Question

Which of the following statements about the box-and-whisker plot below is true?

a. The midrange of the data set shown is.
b. There are more data points inside the data box than are outside the data box.
c. There are more data points in the upper two quartiles than in the lower two quartiles.

Answer 1

The student's question revolves around analyzing box plots and understanding their components such as quartiles and median. Without seeing the actual box plot (Figure A4), we cannot confidently confirm or deny the provided statements, as a box plot's accuracy is highly dependent on the visual representation of the data distribution within the plot.

Step-by-step explanation:

The question the student asked is related to box plots, a type of graph used in statistical analysis to display the distribution of a dataset. A box plot includes a number of key components, such as the minimum value, first quartile, median, third quartile, and the maximum value.

Given the description of the box plot, let's clarify the statements.

• A. Twenty-five percent of the data are at most five - This would be true if the first quartile is at the number 5 on the box plot, as the first quartile represents the 25th percentile of the data.
• B. The statement suggests that the quantities of data from 4-5 and from 5-7 are the same, which can be true if the median is located at 5 and the distance from first to median is equal to the distance from median to third quartile.
• C. A statement about there being no data values of three requires knowledge of individual data points or outliers, which are typically plotted as points outside the 'whiskers' of the box plot.
• D. Fifty percent of the data being four would mean that both the second quartile (median) and the third quartile are at four, which would make the statement true if the box plot reflects this.

Without the visual of Figure A4, we are unable to determine the truth of these statements.