- Calculate the total number of respondents as \(27\).
- Determine the number of individuals in each group: piano players (\(10\)), saxophone players (\(12\)), piano players who prefer jazz (\(2\)), and saxophone players who prefer jazz (\(8\)).
- Apply the percentage formula \(\frac{\text{Group Total}}{27} \times 100\%\) to each group.
- Conclude that the group "piano players" accounts for approximately \(\frac{10}{27} \times 100\% \approx 37\%\).
The correct answer is \(\boxed{a}\).
Explanation
- Analyze the problem and identify the total population
We are given a contingency table representing survey results from 27 musicians regarding their favorite music genre (Jazz or Other). The total number of survey respondents is 27. Our goal is to identify which of the provided groups accounts for approximately 37% of these 27 respondents. The groups to evaluate are:
Apiano players
Bsaxophone players
Cpiano players who preferred jazz
Dsaxophone players who preferred jazz
- Define the calculation method for percentages
To find which group accounts for approximately 37% of the total, we use the formula for percentage:
\[\text{Percentage} = \left( \frac{\text{Number of respondents in the group}}{\text{Total number of respondents}} \right) \times 100\%\]
Given that the total number of respondents is 27, we calculate the percentage for each group provided in the options.
- Calculate the percentage for each option
Let's calculate the percentage for each group identified in the options:
- a. Piano players: The total number of piano players is 10.
\[\frac{10}{27} \times 100\% \approx 37.04\%\]
- b. Saxophone players: The total number of saxophone players is 12.
\[\frac{12}{27} \times 100\% \approx 44.44\%\]
- c. Piano players who preferred jazz: This group has 2 respondents.
\[\frac{2}{27} \times 100\% \approx 7.41\%\]
- d. Saxophone players who preferred jazz: This group has 8 respondents.
\[\frac{8}{27} \times 100\% \approx 29.63\%\]
- Identify the correct group and conclude
Comparing the calculated percentages, we can see that the group "piano players" results in a percentage of approximately 37.04%, which matches the requirement of "approximately 37%". Therefore, the piano players group is the correct answer.
Examples
When conducting a survey, understanding the composition of your data is vital for clear reporting. For example, if you find that a specific subgroup makes up 37% of your participants, you can use that statistic to highlight their influence on the survey results, just as we identified the proportion of piano players relative to the total number of survey respondents. By calculating \(\frac{10}{27} \approx 0.3704\), you can effectively report that piano players represent roughly 37% of your sample.