M3 Chapter 11 Notes: Data Displays
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Academic Note
Packet
Sections 11.1-11.5
Data Analysis
Name_________________Pd___
M3 Chapter 11 Notes: Data Displays
Vocabulary Words
Sections 11.1-11.2
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Stem-and-leaf plot
Frequency
Frequency table
Histogram
Box-and-whisker plot
Lower quartile
Upper quartile
Upper extreme
Lower extreme
Median
Range
Interquartile range
Vocabulary List
Sections 11.3-11.5
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Bar graph
Line graph
Circle graph
Categorical data
Numerical data
Population
Sample
Random sample
Systematic sample
Stratified sample
Convenience sample
Self-selected sample
Biased sample
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M3 Chapter 11 Notes: Data Displays
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Section 11.1: Stem-and-Leaf Plots and Histograms
Learning Goal: We will make stem-and-leaf plots and histograms.
Vocabulary:
 Stem-and-leaf plot –
Example 1: Making a Stem-and-Leaf Plot
The distances (in centimeters) of 11 jumps from the final round of a
women’s long jump competition are listed below. How can you display
the data to show the distribution of the distances?
669, 702, 644, 701, 684, 686, 676, 673, 688, 670, 662
ON YOUR OWN:
The number of passengers on each of 10 city buses is given below.
Display the data in a stem-and-leaf plot.
12, 35, 17, 39, 25, 23, 20, 20, 35, 14
M3 Chapter 11 Notes: Data Displays
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Example 2: Interpreting Stem-and-Leaf Plots
The stem-and-leaf plots show the grades on a history test for two
classes. What can you conclude about the grades?
ON YOUR OWN:
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Vocabulary:
 Frequency –
 Frequency table –
Example 3: Making a Frequency Table
Madison asked 20 classmates how many CDs they own. The numbers
are listed below. Make a frequency table of the data, using intervals
of 5.
12, 12, 12, 2, 6, 7, 18, 19, 7, 4, 13, 13, 7, 8, 9, 4, 10, 14, 14, 14
ON YOUR OWN:
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Vocabulary:
 Histogram –
Example 4: Making a Histogram
Make a histogram using the frequency table in Example 3.
ON YOUR OWN:
Make a histogram using the frequency table in the last ON YOUR OWN
problem.
M3 Chapter 11 Notes: Data Displays
Example 5: Interpreting a Histogram
ON YOUR OWN:
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M3 Chapter 11 Notes: Data Displays
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Section 11.2: Box-and-Whisker Plots
Learning Goal: We will make and interpret box-and-whisker plots.
Vocabulary:
 Box-and-whisker plot –
 Lower quartile –
 Upper quartile –
 Lower extreme –
 Upper extreme –
Example 1: Making a Box-and-Whisker Plot
The ages of nine people at a birthday party are given below. Make a
box-and-whisker plot of the data.
15, 37, 45, 62, 14, 12, 17, 10, 11
M3 Chapter 11 Notes: Data Displays
ON YOUR OWN:
Interpreting Box-and-Whisker Plots:
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M3 Chapter 11 Notes: Data Displays
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Example 2: Interpreting Box-and-Whisker Plots
ON YOUR OWN:
The box-and-whisker plot below displays the cost, in dollars, of a
wetsuit sold by several online diving store.
a. What is the median price for the wetsuit?
b. What is the range of the prices?
M3 Chapter 11 Notes: Data Displays
 Range –
 Interquartile range –
Example 3: Comparing Box-and-Whisker Plots
EXTRA PRACTICE:
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M3 Chapter 11 Notes: Data Displays
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Making Data Displays
Learning Goal: We will prepare for using bar graphs, line graphs, and circle graphs.
Making a Bar Graph:
 Bar graph –
Example 1: Bar Graphs
How are bar graphs different from histograms? What conclusions can
you make about the data?
a.
b.
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Making a Line Graph:
 Line graph –
Example 2: Line Graph
What are the advantages of using a line graph? What trends can be
observed in the data?
a.
b.
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Making a Circle Graph:
 Circle graph –
Example 3: Circle Graph
How would you make a circle graph? What characteristics of circles
would help you determine how large to make each section?
a.
b.
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EXTRA PRACTICE:
1. Make a bar graph showing the percent of people surveyed who enjoy each
kind of entertainment.
2. Make a line graph showing the percent of single women who worked in the
U.S., from 1970 to 2000.
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3. Make a circle graph showing the percent of U.S. curbside
recycling programs in 2000 that existed in each region.
