What is a box plot?

Box plot (also called ‘box and whisker plot’) visualizes the distribution of numerical data and helps in identifying outliers present in the data.

Below, you can see the box plot of a toy data set having just 10 observations – 144, 147, 153, 154, 156, 157, 161, 164, 170, 181.

Notice the following components in the above box plot:

• 1^st Quartile (25^th percentile)
• Median (2^nd Quartile or 50^th percentile)
• 3^rd Quartile (75^th percentile)
• Interquartile Range (IQR – difference between 3^rd and 1^st Quartile)
• Whiskers — marks the lowest data point which lies within 1.5 IQR of the 1^st quartile, and the highest datum which lies within 1.5 IQR of the 3^rd quartile
• Outliers — any data points beyond 1.5 IQR of the 1^st or 3^rd quartile, i.e. values which are greater than 3^rd Quartile + 1.5 * IQR or less than 1^st Quartile – 1.5 * IQR.

In other words, whiskers extend from the quartiles to the rest of the distribution, except for points that are determined to be “outliers”.