Lesson 2.8IntroductionCourse ObjectivesThis lesson will addr.docx

Lesson 2.8
Introduction
Course Objectives
This lesson will address the following course outcomes:
· 7. Read, interpret, and make decisions based upon data from
tables and graphical displays such as line graphs, bar graphs,
scatterplots, pie charts, and histograms. Given data, choose an
appropriate type of graphical display and create it using scales
appropriate to the application.
Specific Objectives
Students will understand that
· the scale on graphs can change perception of the information
they represent.
· to fully understand a pie graph, the reference value must be
known.
Students will be able to
· calculate relative change from a line graph.
· estimate the absolute size of the portions of a pie graph given
its reference value.
· use data displayed on two graphs to estimate a third quantity.
Graphs are a helpful way to summarize data. Often there are
many ways to portray information graphically. Sometimes one
form is easier to read than another. Sometimes the way a graph
is made can affect the impression it gives. Today, you will look
at three examples of such graphs.
Line Graphs
Problem Situation 1: Reading Line Graphs
#1 Points possible: 5. Total attempts: 5
Compare the two graphs below.
Which statement best descries the relationship between the
graphs?
· The data appears to be different - the first graph shows larger
changes in income

· They appear to show the same data, but on different vertical
scales.
What was the average household income in 1999?
$
Based on these two graphs, would it be fair to say that the
average household income was significantly lower in 2009 than
it was in 1999?
Give your answer with an explanation, then compare your
answer to the one provided.
Bar Graphs
Problem Situation 2: Reading Bar Graphs
In this example, we will be looking at bar graphs. Before doing
that, answer the question about Jeff’s Housing so that you can
understand the questions about national debt and GDP that
follow.
Jeff’s Housing: Two pairs of statements are given below.
In 1990, Jeff spent $1,000 per month on housing.
In 2010, Jeff spent $2,000 per month on housing.
In 1990, Jeff spent 20% of his income on housing.
In 2010, Jeff spent 10% of his income on housing.
a. How can both pairs of statements be true?
· It is not possible for both statements to be true, since one
shows his housing costs rising, and the other shows his housing
costs decreasing
· Both statements can be true if his income increased
significantly from 1990 to 2010
· Both statements can be true if his income fell significantly
from 1990 to 2010
b. Calculate Jeff's monthly income in 1990

$
c. Calculate Jeff's monthly income in 2010
$
GDP, or Gross Domestic Product, can be thought of as the
country’s income. It is the value of all goods and services the
country produces. The national debt is how much the country
owes. Just as Jeff’s spending on housing can be calculated as a
percent of income, a country’s national debt can be calculated
as a percent of its GDP.
Using the graphs above,
a) What was the national debt in 2010?
trillion dollars
b) What percent of the GDP was the national debt in 2010?
%
Consider the two graphs above.
Think about the statement, "The 2010 national debt is way out
of hand and has never been higher." Use the graphs above to
evaluate the statement. While of the following is most correct?
· The total debt has never been higher, but as a percentage of
income debt was not at the highest level ever in 2010
· The debt is higher than the last few decades, but was higher in
1950
· The debt has never been higher
· As a percentage of GDP, debt is higher now than in the last
few decades, but it was higher in 1950
Pie Graphs
Problem Situation 3: Reading Pie (Circle) Graphs
Decide if the following statement is true or false based on the
two graphs below.

True or False: This pair of graphs predicts that the number of
non-Hispanics in the United States is expected to decline
between 2010 and 2050.
· True
· False
· Not enough information is given
The U.S. population in 2010 was around 310,000,000. In 2050,
the U.S. population is expected to be around 439,000,000. Using
this information and the pie charts above, find the number of
non-Hispanic Americans at each time, to the nearest million
people.
Non-Hispanic Americans in 2010: million people
Non-Hispanic Americans in 2050: million people
Based on your calculations, now what can you conclude about
this statement?
True or False: This pair of graphs predicts that the number of
non-Hispanics in the United States is expected to decline
between 2010 and 2050.
· True
· False
· Not enough information is given
HW 2.8
Which of the following was one of the main mathematical ideas
of the lesson?
· In the graphs below, you know that Part A2 represents a larger
quantity than Part B2 because the piece of the graph is larger.
· In Graph A, you can find the quantity represented by Part A1
by multiplying the percentage for the section times the total
quantity represented by the circle.

