STATISTICS
Provided by: Susan A. Mellott
A student at Miami University
CONNECTIONS BETWEEN EDUCATION AND POVERTY FOR WOMEN
- 7 5 % of female heads of household with less than a high school diploma are living below the national poverty line.
- 40 % of female single parents have an eighth grade level education or less.
- 35% of displaced homemakers have less than an eighth grade education.
- In 1990, over 67.3 % of women who worked without a high school diploma earned less than $12,400.00 per year.
- One in Eight women workers has less than a high school diploma.
People with less than a high school education will only be able to fill 14 % of the jobs that will be available in the future.
INCOME AND WAGE GAPS CONCERNING WOMEN
- In 1939- women made sixty-three cents for every dollar a man earned,
- In 1 9 8 5- women narrowed this gap by increasing their wages to sixty-four cents for every dollar a man earned.
- Our country offers women less income than other industrialized nations:
-in 1980:
Sweden- women earned eighty one cents for every dollar earned by a man.
Britain- women earned sixty-six cents for every dollar
earned by a man.
In 1 9 8 4- the average yearly income for a woman was $14,479.00, as compared to $23,218 which is the average yearly income for an average man.
GIVE EXAMPLES OF SOME PROBABILITY QUESTIONS
Games are usually interesting. For example, if a friend challenges you to draw an ace on your first pick for a free lunch, how good are your chances of winning? Since there are 4 aces in 52 cards, your chances of winning are 4/52 or 1/13. So the probability of not picking an ace is 48/52 OR 12/13! The odds are against you, but not too impossible.
Now let's say the friend has challenged you to toll dice - two of them. He will buy you lunch if you roll a six on each dice. So what is the probability of getting a free lunch? Your chances of rolling a six on one dice is 1/6. But how about both at the same time? Now we have to multiply the probability of getting a six on each die. Now your chances are 1/6 x 1/6 or 1/36. Your chances of rolling 2 sixes are much worse that drawing an ace out of a deck of cards.
Another example would be a "Pick Three" in the Lottery. If your chances are 1/10 for each number, then your chances of picking all three correct would be 1/10 x 1/10 x 1/10 or 1/1000! Save your money!
In Figmentland, USA, marketing specialists decided that they would promote Smarties Cereal by giving away coupons in specially marked boxes. These coupons could be redeemed for passing scores on the GED Test, Writing Skills, Essay, Social Studies, Science, Literature, and Mathematics coupons were put in Smarties Cereal. Equal numbers of each coupon were placed in boxes and distributed evenly to area stores.
Since your chances of getting any of the coupons are the same, how many boxes of Smarties Cereal would you expect to have to buy in order to collect all six coupons?
Is it possible to get all six coupons in only six boxes?
Is it possible that you might buy 100 boxes and still not get all six? Let's set up a simulation or "act out" the problem.
SPINNERS WITH 6 EQUAL AREAS
CUBES
HANDMADE COUPONS ON 3 X 5 CARDS
OVERHEAD DICE (TRANSPARENT) if doing project with whole class together. Each group should run three trials with their materials and keep track of the number of times it took to get all 6 coupons.
-Using transparent grid paper, plot the data.
-Calculate Mean, Mode, and Range.
-How could the manufacturers of Smarties Cereal make the odds of winning lower?
Tallying the results of the simulation can be done in several different ways. I have used "100" GRID" PAPER. Using that, they star a number when it is a coupon that they have not yet gotten. Then on spins that are duplicates, either just mark out the number or record the duplicate subject name. By recording the name of each spin, at the end other numbers can be tabulated such as how many times was each subject area spun. Also the last number starred will be the total number of attempts that it took to get coupons for all sections of the GED Test.
A CERTAINTY
A.B.L.E. STUDENTS EXAMINE TAXES
Rationale and Overview:
"In this world nothing Is certain but death and taxes."
-- Benjamin Franklin
Adult students deal with tax costs and benefits regularly. Gaining greater understanding of the tax system, where tax money comes from and how it's used, can help them understand and appreciate the application of classroom mathematics to real life situations.
