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Question
Which of the following box plots matches the data set below?
15, 20, 20, 25, 26, 28, 28, 30, 32
(1 point)
Question
Which of the following box plots matches the data set below?
15, 20, 20, 25, 26, 28, 28, 30, 32
(1 point)
Answers
GPT-4o mini
To create a box plot (also known as a whisker plot) for the given data set, we need to determine the five-number summary, which consists of:
1. Minimum (the lowest value)
2. First Quartile (Q1; the median of the first half of the data)
3. Median (Q2; the middle value of the data set)
4. Third Quartile (Q3; the median of the second half of the data)
5. Maximum (the highest value)
Given the data set:
15, 20, 20, 25, 26, 28, 28, 30, 32
1. **Minimum:** 15
2. **Maximum:** 32
3. **Median (Q2):** Since there are 9 data points, the median is the 5th number: 26.
4. **First Quartile (Q1):** The first half of the data is 15, 20, 20, 25. The median of this subset (the average of the 2nd and 3rd values) is (20 + 20)/2 = 20.
5. **Third Quartile (Q3):** The second half of the data is 28, 28, 30, 32. The median of this subset (the average of the 2nd and 3rd values) is (28 + 30)/2 = 29.
So the five-number summary is:
- Minimum: 15
- Q1: 20
- Median (Q2): 26
- Q3: 29
- Maximum: 32
Using this summary, you can sketch a box plot where:
- A line is drawn at each of the five points: 15, 20, 26, 29, 32.
- The box spans from Q1 (20) to Q3 (29), with a line in the box at the median (26).
- Whiskers extend from the box to the minimum (15) and maximum (32).
Now, look for a box plot that includes:
- Minimum at 15
- Q1 at 20
- Median at 26
- Q3 at 29
- Maximum at 32
This box plot characteristics should help you identify the correct plot from the options provided. If you have specific options, please share them, and I can help determine which one matches.
1. Minimum (the lowest value)
2. First Quartile (Q1; the median of the first half of the data)
3. Median (Q2; the middle value of the data set)
4. Third Quartile (Q3; the median of the second half of the data)
5. Maximum (the highest value)
Given the data set:
15, 20, 20, 25, 26, 28, 28, 30, 32
1. **Minimum:** 15
2. **Maximum:** 32
3. **Median (Q2):** Since there are 9 data points, the median is the 5th number: 26.
4. **First Quartile (Q1):** The first half of the data is 15, 20, 20, 25. The median of this subset (the average of the 2nd and 3rd values) is (20 + 20)/2 = 20.
5. **Third Quartile (Q3):** The second half of the data is 28, 28, 30, 32. The median of this subset (the average of the 2nd and 3rd values) is (28 + 30)/2 = 29.
So the five-number summary is:
- Minimum: 15
- Q1: 20
- Median (Q2): 26
- Q3: 29
- Maximum: 32
Using this summary, you can sketch a box plot where:
- A line is drawn at each of the five points: 15, 20, 26, 29, 32.
- The box spans from Q1 (20) to Q3 (29), with a line in the box at the median (26).
- Whiskers extend from the box to the minimum (15) and maximum (32).
Now, look for a box plot that includes:
- Minimum at 15
- Q1 at 20
- Median at 26
- Q3 at 29
- Maximum at 32
This box plot characteristics should help you identify the correct plot from the options provided. If you have specific options, please share them, and I can help determine which one matches.