Question
Calculate the values for the 5-number summary of the skewed dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16.(1 point) Responses The minimum value = 5, the maximum value = 16, the median value = 7.5, the Quartile 1 = 6, and the Quartile 3 = 9. The minimum value = 5, the maximum value = 16, the median value = 7.5, the Quartile 1 = 6, and the Quartile 3 = 9. The minimum value = 5, the maximum value = 16, the median value = 8, the Quartile 1 = 8, and the Quartile 3 = 9. The minimum value = 5, the maximum value = 16, the median value = 8, the Quartile 1 = 8, and the Quartile 3 = 9. The minimum value = 5, the maximum value = 16, the median value = 8, the Quartile 1 = 6.5, and the Quartile 3 = 9. The minimum value = 5, the maximum value = 16, the median value = 8, the Quartile 1 = 6.5, and the Quartile 3 = 9. The minimum value = 4, the maximum value = 16, the median value = 8, the Quartile 1 = 6.5, and the Quartile 3 = 9.
Answers
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GPT-4o mini
To calculate the 5-number summary (minimum, first quartile (Q1), median, third quartile (Q3), and maximum) of the dataset \( 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16 \), we can follow these steps:
1. **Minimum**: The smallest number in the dataset is \( 5 \).
2. **Maximum**: The largest number in the dataset is \( 16 \).
3. **Median**:
- To find the median, we need to locate the middle value. Since there are \( 12 \) numbers (an even count), the median will be the average of the 6th and 7th values.
- The sorted dataset is \( 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16 \).
- The 6th and 7th values are \( 8 \) and \( 8 \).
- Thus, the median is \( \frac{8 + 8}{2} = 8 \).
4. **First Quartile (Q1)**:
- Q1 is the median of the first half of the data (the first 6 numbers): \( 5, 6, 6, 7, 7, 8 \).
- The 3rd and 4th numbers in this subset are \( 6 \) and \( 7 \), so \( Q1 = \frac{6 + 7}{2} = 6.5 \).
5. **Third Quartile (Q3)**:
- Q3 is the median of the second half of the data (the last 6 numbers): \( 8, 8, 9, 9, 14, 16 \).
- The 3rd and 4th numbers here are \( 9 \) and \( 9 \), so \( Q3 = \frac{9 + 9}{2} = 9 \).
Putting it all together, the 5-number summary is:
- Minimum = \( 5 \)
- Q1 = \( 6.5 \)
- Median = \( 8 \)
- Q3 = \( 9 \)
- Maximum = \( 16 \)
So, the correct answer is:
**The minimum value = 5, the maximum value = 16, the median value = 8, the Quartile 1 = 6.5, and the Quartile 3 = 9.**
1. **Minimum**: The smallest number in the dataset is \( 5 \).
2. **Maximum**: The largest number in the dataset is \( 16 \).
3. **Median**:
- To find the median, we need to locate the middle value. Since there are \( 12 \) numbers (an even count), the median will be the average of the 6th and 7th values.
- The sorted dataset is \( 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16 \).
- The 6th and 7th values are \( 8 \) and \( 8 \).
- Thus, the median is \( \frac{8 + 8}{2} = 8 \).
4. **First Quartile (Q1)**:
- Q1 is the median of the first half of the data (the first 6 numbers): \( 5, 6, 6, 7, 7, 8 \).
- The 3rd and 4th numbers in this subset are \( 6 \) and \( 7 \), so \( Q1 = \frac{6 + 7}{2} = 6.5 \).
5. **Third Quartile (Q3)**:
- Q3 is the median of the second half of the data (the last 6 numbers): \( 8, 8, 9, 9, 14, 16 \).
- The 3rd and 4th numbers here are \( 9 \) and \( 9 \), so \( Q3 = \frac{9 + 9}{2} = 9 \).
Putting it all together, the 5-number summary is:
- Minimum = \( 5 \)
- Q1 = \( 6.5 \)
- Median = \( 8 \)
- Q3 = \( 9 \)
- Maximum = \( 16 \)
So, the correct answer is:
**The minimum value = 5, the maximum value = 16, the median value = 8, the Quartile 1 = 6.5, and the Quartile 3 = 9.**
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