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Chapter 2: Problem 175

Put the \(X\) variable on the horizontal axis and the \(Y\) variable on the vertical axis. $$ \begin{array}{rrrrrrrrr} \hline X & 15 & 20 & 25 & 30 & 35 & 40 & 45 & 50 \\ \hline Y & 532 & 466 & 478 & 320 & 303 & 349 & 275 & 221 \\ \hline \end{array} $$

Short Answer

Expert verified
A line graph is constructed with X and Y values given, with X on the horizontal axis and Y on the vertical axis.

Step by step solution

01

Set Up Axes

Set up a graph with X as the horizontal axis ranging from 10 to 55 and Y as the vertical axis ranging from 200 to 600. Make sure the scale is selected in such a way that all the X and Y values can be easily plotted.
02

Plot Points

Plot the points on the graph where each X value corresponds to a Y value. You should plot points like (15, 532), (20, 466), (25, 478), (30, 320) and so on.
03

Construct Line Graph

Using the plotted points, construct the line graph. Connect the points in the order of increasing X values. There should be a series of interconnected straight lines that forms the line graph.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Data Visualization
Data visualization is the graphical representation of information and data. By using visual elements like charts, graphs, and maps, data visualization tools provide an accessible way to see and understand trends, outliers, and patterns in data.

In the given exercise, the visualization in the form of a line graph helps in communicating the relationship between the two variables, which are the X and Y in this case. By plotting the variables visually, it's easier for us to perceive trends, such as increases or decreases in Y values as X changes, and to quickly grasp complex concepts that might be difficult to understand through text-based data alone.

Effective data visualization allows for a more efficient and comprehensible way of communicating numerical information. For students and anyone looking to improve their understanding of graphing data, focusing on clean, effective visualization is crucial. Choosing the right type of graph is a key step, which, for bivariate data, often involves a line graph or scatter plot—both of which clearly show the relationship between two variables.
Bivariate Data
Bivariate data involves two different variables that may be dependent or independent of each other. In the case of the exercise, the two variables are designated as X and Y. The data provided lists the two variables in pairs where each X value is associated with a corresponding Y value.

Bivariate data is crucial to understand because it lays the foundation for determining the interactions between variables. For students, comprehending how to analyze bivariate data means they can predict outcomes based on correlational data. Such skills are fundamental for subjects such as statistics, science experiments, and economics.

In practice, when working with bivariate data, one of the primary considerations is distinguishing between the dependent and independent variables. Generally, the independent variable is plotted along the horizontal axis (in this case, X), and the dependent variable is plotted on the vertical axis (Y). This setup is useful for identifying how changes in the independent variable can affect the dependent variable.
Graphing Techniques
Graphing techniques are tools and processes used to create visual representations of data. The steps to graphing typically include setting up axes, plotting points, and then, if appropriate, connecting these points to form a particular graph such as a line graph or a bar chart. For a line graph, which is what the exercise requires, the points are typically connected by straight lines in the order they appear on the horizontal axis.

Improving Graph Readability

To enhance readability, labels are essential; they ensure that anyone reading the graph can easily understand what each axis represents. Additionally, keeping a consistent scale is paramount to avoid distorting the data. A scale that is too condensed can make it difficult to observe patterns, while one that is too spread out can exaggerate variances.

Another technique involves choosing an appropriate interval for plotting data points. The interval should be consistent to provide a clear, comparative visual of the data. Lastly, when constructing a line graph, it's important to connect the points in the correct sequence to reflect the relationship and the change between the variables accurately.

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Most popular questions from this chapter

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