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 2.75 . 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 the midale 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.
show all of the steps
show all of the steps
Answers
Answered by
GPT 3.5
To find the IQR (Interquartile Range), we first need to find the first quartile (Q1) and the third quartile (Q3) of the dataset.
First, we need to arrange the dataset 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, 10.0
Next, we find the median. The median of the dataset is the middle number when ordered, which in this case is 3.0.
Now, to find Q1, we need to find the median of the lower half of the data. The lower half of the data is:
0.5, 1.0, 1.0, 1.0, 1.5, 2.0, 2.0, 2.0, 2.5, 3.0
The median of this lower half is 1.5, which is Q1.
To find Q3, we need to find the median of the upper half of the data. The upper half of the data is:
3.5, 3.5, 3.5, 4.0, 5.0, 6.0, 8.0, 10.0
The median of this upper half is 4.75, which is Q3.
Now, we can calculate the IQR:
IQR = Q3 - Q1
IQR = 4.75 - 1.5
IQR = 2.75
Therefore, the IQR of the dataset 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.
First, we need to arrange the dataset 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, 10.0
Next, we find the median. The median of the dataset is the middle number when ordered, which in this case is 3.0.
Now, to find Q1, we need to find the median of the lower half of the data. The lower half of the data is:
0.5, 1.0, 1.0, 1.0, 1.5, 2.0, 2.0, 2.0, 2.5, 3.0
The median of this lower half is 1.5, which is Q1.
To find Q3, we need to find the median of the upper half of the data. The upper half of the data is:
3.5, 3.5, 3.5, 4.0, 5.0, 6.0, 8.0, 10.0
The median of this upper half is 4.75, which is Q3.
Now, we can calculate the IQR:
IQR = Q3 - Q1
IQR = 4.75 - 1.5
IQR = 2.75
Therefore, the IQR of the dataset 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.