Question

Interpreting a Boxplot Shown below is a boxplot of a sample of 30 maximal skull breadths (mm) measured from Egyptian skulls from around 4000 B.C. What do the numbers in the box-plot represent?

Short answer

The minimum value is 119 mm.

The maximum value is 141 mm.

The first quartile is 128 mm.

The third quartile is 135 mm.

The median is 131 mm.

Step-by-step solution

Given information

A boxplot for the sample of 30 maximum skull breadths recorded in mm is given.

Description of the boxplot 

A boxplot is described using the following five-number summary:

• Minimum value
• Maximum value
• First quartile
• Third quartile
• Median

The rectangular box is formed using the first and third quartile values as extreme edges, with the median marked in between.

The minimum values are marked using the whiskers extending from the first and third quartile measures.

Interpretation of the boxplot 

The values stated about each vertical line are the values of the observations as per the number line.

The rectangular box has two vertical edges at 128 and 135.

These are the first and third quartiles, respectively.

The vertical line between the box at 131 indicates the median as per the description.

Thus, the median value is 131.

The two whiskers extend up to 119 and 141, which are the minimum and maximum values, respectively, for the dataset.

The results can be summarized as follows:

• The minimum value is 119 mm.
• The maximum value is 141 mm.
• The first quartile is 128 mm.
• The third quartile is 135 mm.
• The median is 131 mm.