Question

Consider the relation Student Performance below which describes student performance in courses. The value stored in the gradePoint column is the grade point that corresponds to the grade received in a course. Assume that students are identified by their student number, and that courses are identified by their course id. Assume each student can take a course only once and so each row is uniquely identified by {stuNum, courseId}. Each student’s overall gpa is stored – gpa is the average of gradePoint for all courses taken by a student.

Short answer

The GPA for each student can be calculated by averaging the `gradePoint` for all courses taken by each student from the StudentPerformance relation. This can be done using the SQL `AVG` function grouped by `stuNum`.

Step-by-step solution

Understand the database structure

Firstly, understand the given relational database structure of the Student Performance. Here, each row is a unique record identified by the {stuNum, courseId}. In this relation, `gradePoint`usually represents the score that the student (`stuNum`) has achieved in a particular course (`courseId`).

Identify the GPA calculation

The GPA or Grade Point Average is the average of `gradePoint` for all courses taken by a student. This means you need to sum up the `gradePoint` for all courses of a single student and then divide the total by the number of courses. This can be represented with the SQL query: `SELECT stuNum, AVG(gradePoint) as GPA FROM StudentPerformance GROUP BY stuNum;`

Examination of the computed GPA

After calculating the GPA for each student, it would need to be ensured that the calculated GPA is correct. This can be done by examining a few records manually, considering the grades for each course a student took and calculating the GPA by taking the average. If the computed GPA matches the manual calculation, the steps can be considered correct.

Key concepts

SQL Query

An SQL Query is a powerful tool used to retrieve and manipulate data stored in a relational database. It's like asking a database a detailed question to get specific results. In our Student Performance example, we use SQL to calculate each student's GPA. Remember, SQL commands are crucial to communicate with a database effectively.
To find the GPA of students, the query is structured as follows: `SELECT stuNum, AVG(gradePoint) as GPA FROM StudentPerformance GROUP BY stuNum;`. This query selects each student's number (`stuNum`) and computes the average of `gradePoint` for courses taken by each student, grouping the results by student.

• SELECT helps specify what information to retrieve.
• AVG(gradePoint) computes the average grade, a crucial part for GPA calculation.
• FROM StudentPerformance specifies the table to perform the query on.
• GROUP BY stuNum ensures that the average is calculated for each student separately.

This structured approach allows the extraction of meaningful insights from data.

Database Structure

Understanding a Database Structure is vital for managing and analyzing data efficiently. It's like knowing the blueprint of a house to understand how everything fits together. In our scenario, the Student Performance table is organized in a way that each entry is uniquely identified by a combination of `stuNum` and `courseId`.
This composite key is essential because it ensures the uniqueness of records, preventing any confusion or overlap between different students' performance records.

• stuNum: This is a unique identifier for each student, ensuring each student's records can be tracked accurately across courses.
• courseId: Identifies each course uniquely, helping in tracking the performance of students in different courses.
• gradePoint: Represents the score a student received, which is key for calculating the GPA.

Such a design not only provides clarity and organization but is the backbone for performing reliable analytics, like calculating students' GPAs.

GPA Calculation

GPA Calculation is a method used to compute a student's overall academic performance across various courses. Think of it as a snapshot of a student's academic journey, summarized with a single number. In our example, the GPA is calculated as the average of all grade points a student has earned.
To calculate the GPA:

• Sum all the `gradePoint` values for a student.
• Count the total number of courses taken by that student.
• Divide the total sum by the number of courses to find the average, which is the GPA.

Mathematically, if a student has grades g₁, g₂, ... g_n over n courses, then the GPA is calculated as $\text{GPA}=\frac{g_1+g_2+...+g_n}{n}$.
This calculation helps in consistently evaluating student performance, allowing educators and institutions to make informed decisions about student progress.