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Table of Content

 1 Overview! 2 What Is An Outlier? 3 Statistical Outlier Test: 4 Inner And Outer Fences: 5 How To Calculate Outliers? 6 What is standard deviation? 7 What do you mean by grouped data? 8 What is regression analysis?

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An online outlier calculator helps you to detect an outlier that exists far beyond the data set at a specific range. Here, you can adopt various methods to figure out the outliers if they exist. But we have made it easy for you to perform the outlier check.

For better understanding, just jump down!

## What Is An Outlier?

In statistical analysis,

“A specific entry or number that is totally different from all other entries in the data set is known as an outlier”

### Statistical Outlier Test:

The outliers usually occur by chance and can cause serious problems in data sorting. You can use our online outlier calculator to determine an outlier absolutely for free. But, you must know the five number summary as well which is explained below:

#### (1) Maximum:

In a data set, the greatest value is always considered a maximum value.

For example:

Let us consider the following data set:

1, 5, 32, 854, 4

In this data set, the maximum is 854 because it is the greatest among all.

#### (2) Minimum:

The smallest value that exist in a data set is known as minimum.

For example:

Consider the same data set as mentioned above:

1, 5, 32, 854, 4

For this data set, the minimum is the 1 as it is the smallest value.

#### (3) Median:

The middle term in a data set is called median.

Rules For Median:

It must be kept in mind that you have two rules defined if you want to find median.

Even Numbers:

If the number of values in your data set are even, then the median is considered as the average of two middle terms.

$$median = \frac{Two Middle Terms}{2}$$

Odd Numbers:

For an odd number of values, the median is simply the term that lies within the data set.

#### (4) Quartiles:

The medians of the smallest and greatest half of the data set are considered as quartiles.

First quartile(Q_{1}):

It is the median of the smallest numbers ( minimum) that contrains 25% of the data volume within it.

Third quartile(Q_{3}):

The median of the greatest numbers (maximum) under which at least 75% of the data lies is known as the third quartile.

It should always be kept in mind that the data must be arranged from least to greatest always before you perform various outliers tests to detect any outlier.

#### (5) Interquartile Range (IQR):

It is the difference between the first and third quartiles.

$$IQR = Q_{3} – Q_{1}$$

### Inner And Outer Fences:

Before you work for outliers, you need to determine inner and outer fences with the help of the following formulas below:

Inner fences:

$$Q_{1} – (1.5 \times IQR) \text{ and } Q_{3} + (1.5 \times IQR)$$

Outer fences:

$$Q_{1} – (3 \times IQR) \text{ and } Q_{3} + (3 \times IQR)$$

Our free online statistical outlier calculator uses all above formulas to figure out outliers if there is/are any.

### How To Calculate Outliers?

Sometimes, it becomes difficult to find any outliers in a data set that produces a significant increase in difficulty. That is why a free q-test calculator is used to escalate your results. But it is very important to practice test for outliers detection. So, what about solving an example to better get a grip!

Example # 01:

Calculate outliers for the following data set defined below:

$$10, 12, 11, 15, 11, 14, 13, 17, 12, 22, 14, 11$$

Solution:

As the given data is unsorted, we need to arrange it in ascending order as follows:

$$10, 11, 11, 11, 12, 12, 13, 14, 14, 15, 17, 22$$

By following five number summary, we have:

(1) Maximum:

For the data given, the maximum or greatest value is 22.

(2) Minimum:

The smallest value for the data set given is 10.

(3) First Quartile (Q1):

As the total number of values is 12. So we divide it into two parts. The first part contains 6 numbers. The median of these numbers gives us the first quartile as follows:

$$10, 11, 11, 11, 12, 12$$

$$Q_{1} = \frac{11+11}{2}$$

$$Q_{1} = \frac{22}{2}$$

$$Q_{1} = 11$$

(4) Third Quartile (Q3):

It is the median of the next 6 numbers and is calculated as:

$$13, 14, 14, 15, 17, 22$$

$$Q_{3} = \frac{14 + 15}{2}$$

$$Q_{3} = \frac{29}{2}$$

$$Q_{3} = 14.5$$

(4) Median:

As the total number of values is even, so the median is calculated as follows:

$$10, 11, 11, 11, 12, 12, 13, 14, 14, 15, 17, 22$$

$$median = \frac{12 + 13}{2}$$

$$median = \frac{25}{2}$$

$$median = 12.5$$

For interquartile range, we have:

$$IQR = Q_{3} – Q_{1}$$

$$IQR = 14.5 – 11$$

$$IQR = 3.5$$

Calculating inner fences as below:

$$Q_{1} – (1.5 \times IQR) \text{ and } Q_{3} + (1.5 \times IQR)$$
$$11 – (1.5 \times 3.5) \text{ and } 14.5 + (1.5 \times 3.5)$$

$$5.75, 19.75$$

Now, we need to determine outer fences with the help of following equations:

$$Q_{1} – (3 \times IQR) \text{ and } Q_{3} + (3 \times IQR)$$

$$11 – (3 \times 3.5) \text{ and } 14.5 + (3 \times 3.5)$$

$$0.5, 25$$

So,

$$The number of prism outlier = 0$$

$$Potential outlier = 22$$

Here, our free statistical outlier test calculator depicts the same results but in a fraction of seconds to avoid time wastage.

### How Outlier Calculator Works?

Our free q test calculator is the best among all calculators and is used widely by students and statisticians. Let us guide you how to use it properly.

Input:

• Enter all the numbers separated by commas in the menu box
• Hit the calculate button

Output:

The outliers calculator determines:

• Maximum and minimum values
• First outlier
• Third outlier
• Interquartile range
• Inner fences
• Outer fences
• Outliers

## FAQ’s:

### What is standard deviation?

The statistical analysis that measures dispersion of a data set from the mean position is called standard deviation.

### What is standard deviation?

It Is a data that is totally defined in a proper manner without containing any raw values.

### What is regression analysis?

The statistical process that describes relationship among dependent variable and one or more independent variables is called regression analysis.

## Conclusion:

There is a broad use of outlier detection in the field of cybersecurity, military surveillance for the sake of preventing attacks, detection of any mishap with credit cards and many more. This is why the use of free online outlier calculator is preferred around the globe to depict any fault in the systems so that any challenging situation could be overcome easily.

From the source of wikipedia: Grubbs’s test, Chauvenet’s criterion, Peirce’s criterion, Dixon’s Q test, Studentized residual

From the source of khan academy: Identifying outliers, Reading box plots, Interpreting box plots, Interpreting quartiles, Judging outliers in a dataset

From the source of lumen learning: Types of Outliers.