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A track-and-field coach recorded the length of each student's standing long jump. The data is summarized in the box plot.

 
Short description, A box plot.,Long description,
The box plot is entitled Standing Long Jumps with a number line that goes from 0 to 10 feet. The whiskers range from 1 to 9 feet, and the box ranges from 3 to 7 feet with a median of 5 feet.
Question
Choose ,begin emphasis,all,end emphasis, of the statements that can be concluded from this data. 
Answer options with 4 options
A.
The median jump length is 5 feet, which is the average length of a standing long jump for the students represented in the box plot.
B.
The median jump length is 5 feet, which is the length of the middle student's long jump if the students were ordered by the length of their long jump.
C.
The interquartile range of the long jumps is 4 feet, which means that about half of the students' long jumps are within 4 feet of the median.
D.
The interquartile range of the long jumps is 4 feet, which means that about half of the students' long jumps are within 2 feet of the median.

1 answer

Based on the information provided about the box plot for the standing long jumps, we can analyze each statement:

A. The median jump length is 5 feet, which is the average length of a standing long jump for the students represented in the box plot.

  • This statement is incorrect because the median is not the average (mean) of the data. The average is calculated differently and may differ from the median.

B. The median jump length is 5 feet, which is the length of the middle student's long jump if the students were ordered by the length of their long jump.

  • This statement is correct. The median represents the middle value of an ordered set of data.

C. The interquartile range of the long jumps is 4 feet, which means that about half of the students' long jumps are within 4 feet of the median.

  • This statement is incorrect. The interquartile range (IQR) is the range between the first quartile (Q1) and the third quartile (Q3) and does not mean that 4 feet are within the median.

D. The interquartile range of the long jumps is 4 feet, which means that about half of the students' long jumps are within 2 feet of the median.

  • This statement is also incorrect. The IQR is a measure of statistical dispersion and encompasses the range from Q1 to Q3, but it does not imply that half of the students' jumps are within 2 feet of the median.

The correct statements that can be concluded from the data are:

  • B: The median jump length is 5 feet, which is the length of the middle student's long jump if the students were ordered by the length of their long jump.