· It is important to consider the gross national product when
considering the size of the national debt. They relate to each
other just as a person's personal debt relates to his/her income.
· In the graphs below, you must know the reference values to
compare the quantities represented by the parts A1 and A2.
Use the graph below to answer the following questions.1
a. Estimate the percentage increase in new housing prices from
1999 to 2007. (Choose the best answer.)
· The prices increased from around $160,000 to around
$245,000, about a 65% increase.
b. Estimate the percentage increase in new housing prices from
2004 to 2007. (Fill in the blanks.)
The prices increased from $ to $. This is about an 12% increase.
c. Estimate the percentage decrease from 2007 to 2009. (Fill in
the blanks.)
The prices decreased from $ to $. This is about a % decrease.
South Central Bank has a policy that limits the amount of debt
customers may have in order to receive a loan. The following
pie chart shows the highest percentage of debt that the bank will
allow.
a. What is the reference value in this situation?
· Other expenses

· Debt
· Total of other expenses and debt
· None of the above
b. Three graphs are given below. Each graph represents a loan
customer. The customers’ debt is broken into three categories:
Car, Credit Card, and Mortgage (the loan on a house). Which
customer(s) meet the bank policy on the limit of the amount of
debt? There may be more than one correct answer.
·
·
·
In Lesson 1.9, you used results from the 2009 Consumer
Expenditure Survey on how Americans spend their income. A
summary of this information is given in Table 12.
Table 1: Percentages of Average Annual Housing Expenditures
Housing
34.43%
Food
12.99%
Transportation
15.61%
Everything Else
36.97%
Which pie graph best represents the data given in Table 1?
·
·
·
·
The following two pie graphs show how two families spend
their money. The Alvarez family has a take-home pay of $3,650

per month and the Martinez family has a take-home pay of
$7,300 per month.
a. Select the statement that best compares how much the
families spend on gasoline.
· The Alvarez family spent more on gasoline than the Martinez
family because 3% of $7,300 is more than 6% of $3,650.
· The two families both spent $200 on gasoline.
· The Alvarez Family spent more on gasoline than the Martinez
Family.
· Both families spend around $200 on gasoline. This is 6% of
the Alvarez budget, but only 3% of the Martinez budget because
the Martinez family starts with about twice as much money as
the Alvarez family.
b. Estimate the actual spending on food and housing for each
family. (Fill in the tables. Be sure to estimate - exact answers
are not accepted.)
Alvarez Family
Food
$
Housing
$
c.
Martinez Family
Food
$
Housing
$
d.
e. Both families spend about the same percentage of their
income on housing. The family with the income can afford a
house that has twice the payment and maintenance costs.
The Center for Disease Control (CDC) published the following

information about respiratory disease in children. Respiratory
disease is an illness that affects a person’s ability to breathe and
use oxygen.3
In 2005, approximately one fourth of the 2.4 million
hospitalizations for children aged < 15 years were for
respiratory diseases, the largest category of hospitalization
diagnoses in this age group. Of these, 31% were for pneumonia,
25% for asthma, 25% for acute bronchitis and bronchiolitis, and
19% for other respiratory diseases, including croup and chronic
disease of tonsils and adenoids.
a. Based on this information, how many children were
hospitalized for pneumonia in 2005?
children
b. Which of the following pie charts accurately represents the
data for children hospitalized for respiratory diseases?
A group of adults were asked how many children they have in
their families. The bar graph below shows the number of adults
who indicated each number of children.
1234567Number of Children012345
How many adults were questioned?
What percentage of the adults questioned had 0 children?
%
Jan23Feb21Mar16Apr12May9Jun7July5Aug7Sept9Oct12Nov16
Dec10MillimetersAverage Monthly Precipitation010203040
Using the bar graph from above to answer the following

questions:
a)The average monthly precipitation in February is how many
times the average monthly precipitation in June?
b) The average monthly precipitation in December is how many
times the average monthly precipitation in July?
Lesson 2.10
Introduction
Course Objectives
· 6. Demonstrate an understanding of the connection between
the distribution of data and various mathematical summaries of
data (measures of central tendency and of variation).
Specific Objectives
Students will understand that
· each statistic—the mean, median, and mode—is a different
summary of numerical data.
· conclusions derived from statistical summaries are subject to
error.
· they can use the measures of central tendency to make
decisions.
· make good decisions using information about data.
· interpret the mean, median, or mode in terms of the context of
the problem.
· match data sets with appropriate statistics.

