🧐 Wait… What’s the Interquartile Range?
Great question!
The Interquartile Range, or IQR, is a way to measure how spread out the middle 50% of your data is. It helps you understand how “tightly packed” or “spread out” your values are—without being tricked by extreme values (aka outliers).
In short:
IQR = Q3 − Q1
Where:
- Q1 (1st Quartile) is the median of the lower half of your data
- Q3 (3rd Quartile) is the median of the upper half of your data
Table of Contents
🧮 Step-by-Step: How to Calculate IQR
Let’s walk through it together with an example!
📊 Example Data Set
4, 7, 10, 15, 18, 21, 25, 29, 33
Arrange the numbers in order
(Already done ✅)
Find the Median (Middle Value)
There are 9 numbers, so the middle one is: Median = 18
(This just helps us split the data into halves.)
Split the data into two halves
- Lower half:
4, 7, 10, 15 - Upper half:
21, 25, 29, 33
(Exclude the median if there’s an odd number of values.)
Find Q1 and Q3
- Q1 = Median of lower half =
(7 + 10)/2 = 8.5 - Q3 = Median of upper half =
(25 + 29)/2 = 27
Subtract to find the IQR
IQR = Q3 − Q1
IQR = 27 − 8.5 = 18.5🎉 So, the IQR is 18.5!
💡 Why Is IQR Useful?
- It tells you where the “middle chunk” of your data lies.
- It ignores outliers (super high or low numbers).
- It’s great for comparing consistency between data sets.
⚠️ Quick Tips
- Always sort your data first!
- If you have an even number of values, finding medians means averaging the middle two.
- IQR is especially handy when you’re looking at box plots or checking for outliers (which are usually 1.5×IQR above Q3 or below Q1).
📦 Wrapping It Up
The Interquartile Range is like the heart of your data—it tells you how tightly your core values are packed. It’s a super handy tool in statistics, data science, and even school test scores.
Just remember: ➡️ IQR = Q3 − Q1
…and you’re golden!