Question

A sports magazine asked 3,600 of its subscribers this question: Which of these sports do you think is most dangerous? Choose one. \(\square\) football \(\square\) ice hockey \(\square\) skiing \(\square\) sky diving \(\square\) rock climbing \(\square\) other Ms. Kelsey's math class decided to conduct the same survey in their class. The table shows the results of the magazine's survey and Ms. Kelsey's class survey. $$\begin{array}{|l|c|c|} \hline \text { Sport } & \begin{array}{c} \text { Fraction of Votes } \\ \text { in Magazine Survey } \end{array} & \begin{array}{c} \text { Fraction of Votes in } \\ \text { Ms. Kelsey's Class } \end{array} \\ \hline \text { Football } & \frac{524}{3,600} & \frac{3}{25} \\ \text { Ice hockey } & \frac{320}{3,600} & \frac{0}{25} \\ \text { Skiing } & \frac{870}{3,600} & \frac{8}{25} \\ \text { Skydiving } & \frac{607}{3,600} & \frac{11}{25} \\ \text { Rock climbing } & \frac{959}{3,600} & \frac{2}{25} \\ \text { Other } & \frac{320}{3,600} & \frac{1}{25} \\ \hline \end{array}$$ a. Find the percent of votes each sport received in the magazine survey. Round to the nearest percent. b. Find the percent of votes each sport received in Ms. Kelsey's class. Round to the nearest percent c. Write a short newspaper article comparing the results of the magazine survey with the results of the survey in Ms. Kelsey's class.

Short answer

Magazine: Football 15%, Ice Hockey 9%, Skiing 24%, Skydiving 17%, Rock climbing 27%, Other 9%. Class: Football 12%, Ice Hockey 0%, Skiing 32%, Skydiving 44%, Rock climbing 8%, Other 4%.

Step-by-step solution

- Convert Fractions to Percentages for Magazine Survey

To find the percentage of votes each sport received in the magazine survey, divide the numerator by the denominator and multiply by 100. For example, for football, the fraction is \( \frac{524}{3600} \). Calculating: \( \frac{524}{3600} \times 100 \approx 14.56\% \). Round to the nearest percent: \( 15\% \). Repeat this process for each sport.

- Calculating Percentages for Each Sport in Magazine Survey

Using the method described in Step 1: - Football: \( \frac{524}{3600} \times 100 \approx 15\% \)- Ice hockey: \( \frac{320}{3600} \times 100 \approx 9\% \)- Skiing: \( \frac{870}{3600} \times 100 \approx 24\% \)- Skydiving: \( \frac{607}{3600} \times 100 \approx 17\% \)- Rock climbing: \( \frac{959}{3600} \times 100 \approx 27\% \)- Other: \( \frac{320}{3600} \times 100 \approx 9\% \)

- Convert Fractions to Percentages for Ms. Kelsey's Class

To find the percentage of votes each sport received in Ms. Kelsey's class, divide the numerator by the denominator and multiply by 100. For football: \( \frac{3}{25} \times 100 = 12\% \). Repeat this process for each sport.

- Calculating Percentages for Each Sport in Ms. Kelsey's Class Survey

Using the method described in Step 3: - Football: \( \frac{3}{25} \times 100 = 12\% \)- Ice hockey: \( \frac{0}{25} \times 100 = 0\% \)- Skiing: \( \frac{8}{25} \times 100 = 32\% \)- Skydiving: \( \frac{11}{25} \times 100 = 44\% \)- Rock climbing: \( \frac{2}{25} \times 100 = 8\% \)- Other: \( \frac{1}{25} \times 100 = 4\% \)

- Write Comparison Article

Compare the results: - Football: Magazine shows higher concern with 15% compared to 12% in class. - Ice Hockey: Only magazine voters chose this, at 9%. - Skiing: Class feels it is more dangerous, 32% v. 24%. - Skydiving: Class shows higher concern with 44% compared to 17% in magazine. - Rock climbing: Magazine shows higher concern, 27% v. 8%. - Other: Both retained minimal votes with 9% in magazine & 4% in class. Write a concise article summarizing these points.

Key concepts

fraction to percentage conversion

Converting fractions to percentages is a vital skill, particularly in survey analysis and data comparison. The conversion process involves the following steps:
1. Divide the numerator by the denominator. For example, with the fraction \( \frac{524}{3600} \), divide 524 by 3600 to get approximately 0.1456.
2. Multiply the result by 100 to convert it to a percentage. Continuing with our example, 0.1456 multiplied by 100 equals 14.56%.
3. Round the percentage to the nearest whole number if required. For instance, 14.56% becomes 15%.

This process is applied to each sport in the given exercise, ensuring that the data is represented in a more accessible format for analysis and comparison.

data comparison

Data comparison is essential when interpreting survey results, allowing us to see patterns, differences, and similarities. To compare data effectively, follow these steps:
1. Convert all data sets to a common format. In this case, we converted fractions to percentages.
2. Analyze each category side-by-side, noting any significant differences.
For example:

• Football received 15% of the votes in the magazine survey but only 12% in Ms. Kelsey's class.
• Skydiving was considered more dangerous by Ms. Kelsey's class (44%) compared to the magazine survey respondents (17%).

3. Summarize the findings, highlighting any notable contrasts or trends.

This method ensures a clear and concise understanding of how different groups perceive the dangers of various sports.

survey analysis

Survey analysis helps make sense of collected data, shedding light on trends and opinions. When analyzing survey results, consider these steps:
1. Collect data systematically, ensuring clarity and consistency.
2. Use statistical tools like conversion to percentages to facilitate comparison.
For instance, converting the fractions of responses to percentages in both the magazine and Ms. Kelsey's class surveys.
3. Identify key findings by looking at the data distribution across categories.
For example, skydiving was ranked as most dangerous by Ms. Kelsey's class but had varied responses in the magazine survey.
4. Present the data in a digestible format, such as a comparison article or bullet points.

By following these steps, you can effectively analyze survey results, drawing meaningful conclusions about public opinion.

percentage calculations

Percentage calculations are fundamental in data representation, particularly in surveys. To calculate percentages:
1. Start with your fraction and divide the numerator by the denominator. For example, \( \frac{3}{25} \) yields 0.12.
2. Multiply the result by 100 to convert it to a percentage. Using our example, 0.12 becomes 12%.
3. Repeat these calculations for all data points to ensure consistency.
In the exercise:

• For football, the fraction \( \frac{3}{25} \) translates to 12%.
• For skiing, \( \frac{8}{25} \) results in 32%.

Converting all survey responses to percentages provides a clear view of the data, making it easier to compare and draw conclusions.