Job Ads
Problem Situation 1: Making Sense of Measures of Central
Tendency
Examine these three job advertisements:
Employment Opportunities
Outdoor Sales
Above Average Sales
Home Sales
Sales Positions Available!
We have immediate need for five enthusiastic self-starters who
love the outdoors and who love people. Our salespeople make
an average of $1,000 per week. Come join the winning team.
Call 555-0100 now!
Are you above average?
Our company is hiring one person this month—will you be that
person? We pay the top percentage commission and supply you
leads. Half of our sales force makes over $3,000 per month.
Join the
Above Average Team!
Call 555-0127 now!
NEED A NEW CHALLENGE?
Join a super sales force and make as much as you want. Five of
our nine salespeople closed FOUR homes last month. Their
average commission was $1,500 on each sale. Do the math—this
is the job for you.
Making dreams real—
call 555-0199
Consider the phrase from each advertisement. Which measure
of central tendency is it most likely describing?
"Our salespeople make an average of $1,000 per week."
"Half of our sales force makes over $3,000 per month."
"Five of our nine salespeople closed FOUR homes last
month."

Consider the set of monthly salaries below. Which company
(which Ad) could these salaries have come from?
$1500, $2000, $2000, $2500, $2500, $2500, $6000, $8000,
$9000
· Outdoor Sales
· Above Average Sales
· Home Sales
For the company "Above Average Sales", create a set of data for
8 employees that fits the measure of center described in the
advertisement. You did this in the previous lesson when you
made a list of credit card debts for the six college students.
, , , , , , ,
Home Prices
Problem Situation 2: Understanding Trends in Data
The median and average sales price of new homes sold in the
United States from 1963–2008 is shown in the following
graphic. Examine the graph.
Looking at the graph above, what was the average (mean) and
median home price in 2005?
Average (mean): $
Median: $
Five possible data sets for the year 2005 are given in Table 2.
Use your knowledge of mean and median to answer the
following questions without calculating the mean of the data
sets. There may be more than one correct answer to any of the
questions. Explain your reasoning.
Table 2: Possible Data Sets for 2005
Set A
Set B
Set C

Set D
Set E
$240,000
$84,000
$120,000
$74,000
$74,000
$245,000
$105,000
$135,000
$95,000
$90,000
$250,000
$125,000
$150,000
$105,000
$120,000
$256,000
$240,000
$168,000
$240,000
$240,000
$267,000
$245,000
$201,000
$242,000
$250,000
$275,000
$469,000
$225,000
$250,000
$635,000
$312,000
$810,000
$336,000
$251,000

$669,000
Which of the data sets could have the same mean and median
shown in the graph for 2005? (Select all that could)
· Set A
· Set B
· Set C
· Set D
· Set E
Which of the data sets would likely have a mean that is less
than the median? (Select all that could)
· Set A
· Set B
· Set C
· Set D
· Set E
Which of the data sets would likely have a mean and median
that are close together? (Select all that could)
· Set A
· Set B
· Set C
· Set D
· Set E
Look back at the home sales price graph and compare 2005 and
2007.
Both the mean and median sales prices decreased from 2005 to
2007. How much did each decrease?
The mean decreased by $
The median decreased by $

What type of changes of home sales prices occurred from 2005
to 2007 so that the mean and median would change in that way?
Since both the median and mean decreased:
· In general all house prices increased
· In general all house prices decreased
· Only high-end home prices decreased
· Only low-end home prices decreased
Since the mean decreased more than the median:
· All home prices decreased about the same amount
· Low-end home prices decreased more than the high-end home
prices decreased
· High-end home prices decreased more than the low-end home
prices decreased
On the sales price graph, for the years 1999 and onward the
mean sales price is greater than the median sales price (which it
had been for many years). What is new is that
the difference between the mean and median prices of the homes
is growing larger, especially so in the years 2003 and 2005.
What type of changes in housing prices in those years after
1999 would make the mean be further above the median?
· Low-end home prices increased faster than high-end home
prices
· High-end home prices increased faster than low-end home
prices
· All home prices increased at the same rate
HW 2.10
of the lesson?
· The median is the middle number when a data set is listed in
order. If there is an even number of points in the data set, the

