The following are the ratings of men by women in an experiment involving speed dating. Use the given data to construct a boxplot and identify the 5-number summary.
1.0
1.0
1.5
2.0
3.0
3.0
4.0
4.0
4.0
4.0
4.0
4.5
4.5
5.0
5.0
5.0
6.0
6.5
7.5
8.0
Question content area bottom
Part 1
The 5-number summary is
enter your response here,
enter your response here,
enter your response here,
enter your response here, and
enter your response here.
(Use ascending order. Type integers or decimals. Do not round.)
1.0
1.0
1.5
2.0
3.0
3.0
4.0
4.0
4.0
4.0
4.0
4.5
4.5
5.0
5.0
5.0
6.0
6.5
7.5
8.0
Question content area bottom
Part 1
The 5-number summary is
enter your response here,
enter your response here,
enter your response here,
enter your response here, and
enter your response here.
(Use ascending order. Type integers or decimals. Do not round.)
Answers
Answered by
GPT-4o mini
To find the 5-number summary (minimum, first quartile, median, third quartile, and maximum) for the given data, we'll follow these steps:
1. **Sort the Data:** The data is already sorted in ascending order:
```
1.0, 1.0, 1.5, 2.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.5, 4.5, 5.0, 5.0, 5.0, 6.0, 6.5, 7.5, 8.0
```
2. **Determine the Minimum and Maximum:**
- **Minimum:** 1.0
- **Maximum:** 8.0
3. **Calculate the Median (Q2):**
- There are 20 data points (even number), so the median will be the average of the 10th and 11th values.
- 10th value: 4.0
- 11th value: 4.0
- Median (Q2) = (4.0 + 4.0) / 2 = 4.0
4. **Calculate the First Quartile (Q1):**
- Q1 is the median of the first half of the data (the 1st to the 10th values).
- First half: 1.0, 1.0, 1.5, 2.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0
- Since there are 10 values in the first half (even), Q1 is the average of the 5th and 6th values.
- 5th value: 3.0
- 6th value: 3.0
- Q1 = (3.0 + 3.0) / 2 = 3.0
5. **Calculate the Third Quartile (Q3):**
- Q3 is the median of the second half of the data (the 11th to the 20th values).
- Second half: 4.5, 5.0, 5.0, 5.0, 6.0, 6.5, 7.5, 8.0
- Since there are 10 values in the second half (even), Q3 is the average of the 5th and 6th values.
- 5th value: 6.0
- 6th value: 6.5
- Q3 = (6.0 + 6.5) / 2 = 6.25
Now, compiling this information, the 5-number summary is:
- Minimum: 1.0
- Q1: 3.0
- Median (Q2): 4.0
- Q3: 6.25
- Maximum: 8.0
Thus, the final 5-number summary can be written as:
**The 5-number summary is**
1.0,
3.0,
4.0,
6.25,
8.0.
1. **Sort the Data:** The data is already sorted in ascending order:
```
1.0, 1.0, 1.5, 2.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.5, 4.5, 5.0, 5.0, 5.0, 6.0, 6.5, 7.5, 8.0
```
2. **Determine the Minimum and Maximum:**
- **Minimum:** 1.0
- **Maximum:** 8.0
3. **Calculate the Median (Q2):**
- There are 20 data points (even number), so the median will be the average of the 10th and 11th values.
- 10th value: 4.0
- 11th value: 4.0
- Median (Q2) = (4.0 + 4.0) / 2 = 4.0
4. **Calculate the First Quartile (Q1):**
- Q1 is the median of the first half of the data (the 1st to the 10th values).
- First half: 1.0, 1.0, 1.5, 2.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0
- Since there are 10 values in the first half (even), Q1 is the average of the 5th and 6th values.
- 5th value: 3.0
- 6th value: 3.0
- Q1 = (3.0 + 3.0) / 2 = 3.0
5. **Calculate the Third Quartile (Q3):**
- Q3 is the median of the second half of the data (the 11th to the 20th values).
- Second half: 4.5, 5.0, 5.0, 5.0, 6.0, 6.5, 7.5, 8.0
- Since there are 10 values in the second half (even), Q3 is the average of the 5th and 6th values.
- 5th value: 6.0
- 6th value: 6.5
- Q3 = (6.0 + 6.5) / 2 = 6.25
Now, compiling this information, the 5-number summary is:
- Minimum: 1.0
- Q1: 3.0
- Median (Q2): 4.0
- Q3: 6.25
- Maximum: 8.0
Thus, the final 5-number summary can be written as:
**The 5-number summary is**
1.0,
3.0,
4.0,
6.25,
8.0.