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Statistics Calculators ▶ Interquartile Range Calculator

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An online interquartile range calculator allows you to calculate IQR statistics (Q1, Q2, Q3) for a set of numerical observations. The IQR calculator performs calculations by using the IQR formula and display the 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)

Itâ€™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 an interquartile calculator, and different parameters related to IQR statistics.

First, we refer to know about the basic interquartile range definition!

Read on!

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 the first quartile(25th percentile).

Other names for the interquartile range(IQR) are,

- Midspread.
- Middle 50%.
- H-spread.

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).

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

IQR = Q3 – Q1

Where,

Q3 = Third quartile (75th percentile)

Q1 = First quartile (25th percentile)

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

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. Apart from Q1 (25%), second quartile Q2 (50%), and third quartile Q3 (75%), the calculator also finds different other important statistics parameters.

**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

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

IQR = Q3 – Q1

Letâ€™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

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. Letâ€™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

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.

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.

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.

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.

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

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.

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.

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

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.

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