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.
2.0
3.0
3.5
4.5
5.5
5.5
6.5
6.5
6.5
6.5
6.5
7.5
8.5
9.5
9.5
9.5
10.0
10.0
10.0
10.0
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.)
Part 2
Which of the following boxplots best represents the data?
A.
0
2
4
6
8
10
Ratings
A boxplot titled Ratings is plotted above a horizontal scale from 0 to 10 in increments of 1. The boxplot consists of a box that extends from 4.5 to 9.75, a vertical line segment drawn through the box at 6.5, and a horizontal line segment extending from 2 to 10 that bisects the box. All values are approximate.
B.
0
2
4
6
8
10
Ratings
A boxplot titled Ratings is plotted above a horizontal scale from 0 to 10 in increments of 1. The boxplot consists of a box that extends from 4.5 to 8.5, a vertical line segment drawn through the box at 5.5, and a horizontal line segment extending from 1 to 10 that bisects the box. All values are approximate.
C.
0
2
4
6
8
10
Ratings
A boxplot titled Ratings is plotted above a horizontal scale from 0 to 10 in increments of 1. The boxplot consists of a box that extends from 5.5 to 9.5, a vertical line segment drawn through the box at 6.5, and a horizontal line segment extending from 2 to 10 that bisects the box. All values are approximate.
D.
0
2
4
6
8
10
Ratings
2.0
3.0
3.5
4.5
5.5
5.5
6.5
6.5
6.5
6.5
6.5
7.5
8.5
9.5
9.5
9.5
10.0
10.0
10.0
10.0
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.)
Part 2
Which of the following boxplots best represents the data?
A.
0
2
4
6
8
10
Ratings
A boxplot titled Ratings is plotted above a horizontal scale from 0 to 10 in increments of 1. The boxplot consists of a box that extends from 4.5 to 9.75, a vertical line segment drawn through the box at 6.5, and a horizontal line segment extending from 2 to 10 that bisects the box. All values are approximate.
B.
0
2
4
6
8
10
Ratings
A boxplot titled Ratings is plotted above a horizontal scale from 0 to 10 in increments of 1. The boxplot consists of a box that extends from 4.5 to 8.5, a vertical line segment drawn through the box at 5.5, and a horizontal line segment extending from 1 to 10 that bisects the box. All values are approximate.
C.
0
2
4
6
8
10
Ratings
A boxplot titled Ratings is plotted above a horizontal scale from 0 to 10 in increments of 1. The boxplot consists of a box that extends from 5.5 to 9.5, a vertical line segment drawn through the box at 6.5, and a horizontal line segment extending from 2 to 10 that bisects the box. All values are approximate.
D.
0
2
4
6
8
10
Ratings
Answers
Answered by
GPT-4o mini
To construct the boxplot and identify the 5-number summary for the given speed dating ratings, we will first determine the five numbers: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
### Given Data:
```
2.0, 3.0, 3.5, 4.5, 5.5, 5.5, 6.5, 6.5, 6.5, 6.5, 6.5, 7.5, 8.5, 9.5, 9.5, 9.5, 10.0, 10.0, 10.0, 10.0
```
### Step 1: Sort the Data
The ratings are already sorted in ascending order.
### Step 2: Identify the 5-number summary
1. **Minimum**: The smallest value = **2.0**
2. **Maximum**: The largest value = **10.0**
3. **Median (Q2)**: The middle value. For n = 20 (even), the median is the average of the 10th and 11th values.
- 10th value = 6.5
- 11th value = 6.5
- Median \( (Q2) = \frac{6.5 + 6.5}{2} = 6.5 \)
4. **First Quartile (Q1)**: The median of the first half (first 10 values).
- First half: 2.0, 3.0, 3.5, 4.5, 5.5, 5.5, 6.5, 6.5, 6.5, 6.5
- Median of this set = average of the 5th and 6th values (5.5 and 5.5)
- First Quartile \( (Q1) = \frac{5.5 + 5.5}{2} = 5.5 \)
5. **Third Quartile (Q3)**: The median of the second half (last 10 values).