median is found by finding the mean of the middle two
numbers.
· Home prices in 2007 were more than 10 times what they were
in the 1960s.
· When using measures of central tendency, it is always
important to ask questions about what the different types of
measurements do and do not tell you about the data set.
· The mean and median of a data set are always very close
together, but the mode might be very different.
The first advertisement discussed in class states that the
salespeople make an average of $1,000 per week. Suppose there
are nine salespeople. What would the ninth person need to earn
for the mean to be $1,000 if the other eight salespeople earned
$550, $600, $600, $800, $950, $950, $1,000, and $1,100?
$
The second advertisement states that half the salespeople make
more than $3,000 per month. Suppose there are eight
salespeople. What would the eighth person need to earn for the
median to be $3,000 if the other seven salespeople earned
$2,400, $2,500, $2,800, $2,800, $3,400, $3,400, and $3,800?
$
Which statistic (mean, median, or mode) is most appropriate in
each of the following situations?
a. Tables in the dining hall are numbered 1 through 12 for
students who eat there. The principal calls out a number for the
table that will go through the buffet line first. The other tables
follow in order of the table numbers. One student is sure the
principal calls certain tables more often. She keeps track of
which numbers are called over a 21-day period.
· Mean

· Median
· Mode
b. The offensive line of a football team is larger than in
previous years. The program will list a statistic to show this
fact.
· Mean
· Median
· Mode
c. A reporter is doing a story on the falling prices of homes in a
large neighborhood. The reporter wants to demonstrate how the
prices have fallen for all homes, not just the most expensive
houses.
· Mean
· Median
· Mode
At a summer camp for kids, the leader asked all the kids their
ages. The results were:
11 12 11 11 10 13 13 13 12 12 12 11 11 13 11 10 13 11 13 12
10 12
The data was summarized into a table. The second column
shows the number of kids who are that age.
Age
Frequency
10
3
11
7
12
6
13
6

a. How many kids in the camp are 11 years old?
b. To calculate the mean, you could start by adding up all the
ages: 11 + 12 + 11 + 11 + 10 + ···, but that would be tedious.
Which of the following calculations would allow you to come
up with the same result more quickly?
· 10(3)+11(7)+12(6)+13(6)10(3)+11(7)+12(6)+13(6)
· 10+11+12+1310+11+12+13
· 3+7+6+63+7+6+6
c. To figure out the total number of kids in the camp, you could
count all the data values. Which of the following calculations
would allow you to come up with the same result more quickly?
· 10(3)+11(7)+12(6)+13(6)10(3)+11(7)+12(6)+13(6)
· 10+11+12+1310+11+12+13
· 3+7+6+63+7+6+6
d. Determine the mean of the data. Round to 1 decimal place.
e. Determine the mode of the data.
Three descriptions of measures of central tendency are given
below. They are labeled A, B, and C. Descriptions of data sets
are listed below that. Match each data set with a description of
measures of central tendency by writing the letter in the blank.
Choices may be used more than once.
A The mean and median are close together.
B The mean is much higher than the median.
C The median is much higher than the mean.
a. The data have a large range, with only a few very high
numbers, but most of the numbers are very small.
b. The data set has a large range with the numbers evenly

spaced.
c. The data set has a small range with most of the numbers
grouped in the middle.
If you lived in Canada in 2008, you might have seen the
following headline:
“Canada Below G7 Average for Productivity!”
Here is some information to help you understand this
headline.
Productivity is a way to measure the economy of a nation. One
way to measure productivity is by Gross Domestic Product
(GDP) per worker. You may recall from Lesson 2.8 that GDP is
the value of all the goods and services produced in a country.
The G7 is a coalition of the major industrial democracies in the
world: United States, United Kingdom, France, Germany, Italy,
Canada, and Japan.
a. Which of the following is most likely what the author of the
headline wanted the reader to think?
· Canada's economy is weak and is falling behind other
countries in the G7.
· Canada's economy is strong and is leading other countries in
the G7.
· Canada's economy is very similar to other countries in the G7.
· Canada's economy should not be compared to other countries.
b. Which of the following can you conclude from the headline?
· Canada is less productive than half of the G7 nations.
· There is at least one G7 nation that is more productive than
Canada.
· There is at least one G7 nation that is less productive than
Canada.
· None of the above.
A graph of the GDP per worker of the G7 nations is shown
below.1

