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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.



A 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

Let’s analyze each of the statements based on the box plot information provided:

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 not correct. The median is not the same as the average (mean), so we cannot conclude that the median jump length is the average.

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 indeed represents the middle value when the data is ordered.

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 not correct in its conclusion about the distribution of the data. The interquartile range (IQR) is defined as the difference between the first quartile (Q1) and the third quartile (Q3). If the box plot shows that Q1 is at 3 feet and Q3 is at 7 feet, then the interquartile range is indeed 4 feet (7 - 3). However, the statement about the jumps being "within 4 feet of the median" is misleading; it is more accurate to say that the middle 50% of the data lies within this range.

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 correct. Given that the IQR is 4 feet (from 3 to 7 feet), and the median is 5 feet, it indicates that half of the students have long jumps that fall within the distance of 2 feet from the median (so from 3 to 7 feet).

Based on this analysis, the correct answers are:

  • B
  • D