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Questions and Answers
What is the distinction between qualitative data and quantitative data? Give a few examples of each.
What is the distinction between qualitative data and quantitative data? Give a few examples of each.
Qualitative data describe categories, while quantitative data represent counts or measures. Examples of qualitative data include brand names of shoes and eye colors. Examples of quantitative data include heights of students and quiz scores.
What two types of graphs are most common when the categories are qualitative data? Describe the construction of each.
What two types of graphs are most common when the categories are qualitative data? Describe the construction of each.
Bar graphs and pie charts. In a bar graph, categories are indicated along the horizontal axis with rectangles representing frequency or relative frequency. In a pie chart, each category corresponds to a wedge of a circle proportional to its relative frequency.
Describe the importance of labeling on a graph, and briefly discuss the kinds of labels that should be included on graphs.
Describe the importance of labeling on a graph, and briefly discuss the kinds of labels that should be included on graphs.
A graph should have a title or caption that explains the content. Labels for vertical and horizontal axes should indicate scale and describe the variables. A legend is needed if multiple data sets are displayed.
I made a frequency table with two columns, one labeled 'State' and one labeled 'State Capitol.' This statement makes sense.
I made a frequency table with two columns, one labeled 'State' and one labeled 'State Capitol.' This statement makes sense.
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Your pie chart must be wrong, because when I added the percentages on your wedges, they totaled 124%. This statement makes sense.
Your pie chart must be wrong, because when I added the percentages on your wedges, they totaled 124%. This statement makes sense.
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Create a table for Grade Frequency, Relative Frequency, Cumulative Frequency, and Total based on the data given: A,A,A,A,A,B,B,B,B,B,B,C,C,C,C,C,C,C,C,D,D,D,D,F.
Create a table for Grade Frequency, Relative Frequency, Cumulative Frequency, and Total based on the data given: A,A,A,A,A,B,B,B,B,B,B,C,C,C,C,C,C,C,C,D,D,D,D,F.
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Choose the correct construction and use of multiple bar graphs.
Choose the correct construction and use of multiple bar graphs.
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Choose the correct construction and use of multiple line charts.
Choose the correct construction and use of multiple line charts.
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Describe the correct construction and use of stack plots.
Describe the correct construction and use of stack plots.
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How can graphics sometimes be misleading?
How can graphics sometimes be misleading?
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How can graphics sometimes be useful?
How can graphics sometimes be useful?
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Explain how a graph showing percentage change can show descending bars even when the variable of interest is increasing.
Explain how a graph showing percentage change can show descending bars even when the variable of interest is increasing.
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My bar chart contains more information than yours, because I made my bars three-dimensional. This statement makes sense.
My bar chart contains more information than yours, because I made my bars three-dimensional. This statement makes sense.
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There's been only a very slight rise in our stock price over the past few months, but I wanted to make it look dramatic so I started the vertical scale from the lowest price rather than from zero. This statement makes sense.
There's been only a very slight rise in our stock price over the past few months, but I wanted to make it look dramatic so I started the vertical scale from the lowest price rather than from zero. This statement makes sense.
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What is a correlation? Give three examples of pairs of variables that are correlated.
What is a correlation? Give three examples of pairs of variables that are correlated.
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Define positive correlation.
Define positive correlation.
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Define negative correlation.
Define negative correlation.
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Define no correlation.
Define no correlation.
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How do we determine the strength of a correlation?
How do we determine the strength of a correlation?
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Briefly describe each of the six guidelines for establishing causality.
Briefly describe each of the six guidelines for establishing causality.
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I had originally suspected that an increase in variable E would cause a decrease in variable F, but I no longer believe this because I found no correlation between the two variables. This statement makes sense.
I had originally suspected that an increase in variable E would cause a decrease in variable F, but I no longer believe this because I found no correlation between the two variables. This statement makes sense.
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Consider the following statement about a correlation: In a large resort city, the crime rate increased as the number of taxi cabs increased. What correlation is this, and what is it likely due to?