c. Find the mean of the GDP per worker for the G7 nations.
Round to the nearest hundred dollars. Hint
$
d. Is the headline correct?
· yes
· no
e. Which of the seven G7 nations have “above average”
productivity?
· Canada
· France
· Germany
· Italy
· Japan
· United Kingdom
· United States
f. Which of the following are correct conclusions based on the
data in the graph? There may be more than one correct answer.
· Canada is in the top half of the G7 in productivity.
· Canada's productivity is relatively close to all the G7 nations
except for the United States and Japan.
· Canada is far behind the G7 nations in productivity.
· None of the above.
Buying power of money: Gasoline costs have varied
significantly in recent months. The American Petroleum
Institute posted an update on gasoline prices for June 15, 2011.1
U.S. PUMP PRICE UPDATE—JUNE 15, 2011
The average U.S. retail price for all grades of gasoline fell this
week for the fifth week in a row by 6.6 cents from the prior
week to $3.767 per gallon, according to the Energy Information
Administration (EIA). This was at the highest level since
August 2008 with the exception of the recent highs in the prior
two months. Compared with the December 29, 2008 low of
$1.670, the all-grade average was higher by $2.097 per gallon,
or 125.6 percent. The average has been above $3.50 per gallon

since the beginning of March 2011. Nominal prices have been
above the year-ago average for 66 weeks—and were up by 101.1
cents or 36.7 percent, from the year-ago average of $2.756 per
gallon.
a. How much was the average retail price for one gallon of
gasoline a week before this article was published?
· $3.701
· $3.518
· $3.833
b. What is the relative change in the retail price for one gallon
of gasoline from
December 29, 2008, to June 15, 2011?
· 225.6%
· 125.6%
· 25.6%
c. If the retail price for one gallon of gasoline was $2.756 a
year before, then what is the absolute change in the retail price
on June 15, 2011?
· $2.097
· $1.086
· $1.670
Lesson 2.9
Introduction
Course Objectives
· 6. Demonstrate an understanding of the connection between

the distribution of data and various mathematical summaries of
data (measures of central tendency and of variation).
Specific Objectives
Students will understand
· that numerical data can be summarized using measures of
central tendency.
· how each statistic—mean, median, and mode—provides a
different snapshot of the data.
· that conclusions derived from statistical summaries are subject
to error.
· calculate the mean, median, and mode for numerical data.
· create a data set that meets certain criteria for measures of
central tendency.
Measures of Center
People often talk about “averages,” and you probably have an
idea of what is meant by that. Now, you will look at more
formal mathematical ways of defining averages. In mathematics,
you call an average, a measure of center because an average is a
way of measuring or quantifying the center of a set of data.
There are different measures of center because there are
different ways to define the center.
Think about a long line of people waiting to buy tickets for a
concert. (Figure A shows a line about 100-feet long and each
dot represents a person in the line.) In some sections of the line
people are grouped together very closely, while in other
sections of the line people are spread out. How would you
describe where the center of the line is?
Would you define the center of the line by finding the point at
which half the people in the line are on one side and half are on
the other (see Figure B)? Is the center based on the length of the
line even though there would be more people on one side of the
center than on the other (see Figure C)? Would you place the
center among the largest groups of people (see Figure D)? The
answer would depend on what you needed the center for. When

working with data, you need different measures for different
purposes.
Measures of Center
Mean (Arithmetic Average)
Find the average of numeric values by finding the sum of the
values and dividing the sum by the number of values. The mean
is what most people call the “average.”
Example
Find the mean of 18, 23, 45, 18, 36
Find the sum of the numbers: 18 + 23 + 45 + 18 +36 = 140
Divide the sum by 5 because there are 5 numbers: 140 ÷ 5 = 28
The mean is 28.
Example
Find the mean of 1.5, 1.2, 3.7, 5.3, 7.1, 2.9
Find the sum of the numbers: 1.5 + 1.2 + 3.7 + 5.3 + 7.1 + 2.9 =
21.7
Divide the sum by 6 because there are 6 numbers: 21.7 ÷ 6 =
3.6166666666
Since the original values were only accurate to one decimal
place, reporting the mean as 3.61666666 would be misleading,
as it would imply we knew the original values with a higher
level of accuracy. To avoid this, we round the mean to one
more decimal place than the original data.
The mean is 3.62.
Median
Find the median of numeric values by arranging the data in
order of size. If there is an odd number of values, the median is
the middle number. If there is an even number of values, the
median is the mean of the two middle numbers.
Example (data set with odd number of values)
Find the median of 18, 23, 45, 18, 36.
Write the numbers in order: 18, 18, 23, 36, 45
There is an odd number of values, so the median is the number
in the middle.
The median is 23.
Example (data set with even number of values)

