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, let's analyze the given box-and-whisker plot to find the range and interquartile range of the data set.
The above represents the ages of the members of a backpacking expedition in the mountains. We can see that the greatest value of the data set is 30 and the least value is 18. Let's calculate the difference of these values to find the range.
Range: 30- 18=12years
This means that ages of the members vary by no more than 12 years. The interquartile range (IQR) is another measure of variation for data. It is given by the difference of the third quartile, Q_3, and the first quartile, Q_1. It represents the range of the middle half of the data. We can see that Q_1 is 23 and Q_3 is 29. Let's calculate the difference of these values to find the interquartile range.
Q_3- Q_1 ⇒ 29- 23=6years
This means that the middle half of the ages of the members varies by no more than 6 years.
