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The calculation of the Interquartile Range (IQR) is a fundamental statistical measure used to analyze and interpret data. It provides valuable insights into the spread or dispersion of a dataset, particularly when outliers or extreme values are present. By understanding how to calculate the IQR, researchers, analysts, and data scientists gain the ability to assess the variability in a set of values and make informed decisions based on these statistics. This article will delve into the concept of the IQR, explain its significance, and provide a step-by-step guide on how to calculate this intermediary spread.
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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
![Image titled Find the IQR Step 1](https://www.wikihow.com/images_en/thumb/1/1c/Find-the-IQR-Step-1-Version-4.jpg/v4-460px-Find-the-IQR-Step-1-Version-4.jpg)
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.
![Image titled Find the IQR Step 2](https://www.wikihow.com/images_en/thumb/9/9e/Find-the-IQR-Step-2-Version-3.jpg/v4-460px-Find-the-IQR-Step-2-Version-3.jpg)
- 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
![Image titled Find the IQR Step 3](https://www.wikihow.com/images_en/thumb/2/28/Find-the-IQR-Step-3-Version-3.jpg/v4-460px-Find-the-IQR-Step-3-Version-3.jpg)
Formula: IQR = Q3 – Q1.
Sort data set
![Image titled Find the IQR Step 4](https://www.wikihow.com/images_en/thumb/3/35/Find-the-IQR-Step-4-Version-3.jpg/v4-460px-Find-the-IQR-Step-4-Version-3.jpg)
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.
![Image titled Find the IQR Step 5](https://www.wikihow.com/images_en/thumb/a/a5/Find-the-IQR-Step-5-Version-3.jpg/v4-460px-Find-the-IQR-Step-5-Version-3.jpg)
- Even-numbered data set (A): 4 7 9 11 12 20
- Odd data set (B): 5 8 10 10 15 18 23
![Image titled Find the IQR Step 6](https://www.wikihow.com/images_en/thumb/b/b5/Find-the-IQR-Step-6-Version-2.jpg/v4-460px-Find-the-IQR-Step-6-Version-2.jpg)
- 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
![Image titled Find the IQR Step 7](https://www.wikihow.com/images_en/thumb/7/76/Find-the-IQR-Step-7-Version-2.jpg/v4-460px-Find-the-IQR-Step-7-Version-2.jpg)
- 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)
![Image titled Find the IQR Step 8](https://www.wikihow.com/images_en/thumb/6/6a/Find-the-IQR-Step-8-Version-2.jpg/v4-460px-Find-the-IQR-Step-8-Version-2.jpg)
- 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] XResearch 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, the Interquartile Range (IQR) is a valuable statistic that helps measure the spread or variability of a dataset. By calculating the IQR, we can identify and analyze the range between the first quartile (25th percentile) and the third quartile (75th percentile), which represents the middle 50% of the data. The IQR is a robust measure because it is not affected by outliers or extreme values, making it particularly useful in analyzing skewed or non-normal distributions. Moreover, the IQR can be used to identify outliers by considering data points that lie outside of the range defined by the lower and upper quartiles. Overall, understanding how to calculate the IQR provides us with a powerful tool for analyzing and interpreting datasets, enabling us to gain insights into the spread and variability of the data.
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