Find the median of 18, 23, 45, 18, 12, 50.
Write the numbers in order: 12, 18, 18, 23, 45, 50
There is an even number of values, so there is no one middle
number. Find the median by finding the mean of the two middle
numbers:
18 + 23 = 41
41 ÷ 2 = 20.5
The median is 20.5.
Mode
Find the mode by finding the number(s) that occur(s) most
frequently. There may be more than one mode.
Example
Find the mode of 18, 23, 45, 18, 36.
The number 18 occurs twice, more than any other number, so
the mode is 18.
For another explanation, watch this video:
· Mean, Median, and Mode [+]
Note on terminology
The terms mean, median, and mode are well defined in
mathematics and each gives a measure of center of a set of
numbers. In everyday usage, the word “average” usually refers
to the mean. But be aware that “average” is not clearly
defined and someone might use it to refer to any measure of
center.
Consider the data set.
5
5
4
4
7
8
3
1
9
6

7
Find the mean:
Find the median:
Consider the data set
7
7
2
6
9
9
1
5
3
5
Find the mean:
Find the median:
Credit Cards
Problem Situation: Summarizing Data About Credit Cards
A revolving line of credit is an agreement between a consumer
and lender that allows the consumer to obtain credit for an
undetermined amount of time. The debt is repaid periodically
and can be borrowed again once it is repaid. The use of a credit
card is an example of a revolving line of credit.
U.S. consumers own more than 600 million credit cards. As of
2015 the average credit card debt per household with a credit
card was $15,863. In total, American consumers owe $901
billion in credit card debt. Worldwide the number of credit card

transactions at merchants was over 135 billion in 2011.
Surveys indicate that the percentage of college freshmen with a
credit card was 21% in 2012, while 60% of college seniors had
a credit card. One-third of the college students reported having
a zero balance on their credit card. The average balance
carried across all students’ cards was $500. However, the
median balance was $136.
At www.creditcards.com it explains that card issuers divide
customers into two groups:
· "transactors" who use their cards for purchases and pay off the
balances each month. Transactors pay off the balance before
any interest charges are applied.
· "revolvers" who carry balances on their cards, paying interest
charges month to month.
The number of people who carry credit card debt, the
“revolvers”, has been steadily decreasing in the U.S. since
2009. By 2014 only one-third of adults surveyed said their
household carries credit card debt. Fifteen percent of adults
carry $2,500 or more in credit card debt each month.
In the first part of this lesson, you will use the information
about credit cards given above to learn about some ways to
summarize quantitative information.
The population of the United States is slightly more than 300
million people. There are about 100 million households in the
United States. Use the information above to find:
a) What is the average number of credit cards per person?
cards per person
b) What is the average number of credit cards per household?
cards per household
In the U.S. the average number of credit cards held by
cardholders is 3.7. Why is this number different than the
average number of credit cards per person you found in the last

question?
· The last question answer was when the credit cards are
averaged over all the people in the country, including children
and people who have no cards. 3.7 is the number of cards for
person when averaged over only the people with cards.
· The last question answer was based on inaccurate, rounded
values
· People lie about how many cards they have
· Some people have lots of cards
Consider the statement, “Average credit card debt per household
with a credit card is $15,863.”
What does this statement tell us? (Assume the "average" they're
using is the mean)
· Half the households with credit cards owe less than $15,863,
and half owe more
· That most households with credit cards owe $15,863
· That if we added up all the credit card debt and spread it
evenly among the households with credit cards, each would owe
$15,863
· That every household with a credit card has this much debt
· That if we added up all the credit card debt and spread it
evenly among all households in the U.S., each would owe
$15,863
If about 45% of households with credit cards carry no debt,
what does that indicate about the amount of debt of some of the
other 55% of households?
· The others must have debt that averages to 15,863
· Since a lot of households have no debt, the others must have
debt much higher than $15,863 so the mean will come out to
15,863
· Since a lot of households have no debt, the others must have
debt much lower than $15,863 so the mean will come out to

15,863
The introduction states that the average balance carried across
all college students’ cards was $500. Imagine you ask four
groups of six college students what their credit card debt is. The
amount of dollars of debt for each student in each group is
shown in the table, values listed in order of size.
Find the mean and median debt of each group of college
students and record it in the table. Make sure the values you
find are reasonable given the values for that group.
Group A
Group B
Group C
Group D
0
500
410
0
100
500
460
0
110
500
480
0
170
500
490
0

