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 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 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.
To find the IQR (Interquartile Range), we first need to determine the quartiles.
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
2. Find the median (Q2):
Since there are 18 data points, the median is the average of the 9th and 10th values:
(2.5 + 3.0) / 2 = 2.75
3. Find the lower quartile (Q1):
The lower quartile is the median of the lower half of the data. Since there are 9 data points in the lower half, the median is the average of the 4th and 5th values:
(1.0 + 1.5) / 2 = 1.25
4. Find the upper quartile (Q3):
The upper quartile is the median of the upper half of the data. Again, there are 9 data points in the upper half, so the median is the average of the 14th and 15th values:
(4.0 + 5.0) / 2 = 4.5
5. Calculate the IQR:
IQR = Q3 - Q1 = 4.5 - 1.25 = 3.25