Question
Question 1 A)Calculate the 5-number summary of the skewed dataset 15, 16, 16, 17, 17, 18, 18, 18, 19, 19, 29. When constructing the box plot on a number line, which explains a reason why the dataset is skewed?(1 point) Responses The median is exactly in the middle of the box. The median is exactly in the middle of the box. The right whisker is much longer than the left whisker. The right whisker is much longer than the left whisker. The whiskers are the same length. The whiskers are the same length. The 5 numbers in the summary are equally spread apart. The 5 numbers in the summary are equally spread apart. Question 2 A)Calculate the 5-number summary of the skewed dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16. Which of the following choices is quartile 3?(1 point) Responses 8 8 9 9 2.5 2.5 6.5 6.5 Question 3 A)Which option is true about the outliers of the skewed dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16?(1 point) Responses There are no outliers in the dataset. There are no outliers in the dataset. The outliers of the dataset are 5, 14, and 16. The outliers of the dataset are 5, 14, and 16. The only outlier of the dataset is 16. The only outlier of the dataset is 16. The outliers of the dataset are 14 and 16. The outliers of the dataset are 14 and 16. Question 4 A)A stock analyst is comparing the interquartile range of the day’s stock prices of Stock A and Stock B. Stock A has an interquartile range of 3, and Stock B has an interquartile range of 11. What interpretation can be made from the interquartile range of each stock?(1 point) Responses Stock B has more variability than Stock A. Stock B has more variability than Stock A. The price of Stock B is higher than the price of Stock A by 7. The price of Stock B is higher than the price of Stock A by 7. Stock A has more variability than Stock B. Stock A has more variability than Stock B. The stock price for Stock B is higher than the price for Stock A. The stock price for Stock B is higher than the price for Stock A. Question 5 A)A video game player had the following scores: 287, 389, 287, 329, 295, 290, 397, 387, 365. What does the IQR indicate about this dataset?(1 point) Responses An IQR of 329 indicates that the center of the data is around this score. An IQR of 329 indicates that the center of the data is around this score. An IQR of 99.5 indicates that the video game player had a relatively small variability for their middle scores. An IQR of 99.5 indicates that the video game player had a relatively small variability for their middle scores. An IQR of 329 indicates that the video game player had a relatively large variability for their middle scores. An IQR of 329 indicates that the video game player had a relatively large variability for their middle scores. An IQR of 99.5 indicates that the average score was 99.5 points. An IQR of 99.5 indicates that the average score was 99.5 points.
Answers
GPT-4o mini
Let's go through each question one by one.
### Question 1 A)
**Calculate the 5-number summary of the dataset 15, 16, 16, 17, 17, 18, 18, 18, 19, 19, 29.**
1. **Minimum:** 15
2. **Q1 (1st Quartile):** The first quartile is the median of the first half of the data. The first half is [15, 16, 16, 17, 17]. The median here is 16.
3. **Median (Q2):** The median of the entire dataset is the middle value, which is 18.
4. **Q3 (3rd Quartile):** The third quartile is the median of the second half of the data, which is [18, 18, 19, 19, 29]. The median is 19.
5. **Maximum:** 29
Thus, the 5-number summary is:
- Minimum: 15
- Q1: 16
- Median: 18
- Q3: 19
- Maximum: 29
**Which explains a reason why the dataset is skewed?**
- The right whisker is much longer than the left whisker.
### Question 2 A)
**Calculate the 5-number summary of the dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16.**
1. **Minimum:** 5
2. **Q1:** The first quartile (first half: [5, 6, 6, 7, 7, 8]) is the median of this half: Q1 = 6.5.
3. **Median (Q2):** The median of the entire dataset (middle values: 8 and 9) is 8.5.
4. **Q3:** The third quartile (second half: [8, 9, 14, 16]) is the median of this half: Q3 = 9.
5. **Maximum:** 16
**Which of the following choices is quartile 3?**
- 9
### Question 3 A)
**Which option is true about the outliers of the dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16?**
To find outliers, we can use the IQR method:
1. **IQR = Q3 - Q1 = 9 - 6.5 = 2.5**
2. Outlier thresholds:
- Lower bound: Q1 - 1.5 * IQR = 6.5 - 1.5 * 2.5 = 6.5 - 3.75 = 2.75
- Upper bound: Q3 + 1.5 * IQR = 9 + 1.5 * 2.5 = 9 + 3.75 = 12.75
Any data points below 2.75 or above 12.75 would be considered outliers. The only outlier is 14 and 16.
**The outliers of the dataset are:**
- 14 and 16.
