Problem 11 - BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Question

In a school district, a survey of 1300 high school students found that 1001 of them like the new, healthy cafeteria food choices.

Step-by-Step Solution

Answer

Approximately 77.00% of students like the new, healthy cafeteria choices.

Step 1. Identifying the total and favorable count

In the exercise, the total number of students surveyed is 1300 and the number of those who like the new, healthy cafeteria food choices is 1001.

Step 2. Applying the percentage formula

The percentage can be calculated by setting up the ratio of the part (students who like the new food) over the whole (total students) and then multiplying by 100. Hence, the formula becomes \(\frac{{1001}}{{1300}} \times 100\%\)

Step 3. Solving the calculation

By computing the formula, the result is approximately 77.00%.

Key Concepts

Survey Data Analysis

Survey data analysis involves collecting, evaluating, and interpreting responses from a group of people to gather insights. In the context of our exercise, analysis starts with identifying the total number of participants, which is 1300 high school students. Next, we discern the number of those who have responded positively to a specific question – in this case, the 1001 students who like the new, healthy cafeteria food choices.

This fundamental step provides the raw data needed to compute statistical measures, such as percentages, and to draw conclusions regarding the preferences of the student population. Survey data analysis allows researchers to transform simple yes-or-no data into valuable information that can influence decision-making processes, such as whether to continue offering the new food choices based on their popularity.

Ratio and Proportion

The concept of ratio and proportion is integral to understanding relationships between numbers. A ratio is a way to compare two quantities by using division, indicating how much of one thing there is compared to another. In our example, the ratio of students who like the new cafeteria food to the total number of surveyed students is 1001 to 1300. A proportion, on the other hand, occurs when two ratios are set equal to each other, allowing for comparison of different groups or for solving for unknown values.

Understanding the ratio of favorable responses to total responses provides a basis for many statistical calculations. For instance, it is the crucial first step before converting that ratio into a percentage to represent the data more meaningfully to individuals who need to interpret the results of the survey.

Mathematical Percentages

Mathematical percentages are a way of expressing a number as a fraction of 100. They are useful for comparing quantities of different sizes in a standardized format. To compute the percentage of students who favor the healthy cafeteria options in our exercise, we divide the number of favorable responses (1001) by the total responses (1300) and then multiply the result by 100, as follows: \(\frac{{1001}}{{1300}} \times 100\%\).

By performing this calculation, we determine that approximately 77% of the students surveyed favor the new cafeteria options. This percentage is imperative for communicating the extent of the favorability clearly and concisely. Percentages are common in data presentations because they are intuitive and easily understood by various audiences, making them a vital tool in both survey analysis and reporting.