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Chapter 3: Problem 6

The price of EX0306 living in the United States has increased dramatically in the past decade, as demonstrated by the consumer price indexes (CPIs) for housing and transportation. These CPIs are listed in the table for the years 1996 through the first five months of \(2007 .^{3}\) $$\begin{array}{lcccccc}\text { Year } & 1996 & 1997 & 1998 & 1999 & 2000 & 2001 \\\\\hline \text { Housing } & 152.8 & 156.8 & 160.4 & 163.9 & 169.6 & 176.4 \\\\\text { Transportation } & 143.0 & 144.3 & 141.6 & 144.4 & 153.3 & 154.3 \\\\\hline \text { Year } & 2002 & 2003 & 2004 & 2005 & 2006 & 2007 \\\\\hline \text { Housing } & 180.3 & 184.8 & 189.5 & 195.7 & 203.2 & 207.8 \\\ \text { Transportation } & 152.9 & 157.6 & 163.1 & 173.9 & 180.9 & 181.0 \\\\\hline\end{array}$$ a. Create side-by-side comparative bar charts to describe the CPIs over time. b. Draw two line charts on the same set of axes to describe the CPIs over time. c. What conclusions can you draw using the two graphs in parts a and b? Which is the most effective?

Short Answer

Expert verified
Additionally, which type of graphical representation (bar graphs or line charts) do you think is more effective in visualizing these trends and allowing for better comparisons between the two categories?

Step by step solution

01

Organize the Data

First, write down the given data in a table consisting of the Year, Housing CPI, and Transportation CPI: Year | Housing | Transportation -----|---------|-------------- 1996 | 152.8 | 143 1997 | 156.8 | 144.3 1998 | 160.4 | 141.6 1999 | 163.9 | 144.4 2000 | 169.6 | 153.3 2001 | 176.4 | 154.3 2002 | 180.3 | 152.9 2003 | 184.8 | 157.6 2004 | 189.5 | 163.1 2005 | 195.7 | 173.9 2006 | 203.2 | 180.9 2007 | 207.8 | 181
02

Create Side-By-Side Comparative Bar Graphs

Using the organized data, create bar graphs for both housing and transportation CPIs for each year from 1996 to 2007. Place the bars corresponding to the same year side-by-side for comparison.
03

Create Line Charts

Using the same data, create two line charts: one for housing CPI and one for transportation CPI. Plot the charts on the same set of axes with the time on the x-axis (1996 to 2007) and the CPI on the y-axis.
04

Analyze the Graphs

Observe both the side-by-side comparative bar graphs and line charts. Analyze the trends depicted in the graphs: whether the CPIs increased or decreased, and the similarity or difference of trends in CPIs for housing and transportation.
05

Compare the Effectiveness of Graphs

Compare the side-by-side comparative bar graphs and line charts to determine which one is more effective in visualizing the trends and allowing better comparison of the CPIs for housing and transportation.
06

Draw Conclusions

Based on the trends and changes observed in the graphs, draw conclusions regarding the CPIs for housing and transportation during the given time period, such as their growth or decline over time and their relationship with each other. Also, state which graph type is most effective for this data set and why.

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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 like storytelling with numbers. It uses images like charts and graphs to show data in a way that's easy to understand. By using these visual tools, we can quickly see patterns, trends, and outliers in data that might be hard to spot in a table. In this exercise, we are looking at how Consumer Price Indexes (CPI) for housing and transportation have changed over time. Instead of just staring at numbers, we use graphs to see this information in a helpful visual way. Data visualization helps make complex data more approachable and insightful, aiding in decision-making and communication.
Comparative Bar Chart
A Comparative Bar Chart is a type of chart used to compare different sets of data side by side. Each set is represented by a bar, and their heights show the value of the data. For this exercise, we create side-by-side bars for the Consumer Price Index of housing and transportation for each year from 1996 to 2007.
This helps us see at a glance which one was higher at various points in time. It's like having a visual list that makes comparing different things quick and easy. A key tip for these charts: Keep the distance equal between the bars within a year, and use different colors or shades for housing and transportation to make them easily distinguishable.
Line Chart
A Line Chart is all about showing how data changes over time. It's perfect for seeing trends because you can clearly watch the upward or downward movement on the graph. In this exercise, we plot two line charts on the same axes: one for housing CPI and another for transportation CPI.
By putting both lines on the same chart, you can easily compare how each has increased or decreased from 1996 to 2007. The x-axis represents the passing years, while the y-axis displays the CPI values. Intersection and divergence points of the lines can highlight moments where the increases were similar or significantly different. A line chart's strength lies in its ability to reveal trends through a continuous flow of data, unlike a bar chart's segmented intervals.
Trend Analysis
Trend Analysis is about understanding how your data changes over time. This can help in guessing future movements. With the graphs drawn in this exercise, we can see if the CPIs have generally been increasing or decreasing.
For example, observing the line charts might show a steady rise in housing CPI, but fluctuations in transportation CPI. With the bar chart, the comparison over each year might be clearer at a glance.
  • Increasing trends: Indicates growth or inflation in prices.
  • Fluctuating trends: Suggest volatility, where prices rise and fall unpredictably.
  • Diverging trends between two data sets show how one may be growing faster than the other.
Trend analysis can aid in making predictions about future economic conditions or costs, and choosing the right type of graph is essential for clarity and understanding these trends effectively.

