The table shows the rate (in percent) at which 2-year...

The table shows the rate (in percent) at which 2-year college students (public) completed a degree within 3 years. (a) Write the data from the table as ordered pairs $(x, y),$ where $x$ represents the year and $y$ represents the percent. (b) What does the ordered pair $(2007,26.9)$ mean in the context of this problem? (c) Make a scatter diagram of the data, using the ordered pairs from part (a) and the given grid. (d) Describe the pattern indicated by the points on the scatter diagram. What is happening to rates at which 2 -year college students complete a degree within 3 years?

The table shows the rate (in percent) at which 2-year college students (public) completed a degree within 3 years.
(a) Write the data from the table as ordered pairs $(x, y),$ where $x$ represents the year and $y$ represents the percent.
(b) What does the ordered pair $(2007,26.9)$ mean in the context of this problem?
(c) Make a scatter diagram of the data, using the ordered pairs from part (a) and the given grid.
(d) Describe the pattern indicated by the points on the scatter diagram. What is happening to rates at which 2 -year college students complete a degree within 3 years?

Key Concepts

Trend Analysis

Trend analysis involves reviewing the plotted data to determine whether there is an increasing, decreasing, or stable pattern over time. This analysis helps in understanding the direction and nature of the relationship between the variables, offering insights into long-term behaviors or changes in the dataset.

Scatter Diagram

A scatter diagram, or scatter plot, is a graphical tool used to display the relationship between two quantitative variables. It plots each ordered pair as a point on a coordinate grid, making it easier to visually identify patterns, clusters, or trends in the dataset, and helping to assess how changes in one variable may be associated with changes in another.

Ordered Pairs Representation

Ordered pairs are a way of representing data values where each pair consists of two elements, typically representing independent and dependent variables. In the context of data from a table, this means pairing each key measurement (such as a specific year) with its corresponding value (such as a percentage rate), allowing one to plot and analyze the relationship systematically.

Contextual Interpretation of Data

Understanding an ordered pair in a real-world context involves interpreting what the numerical values represent with respect to the situation. In many cases, one value might correspond to a time period or category while the other indicates a quantitative measure, such as a percentage or rate. This interpretation is critical for making informed conclusions based on the data.

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