# Outlier Calculator

## Table of Content

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An online outlier calculator is used to find the outlier of various data sets. The q test calculator takes into service the different ways to measure the variance of the underlying data to determine their underlying low and high values.

## What is an Outlier?

The outlier is the data point that is different from the other data point. An outlier may be due to:

• Variability in the measurement
• Due to an indication of novel data
• It may be the result of experimental error

Example: Place the data set in ascending order 4, 7, 11, 13, and 47 and this might be an outlier test because it is higher than the other data points.

## Ways to Find the Outliers From the Data:

The unusual value in the data set can be calculated by using the Outlier calculator because it is designed to keep the user's needs.

### 1. Z-Score:

The distribution of the data is normal and it evaluates the number of valid outliers. Z-score finds the raw value of X value and determines how many standard deviations away from the mean.

z = (x-μ) / σ

### 2. Grubbs Test:

The Grubbs test is used to find the single test for outliers in the univariate data set that follows an approximation of normal distribution. This test is used to find its minimum and maximum values.

### 3. By using the IQR Method:

It is the measure of data dispersion that is equal to the difference between the first and third quartiles. In other words, it is used to say that it is the measure of the “middle fifty” in the given set of data.

This difference can be easy to evaluate by using the outlier calculator or by manually following the formula is helpful.

IQR = Q3 - Q1

This also uses the inner and outer fences that are figured out using the below formulas:

Inner fence:

The first quartile also known as the lower quartile is equal to the 25th percentile of the data.

Q1 - ( 1.5 x IQR )
Q3 + ( 1.5 x IQR )

Outer Fence:

The third quartile also known as the upper quartile is equal to the 75th percentile of the data.

Q1 - ( 3 x IQR )
Q3 + ( 3 x IQR )

### 4. Find the Outliers by Hypothesis Testing:

Hypothesis testing can also be used to find the outliers which is the choice for single outliers. This test has one and two-sided versions mean null hypothesis and alternative.

Null: All sample values were drained from a single population that follows the same normal distribution.

Alternative: A single sample value was not concluded from the normally distributed population as by the other values.

### 5. Graphing Outliers:

The graphic identification can also be identified by the box plot. Scatter plots also be used to clearly detect when a dataset or particular feature contains outliers.

## Practical Example:

To determine whether the most extreme value in the list of values is a significant outlier from the rest we suppose a set of data:

5, 12, 8, 3, 7, 18, 19

### Solution:

Your Input Data in Sorted form: 3, 5, 7, 8, 12, 18, 19

The interquartile range, IQR

IQR = Q3 - Q1

Q1 = 5

Q3 = 18

IQR = 18 - 5 = 13

To calculate outlier tests and potential outliers, we have to find the inner fences and outer fences by using the outliers calculator. The inner fences are defined by:

Q1 - ( 1.5 x IQR ) and Q3 + ( 1.5 x IQR )

5 - ( 1.5 x 13 ) and 18 + ( 1.5 x 13 )

So it is evaluated that there are no outliers

Outliers and potential outliers = none
Outer Fences = -34 and 57
Median: 12

## Working of an Outlier Calculator:

To get fast results, you need to use the q test calculator. This functions well when you provide the below value.

Input:

• Insert all the values in the tool-designated field
• Tap the “Calculate” button

Output:

• All outlier values
• Minimum and Maximum values
• First and third outliers
• Inner and outer fences
• Interquartile range
• Complete calculation with given steps

## References:

From the source Wikipedia: Outlier, Occurrence and causes, Working with outliers.

From the source Khan Academy: Outliers in scatter plots, Practice problems.

### Shaun Murphy

I'm graduated in biomedical and electrical engineering. Specialization in sports and medical topics but will gladly tackle everything you throw at him. He is a sailor, hiker, and motorcyclist in his free time.