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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.

Interquartile range (IQR)

 

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:

Interquartile range boxplot 

Learnings on IQR

Khan Academy video: Interquartile range (IQR)

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