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Most popular questions from this chapter

When you were growing up, did you feel that you did not have enough free time? Parents and children have differing opinions on this subject. A research group surveyed 198 parents and 200 children and recorded their responses to the question, "How much free time does your child have?" or "How much free time do you have?" The responses are shown in the table below: $$\begin{array}{lcccc} & \text { Just the } & \text { Not } & \text { Too } & \text { Don't }^{\prime} t \\\& \text { Right Amount } & \text { Enough } & \text { Much } & \text { Know } \\\\\hline \text { Parents } & 138 & 14 & 40 & 6 \\\\\text { Children } & 130 & 48 & 16 & 6\end{array}$$ a. Define the sample and the population of interest to the researchers. b. Describe the variables that have been measured in this survey. Are the variables qualitative or quantitative? Are the data univariate or bivariate? c. What do the entries in the cells represent? d. Use comparative pie charts to compare the responses for parents and children. e. What other graphical techniques could be used to describe the data? Would any of these techniques be more informative than the pie charts constructed in part d?

Access the applet in How a Line Works. a. Use the slider to change the \(y\) -intercept of the line, but do not change the slope. Describe the changes that you see in the line. b. Use the slider to change the slope of the line, but do not change the \(y\) -intercept. Describe the changes that you see in the line.

The EX0333 table below (Exercise 1.50) shows the predicted rise of home networking of \(\mathrm{PCs}\) in the next few years. \({ }^{13}\) $$\begin{array}{lcc}\multicolumn{2}{l} {\text { U.S Home Networks (in millions) }} \\\\\hline \text { Year } & \text { Wired } & \text { Wireless } \\\\\hline 2002 & 6.1 & 1.7 \\\2003 & 6.5 & 4.5 \\\2004 & 6.2 & 8.7 \\\2005 & 5.7 & 13.7 \\\2006 & 4.9 & 19.1 \\\2007 & 4.1 & 24.0 \\\2008 & 3.4 & 28.2 \\\\\hline\end{array}$$ a. What variables have been measured in this experiment? Are they qualitative or quantitative? b. Use one of the graphical methods given in this chapter to describe the data. c. Write a sentence describing the relationship between wired and wireless technology as it will be in the next few years.

In Exercise \(2.12,\) ConEX0319 \(\quad\) sumer Reports gave the prices for the top 10 LCD high definition TVs (HDTVs) in the 30 - to 40 -inch category. Does the price of an LCD TV depend on the size of the screen? The table below shows the 10 costs again, along with the screen size. $$\begin{array}{lcl}\text { Brand } & \text { Price } & \text { Size } \\\\\hline \text { JVC LT-40FH96 } & \$ 2900 & 40^{\prime \prime} \\\\\text { Sony Bravia KDL-V32XBR1 } & 1800 & 32^{\prime \prime} \\\\\text { Sony Bravia KDL-V40XBR1 } & 2600 & 40^{\prime \prime} \\\\\text { Toshiba 37HLX95 } & 3000 & 37^{\prime \prime} \\\\\text { Sharp Aquos LC-32DA5U } & 1300 & 32^{\prime \prime} \\\\\text { Sony Bravia KLV-S32A10 } & 1500 & 32^{\prime \prime} \\\\\text { Panasonic Viera TC-32LX50 } & 1350 & 32^{\prime \prime} \\\\\text { JVC LT-37X776 } & 2000 & 37^{\prime \prime} \\\\\text { LG 37LP1D } & 2200 & \text { 37" } \\\\\text { Samsung LN-R328W } & 1200 & \text { 32" }\end{array}$$ a. Which of the two variables (price and size) is the independent variable, and which is the dependent variable? b. Construct a scatterplot for the data. Does the relationship appear to be linear?

Consider this set of bivariate data: $$\begin{array}{c|cccccc}x & 1 & 2 & 3 & 4 & 5 & 6 \\\\\hline y & 5.6 & 4.6 & 4.5 & 3.7 & 3.2 & 2.7\end{array}$$ a. Draw a scatterplot to describe the data. b. Does there appear to be a relationship between \(x\) and \(y\) ? If so, how do you describe it? c. Calculate the correlation coefficient, \(r\). Does the value of \(r\) confirm your conclusions in part b? Explain.
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