Statistics Chapter 5 Review Quiz
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Questions and Answers

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.

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.

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.

<p>False</p> Signup and view all the answers

Your pie chart must be wrong, because when I added the percentages on your wedges, they totaled 124%. This statement makes sense.

<p>True</p> Signup and view all the answers

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.

<p>Grade Frequency: A-5, B-6, C-8, D-4, F-1; Relative Frequency: A-0.208, B-0.25, C-0.333, D-0.167, F-0.042; Cumulative Frequency: A-5, B-11, C-19, D-23, F-24; Total: 24.</p> Signup and view all the answers

Choose the correct construction and use of multiple bar graphs.

<p>It is a simple extension of a regular bar graph with two or more sets of bars that allows comparison of two or more data sets.</p> Signup and view all the answers

Choose the correct construction and use of multiple line charts.

<p>It is a simple extension of a regular line chart using different lines for different data sets, each based on a different level.</p> Signup and view all the answers

Describe the correct construction and use of stack plots.

<p>Stack plots show different data sets stacked in bar graphs and line charts, using sections that are color-coded according to a legend, useful for showing trends over time.</p> Signup and view all the answers

How can graphics sometimes be misleading?

<p>The variation can seem to be larger than it really is.</p> Signup and view all the answers

How can graphics sometimes be useful?

<p>It can make it easier to show small scale trends in the data.</p> Signup and view all the answers

Explain how a graph showing percentage change can show descending bars even when the variable of interest is increasing.

<p>The vertical axis represents percentage change, so a drop-off can indicate that the actual value rises by smaller amounts.</p> Signup and view all the answers

My bar chart contains more information than yours, because I made my bars three-dimensional. This statement makes sense.

<p>False</p> Signup and view all the answers

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.

<p>True</p> Signup and view all the answers

What is a correlation? Give three examples of pairs of variables that are correlated.

<p>A correlation exists when higher values of one variable consistently match higher or lower values of another. Examples include: amount of smoking and lung cancer, height and weight of people, price of a good and demand for the good.</p> Signup and view all the answers

Define positive correlation.

<p>Positive correlation means that both variables tend to increase or decrease together.</p> Signup and view all the answers

Define negative correlation.

<p>Negative correlation means that two variables tend to change in opposite directions, with one increasing while the other decreases.</p> Signup and view all the answers

Define no correlation.

<p>No correlation means that there is no apparent relationship between the two variables.</p> Signup and view all the answers

How do we determine the strength of a correlation?

<p>The strength of a correlation is determined by how closely the variables follow a general trend, which can be positive or negative.</p> Signup and view all the answers

Briefly describe each of the six guidelines for establishing causality.

<ol> <li>Look for correlation with suspected cause; 2. Check if effect is present/absent among groups with/without cause; 3. Larger amounts of cause produce larger effects; 4. Isolate potential causes to see if effect remains; 5. Test suspected cause with experiments; 6. Determine the mechanism by which the suspected cause induces the effect.</li> </ol> Signup and view all the answers

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.

<p>True</p> Signup and view all the answers

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?

<p>There is a positive correlation between the crime rate and the number of taxi cabs, likely due to a common underlying cause such as increased tourism.</p> Signup and view all the answers

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?

<p>This correlation is due to a direct cause because lower tire pressure requires more gasoline to roll.</p> Signup and view all the answers

There is a strong correlation between tobacco smoking and incidence of lung cancer. Why do not all smokers get lung cancer?

<p>Not all smokers get cancer because cancer is caused by cell mutation, and while smoking increases the chances of such mutation occurring, it does not occur in every smoker.</p> Signup and view all the answers

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?

<p>You cannot conclude causality because a mechanism must be confirmed. Further research should focus on the effect of electricity on cell growth mechanisms.</p> Signup and view all the answers

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.

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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!

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