Math 5 – Bid is non negotiable

 Read first before bidding.  Accept Bid as is or don’t Bid at all.  I’m not increasing so don’t ask and don’t waste my time

Lesson

2

.

9

Introduction

Course Objectives

This lesson will address the following course outcomes:

·

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.

Students will be able to

· 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 

1

00-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 1

8

, 2

3

,

4

5

, 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.

#1 Points possible: 10. Total attempts: 5

Consider the data set

.

5

4

7

5

4

7

8

3

1

9

6

Find the mean:  
Find the median: 

#2 Points possible: 10. Total attempts: 5

Consider the data set

7

7

6

9

9

1

5

3

5

2

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.

#3 Points possible: 10. Total attempts: 5

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 

#4 Points possible: 5. Total attempts: 5

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

#5 Points possible: 5. Total attempts: 5

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

#6 Points possible: 5. Total attempts: 5

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

#7 Points possible: 24. Total attempts: 5

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

#8 Points possible: 10. Total attempts: 5

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.        

#9 Points possible: 5. Total attempts: 5

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

#10 Points possible: 5. Total attempts: 5

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

#11 Points possible: 5. Total attempts: 5

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

#12 Points possible: 5. Total attempts: 5

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

#1 Points possible: 5. Total attempts: 5

Which of the following was one of the main mathematical ideas 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 Points possible: 10. Total attempts: 5
Consider the data set

2

6

1

2

1

4

Find the average (mean): 
Find the median: 

#3 Points possible: 10. Total attempts: 5
Consider the data set

8

9

4

1

6

8

6

3

3

2

2

Find the average (mean): 
Find the median: 

#4 Points possible: 24. Total attempts: 5

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.

#5 Points possible: 10. Total attempts: 5

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.

#6 Points possible: 5. Total attempts: 5

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.

#7 Points possible: 12. Total attempts: 5

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. 
   

#8 Points possible: 9. Total attempts: 5

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
#9 Points possible: 5. Total attempts: 5

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?
%

#10 Points possible: 12. Total attempts: 5

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.

#11 Points possible: 5. Total attempts: 5

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 = 

#12 Points possible: 5. Total attempts: 5

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 = 

Lesson 2.

1

0

Introduction

Course Objectives

This lesson will address the following course outcomes:

·

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.

Students will be able to

· 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 555-0

10

0 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 555-0

12

7

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

#1 Points possible: 12. Total attempts: 5

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.”       

#2 Points possible: 5. Total attempts: 5

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

#3 Points possible: 5. Total attempts: 5

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.

#4 Points possible: 8. Total attempts: 5

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  

$

13

5,000  

$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

#5 Points possible: 5. Total attempts: 5

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

#6 Points possible: 5. Total attempts: 5

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

#7 Points possible: 5. Total attempts: 5

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.

#8 Points possible: 8. Total attempts: 5

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 $

#9 Points possible: 10. Total attempts: 5

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

 

#10 Points possible: 5. Total attempts: 5

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

#1 Points possible: 5. Total attempts: 5

Which of the following was one of the main mathematical ideas 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.

#2 Points possible: 5. Total attempts: 5

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?

$
#3 Points possible: 5. Total attempts: 5

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?
$

#4 Points possible: 9. Total attempts: 5

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

#5 Points possible: 25. Total attempts: 5

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.

6

Age	Frequency
10	3
11	7
12		6
13

 

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

· None of the above

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
· None of the above

d. Determine the mean of the data. Round to 1 decimal place.

e. Determine the mode of the data.

#6 Points possible: 9. Total attempts: 5

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.

#7 Points possible: 24. Total attempts: 5

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.

#8 Points possible: 12. Total attempts: 5

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

· None of the above

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%

· None of the above

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

· None of the above

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.

#2 Points possible: 5. Total attempts: 5

What was the average household income in 1999?

$

#

3

Points possible: 5. Total attempts: 5

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.

#4 Points possible: 15. Total attempts: 5

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.

#5 Points possible: 10. Total attempts: 5

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?

 % 

#6 Points possible: 5. Total attempts: 5

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

#7 Points possible: 5. Total attempts: 5

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

#8 Points possible: 10. Total attempts: 5

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

#9 Points possible: 5. Total attempts: 5

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

#1 Points possible: 5. Total attempts: 5

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.

 

#2 Points possible: 14. Total attempts: 5

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.

· The prices increased from around $160,000 to around $220,000, about a 35% increase.

· The prices increased from around $160,000 to around $220,000, about a 38% increase.

· The prices increased from around $160,000 to around $245,000, about a 53% 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.

#3 Points possible: 10. Total attempts: 5

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.

·

·
·

#4 Points possible: 5. Total attempts: 5

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?

·
·
·
·

#5 Points possible: 20. Total attempts: 5

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.

Food

$

Housing

$

Martinez Family

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.

#6 Points possible: 10. Total attempts: 5

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?      

#7 Points possible: 5. Total attempts: 5

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?
 %

#8 Points possible: 5. Total attempts: 5

Jan23Feb21Mar16Apr12May9Jun7July5Aug7Sept9Oct12Nov16Dec10MillimetersAverage 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?