Box plots (also known as boxandwhisker plots) are a way of showing the fivenumber summary for a data set. The five number summary consists of the following five statistics:
Minimum  $17$17 
Lower Quartile  $52$52 
Median  $69$69 
Upper Quartile  $87$87 
Maximum  $100$100 
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 boxandwhisker 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.
Do:
$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:
Minimum  $5$5 
Lower Quartile  $25$25 
Median  $40$40 
Upper Quartile  $45$45 
Maximum  $65$65 
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 boxandwhisker plot.
Box plots are a graphical representation showing the fivenumber summary for a data set.

For the box plot shown below, find each of the following:
0 2 4 6 8 10 12 14 16 18 20 score 
Complete the table for the given data:
Minimum  $\editable{}$ 

Lower Quartile  $\editable{}$ 
Median  $\editable{}$ 
Upper Quartile  $\editable{}$ 
Maximum  $\editable{}$ 
Create a box plot to represent the data in the table below.
Minimum  $10$10 

Lower quartile  $20$20 
Median  $40$40 
Upper quartile  $55$55 
Maximum  $75$75 
Construct and interpret box plots and use them to compare data sets.