Question
The players on Matthew's soccer team each bring a water bottle with them to practice. For a statistics project, Matthew asked each player how much water his bottle held. This box plot shows the results.
Water bottle volume (oz.)
12
16
20
24
28
32
What fraction of the water bottles held at least 24 ounces?
Water bottle volume (oz.)
12
16
20
24
28
32
What fraction of the water bottles held at least 24 ounces?
Answers
GPT-4o mini
To determine the fraction of water bottles that held at least 24 ounces using the box plot data, we need to analyze the information provided.
The box plot suggests that the water bottle volumes range from a minimum (12 oz.) up to a maximum (32 oz.) and also shows quartiles and potentially median data points:
- The first quartile (Q1) is likely around 16 oz.
- The median (Q2) is typically near 20 oz.
- The third quartile (Q3) is typically around 24 oz. or may vary slightly according to specific box plot details.
The data indicates the following:
1. **Minimum volume:** 12 oz.
2. **First quartile (Q1):** 16 oz.
3. **Median (Q2):** 20 oz.
4. **Third quartile (Q3):** 24 oz.
5. **Maximum volume:** 32 oz.
From the quartiles, we can conclude that:
- Approximately 25% of the data is below Q1 (16 oz.).
- Approximately 50% of the data is between Q1 (16 oz.) and Q3 (24 oz.) — which covers 25% of the players at or above 16 oz.
- The remaining 25% of the data is above Q3 (24 oz.).
If the third quartile (Q3) is indeed 24 oz., this indicates that 75% of the players have water bottles that hold less than 24 oz., and thus, 25% have water bottles that hold at least 24 oz.
Therefore, the fraction of water bottles that held at least 24 ounces is:
\[
\frac{number \ of \ bottles \ holding \ at \ least \ 24 \ ounces}{total \ number \ of \ bottles} = \frac{25}{100} = \frac{1}{4}.
\]
So the answer is **\(\frac{1}{4}\)**.
The box plot suggests that the water bottle volumes range from a minimum (12 oz.) up to a maximum (32 oz.) and also shows quartiles and potentially median data points:
- The first quartile (Q1) is likely around 16 oz.
- The median (Q2) is typically near 20 oz.
- The third quartile (Q3) is typically around 24 oz. or may vary slightly according to specific box plot details.
The data indicates the following:
1. **Minimum volume:** 12 oz.
2. **First quartile (Q1):** 16 oz.
3. **Median (Q2):** 20 oz.
4. **Third quartile (Q3):** 24 oz.
5. **Maximum volume:** 32 oz.
From the quartiles, we can conclude that:
- Approximately 25% of the data is below Q1 (16 oz.).
- Approximately 50% of the data is between Q1 (16 oz.) and Q3 (24 oz.) — which covers 25% of the players at or above 16 oz.
- The remaining 25% of the data is above Q3 (24 oz.).
If the third quartile (Q3) is indeed 24 oz., this indicates that 75% of the players have water bottles that hold less than 24 oz., and thus, 25% have water bottles that hold at least 24 oz.
Therefore, the fraction of water bottles that held at least 24 ounces is:
\[
\frac{number \ of \ bottles \ holding \ at \ least \ 24 \ ounces}{total \ number \ of \ bottles} = \frac{25}{100} = \frac{1}{4}.
\]
So the answer is **\(\frac{1}{4}\)**.