The box extends from the first to the third quartiles (Q_1 and Q_3), with a line in the middle indicating the median (second quartile, Q_2) of the data.
The first segment extends from the least value of the data set to Q_1, while the second one extends from Q_3 to the greatest value of the data.
The set of numbers used to draw the box plot is called the five-number summary of the data set. Each of the five numbers is labeled accordingly.
By using the above diagram we can interpret the given box-and-whisker plot.
The above describes the body mass indices (BMI) of students in a ninth-grade class. Let's write the five-number summary of this data set.
Least Value: 17& First Quartile: 19
Median: 21& Third Quartile: 22
Greatest Value: 28
These values divide the data set into four equal parts. With this information we can state
that a quarter of the ninth-grade students have a BMI between 17 and 19. Additionally, half of the students have a BMI between 19 and 22, and the last quarter has a BMI between 22 and 28.
b In the same way, we can interpret the next box-and-whisker plot.
The above describes the heights of roller coasters at an amusement park. Let's write the five-number summary of this data set.
Least Value: 120& First Quartile: 140
Median: 180& Third Quartile: 220
Greatest Value: 240
Similarly, we can state that a quarter of the roller coasters have a height between 120 and 140. Half of the roller coasters have a height between 140 and 220, and the last quarter has a height between 220 and 240.
