We are asked to create a data set that this box-and-whisker plot can represent. To do so, let's use the graph to find the five-number summary of the data. These are the least value, first quartile, median, third quartile, and greatest value. Following this order, these are the points marked on the box plot from left to right.
Five-Number Summary
Least Value
3
First Quartile (Q_1)
4
Median
≈ 10.5
Third Quartile (Q_3)
15
Greatest Value
18
Our data set must have 3 as the least value and 18 as the greatest value. The median of the data must be about 10.5. Additionally, the first quartile must be 4 and the third quartile must be 15. Recall that the first and third quartiles are the medians of the lower and upper halves of the data, respectively. With this information, we can create an example data set that follows this criteria.
{ 3, 3, 4, 5, 6, 10.5, 11, 12, 15, 17, 18 }
Please note that this is only one of the many possible data sets.
