91Ó°ÊÓ

In algebra, a data set is essentially a collection of numbers or values that are gathered to provide information about a particular subject. When dealing with algebraic problems involving coordinate points, organizing these points into a structured data set is crucial. This helps in effectively analyzing and interpreting the data.
For this exercise, we created a data set with specific conditions. Initially, we had two coordinate points: \((4,28)\) and \((12,47)\). However, the task required us to include only one of these points in our set. By choosing \((4,28)\), our data set is now:

• \(\{ (4,28) \}\)

This kind of selective inclusion is not uncommon in data tasks, where specific criteria dictate which elements belong in the set.

Coordinate points are a fundamental part of algebra, as they help locate positions in a two-dimensional space. Each point is defined by a pair of numerical values, usually written as \((x, y)\). Here, the first number, \(x\), indicates the horizontal position (also known as the abscissa), while the second number, \(y\), shows the vertical position (also referred to as the ordinate).
In the context of our problem, the points \((4,28)\) and \((12,47)\) denote two specific locations in a Cartesian plane. Deciding which of these points to include in a data set can depend on various factors such as the nature of the data being analyzed or specific problem-solving conditions. Understanding the role of coordinate points is key to successfully managing algebraic data.

Problem solving in mathematics often involves a clear understanding of the requirements, followed by a systematic approach to address those requirements. This process is crucial when constructing a data set with specified conditions.
In this exercise, the problem was clearly defined: select only one coordinate point from the given options for inclusion in a data set. The solution involved:

• Identifying the provided points, \((4,28)\) and \((12,47)\).
• Deciding which point to include (in this case, \((4,28)\)).
• Constructing a new data set with the chosen point.
• Verifying that the solution meets the given criteria.

Through this structured process, we ensure that the solution effectively fits the problem's requirements and conditions.

Data analysis involves examining and interpreting data sets to draw useful conclusions. In algebra, especially with coordinate points, this often means considering each element in relation to others or to specified criteria.
In our scenario, once the point \((4,28)\) was included in the data set, part of the data analysis involved verifying that only this point was included, meeting the exercise's conditions. Such analysis might also explore how including or excluding certain points affects the overall understanding of the data.
By adhering to a defined set of criteria and thoroughly checking our data structures, we ensure the integrity and usefulness of our data sets. This illustrates the importance of precise data analysis skills in mathematical problem-solving.