4. Explain why you cannot use a circle graph to display the data in
Exercise 1.
M3 Chapter 11 Notes: Data Displays
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Section 11.3: Using Data Displays
Learning Goal: We will choose appropriate data displays.
Vocabulary:
 Categorical data –
 Numerical data –
Example 1: Choosing an Appropriate Data Display
What data display would you use to display the heights (in meters) of
different palm trees?
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A student group solicited pledges for the number of kilometers they
walked during a fundraiser. Ashley created a table listing the students
who participated, their age, and the number of kilometers each student
walked. Which display(s) could Ashley use to display the data?
ON YOUR OWN:
Example 2: Comparing Data Displays
M3 Chapter 11 Notes: Data Displays
ON YOUR OWN:
MISLEADING DATA DISPLAYS:
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M3 Chapter 11 Notes: Data Displays
Example 3: Identifying Misleading Data Displays
ON YOUR OWN:
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M3 Chapter 11 Notes: Data Displays
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Section 11.4: Collecting Data
Learning Goal: We will identify populations and sampling methods.
Vocabulary:
 Population –
 Sample –
SAMPLING METHODS:
Random Sample
Systematic Sample
Stratified Sample
Convenience Sample
Self-selected Sample
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Example 1: Identifying Populations and Sampling Methods
For each survey, describe the population and the sampling method.
a. A school newspaper reporter asks every fifth student entering a
school building whether a new gymnasium should be built.
b. A manager at a television station randomly telephones 75
residents under 30 years old and 75 residents 30 years old and
over to determine the station’s most watched programs.
c. During an airplane flight, a newspaper reporter surveys ten
passengers seated near him about airport security.
d. A magazine invites its readers to mail in their answers to a
questionnaire.
 Biased sample –
**The sampling method can affect how _______________________
a sample is.
**The most reliable way to have a representative sample is to use
_______________________.
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Example 2: Identifying Potentially Biased Samples
The board of trustees for a city library is considering extending the
library’s hours and wants to survey some of the city’s residents
regarding their proposed changes. Tell whether the survey method
could result in a biased sample. Explain.
a. Survey all library patrons who visit the library on one particular
evening.
b. Survey people at a city park each morning for one week.
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ON YOUR OWN:
 Biased questions –
Example 3: Identifying Potentially Biased Questions
Tell whether the question is potentially biased. Explain your answer.
If it is biased, rewrite it so it is not. How many times per month do
you use the city’s new library?
ON YOUR OWN:
M3 Chapter 11 Notes: Data Displays
EXTRA PRACTICE:
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M3 Chapter 11 Notes: Data Displays
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Section 11.5: Interpreting Data
Learning Goal: We will make conclusions about populations using surveys.
**You can use a sample to make a prediction about a population. If p%
of a sample gives a particular response and the sample is
representative of the population, then:
Example 1: Making a Population Prediction
Television networks rely on surveys to determine how many people
watch their programs. In a survey of 5000 randomly selected
American households watched a certain program. Of all American
households, how many watched the program? (There are about 105
million households in the United States.)
ON YOUR OWN:
One student out of a class of 20 was absent with a cold. What percent
of the class was absent and how many students out of a school of 1600
would you estimate to be absent based on this percent?
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 Margin of Error – defines an interval centered on a sample
percent in which a population percent is most likely to lie
 Remember: a survey collects data from only a portion of a
population (sample)
 Different surveys of the same population may have different
results
 Due to such variation, a survey should include a margin of error to
estimate an interval in which the actual population percent is most
likely to lie.
 Example: a sample percent of 32% with a margin of error of
 5% means that the population percent is most likely between 27%
and 37%.
Example 2: Interpreting a Margin of Error
The mayor of a city is running for re-election. A survey of some city
residents predicts that the mayor will receive 58% of the votes from
likely voters and her challenger will receive 42% of the votes. The
margin of error for the survey is  5% . Can you predict who will win
the election? Explain.
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ON YOUR OWN:
Example 3: Interpreting a Report
Tell what conclusions you can make from the following report.
Recently, researchers surveyed 1000 patrons of a local shopping mall
and asked them if they were “strongly for”, “mildly for”, or “against”
the city’s plans to buy some residents’ houses and demolish them to
make room for a new upscale mall. Most residents – 780 out of 1000 –
were for having the new mall.
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ON YOUR OWN: Interpreting a Newspaper Survey
Tell what conclusions you can make from the following newspaper
article.