1000
500
550
0
1620
500
610
3000
Mean
Median
Observe the medians and the data values of each of the groups.
For each statement below, indicate if it is true for: None of the
groups, Some but not all of the groups, or All of the groups.
i) Half of the data values are less than the median.
ii) Half of the data values are either less than or equal to the
median.
iii) Half of the data values are greater than the median.
iv) Half of the data values are either greater than or equal to the
median.
v) Half of the data values equal the median.
Recall that college students’ credit cards carry a mean balance

of $500 while having a median balance of $136. What does this
indicate about the distribution of credit card debt among various
students? Does one of the Groups in the table have a
distribution similar to this?
· Group A
· Group B
· Group C
· Group D
A survey in 2012 indicated that college freshmen carry a mean
credit card debt of $611 but the median of their credit card debt
is $47. Create a data set of five freshmen students so that the
data set has a mean and median that is the same as that of the
surveyed college freshmen.
, , , ,
Weighted Mean
Problem Situation 2: Weighted Means
Sometimes you want to find the mean average of some numbers,
but the numbers are not “equally important” or in other words
they don’t have the same “weight” or “frequency”. In that case
we find the “weighted average” of the numbers.
Example: mean credit card debt:
Suppose researchers at a small two-year college surveyed
students who have credit cards and report the following:
Mean credit card debt of $350 for 114 freshmen surveyed
Mean credit card debt of $285 for 220 sophomores surveyed
If we want to know overall for all the surveyed students what
their mean credit card debt was, we cannot simply average $350
and $285 since these numbers are not equally “weighted”. The
$350 was an average for only 114 people while the $285 was an
average for a larger group of 220 people. The way to find the
overall average credit card debt for all students surveyed is to
multiply each of the values by its “weight” or “frequency” or
“importance” before adding them together, and then divide by

the total “weight” or “frequency”.
Overall mean
= 350(114)+285(220)114+220=102600334=307.19350(114)+285
(220)114+220=102600334=307.19
Conclude: The mean credit card debt of all the students
surveyed was about $307
Example: Weighted grade averages in a course:
Suppose a History course has a midterm, a final exam, and a 20
page report, and the syllabus states they have these weights in
determining the final course grade:
midterm - 20%; final exam - 45%; report - 35%.
Kim’s grades in the course were these:
Midterm – 82; final exam – 89; report – 93.
Kim’s final grade in the course is found by the weighted
average:
82(.20)+89(.45)+93(.35).20+.45+.35=891.00=8982(.20)+89(.45)
+93(.35).20+.45+.35=891.00=89 Kim’s final course grade is
89.
Note: If the grades were not weighted, Kim’s average would be
(82 + 89 + 93)/3 = 88
Researchers at Acme groceries studied how long customers had
to stand in the check-out line. One day 35 customers spent on
average 7.7 minutes each in the check-out line. The next day 24
customers spent an average of 6.5 minutes each. What is the
overall average time customers spent in line? Round your
answer to two decimal places.
minutes
Your college GPA is a weighted mean. The grade earned in each
class needs to be weighted by the number of credits for the
class. Compute the GPA for a student who has earned the
following credits:
· English 101 (5 credits) with a grade of 3.0,

· Math 96 (7 credits) with a grade of 3.2,
· Public Speaking (5 Credits) with a grade or 3.6,
· Chemistry 100 (5 credits) with a grade of 2.7, and
· College Success (3 credits) with a grade of 3.8.
Round the GPA to two decimal places.
GPA:
HW 2.9
of the lesson?
· U.S. college students carry far too much credit card debt.
· The mean is calculated by adding all the numbers and dividing
by the number of data points.
· The mean, median, and mode all give important information
about a data set, but they do not give a complete picture of the
data set.
· Any of the three measures of central tendency (mean, median,
and mode) are good representations of data. It does not matter
which one you use.
2
6
1
2
1
4
Find the average (mean):
Find the median:

