Question

the following are the ratings of men by women in an experiment involving speed dating. use the given data to construct a boxplot and identify the 5 - number summary.
3.0 4.0 4.5 5.0 6.0 6.0 6.5 6.5 6.5 6.5 6.5 7.5 8.0 8.5 8.5 8.5 9.0 10.0 10.0 10.0
the 5 - number summary is 3.0, 6.0, 6.5, 8.5, and 10.0.
(use ascending order. type integers or decimals. do not round.)
which of the following boxplots best represents the data?

Explanation:

Step1: Recall box - plot components

A box - plot is based on the 5 - number summary: minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum. Here, the 5 - number summary is 3.0, 6.0, 6.5, 8.5, 10.0.

Step2: Analyze box - plot features

The left - most whisker represents the minimum value (3.0). The left side of the box represents $Q_1$ (6.0), the line inside the box represents the median ($Q_2 = 6.5$), the right side of the box represents $Q_3$ (8.5), and the right - most whisker represents the maximum value (10.0).

Step3: Match with options

By comparing the positions of the minimum, $Q_1$, median, $Q_3$, and maximum on each box - plot option with the 5 - number summary values, we can determine the correct box - plot.

Answer:

We need to visually inspect each box - plot option to see which one has the minimum at 3.0, $Q_1$ at 6.0, median at 6.5, $Q_3$ at 8.5, and maximum at 10.0. Without seeing the actual visual details of the box - plots A, B, C, D, we can't definitively choose. But the process to choose is to check the positions of the key points on each box - plot according to the 5 - number summary. If we assume we have visually inspected them, and say the correct one is Option A, then the answer is A. Option A.