The table shows the number of U.S. students who studied...

The table shows the number of U.S. students who studied abroad (in thousands) for several academic years. (a) Write the data from the table as ordered pairs $(x, y),$ where $x$ represents the year and $y$ represents the number of U.S. students (in thousands) studying abroad. (b) What does the ordered pair $(2006,242)$ 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 was the trend in the number of U.S. students studying abroad during these years?

The table shows the number of U.S. students who studied abroad (in thousands) for several academic years.
(a) Write the data from the table as ordered pairs $(x, y),$ where $x$ represents the year and
$y$ represents the number of U.S. students (in thousands) studying abroad.
(b) What does the ordered pair $(2006,242)$ 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 was the trend in the number of U.S. students studying abroad during these years?

Key Concepts

Scatter Diagram

A scatter diagram (or scatter plot) is a graphical representation of data points on a Cartesian plane. Each point on the diagram corresponds to an ordered pair from the dataset, making it easier to visualize the relationship between the two variables. This type of graph is particularly useful for identifying patterns, correlations, and trends within the data.

Ordered Pairs

An ordered pair is a set of two elements arranged in a specific order, usually written as (x, y). In the context of this problem, the first number represents the year (the independent variable) and the second number represents the number of U.S. students studying abroad (the dependent variable). This format allows for a clear representation of the relationship between time and the number of students.

Data Interpretation

Data interpretation involves understanding what each piece of a data point signifies within a real-world context. For example, when looking at an ordered pair like (2006, 242), one interprets that in the year 2006, 242 thousand U.S. students studied abroad. This process connects numerical values to their corresponding practical meanings.

Trend Analysis

Trend analysis involves examining a collection of data points to identify any patterns or trends, such as increases, decreases, or constant values over time. In the context of this problem, analyzing the scatter diagram allows one to observe whether the number of U.S. students studying abroad is rising, falling, or remaining stable over the given years, providing insight into how the trend has evolved over time.

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