Question

the box plot below represents some data set. approximately what percentage of the data values are less than 32?

Explanation:

Step1: Recall box - plot properties

In a box - plot, the box is divided into quartiles. The left - most part of the box (the lower quartile, \(Q_1\)) represents the value below which 25% of the data lies. The median (the line inside the box) divides the data into two halves (50% below and 50% above), and the upper quartile (\(Q_3\)) represents the value below which 75% of the data lies.

Step2: Analyze the position of 32

From the box - plot, we can see that 32 is at the lower quartile (\(Q_1\)) position. By the definition of quartiles in a box - plot, approximately 25% of the data values are less than the lower quartile. So, if 32 is the lower quartile, then approximately 25% of the data values are less than 32.

Answer:

25