A study of taxes can help students integrate understandings from the areas of social studies and mathematics. Students are interested In how their own money Is spent. This unit could logically follow a study of family budgets, emphasizing the need for the government unit to also budget its income and expenses. As students develop an interest In how tax money is spent, they may also develop an Interest in participating In the system to help influence how the government allocates financial priorities.
When my 14-year-old daughter collected her first paycheck, she quickly noticed that several deductions had lessened the amount she'd expected. she wanted to know why that money was taken away from her, who said they could do that, who decided how much money to take, what did those people do with her money, and what did she get out of the-deal. After a lot of discussion, her final comment was, "No wonder you guys vote." We and our students have wondered the same things, and this unit gives everyone an opportunity to develop and express opinions, quantify them, and compete their ideas to reality.
Discussing what students already know about taxes, using math skills to analyze their opinions, and comparing their concepts to real life examples gives them many opportunities to build new understandings and grow.
APPLICATIONS
Connections to past learning:
Give students some time to consider what they already know about taxes. Encourage them to share their experiences with taxes -both as payers and consumers. This is a good opportunity to correlate previous learning about taxation and government and information about the history of the United States that relates to this issue. Students use critical thinking, communication skills and reasoning during the discussion. If the need arises, they may want to use Information gathering and research skills.
As the unit develops, students practice previously learned math skills in estimating, calculation of whole numbers and percents, averaging, and chart and graph development.
Connections to the real world;
Taxes are a certainty. Income taxes have been collected in the U.S. since 1913, and the Social Security Act of 1935 created the Internal Revenue Service which supervises the collection of federal income taxes. Looking at a sample paycheck will show many deductions for various taxes. Students will be able to name other kinds of taxes from their experience.
Even If a student doesn't currently pay income taxes, other taxes are a reality. Each student can consider how government activities are funded. Then each can consider himself as a consumer of tax money in benefits. The A.B.L.E. classroom itself may enter the discussion.
Students can be encouraged to analyze their own paychecks or tax forms. And they can look for ways their lives benefit from government spending.
Each student has the opportunity to think about how tax money should be allocated, then to compare those opinions to the others in the group and to the real applications of government. Students can be encouraged to understand how taxes (collection and expenditure) may influence Individual lives.
Connections to adult life skills:
Adult students participating In this unit will practice language skills. During discussions they'll offer opinions and adjust those opinions based on other input. They'll also use critical thinking and analysis skills as they compare their ideas to actual tax sources and expenditures. Learning about the tax system will help them develop their ability to read, evaluate and understand information from periodicals and broadcasts. Perhaps they will want to express the opinions they develop to their government representatives.
During the unit each student will have many opportunities to apply math skills In reading and writing numbers, comparing and estimating amounts, calculating totals and averages, converting whole numbers to fractions and percents and reading various charts and graphs. Some students may want to learn how to fill out their own IRS forms.
Connections to work:
Using a paycheck to compute the amount or percent of tax contribution can emphasize the importance of learning about taxes. Some students may want information on adjusting their deductions.
As students become aware of how tax money is spent, they may become quite interested in how government spending of tax money both creates and influences their own Jobs and the Jobs of others. Some students may want to learn more about the Jobs of the people who collect, disburse and allocate their tax money.
Follow-up:
Create graphs from the class or student charts (on computer?).
Fill out sample tax forms.
Compare graphs showing spending of tax money in previous years to current graphs. Compute the changes and/or discuss what has influenced the differences.
Consider how to reduce the deficit and pay off the federal debt by reducing taxes or reducing spending in certain categories.
Find tax-related articles in periodicals and compare them to the worksheet information.
Contact the budget office for the government unit and ask for budget projections for the coming year.