Consider the following statement about a correlation: In a large resort city, the crime rate increased as the number of taxi cabs increased. What correlation is this, and what is it likely due to?
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Consider the following statement about a correlation: Automobile gas mileage decreases with tire pressure. What correlation is this and what type of cause is it?
Consider the following statement about a correlation: Automobile gas mileage decreases with tire pressure. What correlation is this and what type of cause is it?
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There is a strong correlation between tobacco smoking and incidence of lung cancer. Why do not all smokers get lung cancer?
There is a strong correlation between tobacco smoking and incidence of lung cancer. Why do not all smokers get lung cancer?
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Suppose that people living near a high-voltage power line have a higher incidence of cancer than those living farther from it. Can you conclude that the power line is the cause of the elevated cancer rate? What other research would you like to see?
Suppose that people living near a high-voltage power line have a higher incidence of cancer than those living farther from it. Can you conclude that the power line is the cause of the elevated cancer rate? What other research would you like to see?
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Study Notes
Data Types
- Qualitative data categorize characteristics (e.g., shoe brands, eye colors).
- Quantitative data involve numerical values or measurements (e.g., student heights, quiz scores).
Graphical Representations
-
Bar Graphs:
- Categories on the horizontal axis.
- Rectangles indicate frequency or relative frequency.
- Vertical axis includes a clear scale.
-
Pie Charts:
- Each category represented as a wedge in a circle.
- Wedge size correlates with relative frequency.
Importance of Graph Labels
- Graphs require a title or caption to clarify content and data source.
- Vertical axis should indicate scale and label the depicted variable.
- Include a legend if multiple data sets are present to avoid confusion.
Frequency Tables
- A valid frequency table must include a column for category frequency.
- Example given does not conform since it lacks frequency data.
Pie Chart Totality
- A pie chart must represent 100% of relative frequencies; totals exceeding this indicate errors.
Multiple Graph Types
- Multiple Bar Graphs: Extend regular bar graphs for comparing two or more data sets with qualitative categories.
- Multiple Line Charts: Use different lines for various quantitative data sets, showing trends over time.
- Stack Plots: Represent data sets stacked either in bar graphs or line charts, useful for trend analysis.
Misleading Graphics
- Variations in data can appear exaggerated through improper scaling or formatting.
Graphics Utility
- Effective in illustrating small-scale trends, making complex data more digestible.
Percentage Change in Graphs
- A descending graph may indicate an increasing variable if the vertical axis shows percentage change, reflecting smaller increments.
Correlation Concepts
- Correlation: Exists when a change in one variable consistently associates with changes in another (e.g., smoking and lung cancer).
- Positive Correlation: Both variables increase or decrease simultaneously.
- Negative Correlation: One variable increases while the other decreases.
- No Correlation: No apparent relationship between two variables.
Determining Correlation Strength
- Stronger correlations are indicated by how closely two variables follow an expected trend.
Causality Guidelines
- Look for correlation with suspected causes and consider effects seen exclusively in the presence of these causes.
- Larger amounts of the cause should correlate with larger effects, while ruling out other causes.
- Experimental tests are vital, along with establishing a mechanism for the cause-effect relationship.
Correlation Clarifications
- No correlation suggests no relationship, even with previous assumptions.
- Increases in crime rate alongside more taxi cabs may be due to tourism (common cause).
- Reduced gas mileage with lower tire pressure is a direct causal relationship.
Smoking and Cancer Relation
- Smoking enhances the risk of cancer due to cell mutation, which doesn't uniformly affect all smokers.
High-Voltage Power Lines and Cancer
- Correlation does not imply causation regarding cancer rates near power lines.
- Other explanations, such as lifestyle or environmental factors, must be considered, along with research to confirm mechanisms.
Studying That Suits You
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Description
Test your understanding of qualitative and quantitative data with this review quiz based on Chapter 5. Explore definitions, examples, and the most common types of graphs used to represent categorical data. Challenge yourself and reinforce your knowledge!