Box plots (also known as box-and-whisker plots) are a way of showing the five-number summary for a data set. The five number summary consists of the following five statistics:
The box plot below shows a nice summary of all this information:
As you can see the box plot consists of a number line, a rectangle with a line inside (the box), and 2 horizontal lines (the whiskers). The box represents the middle $50%$50% of the scores and its size tells us the interquartile range.
Using the box-and-whisker plot above:
a) what percentage of scores lie between:
$10.9$10.9 and $11.2$11.2
$10.8$10.8 and $10.9$10.9
$11.1$11.1 and $11.3$11.3
$10.9$10.9 and $11.3$11.3
$10.8$10.8 and $11.2$11.2
Think: For these five questions, think about how many quartiles are in that range. Remember that one quartile represents $25%$25% of the data set.
$50%$50% of the scores lie between Q1 to Q3.
$25%$25% of the scores lie between the lowest score and Q1.
$50%$50% of the scores lie between the median and the highest score.
$75%$75% of the scores lie between Q2 and the highest score.
$75%$75% of the scores lie between the lowest score and Q3.
b) In which quartile (or quartiles) is the data the most spread out?
Think: Which quartile takes up the longest space on the graph?
Do: The second quartile is the most spread out.
Using the information in the table, create a box plot to represent this data:
Think: Where do each of these values sit on a box and whisker plot?
Do: Here is our graph. Notice how the values in our table correspond to particular places on the box-and-whisker plot.
Box plots are a graphical representation showing the five-number summary for a data set.
For the box plot shown below, find each of the following:
Complete the table for the given data:
Create a box plot to represent the data in the table below.
Construct and interpret box plots and use them to compare data sets.