# Boxplots

Before viewing this page, it would be helpful to learn how to calculate Quartiles.

**Box-and-whisker plots** are graphs showing **five-number summary statistics** (lowest score, 1st quartile, median or 2nd quartile, 3rd quartile, highest score) as follows:

**Lowest Score** - the lowest score or number in the data
**1st Quartile (also called Q**_{1} or Lower Quartile) - the score below which lies one quarter of the data
**Median (also called Q**_{2} or 2nd Quartile) - the score below which lies one half of the data
**3rd Quartile (also called Q**_{3} or Upper Quartile) - the score below which lies three quarters of the data
**Highest Score** - the highest score or number in the data

## Did You Know That...?

People from the Netherlands (Dutch people) are the world's tallest people with an average height of 1.85 metres.
As a nation, people from Japan are the world's shortest people with an average height of 1.63 metres.

## Example - Boxplot of Dutch Jeans' Sizes

The waist to ankle lengths (in cm) for 15 Dutch men are listed below. By first calculating the five-number summary, show this information as a boxplot.

Ordered Data (from smallest to largest) -

**90**, 91, 92, **94**, 97, 98, 98, **100**, 100, 105, 106, **107**, 110, 111, **112**

**Answer:**

n = 15

Lowest Score = 90 cm

1st Quartile | = (n + 1) ÷ 4 | = (15 + 1) ÷ 4 | = 4th man | = 94 cm |

Median | = (n + 1) ÷ 2 | = (15 + 1) ÷ 2 | = 8th man | = 100 cm |

3rd Quartile | = (n + 1) ÷ 4 × 3 | = (15 + 1) ÷ 4 × 3 | = 12th man | = 107 cm |

Highest Score = 112 cm

## Question - Boxplot of Japanese Jeans' Sizes

The waist to ankle lengths for 11 Japanese men are listed below. By first calculating the **five-number summary**, show this information as a **boxplot**.

Ordered Data (in cm) - 70, 71, 73, 75, 75, 78, 79, 82, 85, 86, 88