South Georgia College



Making Connections to the Lesson

(1) Which of the following was one of the main mathematical ideas of the lesson?

(i) Home prices in 2007 were more than 10 times what they were in the 1960s.

(ii) The mean and median of a data set are always very close together, but the mode might be very different.

(iii) When using averages or 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.

(iv) 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.

(2) Refer back to the OCE for Lesson 2.1.4. Question 3 contains a graph about housing prices.

(a) Explain what the data for 2007 tells you about the cost of a house.

(b) Compare this graph to the graph of house prices used in Lesson 2.2.2. What is similar about the information? What is different?

Developing Skills and Understanding

(3) 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?

(4) 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?

(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.

(i) Mean

(ii) Median

(iii) 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.

(i) Mean

(ii) Median

(iii) 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.

(i) Mean

(ii) Median

(iii) Mode

(6) Lines at the Department of Motor Vehicles are so long! A supervisor decided to do a study on the number of people standing in line. At the beginning of each hour for an entire week, the supervisor counted the number of people in line and recorded the number. At the end of the week, the supervisor made the frequency table below. Note that the first column shows the number of people in line at the beginning of the hour. The second column shows the number of times that length of line occurred in the 40 observations.

|Number of People in |Frequency |

|Line | |

|1 |1 |

|2 |0 |

|3 |2 |

|4 |2 |

|5 |2 |

|6 |4 |

|7 |4 |

|8 |4 |

|9 |8 |

|10 |4 |

|11 |9 |

(a) How many times did the supervisor observe six people in line?

(b) Which calculation could be used to determine how many people the supervisor observed standing in line all together?

(i) 1 x 1 + 2 x 0 + 3 x 2 + 4 x 2 + 5 x 2 + 6 x 4 + 7 x 4 + 8 x 4 + 9 x 8 + 10 x 4 + 11 x 9

(ii) 1 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11

(iii) 3 + 2 + 2 + 2 + 4 + 4 + 4 + 8 + 4 + 9

(iv) None of the above

(c) How many observations did the supervisor make?

(d) Determine the mode of the data in the frequency table.

(e) Determine the median of the data in the frequency table.

(f) Determine the mean of the data in the frequency table.

(g) The supervisor made observations again the following week. The table below shows the observations.

|Number of People in |Frequency |

|Line | |

|1 |3 |

|2 |4 |

|3 |5 |

|4 |4 |

|5 |5 |

|6 |1 |

|7 |2 |

|8 |1 |

|9 |2 |

|10 |6 |

|11 |8 |

The mean for the second week was 6.366, the median was 5, and the mode was 11. The supervisor wanted to make the argument that additional personnel were needed. Which of these arguments is correct?

(i) Most of the time, there are 11 people in line!

(ii) Most of the time, there are 5 or more people in line!

(iii) Most of the time, there are more than 6 people in line!

(7) 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 some very high numbers and many small numbers.

(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.

(d) _____ The data set has a large range with a few very low numbers.

(8) 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 2.1.4 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?

(i) Canada’s economy is weak and is falling behind other countries in the G7.

(ii) Canada’s economy is strong and is leading other countries in the G7.

(iii) Canada’s economy is very similar to other countries in the G7.

(iv) Canada’s economy should not be compared to other countries.

(b) Which of the following can you conclude from the headline?

(i) Canada is less productive than half of the G7 nations.

(ii) There is at least one G7 nation that is more productive than Canada.

(iii) There is at least one G7 nation that is less productive than Canada.

(iv) None of the above.

A graph of the GDP per worker of the G7 nations is shown below.[1]

[pic]

(c) Find the mean of the GDP per worker for the G7 nations. Round to the nearest hundred dollars.

(d) Is the headline correct?

(e) Which of the seven G7 nations have “above average” productivity?

(f) Which of the following are correct conclusions based on the data in the graph? There may be more than one correct answer.

(i) Canada is in the top half of the G7 in productivity.

(ii) Canada’s productivity is relatively close to all the G7 nations except for the United States and Japan.

(iii) Canada is far behind the G7 nations in productivity.

(iv) None of the above.

Making Connections Across the Course

Themes explored in Lesson 2.2.3 include buying power of money, the role of the Urban Consumer Price Index, and the concept of index numbers.

(9) 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.[2]

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?

