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)
Responses
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.
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.
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 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 2.5. 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 the middle 50% of the students.
and show work
To find the Interquartile Range (IQR), we first need to find the first quartile (Q1) and the third quartile (Q3).
Step 1: Arrange the data in ascending order:
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
Step 2: Find the median (Q2):
Since there are 18 data points, the median is the average of the 9th and 10th value:
Q2 = (2.5 + 3.0) / 2 = 2.75
Step 3: Find Q1 and Q3:
Q1 is the median of the lower half of the data:
Q1 = (1.0 + 1.0) / 2 = 1.0
Q3 is the median of the upper half of the data:
Q3 = (4.0 + 5.0) / 2 = 4.5
Step 4: Calculate the IQR:
IQR = Q3 - Q1
IQR = 4.5 - 1.0
IQR = 3.5
Therefore, the IQR of the dataset is 3.5. This means that 3.5 hours is the range of the number of hours spent on the project for the middle 50% of the students.