Content

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IQR (short for "interquartile range") is the middle spread, also known as the quartile range of the 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 excludes most outliers of data. Let's learn how to determine IQR.

Steps

Method 1 of 3: Understanding IQR

1. 

   Know how to use IQR. Basically, the middle spread represents the width or "dispersion" of the set. The quartile interval is determined by the difference between the upper quartile (25% highest) and lower quartile (25% lowest) of the data set.

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

   
   

2. 

   Understand quartiles. To visualize a quartile, divide the list into four equal parts. Each section will be a "quartile". For example in the 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

3. 

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

   Formula: IQR = Q3 - Q1.

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Method 2 of 3: Sort the data set

1. 

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

   You need to make sure that each number represents a data type: for example, the number of eggs in a particular nest or the number of parking positions per house in a building.

   
   

2. 

   Sort the data set in ascending order. In other words, you need to sort the numbers from baby to big. Draw conclusions from the following examples.
   • Set of even data numbers (A): 4 7 9 11 12 20
   • Set of odd data numbers (B): 5 8 10 10 15 18 23

3. 

   Divide the data into two parts. To do this, you find the midpoint of the data - this will be one or more numbers in the middle of the sequence. If you have an odd quantity, choose the exact middle number. With an even amount of data, the midpoint will be between two numbers in the center.
   • In the example of an even number (set A), the midpoint between 9 and 11 is as follows: 4 7 9 | 11 12 20
   • In the odd number example (population B) then (10) is the midpoint. We have: 5 8 10 (10) 15 18 23
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Method 3 of 3: Calculate IQR

1. 

   Find the median of the upper and lower halves in the data set. Median is the "midpoint" or number between the data set. In this case, you would 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 number in the middle - for example, in set B, you don't need to count the number 10.
   • In the example of an even number (set A):
     • Median of lower half = 7 (Q1)
     • Median of upper half = 12 (Q3)
   • In the odd quantity example (set B):
     • Median of lower half = 8 (Q1)
     • Median of upper half = 18 (Q3)

2. 

   Take Q3 - Q1 to find the middle spread. So you know how many numbers are between the 25th and 75th percentiles. You can use this to visualize how widely the data is spread. For example, if the test has a scale of 100 and the IQR of the score is 5, you will have grounds to believe that the participants are of the same level because the highs and lows are not too different. But if the spread of test scores goes up to 30, you might question why some people score so high and others so low.
   • In the example of an even number (set A): 12 - 7 = 5
   • In the odd number example (set B): 18 - 8 = 10
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Advice

• It is important to master your knowledge, because there are also many IQR calculators online, use them to check the results. Do not rely too much on the calculation application when studying! If you run into a test of mid spread, you need to know how to do it yourself by hand.