(i) $3.701

(ii) $3.518

(iii) $3.833

(iv) 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?

(i) 225.6%

(ii) 125.6%

(iii) 25.6%

(iv) 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?

(i) $2.097

(ii) $1.086

(iii) $1.670

(iv) None of the above

(10) A key idea of the previous question is that the buying power of a dollar is not constant. For example, the price of gasoline varies greatly, so the amount of gas you can buy with $1 varies over time. The Urban Consumer Price Index (CPI-U) is a tool designed to compare the price of goods and services in terms of base-year dollars. You will be using the CPI-U in your next lesson. The following questions will help you learn about it.

Refer to the website cpi to answer the following questions.

(a) Complete the following description of the Urban Consumer Price Index.

The Consumer Price Indexes (CPI) program produces monthly data on …

Go to the CPI Overview.

(b) Read the Data Available section. What percentage of the population is represented by the

CPI-U?

(c) Read the Coverage section. Are user fees for services like water and sewer included in the CPI?

(d) Are income taxes included in the CPI?

(e) Read the Uses section. The website states that the CPI affects the income of almost 80 million people because their incomes are tied to changes in the CPI. Which option is the best estimate for the percentage of these people who receive Social Security benefits?

(i) A little less than 48%

(ii) More than 50%

(iii) Around 80%

(f) Which option is the best estimate for the fraction of these people who receive food stamps?

(i) About a third

(ii) About three-fourths

(iii) About half

(g) State one use for the CPI-U, based on information from the website.

Preparing for the Next Lesson (2.2.3)

The following information will be used in the next lesson.

The United States has a federal minimum wage. This means that there is a law that requires employers to pay employees a certain amount. Many states also have their own minimum wage laws that require a higher wage than the federal law. The minimum wage started in 1938 as a part of a law that protected the rights of workers in many ways. The minimum wage in 1938 was set at $0.25 per hour.[3]

Since 1938, Congress has increased the minimum wage many times to account for inflation. Inflation is when prices increase over time. Maybe you have heard stories from older people about how a cup of coffee used to cost a dime or a gallon of gasoline was less than a dollar. Prices for these items have increased due to inflation.

When deciding if the minimum wage should be increased, people often talk about the buying power of the wage. Buying power refers to how much you can actually buy with a dollar. Because of inflation, a dollar bought more in 1938 than it did in 2009. In Lesson 2.2.3, you will answer the question: Did the minimum wage in 1938 have more buying power than the minimum wage in 2009? You will start by thinking about the specific example of buying a movie ticket.

(11) The minimum wage from 1997 through 2006 was $5.15 per hour. In 2009, the minimum wage increased to $7.25 per hour.

(a) What was the absolute change in the minimum wage from 1997 to 2009?

(b) What was the relative change in the minimum wage from 1997 to 2009? Round to the nearest tenth of one percent.

(12) The average price of a movie ticket in 1997 was $4.59.[4] Which statement is correct? Be prepared to explain your answer in class.

(i) In 1997, a person earning minimum wage had to work less than an hour to earn enough for a movie ticket.

(ii) In 1997, a person earning minimum wage had to work more than an hour to earn enough for a movie ticket.

(13) The average price of a movie ticket in 2009 was $7.50. Which statement is correct? Be prepared to explain your answer in class.

(i) In 2009, a person earning minimum wage had to work less than an hour to earn enough for a movie ticket.

(ii) In 2009, a person earning minimum wage had to work more than an hour to earn enough for a movie ticket.

(14) Did you read and understand the information to be used in class?

_____Yes _____No

(15) Did you complete the work that you need to take to class?

_____Yes _____No

(16) You should be able to do the following things for the next class. Rate how confident you are on a scale of 1–5 (1 = not confident and 5 = very confident).

Before beginning Lesson 2.2.3, you should understand the concepts and demonstrate the skills listed below:

|Skill or Concept: I can … |Rating from 1 to 5 |

|Calculate and interpret relative change. | |

|Understand the minimum wage. | |

-----------------------

[1]Retrieved from fls/flsgdp.pdf.

[2]Retrieved from aboutoilgas/gasoline/upload/PumpPriceUpdate.pdf

[3]Retrieved from oasam/programs/history/flsa1938.htm.

[4]Retrieved from .

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download