Content

• To step
• Method 1 of 3: Understanding the interquartile range
• Method 2 of 3: Organize the data collection
• Method 3 of 3: Calculate the interquartile range
• Tips

With the interquartile range you calculate the spread of a data set. The interquartile range is used in statistical analyzes to draw conclusions about a data set. It is often preferred to calculate the interquartile range rather than the range, because most of the outliers are then not included. Read on to find out how to determine interquartile range.

To step

Method 1 of 3: Understanding the interquartile range

1. Understand how interquartile range is used. In essence, it is a way of understanding the dispersion of a data set. The interquartile range is the difference between the top quartile (the top 25%) and the bottom quartile (the bottom 25%) of a data set. The lowest quartile is usually referred to as Q1 and the highest quartile as Q3, which theoretically makes Q2 the center of the data set, and Q4 the highest point.
2. Understand quartiles. To visualize a quartile, divide a list of numbers into four equal parts. Each of these parts is a "quartile." Consider the following data set: 1, 2, 3, 4, 5, 6, 7, 8.
   • 1 and 2 make up the first quartile, or Q1.
   • 3 and 4 make up the second quartile, or Q2.
   • 5 and 6 make up the third quartile, or Q3.
   • 7 and 8 make up the fourth quartile, or Q4.
3. Learn the formula. To find the difference between the top and bottom quartiles, you must subtract the 75th percentile from the 25th percentile. The formula is written as follows: Q3 - Q1 = interquartile range.

Method 2 of 3: Organize the data collection

1. Collect your data. If you have to learn this for school and you get a test on it, you will likely get a ready-made data set, such as 1, 4, 5, 7, 10. This is your data set, or the numbers you will go with to work. However, you may have to order the numbers yourself using a table or a story sum. Make sure that each number refers to the same thing, for example the number of eggs in each nest within a group of birds, or the number of parking spaces each house has on a particular street.
2. Sort your data collection in ascending order. This means that you order the data from the lowest to the highest number. Consider the following examples:
   • Example with an even number of numbers (set A): 4 7 9 11 12 20
   • Example with an odd number of numbers (set B): 5 8 10 10 15 18 23
3. Divide the data in half. To do this, you need to determine the center of the data - the number or numbers that are right in the middle of the data set. If you have an odd number of numbers, choose the number that is exactly in the middle. If you have an even number of numbers, the midpoint will be between the two middle numbers.
   • Example with an even number of numbers (set A), in which the midpoint is between 9 and 11: 4 7 9 | 11 12 20
   • Example with an odd number of numbers (set B), where (10) is the center: 5 8 10 (10) 15 18 23

Method 3 of 3: Calculate the interquartile range

1. Determine the median of the bottom and top half of your data set. The median is the "center," or number at the center of a data set. In this case, you are not looking for the center of the entire data set, but the relative center of both the top and bottom halves. If you have an odd number of numbers, don't include its center. For example, with data set B, you would not include one of the ten.
   • Example with an even number of numbers (set A):
     • Median of the bottom half = 7 (Q1)
     • Median of the top half = 12 (Q3)
   • Example with an odd number of numbers (set B):
     • Median of the bottom half = 8 (Q1)
     • Median of the top half = 18 (Q3)
2. Solve Q3 - Q1 to determine the interquartile range. Now you know how many numbers there are between the 25th and 75th percentiles. You can use this to understand the spread of the data. For example, if you can score a maximum of 100 points on a test and the interquartile distance of the marks obtained is 5, then you can assume that most people who took this test knew about the same amount of the subject matter. There is little difference between the high and low numbers. However, if the interquartile range of the grades obtained is 30, you might wonder why some people had such a high grade and others had such a low grade.
   • Example with an even number of numbers (set A): 12 - 7 = 5
   • Example with an odd number of numbers (set B): 18 - 8 = 10

Tips

• It's important to learn how to calculate this on your own, but there are a number of online calculators you can use to make sure you've calculated the interquartile range correctly. Don't rely too much on a calculator app if you need to learn this for math class at school. If you are asked about the interquartile range on a test, you will have to be able to calculate this by heart.