    # Interquartile Range Calculator

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Table of Content
 1 What is Interquartile Range(IQR)? 2 What is Quartiles? 3 What is Range? 4 What is Geometric mean? 5 What is Standard deviation? 6 How to find Interquartile range manually (Step-by-Step)? 7 How do you calculate the quartile and interquartile range? 8 What does the interquartile range tell you? 9 How are quartiles calculated? 10 What is the 1.5 IQR rule? 11 Does a box plot show the interquartile range? 12 How do you find Q1 and Q3 in quartile deviation? 13 Why is the interquartile range important? 14 Why is IQR better than range? 15 How do you calculate the interquartile range in excel?
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An online interquartile range calculator that helps to calculate IQR statistics along with quartile Q1 (25%), second quartile Q2 (50%), and third quartile Q3 (75%). This IQR calculator uses simple IQR formula to find the quartile (Q1), median (Q2), and upper (Q3) from the groups of the data set.

It’s time to give a thorough read to this helpful stuff; we are going to discuss how to find the interquartile range step-by-step and with interquartile calculator, interquartile range excel, and different parameters related to IQR statistics.

First, we refer to know about the basic interquartile range definition!
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## What is Interquartile Range(IQR)?

The interquartile range of a data set tells us how the values of the data set are spread or bunched.IQR is the difference between the third quartile(75th percentile) and first quartile(25th percentile).

Other names for the interquartile range(IQR) are,

• Middle 50%.

If you only want to find the quartile of the dataset, then this free and simple quartile calculator allows you to find the first quartile (q1), second quartile (q2), third quartile (q3).

### Interquartile range (IQR) formula:

The formula used by this online IQR calculator to calculate interquartile range is as follow,

IQR = Q3 – Q1

Where,

Q3 = Third quartile (75th percentile)

Q1 = First quartile (25th percentile)

## What is Quartiles?

The quartile determines the values spread of values left and right to the mean by dividing into four groups. The quartile splits the data set into three points, first quartile(lower quartile), median and third quartile(upper quartile).

### First quartile and Third quartile:

The first quartile is the 25th percentile of the data, also called the lower quartile. The third quartile, also called the upper quartile, is the 75th percentile of the data.

There are many different methods to find out the quartiles, but this quartile finder uses a method by Moore & McCabe to find quartiles.

#### Moore & McCabe method:

According to this method, the lower quartile (Q1) is the median of the numbers below the median, and the upper quartile (Q3) is the median of numbers above the median.

## What is Range?

The range is the difference between the maximum value and the minimum value of the data set. The range of the dataset can be determined by the following formula,

R =Xm – Xi

Where,

Xm = Maximum value

Xi = Minimum value

You can give a try to this free mean, median, mode and range calculator to find the mean median mode and range for any dataset values.

## What is Average?

The number expressed the central value in the set of data is termed as its average or the median of the data or most commonly it is the mean.

The average numbers obtained by dividing the sum of all numbers by the total numbers in the data set. The formula of average is as follow,

Average = Sum of all numbers / Total numbers

For convenience, this online average calculator will help you to find the average or mean value of any given data set of numbers.

## What is Geometric mean?

The geometric mean for numbers is defined as “the nth root of a product of n numbers ”.
The formula for the set of numbers x1, x2 ,x3,………, xn is as follow,

G.M = n√x1, x2 ,x3,………, xn

## What is Standard deviation?

The standard deviation of the data set is the calculation of the dispersion of numbers. If standard deviation has a small value, then data points are close to their average or mean. The formula for the standard deviation is as,

S.D=√(∑(x-µ))/N

Where,

µ is the population mean.

N is the total numbers.

x is the value from population.

The simple, but highly accurate interquartile range calculator enables you to find the interquartile range (Q1, Q2, Q3) for a set of numerical observations. This IQR finder not only finds the interquartile range but also different other important statistics parameters. The IQR calculator displays the IQR graph for a data set values including:

• Q1 (lowest 25% of numbers)
• Q2 (between 25.1% and 50%)
• Q3 (51% to 75%)
• Q4 (highest 25% of numbers)

### How to find the interquartile range by IQR Calculator:

So, calculating IQR becomes easy, all you need to stick to the given steps of this interquartile range calculator to get accurate IQR statistics calculations.

Inputs:

First of all, you have to select the standard from which the group of numbers (dataset) are separated from the dropdown of this tool.

• Then, enter the group of numbers below in the designated field.
• Lastly, hit the calculate button.

