Problem 9 - Algebra 1: Concepts and Skills

Question

SCHOOL ENROLLMENT The table shows the number of students (in millions) enrolled in school in the United States by age. Make a table showing the total number of students enrolled for each given year. $$ \begin{array}{|c|c|c|c|c|c|} \hline \text { Age } & {1980} & {1985} & {1990} & {1995} & {2000} \\ \hline 14-15 \text { years old } & {7282} & {7362} & {6555} & {7651} & {8100} \\\ \hline 16-17 \text { years old } & {7129} & {6654} & {6098} & {6997} & {7600} \\\ \hline 18-19 \text { years old } & {3788} & {3716} & {4044} & {4274} & {4800} \\\ \hline \end{array} $$ Which year had the least number of students enrolled? Which had the greatest number of students enrolled?

Step-by-Step Solution

Answer

The year with the least number of students enrolled will be the one with the lowest sum from Step 1; similarly, the year with the greatest number of students enrolled will be the one with the highest sum from Step 1.

Step 1: Sum the enrollment for each year

In this step, sum the number of students of all age brackets for each year. For example, for year 1980, the total enrollment would be \(7282 + 7129 + 3788 = 18199\). Repeat this process for all other years (1985, 1990, 1995, and 2000).

Step 2: Identify the year with the least enrollment

After getting the total enrollment for each year, look through the sums to find the year with the least number of students. This is the year that has the smallest total enrollment figure.

Step 3: Identify the year with the greatest enrollment

Likewise, to find the year with the greatest number of students, look through the sums from step 1 and find the year with the largest total enrollment.

Key Concepts

Data Interpretation

Data interpretation is the process of making sense of numerical information. In the context of school enrollment numbers, you're tasked to analyze data to determine trends or make comparisons.
This skill is important because raw data often don't directly convey messages. You have to gather, process and extract insights to help in decision-making.
When dealing with our school enrollment exercise, start by closely examining the table of enrollment figures provided. Focus on each column to understand the number of students across different years and ages.

• Look for patterns or anomalies across ages within the same year.
• Besides the main question, consider trends over the years. Is the enrollment increasing or decreasing?

This scrutiny helps in tackling not just the problem at hand, but also builds skill for future data interpretation exercises.

Comparing Data

Comparing data involves examining datasets to identify similarities and differences. When comparing school enrollment numbers, you need to grasp the variations across different years. It requires assessing numbers to find patterns or significant changes.
From our exercise, we compare the total enrollments for each year. This is achieved by summing up the number of students for all age groups in a given year. For example, for 1980, you calculate the total by adding each age group's figures.
The aim is to pinpoint years with the least and greatest enrollments. By comparing these totals for each year, we understand the trends and possible causes behind these numbers, such as demographic shifts or policy changes.

• Identify any significant rise or drop in student numbers.
• Reflect on external factors that might affect these numbers (e.g., population growth, economic conditions).

Understanding how to compare data accurately can uncover useful insights from numeric information.

Educational Statistics

Educational statistics serve as a crucial tool for understanding and analyzing school enrollments. These statistics help schools, policymakers, and researchers gauge educational trends and make informed decisions. Statistics like the ones from our exercise shed light on aspects like age group-specific trends or overall enrollment growth.
In the exercise, calculating total enrollments informs us about the education landscape over time. Educational statistics usually involve:

• Collecting data - for instance, gathering numbers of enrolled students.
• Analyzing data - totaling enrollments for each year.
• Reporting findings - identifying peak years or those with lowest enrollments.

Such statistics help in spotting demographic changes, assessing future educational needs, or planning resource allocation.
By understanding how to use educational statistics effectively, it becomes easier to derive meaningful conclusions from data, which is essential for academic planning and resource management.