset. Also known as outlier detection, it’s an important step in data analysis, as it removes erroneous or inaccurate observations which might otherwise skew conclusions.
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     Outlier Analysis: Definition, Techniques, How-To, and More

2. Top results related to definition of outlier analysis in math

   • Outlier Analysis in R

     This article will focus on the outlier analysis, including Outlier detection and removal in the R programming language.

     What are outliers?

     Data points far from the dataset’s other points are considered outliers. This refers to the data values dispersed among other data values and upsetting the dataset’s general distribution. Outlier detection is a statistical approach used to find outliers in datasets. Measurement errors, incorrect data entry, or really anomalous data values are just a few of the causes of outliers.

     Effects of an outlier on the model:

     • The format of the data appears to be skewed.
     • Modifies the mean, variance, and other statistical characteristics of the data’s overall distribution.
     • Leads to the model’s accuracy level being biased.

     Steps involving Outlier detection:

     Step 1: In this step, we will be, by default creating the data containing the outliner inside it using the rnorm() function and generating 500 different data points. Further, we will be adding 10 random outliers...

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     1/5

   • Definition of math_sin function in the CPython source code?

     Top Answer

     Answered Apr 18, 2019 · 9 votes

     math_sin is defined via the FUNC1

     macro:

     FUNC1(sin, sin, 0, "sin($module, x, /)\n--\n\n" "Return the sine of x (measured in radians).")-

     where FUNC1

     is defined as:

     #define FUNC1(funcname, func, can_overflow, docstring) \ static PyObject * math_##funcname(PyObject *self, PyObject *args) { \ return math_1(args, func, can_overflow); \ }\ PyDoc_STRVAR(math_##funcname##_doc, docstring);

     so the preprocessor expands this to:

     static PyObject * math_sin(PyObject *self, PyObject *args) { return math_1(args, sin, 0); } PyDoc_STRVAR(math_sin_doc, "sin($module, x, /)\n--\n\n" "Return the sine of x (measured in radians).");

     (but then all on one line, and with the PyDoc_STRVAR macro also having been expanded)

     So math_sin(module, args) basically is a call to math_1(args, sin, 0), and math_1(args, sin, 0)

     calls math_1_to_whatever(args, sin, PyFloat_FromDouble, 0)

     which takes care of validating that a Python float was passed in, converting that to a C double, calling sin(arg_as_double), raising exceptions as needed or wrapping the double return value from sin() with the PyFloat_FromDouble function passed in by math_1() before returning that result to the caller.

     sin() here is the double sin(double x)

     function defined in POSIX math.h

     .

     You can, in principle, preprocess the whole Python source tree and dump the output into a new directory; the following does presume you successfully built the python binary already, as it is used to extract the necessary include flags for gcc:

     find . -type d -exec mkdir -p /tmp/processed/{} \;(export FLAGS=$(./python.exe -m sysconfig | grep PY_CORE_CFLAGS | cut -d\" -f2) && \ find . -type f \( -name '*.c' -o -name '*.h' \) -exec gcc -E $FLAGS {} -o /tmp/processed/{} \;)-

     and then math_sin will show up in /tmp/preprocessed/Modules/mathmodule.c.

     Or you can tell the compiler to save preprocessor output to .i files with the -save-temps flag:

     make clean && make CC="gcc -save-temps"-

     and you'll find make_sin in Modules/mathmodule.i.

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     2/5

   • Outlier Analysis on a 2D array in Matlab

     Top Answer

     Answered Feb 11, 2018 · 1 votes

     Normally, this operation on Matlab is performed using the isoutlier function. The mean-variance approach for detecting outliers (the one your are refering to in your question) is applied on the observations when the method parameter is passed as mean to the function call:

     method — Method for determining outliers 'median' (default) | 'mean' | 'quartiles' | 'grubbs' | 'gesd'

     'mean' Returns true for elements more than three standard deviations from the mean. This method is faster but less robust than 'median'.

     Unfortunately, it is based on 3 standard deviations away from the mean instead of only 1 standard deviation away from the mean. Hence, a custom code must be implemented. Given the matrix of observations A, this should work fine:

     m = nanmean(A,1);s = nanstd(A,1); lb = m - s;ub = m + s;is_outlier = ((A < lb) | (A > ub));

     The is_outlier variable will be a matrix of logical values of the same size of A, in which true values indicate an outlier:

     A = [ 10.836126 6.342457 6.359280 4.865735 11.332891; 13.228078 17.779455 11.021488 10.057800 13.371285; 11.350769 15.052270 10.556633 7.909101 7.627935; 11.841888 4.655980 8.363947 10.808192 12.761605; 2.534398 6.189042 6.987835 8.412396 8.166305];m = nanmean(A,1);s = nanstd(A,1); lb = m - s;ub = m + s;is_outlier = ((A < lb) | (A > ub))is_outlier = 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 0 1

