Question
Find the interquartile range
A dataset of homework time spent by students in minutes per week is presented. The dataset, listed numerically, ranges from 25 to 85 minutes. The text above the dataset clarifies that the numbers represent the time in minutes.
The dataset is: 25, 30, 32, 35, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85.
35
45
55
65
A dataset of homework time spent by students in minutes per week is presented. The dataset, listed numerically, ranges from 25 to 85 minutes. The text above the dataset clarifies that the numbers represent the time in minutes.
The dataset is: 25, 30, 32, 35, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85.
35
45
55
65
Answers
Answered by
GPT-4o mini
To find the interquartile range (IQR) of the dataset, we first need to determine the first quartile (Q1) and the third quartile (Q3).
1. **Sort the dataset**: The dataset is already sorted:
- 25, 30, 32, 35, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85
2. **Determine the number of data points (n)**: There are 15 data points.
3. **Find the median (Q2)**: The median is the middle value of the dataset. For an odd number of values (n = 15), Q2 is the value at position (n + 1) / 2 = 16 / 2 = 8.
- The median (Q2) is the 8th value: **50**.
4. **Find Q1**: Q1 is the median of the first half of the dataset (the first 7 values):
- First half: 25, 30, 32, 35, 35, 40, 45
- There are 7 values here. The median is the 4th value (n + 1) / 2 = 4.
- The value at position 4 is: **35**.
5. **Find Q3**: Q3 is the median of the second half of the dataset (the last 7 values):
- Second half: 50, 55, 60, 65, 70, 75, 80, 85
- There are 7 values here. The median is the 4th value (n + 1) / 2 = 4.
- The value at position 4 is: **70**.
6. **Calculate the interquartile range (IQR)**:
\[
\text{IQR} = Q3 - Q1 = 70 - 35 = 35
\]
Thus, the interquartile range of the dataset is **35 minutes**.
1. **Sort the dataset**: The dataset is already sorted:
- 25, 30, 32, 35, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85
2. **Determine the number of data points (n)**: There are 15 data points.
3. **Find the median (Q2)**: The median is the middle value of the dataset. For an odd number of values (n = 15), Q2 is the value at position (n + 1) / 2 = 16 / 2 = 8.
- The median (Q2) is the 8th value: **50**.
4. **Find Q1**: Q1 is the median of the first half of the dataset (the first 7 values):
- First half: 25, 30, 32, 35, 35, 40, 45
- There are 7 values here. The median is the 4th value (n + 1) / 2 = 4.
- The value at position 4 is: **35**.
5. **Find Q3**: Q3 is the median of the second half of the dataset (the last 7 values):
- Second half: 50, 55, 60, 65, 70, 75, 80, 85
- There are 7 values here. The median is the 4th value (n + 1) / 2 = 4.
- The value at position 4 is: **70**.
6. **Calculate the interquartile range (IQR)**:
\[
\text{IQR} = Q3 - Q1 = 70 - 35 = 35
\]
Thus, the interquartile range of the dataset is **35 minutes**.