Outputs:

When you enter values in all the fields, the IQR finder will show you,

• Interquartile range of the numbers.
• Quartile Q1
• Quartile Q2
• Quartile Q3
• Average of the given numbers.
• Geometric mean of the numbers
• Total sum of numbers.
• Population standard deviation.
• Sample standard deviation.
• Range of the numbers.
• Count the total numbers.
• The Interquartile range (IQR) Graph

## How to find Interquartile range manually (Step-by-Step)?

The formula used to find out the IQR is as follow,

IQR = Q3 – Q1

Let’s look at the step by step calculation of IQR with the help of an example!

Example:

You have the numbers 7,5,13,1,3,27,18,2,15,6,19,then find out the IQR of this data set?

Solution:

Step 1:

First of all, you have to put the numbers in ascending order.

1,2,3,5,6,7,13,15,18,19,27

Step 2:

Find out the median of this data set.

1,2,3,5,6,7,13,15,18,19,27

Step 3:

For easiness in finding the Q1 and Q3, place the parentheses around the numbers above and below the median.

(1,2,3,5,6),7,(13,15,18,19,27)

Step 4:

Q1 is the median of the lower part and Q3 is the median of the upper part of the data set.

(1,2,3,5,6),7,(13,15,18,19,27)

Here,

Q1 = 3

Q3 = 18

Step 5:

Putting the values in the formula of interquartile range,

IQR = 18 – 3

IQR = 15

### Calculations for the even numbers of data set:

If you have an even set of numbers, then quit worrying this IQR finder will assist you to calculate the IQR of even set of numbers. Let’s have an example,

Example:

You have the numbers 37,13,24,49,6,19,7,45,33,29,then find out the IQR of this data set?

Solution:

Step 1:

First of all, you have to put the numbers in ascending order.

6,7,13,19,24,29,33,37,45,49

Step 2:

Make a mark at the centre of the numbers.

6,7,13,19,24 / 29,33,37,45,49

Step 3:

For easiness in finding the Q1 and Q3, place the parentheses around the numbers above and below the median.

(6,7,13,19,24) / (29,33,37,45,49)

Step 4:

Q1 is the median of the lower part and Q3 is the median of the upper part of the data set.

(6,7,13,19,24) / (29,33,37,45,49)

Here,

Q1 = 13

Q3 = 37

Step 5:

Putting the values in the formula of interquartile range,

IQR = 37 – 13

IQR = 24

### How do you calculate the quartile and interquartile range?

As the interquartile range is the difference between the upper quartile value and the lower quartile value. To find the IQR, simply take the value of the upper quartile and subtract to the lower quartile value.

### What does the interquartile range tell you?

The interquartile range tells how the middle values are spread,it also tells the value is how far from the middle value. In the Box-&-Whisker plot, IQR determines the width of the box.

### How are quartiles calculated?

Quartiles are the values that divided the data set into four equal parts. There are 3 quartiles(Q1, Q2, Q3) in a single dataset. The formulas for calculations of every quartile are as follows,

Q1 = n / 4

Q2 = n / 2

Q3 =3 n / 4

### What is the 1.5 IQR rule?

By multiplying the interquartile range with 1.5, you can determine the outliers of the dataset. Add IQR*1.5 to the third quartile, any number greater than the result is an outlier. Subtract IQR*1.5 from the first quartile, any number smaller than the result is an outlier.

### Does a box plot show the interquartile range?

Box plots do not clearly show the interquartile range, but it is helpful to find out the IQR. With the assistance of the box plot we can easily find out the third & first quartile that are helpful to determine the IQR.

### How do you find Q1 and Q3 in quartile deviation?

The quartile deviation is half of the difference between the third and the first quartile. Quartile deviation is also known as semi-interquartile. The formula for the quartile deviation is as follows,

Q.D = Q3 – Q1 / 2

### Why is the interquartile range important?

Apart from being a less sensitive measure of the spread of data, IQR has another important use. Interquartile range is useful to identify whether a value is an outlier or not. Also, it informs us whether we have a strong or weak outlier.

### Why is IQR better than range?

IQR is a better measure of central tendency than the range because it left the extreme values and only divides the dataset into four equal parts.

### How do you calculate the interquartile range in excel?

To calculate IQR in excel, use the =QUARTILE function to find out the quartiles Q1 & Q3, then find the difference between these two values.

## Takeaway:

This online interquartile range calculator allows you to enter the unarranged data set and find out the interquartile range (IQR) within a fraction of seconds. This tool accurately divides the data into three quartiles. To avoid the error risks, the online IQR finder is the best tool for learning purposes for the students as well as the professionals.

## References:

From the source of Wikipedia: Interquartile range, Use and Examples

From the source of sciencing: How to Calculate the Interquartile Range easily

From the source of scribbr: Best Methods for finding the interquartile range