### Question 4 A)
**Interpret the interquartile range (IQR) of Stock A (3) and Stock B (11).**
The IQR represents the variability of the middle 50% of the data.
**What interpretation can be made from the interquartile range?**
- Stock B has more variability than Stock A.
### Question 5 A)
**A video game player had the following scores: 287, 389, 287, 329, 295, 290, 397, 387, 365. What does the IQR indicate about this dataset?**
1. **Organize the scores:** 287, 287, 290, 295, 329, 365, 387, 389, 397.
2. **Minimum = 287**
3. **Q1 = 290** (1st half: [287, 287, 290, 295])
4. **Median = 365** (middle value: 365)
5. **Q3 = 389** (2nd half: [365, 387, 389, 397])
6. **IQR = Q3 - Q1 = 389 - 290 = 99.**
The IQR of 99 indicates the range of variability for the middle 50% of scores.
**The correct response is:**
- An IQR of 99.5 indicates that the video game player had a relatively small variability for their middle scores. (This might be inaccurate as the IQR is 99 not 99.5).
In summary, here are the answers:
1. The right whisker is much longer than the left whisker.
2. 9
3. The outliers of the dataset are 14 and 16.
4. Stock B has more variability than Stock A.
5. An IQR of 99 indicates that the video game player had a relatively small variability for their middle scores.
### Question 1 A)
**Calculate the 5-number summary of the dataset 15, 16, 16, 17, 17, 18, 18, 18, 19, 19, 29.**
1. **Minimum:** 15
2. **Q1 (1st Quartile):** The first quartile is the median of the first half of the data. The first half is [15, 16, 16, 17, 17]. The median here is 16.
3. **Median (Q2):** The median of the entire dataset is the middle value, which is 18.
4. **Q3 (3rd Quartile):** The third quartile is the median of the second half of the data, which is [18, 18, 19, 19, 29]. The median is 19.
5. **Maximum:** 29
Thus, the 5-number summary is:
- Minimum: 15
- Q1: 16
- Median: 18
- Q3: 19
- Maximum: 29
**Which explains a reason why the dataset is skewed?**
- The right whisker is much longer than the left whisker.
### Question 2 A)
**Calculate the 5-number summary of the dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16.**
1. **Minimum:** 5
2. **Q1:** The first quartile (first half: [5, 6, 6, 7, 7, 8]) is the median of this half: Q1 = 6.5.
3. **Median (Q2):** The median of the entire dataset (middle values: 8 and 9) is 8.5.
4. **Q3:** The third quartile (second half: [8, 9, 14, 16]) is the median of this half: Q3 = 9.
5. **Maximum:** 16
**Which of the following choices is quartile 3?**
- 9
### Question 3 A)
**Which option is true about the outliers of the dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16?**
To find outliers, we can use the IQR method:
1. **IQR = Q3 - Q1 = 9 - 6.5 = 2.5**
2. Outlier thresholds:
- Lower bound: Q1 - 1.5 * IQR = 6.5 - 1.5 * 2.5 = 6.5 - 3.75 = 2.75
- Upper bound: Q3 + 1.5 * IQR = 9 + 1.5 * 2.5 = 9 + 3.75 = 12.75
Any data points below 2.75 or above 12.75 would be considered outliers. The only outlier is 14 and 16.
**The outliers of the dataset are:**
- 14 and 16.
### Question 4 A)
**Interpret the interquartile range (IQR) of Stock A (3) and Stock B (11).**
The IQR represents the variability of the middle 50% of the data.
**What interpretation can be made from the interquartile range?**
- Stock B has more variability than Stock A.
### Question 5 A)
**A video game player had the following scores: 287, 389, 287, 329, 295, 290, 397, 387, 365. What does the IQR indicate about this dataset?**
1. **Organize the scores:** 287, 287, 290, 295, 329, 365, 387, 389, 397.
2. **Minimum = 287**
3. **Q1 = 290** (1st half: [287, 287, 290, 295])
4. **Median = 365** (middle value: 365)
5. **Q3 = 389** (2nd half: [365, 387, 389, 397])
6. **IQR = Q3 - Q1 = 389 - 290 = 99.**
The IQR of 99 indicates the range of variability for the middle 50% of scores.
**The correct response is:**
- An IQR of 99.5 indicates that the video game player had a relatively small variability for their middle scores. (This might be inaccurate as the IQR is 99 not 99.5).
In summary, here are the answers:
1. The right whisker is much longer than the left whisker.
2. 9
3. The outliers of the dataset are 14 and 16.
4. Stock B has more variability than Stock A.
5. An IQR of 99 indicates that the video game player had a relatively small variability for their middle scores.