Interquartile range (IQR)
The interquartile range (IQR) is how wide the middle half of your data is: the third quartile minus the first. It tells you how spread out the typical values are.
Select any words here to ask your Maestro about them.
In one Tuesday's deliveries, Q1 is 20 minutes and Q3 is 30. If anything past Q3 + 1.5 × IQR counts as an outlier, is a 44-minute delivery one?
How to find it: sort the data, find the first quartile (Q1, a quarter of the values below it) and the third (Q3, three quarters below). IQR = Q3 − Q1. It's the box in a box plot.
What it's for: describing how spread out your data is when there are extremes, alongside the median. Standard deviation uses every value; the IQR uses only the middle half.
Where you see it: in the rule that flags an outlier on a box plot, and when comparing groups with long tails, like salaries or wait times.
How it's used
One in Excel
IQR in Excel
- Put the times in B2:B14
- =QUARTILE.INC(B2:B14, 1)The first quartile: a quarter of the data falls below it.
- =QUARTILE.INC(B2:B14, 3)The third quartile: three quarters fall below it.
- marked: Subtract the first from the third: that's the IQRHow wide the middle half of your data is, with the extremes left out.
When to look closer
Which quartile formula?
The same 13 times
- marked: =QUARTILE.INC: Q1 = 20, Q3 = 30, IQR = 10
Excel has QUARTILE.INC and QUARTILE.EXC. On the same 13 delivery times, do they give the same IQR?
Ask your Maestro about Interquartile range
It answers from the free course page closest to this word, the way it answers while you study.
You: What does "Interquartile range" mean, in plain words?
Your Maestro: I'll explain it with a case of yours: it sticks better than a definition. Which times or amounts at work have long tails?
Asking about: Answers from the page "What is exploratory data analysis, and what do I do first with a new table?"
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Related terms
- Percentile (and quartiles)
A percentile is the value a given share of the data falls at or below: 90% falls at or below the 90th. Quartiles are the 25th, 50th and 75th.
- Median
The median is the middle value when you sort the data from lowest to highest: half sit below it and half above. In Excel you get it with =MEDIAN(B2:B11).
- Box plot
A box plot sums up a variable in five numbers: the minimum, the first quartile, the median, the third quartile and the maximum. The box runs from the first to the third quartile and holds the middle half of the data.
- Outlier
An outlier is a value that sits far from the rest, like a $9,800 order among $300 ones. It can be a data-entry error or a real, important case: before you drop it, find out which.