     The only doubt I have concerns the means and variances you provided. They differ from the ones you calculate on the given data:

     A = [ 10.836126 6.342457 6.359280 4.865735 11.332891; 13.228078 17.779455 11.021488 10.057800 13.371285; 11.350769 15.052270 10.556633 7.909101 7.627935; 11.841888 4.655980 8.363947 10.808192 12.761605; 2.534398 6.189042 6.987835 8.412396 8.166305];m = nanmean(A,1)s = nanstd(A,1)m = 9.9582518 10.0038408 8.6578366 8.4106448 10.6520042s = 3.79639885205053 5.33862997268428 1.86284269833871 2.062972979429 2.35083838144151

     So if you have to use those instead, you can simply proceed as follows:

     A = [ 10.836126 6.342457 6.359280 4.865735 11.332891; 13.228078 17.779455 11.021488 10.057800 13.371285; 11.350769 15.052270 10.556633 7.909101 7.627935; 11.841888 4.655980 8.363947 10.808192 12.761605; 2.534398 6.189042 6.987835 8.412396 8.166305];m = [9.9900 10.0057 10.0180 10.0051 9.9312];s = [3.0257 3.0208 3.0119 2.9924 2.9868];lb = m - s;ub = m + s;is_outlier = ((A < lb) | (A > ub))is_outlier = 0 1 1 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 1 1 1 0 0

     Once you know which elements of A must be considered as outliers, you can proceed treating them as you prefer. For example, you could set them to NaN as follows:

     A(is_outlier) = NaN;-

     or you could remove all the columns containing one or more outlier as follows:

     A(any(is_outlier),:) = [];-

     Consider that the more you increase the tolerance from the mean, the more the outliers become rare. Using the built-in isoutlier function, which is based on 3 standard deviations away from the mean, very few outliers are detected:

     A = [ 10.836126 6.342457 6.359280 4.865735 11.332891; 13.228078 17.779455 11.021488 10.057800 13.371285; 11.350769 15.052270 10.556633 7.909101 7.627935; 11.841888 4.655980 8.363947 10.808192 12.761605; 2.534398 6.189042 6.987835 8.412396 8.166305];isoutlier(A) % lb = m - (3 * s) AND ub = m + (3 * s)ans = 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0

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   • analysis of variance in R

     Top Answer

     Answered Apr 12, 2012 · 0 votes

     To expand on @MYaseen208's response:

     Back in the old days computer programs did not deal well with non-numeric data, so it was common to recode categorical variables as numeric variables to enter the data into the computer. These programs then needed the user to tell them that this variable that looks like a numeric variable is really representing categories. This can be done in either of 2 ways: as an attribute of the data, or an attribute of the analysis. R takes the approach that things like this are attributes of the data rather than the analysis (which makes a lot more sense to me) so the aov function does not have any arguments to specify which predictors are categorical but rather looks at the data to determine this. Since the aov function can also do analysis of covariance and more general linear models it can accept both categorical and numeric predictors (so will not assume everything is categorical). You did not tell us how you entered your data, but however you did it it looked like numeric data to R and you never told it otherwise so it keeps assuming that it is numeric. You need to tell R that it is categorical factor(V1). It is possible to do this with every analysis, but it is better to do it once, either when creating/reading the data or once right after ex2$V2 <- factor(ex2$V2) so that every analysis/graph/summary on this data realizes that it is categorical and treats it appropriately.

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   • Outlier Analysis for Ordinal Data

     Top Answer

     Answered Mar 20, 2014 · 1 votes

     your data looks something like this:

     x = rep(1:7, c(3, 4,17, 21, 48, 118, 93)) y = c( rep(1:7,c(1,2,0,0,0,0,0)), rep(1:7,c(2,0,1,1,0,0,0)), rep(1:7,c(10,3,2,1,0,0,1)), rep(1:7,c(15,3,1,1,1,0,0)), rep(1:7,c(20,10,2,10,3,2,1)), rep(1:7,c(40,20,20,30,3,4,1)), rep(1:7,c(50,25,10,5,3,0,0)))

     the plot:

     library(car)sp(x,y, jitter = list(x=0.8, y=0.8), smoother=F, reg.line = F)-

     If you just want to know whether a given value is an outlier in your data (i.e. a univariate outlier analysis), you can use:

     library(outliers)grubbs.test(x)-

     or simply use boxplot which values are plotted as outliers:

     boxplot(x, plot=F)$out-

     If you need multivariate outliers, you can use the mvoutlier package (see functions ?chisq.plot and ?pcout):

     library(mvoutlier)pcout(x=data.frame(x,y))-

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     5/5

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3. People also ask

   What is an outlier in statistics?

