School newspaper staff went to three different sports games to survey students on their favorite sport, and the results are shown in the table below. Are these samples biased? Why or why not?
| | Sample 1 | Sample 2 | Sample 3 |
| :--------- | :------- | :------- | :------- |
| Basketball | 23 | 1 | 1 |
| Football | 2 | 24 | 2 |
| Volleyball | 0 | 0 | 22 |
A. These samples are not biased because students like different sports and the samples reflect the different opinions.
B. These samples are biased because the newspaper staff went to a basketball game, football game, and volleyball match to interview the students.
C. These samples are not biased because each has a total of 25 students, which makes them equal.
D. These samples are biased because 0 should never appear in a sample as it is not possible.
Answer (1)
The samples are biased because the location of the survey influenced the results. Surveying students at a basketball game, football game, and volleyball game will likely result in a sample that is not representative of the entire student population's preferences. Therefore, the samples are biased because the newspaper staff went to a basketball game, football game, and volleyball match to interview the students.
Explanation
Analyze the data Let's analyze the data. The school newspaper staff conducted surveys at three different sports games: basketball, football, and volleyball. Sample 1 was taken at a basketball game, with 23 students preferring basketball, 2 preferring football, and 0 preferring volleyball. Sample 2 was taken at a football game, with 1 student preferring basketball, 24 preferring football, and 0 preferring volleyball. Sample 3 was taken at a volleyball game, with 1 student preferring basketball, 2 preferring football, and 22 preferring volleyball.
Define biased sample Now, let's think about what it means for a sample to be biased. A biased sample is one that does not accurately represent the population from which it was drawn. In this case, the population is the students at the school. If the samples are biased, it means that the opinions of the students surveyed do not accurately reflect the opinions of all students at the school.
Consider the location of each survey Let's consider the location of each survey. Sample 1 was taken at a basketball game. It is likely that students attending a basketball game are more likely to prefer basketball than students who do not attend basketball games. Similarly, Sample 2 was taken at a football game, and Sample 3 was taken at a volleyball game. Therefore, the location of the survey likely influenced the results.
Conclusion Since the location of the survey influenced the results, the samples are biased. The newspaper staff should have surveyed students in a variety of locations to get a more accurate representation of the opinions of all students at the school.
Examples
Imagine you're trying to find out what kind of music students at your school like. If you only ask students in the school band, you're likely to get a biased sample because those students probably like music more than the average student and are more likely to have specific musical tastes. To get a better idea of what all students like, you should ask students in different places, like the cafeteria, the library, and after school activities.
