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A skater conducted a survey at his school. The data he collected is in the table below. If his sample was random, which conclusion below is the most reasonable based on the sample?

| Gender (M/F) | Have you ever ridden a skateboard? (Y/N) | Do you own a skateboard? (Y/N) | Do you skateboard at least once a week? (Y/N) |
|--------------|---------------------------------------|-------------------------------|--------------------------------------------|
| M | N | N | N |
| F | N | N | N |
| M | Y | Y | N |
| M | Y | Y | Y |
| F | Y | N | N |
| M | Y | N | N |
| M | Y | Y | N |
| F | Y | Y | N |
| F | Y | N | Y |
| F | N | | N |

Based on the sample, which conclusion is most reasonable?

A. Most boys own a skateboard.
B. Most girls own a skateboard.
C. Most students skateboard at least once a week.
D. Most students have ridden a skateboard but do not own one.



Answer :

GinnyAnswer
Sure, let's analyze the data provided and make an appropriate conclusion based on the sample.

### Survey Data Analysis

Below is the survey data provided in the table:

| Gender | Have you ever ridden a skateboard? | Do you own a skateboard? | Do you skateboard at least once a week? |
|--------|------------------------------------|-------------------------|----------------------------------------|
| M | N | N | N |
| F | N | N | N |
| M | Y | Y | N |
| M | Y | Y | Y |
| F | Y | N | N |
| M | Y | N | N |
| M | Y | Y | N |
| F | Y | Y | N |
| F | Y | N | Y |
| F | N | N | N |

### Steps to Analyze the Data

1. Count the total number of respondents:
Total respondents are simply the number of rows in the table, which is 10 in this case.

2. Calculate the number of girls (F) in the sample:
Count the number of rows where the gender is 'F'.
- In this sample, there are 5 girls.

3. Calculate the number of girls who own a skateboard (Y for owning a skateboard):
Count the number of rows where the gender is 'F' and they own a skateboard.
- There are 2 instances where girls own a skateboard.

4. Calculate the ratio of girls who own a skateboard:
This is the number of girls who own a skateboard divided by the total number of girls in the sample.
- Ratio = Number of girls who own a skateboard / Number of girls in sample
- Ratio = 2 / 5 = 0.4

5. Estimate the total number of girls in the school who own a skateboard:
- Total girls owning skateboards in the school = Ratio * Total number of girls in the school.
- Given that there are 103 girls in the school who own a skateboard, use the ratio to estimate the total number of girls in the school.

### Final Calculation and Conclusion

Given:
- Total number of girls in the sample: 5
- Number of girls owning a skateboard in the sample: 2
- Ratio = [tex]\(\frac{2}{5} = 0.4\)[/tex]
- Total number of girls owning a skateboard in the school: 103

We can estimate the total number of girls in the school:
- If 0.4 of the total girls in the school own a skateboard, and we know 103 girls own a skateboard:
[tex]\[ \text{Total number of girls in school} = \frac{103}{0.4} = 257.5 \][/tex]

Since we can’t have a fractional number of students, we would round to the nearest whole number:
[tex]\[ \text{Total number of girls in the school} \approx 258 \][/tex]

### Conclusion

Based on the random sample data, the most reasonable conclusion is that there are approximately 258 girls in the school, given that 103 girls own a skateboard.

If you have any other questions or need further clarification, feel free to ask!

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