Question

I saw it class recorded the number of minutes each student had spent on a project
Student 1. 30 minutes
Student 2. 45 minutes
Student 3. 40 minutes
student 4. 50 minutes
Student 5. 35 minutes
Student 6. 60 minutes
Student 7. 55 minutes
What is the interquartile range

Answer 1

To find the interquartile range (IQR), we first need to order the minutes each student spent on the project from least to greatest:

1. Student 1: 30 minutes
2. Student 5: 35 minutes
3. Student 3: 40 minutes
4. Student 2: 45 minutes
5. Student 4: 50 minutes
6. Student 7: 55 minutes
7. Student 6: 60 minutes

Ordered list: **30, 35, 40, 45, 50, 55, 60**

Next, we find the first quartile (Q1) and the third quartile (Q3):

1. **Finding Q1 (the median of the first half)**:
- The first half of the data is: 30, 35, 40
- The median of this data (Q1) is 35 minutes.

2. **Finding Q3 (the median of the second half)**:
- The second half of the data is: 45, 50, 55, 60
- The median of this data (Q3) is the average of 50 and 55:
\[
Q3 = \frac{50 + 55}{2} = \frac{105}{2} = 52.5 \text{ minutes}.
\]

3. **Calculating the Interquartile Range (IQR)**:
\[
IQR = Q3 - Q1 = 52.5 - 35 = 17.5 \text{ minutes}.
\]

Thus, the interquartile range is **17.5 minutes**.