# Interquartile range (IQR)

The interquartile range (IQR) measures the **variability** in a dataset splitting the dataset into quartiles.

Quartiles divide a rank-ordered dataset into 4 equal portions typically denoted by Q1, Q2 and Q3.

- Q1 is the median, or the “middle” value, of the
**first half**of the dataset - Q2 is the median of the
**entire dataset** - Q3 is the median, or the “middle” value, of the
**second half**of the dataset

And the IQR = Q3 – Q1

## Interquartile range (IQR) visualized

Say we have the following dataset: 1, 3, 5, 8, 10, 12, 15, 16, 19

The median is **10 as it is the middle number**. It has **four digits to the left and four digits to the right**. The IQR is the difference between the median of the first half of the upper side of the median of the dataset and the median of the lower half of the dataset.

**Boxplots**

The IQR is usually illustrated graphically with a Boxplot. Let’s see a boxplot illustrating the dataset above: 1, 3, 5, 8, 10, 12, 15, 16, 19:

## Learnings on IQR

Khan Academy video: Interquartile range (IQR)

#### Carsten Grube

Freelance Data Analyst

##### Normal distribution

##### Two-sample inference

##### Confidence intervals

##### Simple linear regression, fundamentals

##### ANOVA & the F-distribution

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