TITLE: STATISTICS, PROBABILITY AND CONNECTIONS USING THE MORTALITY TABLE
Materials: Mortality tables from different periods
Computer software for creating tables or spreadsheets
Calculators
Graph paper
Color markers or pencils
Target
Audience: ABLE/JOBS Adult Students
Mode of
Instruction: Small group or whole class
Rationale: Adult education should put less emphasis on teaching isolated mathematical skills and increase emphasis on teaching the math of life skills and the world of work. Investigation of statistics and probability should actively engage learners in exploring events and making predictions about situations relevant to their daily lives. Adults know that decisions made on the basis of various statistics affect them daily. Collection, organization, calculation, and interpretation of data are fundamental to our personal lives and the lives of most adults in the workplace. Adults use and analyze statistics and, formally or informally, predict outcomes daily.
Therefore, it is important that adult learners understand how statistical representations and calculations are used. There is
nothing more indigenous or relevant to human life than mortality. Using mortality tables from different time periods is an effective way to investigate changes and predict future change. It also is a means of getting adults who smoke (many of our students do) or have other dangerous lifestyles to consider their own mortality
Statistics, Probability, Data Collection, and Insurance
One of the largest businesses in the United States which relies heavily on statistics and probability is insurance. It is very important to an insurance company to know how to measure the risks against which people are buying the insurance. In order to set the premiums, a fire insurance company must have some way of knowing how many fires will occur. An automobile insurance company must be able to predict the number of accidents involving injury, loss of life, and property damage. A life insurance company must know what the expected number of deaths will be in a given group of policyholders.
ACTIVITY
1) Class or Small Group Discussion - List of Ideas or Plans-
Discussion of Feasibility of Ideas, Collection of Data
How then will companies such as these make their estimates? How will they, how would you estimate the probability:
-that an 18-year old male driver will be involved in an automobile accident this year.?
-that a new all brick house in your community will burn?
-that a 70-year old man will be hospitalized this year.?
-that a 16-year old person will die before reaching age 17?
Summary Implications:
You know immediately that in order to arrive at estimates such as these, some data must be collected. The automobile Insurance company will have to gather data on the 18-year old male drivers in order to tell what the experience is likely to be - how many accidents this group of drivers has, on the average. Or the fire insurance company must compile statistics on fires among all-brick houses in communities having adequate fire departments. And life insurance companies must have available some statistics that will show how many 16-year olds die, on the average.
Data such as these must be based on large numbers of events. Operating in cases such as these is the Law of Large Numbers, which, stated simply, means that with large groups we can predict fairly accurately what is likely to happen. With a large number of experiments, the ratio of the number
Life insurance companies use sets of statistics called mortality tables to predict how many people of the same age will die in a particular year. The companies assume that what will happen in the future will be similar to what happened in the recent past. A mortality table is based on the lives and deaths of policyholders of several large life Insurance companies. It has a margin of safety added, and although it might not be used for premium calculations, it is used for making other calculations necessary to life insurance company operations. It is a table of probabilities, also.
ACTIVITY
2) Creating Tables and Graphs - Organizing Data
if available, have students use computer programs to create tables and graphs of the selected information below. 9 computers are not available, have students draw a table of the Information below and create a graph, using graph or lined paper and color pencils or markers, based on the table.
A 1958 United States Commissioners Standard Ordinary Table of Mortality (Table I ) listed the following selected probabilities:
-At age 0, the probability that death would occur within 1 year was 7.08/1000
-At age 1, the, probability that death would occur within 1 year was 1.76/1000
-At age 15, the probability that death would occur within 1 year was 1.46/1000
-At age 30, the probability that death would occur within 1 year was 2.13/1000
-At age 45, the probability that death would occur within 1 year was 5.35/1000
-At age 60 the probability that death would occur within 1 year was 20.34/1000
-At age 75 the probability that death would occur within 1 year was 73.37/1000
-At age 90 the probability that death would occur within 1 yr. was 228.14/1000
-At age 99 the probability that death would occur within 1 yr. was 1000/1000
It is customary in the table to speak of the annual rate of death per 1000 persons rather than to call this the probability of death at a given age.
ACTIVITY
3) Interpreting Data - Questions for class or small group
discussion, group reports, or writing assignment.
-Why was the probability of death at birth so much greater than at age one?
-Why would the probability almost quadruple between ages 45 and 60?
-Why would the probability almost quadruple between ages 75 and 90?