- Second half: 6.5, 6.5, 7.5, 8.5, 9.5, 9.5, 9.5, 10.0, 10.0, 10.0
- Median of this set = average of the 5th and 6th values (9.5 and 9.5)
- Third Quartile \( (Q3) = \frac{9.5 + 9.5}{2} = 9.5 \)
### 5-number summary:
- Minimum: **2.0**
- Q1: **5.5**
- Median (Q2): **6.5**
- Q3: **9.5**
- Maximum: **10.0**
Thus, the 5-number summary is:
**2.0, 5.5, 6.5, 9.5, 10.0**
### Part 1
The 5-number summary is:
- Minimum: **2.0**
- Q1: **5.5**
- Median: **6.5**
- Q3: **9.5**
- Maximum: **10.0**
### Part 2: Constructing the Box Plot
- The boxplot will have:
- The box stretching from Q1 (5.5) to Q3 (9.5)
- The median line inside the box at 6.5
- "Whiskers" extending from the minimum (2.0) to the maximum (10.0)
### Identify the correct boxplot:
Let's analyze the options:
- **Option A**: Box from 4.5 to 9.75 is incorrect; whiskers don't match.
- **Option B**: Box from 4.5 to 8.5 is incorrect; whiskers don't match.
- **Option C**: Box from 5.5 to 9.5, median at 6.5, and extends from 2 to 10 are correct.
- **Option D**: No details available here, but if it's not option C, it's likely incorrect.
### Conclusion:
The correct answer for the **5-number summary** is:
**2.0, 5.5, 6.5, 9.5, 10.0**
The best boxplot that represents the data is **Option C**.
### Given Data:
```
2.0, 3.0, 3.5, 4.5, 5.5, 5.5, 6.5, 6.5, 6.5, 6.5, 6.5, 7.5, 8.5, 9.5, 9.5, 9.5, 10.0, 10.0, 10.0, 10.0
```
### Step 1: Sort the Data
The ratings are already sorted in ascending order.
### Step 2: Identify the 5-number summary
1. **Minimum**: The smallest value = **2.0**
2. **Maximum**: The largest value = **10.0**
3. **Median (Q2)**: The middle value. For n = 20 (even), the median is the average of the 10th and 11th values.
- 10th value = 6.5
- 11th value = 6.5
- Median \( (Q2) = \frac{6.5 + 6.5}{2} = 6.5 \)
4. **First Quartile (Q1)**: The median of the first half (first 10 values).
- First half: 2.0, 3.0, 3.5, 4.5, 5.5, 5.5, 6.5, 6.5, 6.5, 6.5
- Median of this set = average of the 5th and 6th values (5.5 and 5.5)
- First Quartile \( (Q1) = \frac{5.5 + 5.5}{2} = 5.5 \)
5. **Third Quartile (Q3)**: The median of the second half (last 10 values).
- Second half: 6.5, 6.5, 7.5, 8.5, 9.5, 9.5, 9.5, 10.0, 10.0, 10.0
- Median of this set = average of the 5th and 6th values (9.5 and 9.5)
- Third Quartile \( (Q3) = \frac{9.5 + 9.5}{2} = 9.5 \)
### 5-number summary:
- Minimum: **2.0**
- Q1: **5.5**
- Median (Q2): **6.5**
- Q3: **9.5**
- Maximum: **10.0**
Thus, the 5-number summary is:
**2.0, 5.5, 6.5, 9.5, 10.0**
### Part 1
The 5-number summary is:
- Minimum: **2.0**
- Q1: **5.5**
- Median: **6.5**
- Q3: **9.5**
- Maximum: **10.0**
### Part 2: Constructing the Box Plot
- The boxplot will have:
- The box stretching from Q1 (5.5) to Q3 (9.5)
- The median line inside the box at 6.5
- "Whiskers" extending from the minimum (2.0) to the maximum (10.0)
### Identify the correct boxplot:
Let's analyze the options:
- **Option A**: Box from 4.5 to 9.75 is incorrect; whiskers don't match.
- **Option B**: Box from 4.5 to 8.5 is incorrect; whiskers don't match.
- **Option C**: Box from 5.5 to 9.5, median at 6.5, and extends from 2 to 10 are correct.
- **Option D**: No details available here, but if it's not option C, it's likely incorrect.
### Conclusion:
The correct answer for the **5-number summary** is:
**2.0, 5.5, 6.5, 9.5, 10.0**
The best boxplot that represents the data is **Option C**.