8
9
4
1
6
8
6
3
3
2
2
Find the average (mean):
Find the median:
Use the following data set to answer the questions.
13 15 20 20 20 20 20 20 20 23 27 31
a. What is the mean?
b. What is the mode?
c. What is the median?
d. What fraction of the numbers in the data set are less than the
median?
e. What fraction of the numbers in the data set are greater than
the median?
f. Which of the following statements are correct?
· The median is the middle of a data set. Half of the data points
are always less than the median, and half are always greater

than the median.
· The median is the middle of a data set. Half of the data points
are either less than or equal to the median.
· The median is the middle of a data set. At least half of the
data points are always equal to the median.
· The median is not the middle of a data set. You cannot predict
the distribution of the numbers in relationship to the median.
Consider the statement “Worldwide, there are more than $2.5
trillion in credit card transactions annually.”
a. What is the daily average dollar amount of transactions?
Round to the nearest hundred million dollars.
$
b. How many dollars in credit card transactions are made on any
particular day?
· $6,849,315
· $6,849,315,068
· $1,460,000,000
· $1,460,000
· It is impossible to know.
Students at Dover Community College (DCC) have a mean
credit card debt of $3,600 with a median of $1,500. Students at
Ralton Community College (RCC) have a mean credit card debt
of $3,000 with a median of $2,800. Which statements about the
two groups are true based on this information? There may be
more than one correct answer.
· About three-fourths of DCC students have debt less than
$3,600.
· The total debt of RCC students is less than the total debt of
DCC students.
· No more than half of RCC students have debt less than $2,800.
· The total debt of RCC students is larger than the total debt of

DCC students.
· At least one DCC student has debt in excess of $3,600.
· The largest debt of the RCC students is less than the largest
debt of the DCC students.
Decide whether the following statements must be true or might
be false, based on the information provided. Be prepared to
explain your reasoning.
a. The median of 25 numbers is 13. Twelve of the numbers must
be greater than 13.
b. The average of 11 numbers is 130. None of the 11 numbers
are more than 260.
c. The average of 25 numbers is 100, and the median of those 25
numbers is also 100. The mode of the 25 numbers must be 100.
d. The mean of 45 numbers is 70. If you pick any group of 10
numbers from the 45, the mean will be 70.
e. The average of 42 numbers is 20. The sum of all 42 numbers
is 840.
f. The average of 49 numbers is 100. If a 50th number is added
and the average remains at 100, the 50th number must have been
100.
Rio Blanca City Hall publishes the following statistics on
household incomes of the town’s citizens. The mode is given as
a range.
Mean: $257,000 Median: $65,000 Mode: $20
,000–$30,000
Which measure would be the most useful for each of the

following situations?
a. State officials want to estimate the total amount of income of
the citizens of Rio Blanca.
· mean
· median
· mode
b. The school district wants to know the income level of the
largest number of students.
· mean
· median
· mode
c. A businesswoman is thinking about opening an expensive
restaurant in the town. She wants to know how many people in
town could afford to eat at her restaurant.
· mean
· median
· mode
A course has five exams, and passing the course requires a 75%
average on the exams. Maria scored 60%, 72%, 80%, and 70%
on the first four exams. What is the minimum score on the fifth
exam that will let Maria pass the class?
%
Use Figures 1 and 2 for the following questions.
a. Select the figure(s) with 40% shaded.
· Figure 1
· Figure 2
· Both Figure 1 and Figure 2

· Neither Figure 1 or Figure 2
b. Which of the following statements are correct? There may be
more than one correct answer.
· The shaded area of Figure 1 is larger than the shaded area of
Figure 2 because Figure 1 is larger than Figure 2.
· The shaded area of Figure 1 is the same as the shaded area of
Figure 2 because they are both 40% of the square.
· The shaded area of Figure 1 is the same proportion of the
figure as the shaded area of Figure 2 because they are both 40%
of the square.
c. These figures illustrate what important concept?
· Percentages cannot be used for comparisons unless the
reference values are equal.
· Percentages compare measures relative to the size of the
reference values, but do not give information about absolute
measures.
· Percentages are a ratio out of 100, so they can always be
compared directly. In other words, 60% of one value is equal to
60% of another value.
In a psychology class, 58 students have a mean score of 81.4 on
a test. Then 21 more students take the test and their mean score
is 73.7.
What is the mean score of all of these students together? Round
to one decimal place.
mean of the scores of all the students =
To compute a student's Grade Point Average (GPA) for a term,
the student's grades for each course are weighted by the number
of credits for the course. Suppose a student had these grades:

4.0 in a 5 credit Math course
2.6 in a 2 credit Music course
2.6 in a 4 credit Chemistry course
3.1 in a 6 credit Journalism course
What is the student's GPA for that term? Round to two decimal
places. Student's GPA =

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