We want to make a box-and-whisker plot for the given data.

39, 42, 40, 47, 38, 39, 44, 55, 44, 58, 45

To do this, we need to identify the minimum, the first quartile, the median, the third quartile, and the maximum of the given data set. Let's do these things one at a time. Quartiles are values that divide a data set into four equal parts.

The median, which is also called the second quartile, separates the data into upper and lower halves.
The first quartile is the median of the lower half of the data.
The third quartile is the median of the upper half of the data.

These three quartiles together with the least and greatest values are often called the five-number summary of the data set. Let's identify the five-number summary of the given data set. First, we will order the data from least to greatest.

The minimum and maximum values are

38

and

58,

respectively. Because the number of values is odd, there is one middle value —

44 .

Median : 44

The median splits our data set into two even parts. Each part has one middle value — the first and third quartiles.

First Quartile : 39 Third Quartile : 47

Let's list all of the information we have found for our plot.

Minimum : First Quartile : Median : Third Quartile : Maximum : 3839444758

Now we are ready to make the box-and-whisker plot. This type of graph summarizes a set of data by displaying it along a number line. It consists of three parts — a box and two whiskers.

The left whisker extends from the minimum to the first quartile.
The box extends from the first to the third quartile and has a vertical line through the median.
The right whisker extends from the third quartile to the maximum.

Let's make our box-and-whisker plot!

Now we want to identify the shape of a distribution. Let's recall some information about box-and-whiskers plot and the shape of a distribution.

Shape	Whiskers	Data
Skewed left	The left whisker is longer than the right whisker.	Most data are on the right.
Symmetric	The whiskers are about the same length.	Most data are on the left.
Skewed right	The right whisker is longer than the left whisker.	Most data are on the left.

In our case right whisker is longer than the left one. This means that most data are on the left — our distribution is skewed right.

Exercise