Question

which box plot correctly displays the data set with a maximum of 48, a minimum of 27, a median of 36, an upper quartile of 45, and a lower quartile of 32?

Explanation:

Step1: Recall box - plot components

A box - plot has a minimum value (left - most point), a lower quartile ($Q_1$, left - end of the box), a median ($Q_2$, line inside the box), an upper quartile ($Q_3$, right - end of the box), and a maximum value (right - most point).

Step2: Match the given values to the box - plot

We are given minimum $=27$, lower quartile $Q_1 = 32$, median $Q_2=36$, upper quartile $Q_3 = 45$, and maximum $=48$.

• Look at the left - most point (minimum) and right - most point (maximum).
• Check the left - end of the box (lower quartile), the line inside the box (median), and the right - end of the box (upper quartile).

Answer:

The box - plot where the left - most point is at 27, the left - end of the box is at 32, the line inside the box is at 36, the right - end of the box is at 45, and the right - most point is at 48. (Since the actual options are not labeled, but based on the described values, we match these positions on the box - plots)