This online Outlier Calculator calculates the outliers of a set of numbers. You can paste the input data copied from a spreadsheet or csv-file or enter manually using comma, space or enter as separators.
What is outlier in math
The outlier is a statistics term meaning a data point that differs significantly from other points of a data set. Outlier points can indicate incorrect data, experimental errors, or areas where a certain assumption or theory can not be applied. In large samples, however, a small number of outliers is to be expected due to various factors.
Outliers can cause serious problems in statistical analyses and, therefore, it is important to detect and eliminate them. The most widely used criterion for detection of an outlier data point in a distribution is based on interquartile range. An outlier is considered a number that is sufficiently away from either the lower or upper quartiles of the data set. Specifically, a particular number is an outlier if it’s less than Q1 – 1.5×(Q3 – Q1) or greater than Q3 + 1.5×(Q3 – Q1), where Q1 and Q3 are the first and third quartiles respectively.
This algorithm is used in our Outlier Calculator. For calculation of the first and third quartiles we use the Method 2 (see our Quartile Calculator), which means that in case of an odd number of data points, when dividing this set into two halves we do include the median value of the sorted initial data set to each of these two halves. This method yields better results in case of low population discrete distributions, while in case of high population discrete distributions there are no significant differences between all the methods.
Outliers should be investigated with great caution. Sometimes they contain substantial information about the process under investigation or the data gathering and recording process. Before the possible elimination of these points from the data set, it is important to understand why these outliers appeared and whether it’s likely similar values will continue to appear.
Example
As an example in which outliers often appear, consider the distribution of annual household income in the US for 2021.
According to CPI Adjusted ASEC Data, the 25th percentile (Q1) of annual income was $34,554 and the 75th percentile (Q3) was $128,258.
The Interquartile Range (IQR) would be calculated as $128,258 – $34,554 = $93,704.
This means that any household with an income outside the boundaries below would be considered an outlier:
Lower boundary: Q1 – 1.5*IQR = $34,554 – 1.5 * $93,704 = -$106,002
Upper boundary: Q3 + 1.5*IQR = $128,258 + 1.5 * $93,704 = $268,814
Thus, it is obvious that any person whose net worth is in the millions of dollars will be considered an outlier in terms of annual household income.
Note that the calculated value for outliers does not always make sense, for example, in our case, it is impossible to have a negative annual household income.
Related calculators
Check out our other statistics calculators such as Linear Regression Calculator or Correlation Coefficient Calculator.