Question

Niran surveyed the students in his class on how many hours they spent on their project Here are the
results:
0.5, 1.0, 1.0, 1.0, 1.5, 2.0, 2.0, 2.0, 2.5, 3.0, 3.5, 3.5, 3.5, 4.0, 5.0, 6.0, 8.0, 10
Which of the following is the IQR of the dataset and explains what the value means for this dataset?
(1 point)
The IQR is 2.5. This means that 2.5 hours is the range of the number of hours spent on the project for 50%
of the students.
The IQR is 2.5. This means that 2.5 hours is the range of the number of hours spent on the project for the
middle 50% of the students.
The IQR is 2.75. This means that 2.75 hours is the range of the number of hours spent on the project for
the middle 50% of the students.
The IQR is 2.75. This means that 2.75 hours is the range of the number of hours spent on the project for
50% of the students.

Answer 1

Correct choice: "The IQR is 2.5. This means that 2.5 hours is the range of the number of hours spent on the project for the middle 50% of the students."

Work: n = 18, median = average of 9th and 10th values = (2.5 + 3.0)/2 = 2.75.
Lower half (first 9 values) median (Q1) = 5th value = 1.5.
Upper half (last 9 values) median (Q3) = 5th value = 4.0.
IQR = Q3 − Q1 = 4.0 − 1.5 = 2.5, which is the spread covering the middle 50% of students.