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:
- Minimum (the lowest value)
- First Quartile (Q1; the median of the first half of the data)
- Median (Q2; the middle value of the data set)
- Third Quartile (Q3; the median of the second half of the data)
- Maximum (the highest value)
Given the data set:
15, 20, 20, 25, 26, 28, 28, 30, 32
- Minimum: 15
- Maximum: 32
- Median (Q2): Since there are 9 data points, the median is the 5th number: 26.
- 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.
- 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 answer