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Calculating the Interquartile Range (IQR) is a widely used statistical measure that provides valuable insights into the spread and variability of a dataset. The IQR allows us to understand the range within which the middle 50% of values lie, capturing the dispersion of the data without being influenced by outliers. It is particularly useful in analyzing skewed or non-normally distributed data sets, as it provides a more robust measure of spread compared to the range or standard deviation. In this guide, we will delve into the step-by-step process of calculating the Interquartile Range, exploring its significance and application in statistical analysis.

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IQR (short for “interquartile range”) is the spread between, or interquartile range, of a data set. This concept is used in statistical analysis to help draw conclusions about a set of numbers. IQR is often used for the range of variation because it eliminates most outliers in the data. Let’s learn how to determine IQR.

## Steps

### Understanding IQR

**Know how to use IQR.**Essentially, the spread represents the width or “dispersion” of the set of numbers.

^{[1] X Research Source}The interquartile range is defined as the difference between the upper quartile (25% highest) and the lower quartile (25% lowest) of the data set.

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**Tip:** The lower quartile is usually denoted Q1, the upper quartile is Q3 – so the midpoint of the data set will be Q2 and the highest is Q4.

**Understanding quartiles.**To visualize a quartile, divide the list into four equal parts. Each part will be a “quartile”.

^{[3] X Research Source}For example in data set: 1, 2, 3, 4, 5, 6, 7, 8.

- 1 and 2 are the first quartile – Q1
- 3 and 4 are the second quartile – Q2
- 5 and 6 are the third quartile – Q3
- 7 and 8 are the fourth quartile – Q4

**Memorize the formula.**To determine the difference between the upper and lower quartiles, you need to subtract the 75th percentile (Q3) from the 25th percentile (Q1).

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**Formula: IQR = Q3 – Q1.**

### Sort data set

**Gather your data.**If you are learning about IQR to study and take a test, the test will provide a set of numbers, for example: 1, 4, 5, 7, 10. You will calculate based on these numbers. However, you may need to rearrange numbers from a table or puzzle.

^{[5] X Research Sources}

**You need to make sure that each number represents one type of data:** for example, the number of eggs in a particular bird’s nest or the number of parking spaces per house in a block.

**Sort the data set in ascending order.**In other words, you need to arrange the numbers in order from smallest to largest. Draw conclusions from the following examples.

- Even-numbered data set (A): 4 7 9 11 12 20
- Odd data set (B): 5 8 10 10 15 18 23

**Divide the data into two parts.**To proceed, you find the midpoint of the data – this will be one or more numbers in the middle of the series. If you have an odd number, choose the exact middle number. With an even number of data, the midpoint will be between the two central numbers.

- In the even number example (set A), the midpoint between 9 and 11 looks like this: 4 7 9 | 11 12 20
- In the odd number example (set B) then (10) is the midpoint. We have: 5 8 10 (10) 15 18 23

### Calculate IQR

**Find the median**

**of the top and bottom half in the data set.**Median is the “midpoint” or number in the middle of a data set.

^{[6] X Research Source}In this case, you will not find the midpoint of the entire data, but only the relative medians of the upper and lower subsets. If you have an odd number of data, exclude the middle number – for example, in set B you don’t need to count 10.

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- In the even number example (set A):
- Median of bottom half = 7 (Q1)
- Median of upper half = 12 (Q3)

- In the odd number example (set B):
- Median of bottom half = 8 (Q1)
- Median of upper half = 18 (Q3)

**Take Q3 – Q1 to find the mid spread.**So you know how many numbers are between the 25th and 75th percentiles. You can use this to get an idea of how widely distributed the data is. For example, if the test has a scale of 100 and the IQR of the score is 5, you would have reason to believe that the participants have similar qualifications because the highs and lows are not too different. But if the mid-range of test scores is up to 30, you can question why some people score so high while others score so low.

- In the even number example (set A): 12 – 7 = 5
- In the odd number example (set B): 18 – 8 = 10

## Advice

- It is important that you master the knowledge, because there are many IQR calculators online, use them to check the results.
^{[8] X Research Source}Do not rely too much on calculation applications when studying! If you run into a mid-spread test, you need to know how to calculate it by hand.

wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 31 people, some of whom are anonymous, have edited and improved the article over time.

There are 8 references cited in this article that you can see at the bottom of the page.

This article has been viewed 36,437 times.

IQR (short for “interquartile range”) is the spread between, or interquartile range, of a data set. This concept is used in statistical analysis to help draw conclusions about a set of numbers. IQR is often used for the range of variation because it eliminates most outliers in the data. Let’s learn how to determine IQR.

In conclusion, calculating the Intermediary Spread or Interquartile Range (IQR) is an effective statistical measure that provides valuable information about the distribution and spread of a dataset. By taking into account the middle 50% of the data points, it allows us to understand the range within which most of the data falls and identify any outliers. The IQR is calculated by finding the difference between the upper quartile and the lower quartile, and it therefore provides a robust measure of spread that is not affected by extreme values. This makes it particularly useful in comparing distributions and identifying any potential patterns or anomalies. Overall, understanding how to calculate and interpret the IQR is crucial in data analysis and can help to draw meaningful conclusions from datasets.

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