Question

An article in the Winter 2003 issue of Chance magazine reported on the Houston Independent School District's magnet schools programs. Of the 1755 qualified applicants, 931 were accepted, 298 were waitlisted, and 526 were turned away for lack of space. Find the relative frequency distribution of the decisions made, and write a sentence describing it.

Short answer

53% were accepted, 17% were waitlisted, and 30% were turned away.

Step-by-step solution

Understand the Problem

The problem requires us to calculate the relative frequency distribution of the decisions made (accepted, waitlisted, or turned away) for qualified applicants. This involves calculating what fraction or percentage of the applicants fall into each category.

Total Number of Applicants

Identify the total number of qualified applicants mentioned, which is 1755. This number will be used as the denominator when calculating the relative frequencies.

Calculate Relative Frequency for Each Category

For each category (accepted, waitlisted, turned away), divide the number in that category by the total number of applicants (1755) and express it as a percentage.

Step 3a: Accepted Applicants

The number of accepted applicants is 931. The relative frequency is calculated as follows:\[\text{Relative frequency of accepted} = \frac{931}{1755} \approx 0.53 \text{ or } 53\%\]

Step 3b: Waitlisted Applicants

The number of waitlisted applicants is 298. The relative frequency is calculated as follows:\[\text{Relative frequency of waitlisted} = \frac{298}{1755} \approx 0.17 \text{ or } 17\%\]

Step 3c: Turned Away Applicants

The number of applicants turned away is 526. The relative frequency is calculated as follows:\[\text{Relative frequency of turned away} = \frac{526}{1755} \approx 0.30 \text{ or } 30\%\]

Compile the Relative Frequency Distribution

Now, compile all these relative frequencies to form the distribution: - Accepted: 53% - Waitlisted: 17% - Turned away: 30%

Key concepts

Statistical Analysis

Statistical analysis is the process of collecting and processing data to identify patterns and trends. In the context of the exercise, we are tasked with understanding how to calculate a relative frequency distribution. This analysis provides insights into how often specific outcomes occur relative to a whole dataset.

Relative frequency distribution is an essential tool in statistics. It shows the proportion of occurrences of each category compared to the total number of occurrences. This makes it easier to compare the sizes or importance of categories without getting bogged down in actual numbers.

In this example, by determining the relative frequency of each decision category (accepted, waitlisted, turned away), we can see which category is most prevalent. Such information can be valuable not only for statistical reporting but also for strategic planning. Knowing that 53% of applicants are accepted, for instance, can help schools predict future trends and adjust their policies accordingly.

Data Interpretation

Data interpretation involves making sense of the numerical results obtained from statistical analysis. Here, we take calculated percentages from the relative frequency distribution and translate them into meaningful insights.

• Accepted: 53% - Over half of the applicants were accepted, which signifies a relatively high acceptance rate. This suggests that the program has the capacity to accommodate a significant portion of qualified applicants.
• Waitlisted: 17% - A smaller segment finds itself in limbo, reflecting a challenge in matching demand with capacity or indicating selective acceptance criteria.
• Turned away: 30% - This portion indicates limited space availability or highly selective criteria. Turning away nearly a third of applicants points to potential improvements in capacity planning or expectations management.

These interpretations help us understand beyond the numbers, providing insights into how the application process impacts applicants and the institution. When we interpret data, it's about more than crunching numbers—it's about storytelling perspectives through those numbers.

Educational Statistics

Educational statistics refer to the application of statistical methods to analyze and interpret data within educational settings. This includes evaluating processes like school admissions, student performance, and program effectiveness.

In this exercise, the focus was on admissions data. By using educational statistics, we gain insights into the efficiency and fairness of the admission process. It gives educators, administrators, and policymakers a clear picture of how well the system is working and where there might be room for improvement.

The admission statistics from the Houston Independent School District's magnet programs offer a snapshot of how competitive the programs are. This data can drive conversations about increasing access to programs, investing in resources, or tweaking policies to ensure educational equality.

Educational statistics thus play a pivotal role in shaping educational strategies and ensuring that decisions made are data-driven and impactful. They help in measuring progress and spearheading reforms that ultimately improve the learning experience.