   • A convenient definition of an outlier is a point which falls more than 1.5 times the interquartile range above the third quartile or below the first quartile . Outliers can also occur when comparing relationships between two sets of data. Outliers of this type can be easily identified on a scatter diagram .

   Outlier -- from Wolfram MathWorld

   mathworld.wolfram.com/Outlier.html

   See all results for this question

   What happens if a data point is outlier?

   • This action is not available. Outliers, what to do? An outlier is a data point that is far removed from the other entries in the data set. Outliers could be caused by: The first two cases are simple to deal with as we can correct errors or remove data that that does not belong in the population.

   3.5: Working with Outliers - Statistics LibreTexts

   stats.libretexts.org/Bookshelves/Introductory_Statistics/Inferential_Statistics_and_Probability_-_A_Holistic_Approach_(Geraghty)/03:_Descriptive_Statistics/3.05:_Working_with_Outliers

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   What is an example of an outlier?

   • What Is an Outlier? The extreme values in the data are called outliers. Example: For a data set containing 2, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 84 In the above number line, we can observe the numbers 2 and 84 are at the extremes and are thus the outliers.

   Outlier - Definition and examples - Cuemath

   www.cuemath.com/data/outlier/

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   When do outliers occur?

   • Outliers can also occur when comparing relationships between two sets of data. Outliers of this type can be easily identified on a scatter diagram . When performing least squares fitting to data, it is often best to discard outliers before computing the line of best fit.

   Outlier -- from Wolfram MathWorld

   mathworld.wolfram.com/Outlier.html

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4. www.cuemath.com › data › outlierOutlier - Definition and examples - Cuemath

   www.cuemath.com › data › outlier

   • Cached

   Lesson Plan. What Is an Outlier? The extreme values in the data are called outliers. Example: For a data set containing 2, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 84. In the above number line, we can observe the numbers 2 and 84 are at the extremes and are thus the outliers.

5. www.geeksforgeeks.org › outlierOutlier in Statistics: Definition, Meaning, Examples ...

   www.geeksforgeeks.org › outlier

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   May 29, 2024 · Outliers stand for data points that are indicative of a much higher variability than other observations in a given dataset. This can result in skewing statistical studies and wrong conclusions after all the variables are not adequately identified and handled.

6. math.libretexts.org › Courses › Coastline_College3.7: Outliers - Mathematics LibreTexts

   math.libretexts.org › Courses › Coastline_College

   • Cached

   In some data sets, there are values ( observed data points) called outliers. Outliers are observed data points that are far from the least squares line. They have large "errors", where the "error" or residual is the vertical distance from the line to the point. Outliers need to be examined closely.

7. Videos

   • 

     2:38

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     Determining an Outlier Using the 1.5 IQR Rule

     Sep 27, 2020

     49.1K Views

   • 

     articles.outlier.org

     Calculate Outlier Formula: A Step-By-Step Guide | Outlier

     Jan 24, 2022

   • 

     4:45

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     Statistics - How to find outliers

     Oct 20, 2012

     910.2K Views

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8. stats.libretexts.org › Courses › Las_Positas_College10.3: Outliers - Statistics LibreTexts

   stats.libretexts.org › Courses › Las_Positas_College

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   Jul 1, 2020 · In some data sets, there are values ( observed data points) called outliers. Outliers are observed data points that are far from the least squares line. They have large "errors", where the "error" or residual is the vertical distance from the line to the point. Outliers need to be examined closely.

9. mathworld.wolfram.com › OutlierOutlier -- from Wolfram MathWorld

   mathworld.wolfram.com › Outlier

   • Cached

   May 24, 2024 · A convenient definition of an outlier is a point which falls more than 1.5 times the interquartile range above the third quartile or below the first quartile. Outliers can also occur when comparing relationships between two sets of data.

10. study.com › learn › lessonOutlier in Statistics | Definition & Examples - Lesson ...

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    Nov 21, 2023 · An outlier, in statistics, can be defined as a value that is distant from the majority of the values in a data set. The image below shows how an outlier can be...

11. stats.libretexts.org › Bookshelves › Introductory3.5: Working with Outliers - Statistics LibreTexts

    stats.libretexts.org › Bookshelves › Introductory

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    Apr 9, 2022 · An outlier is a data point that is far removed from the other entries in the data set. Outliers could be caused by: Mistakes made in recording data; Data that don’t belong in the population; True rare events ; The first two cases are simple to deal with as we can correct errors or remove data that that does not belong in the population.