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# Week 1 – Discussion

Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Refer to the Discussion Forum Grading Rubric under the Settings icon above for guidance on how your discussion will be evaluated.

 Video 3: Sampling

You will find Video 3: Sampling by navigating to the MSL Tools for Success link under Course Home. This video discusses sampling in the context of how estimates of population parameters are obtained. It refers to Video 1: What is an Average? where we obtained an “average of 1.89 feet per person.” It points out that applying this statistic depends on thinking through whom the population is meant to be, and that depends on the study question (i.e., “If you want to understand your answer, you really have to work out carefully what your question is.”).

As the sample statistic was derived from a bunch of kids heading to the playground, plus a one-legged man who we asked to show up, we conclude that the sample was a bad one. We explain that random sampling is generally a good way of obtaining a representative sample such that you can be confident that the sample statistic is a good estimate of the population parameter.

Respond to one of the following questions in your initial post:

• Are all good samples random? This is an opportunity to bring up opinion polling, which typically tries to obtain views from particular groups (e.g., men, women, older, younger, employed, unemployed, Democrat, Republican, etc.) and then “weights” the results by the prevalence in the population.
• Magazines often report surveys giving statistics such as “63% of women expect the man to pay on the first date.” Are these random samples? These surveys are most definitely not random – they are typically click-through from the magazine website – and so can provide an opportunity to discuss the sort of biases that can result from lack of random sampling.

Your initial post should be 150 to 250 words in length. Respond to at least two of your classmates’ posts by Day 7 in at least one paragraph.

# Week 2 – Discussion

Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Refer to the Discussion Forum Grading Rubric under the Settings icon above for guidance on how your discussion will be evaluated.

 Video 4: Variation 1: Introduction and Quartiles

You will find Video 4: Variation 1: Introduction and Quartiles by navigating to the MSL Tools for Success link under Course Home. The video begins at the park, with cyclists and joggers going by. We show a very slow old woman going by on a bike, and then a bunch of racing cyclists. We point out that sometimes, what is interesting about a data set is not its average but how much it varies. We then discuss the weather in New York and San Francisco, which have pretty much the same average annual temperature, even though New York has hot summers and cold winters. Quartiles as a measure of variation are introduced by way of the price of food on take-out menus. The video ends with a practical application in medical research, where mean exposure to a toxin is far less interesting than the fact that a small number of individuals are exposed to very high levels.

Respond to one of the following questions in your initial post:

• What are some examples, other than temperature, where similar averages can be associated with very different distributions? A few thoughts: costs (e.g., cost of illegally downloading a song online is the same average cost of driving above the speed limit, assuming that you are only caught speeding occasionally); ERA of pitchers (i.e., some are very consistent, others are sometimes brilliant, sometimes horrible); success rates in surgery (i.e., do we want an operation that most surgeons can do pretty well, or one in which a few surgeons are nearly perfect and some have very poor results?)
• Give some practical uses of knowing variation. A few thoughts: You are traveling to a job interview; what clothes do you need to pack for a trip? Doctors need to know distributions of blood values to know whether a patient is out of range; industrial engineers need to know distributions, for example the strength of a certain part to see if there is a problem with a manufacturing machine; clothing manufacturers need to know the distribution of sizes, for example children’s clothes for a certain age.
• For many years, the New York subway had no air conditioning on the grounds that the average trip was only 15 minutes, and 15 minutes without air conditioning is no hardship, even in the New York summer. Critique this reasoning.

Your initial post should be 150 to 250 words in length. Respond to at least two of your classmates’ posts by Day 7 in at least one paragraph.

# Week 3 – Discussion

Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Refer to the Discussion Forum Grading Rubric under the Settings icon above for guidance on how your discussion will be evaluated.

 Video 2: When Should You Use the Mean and When Should you Use the Median.

You will find Video 2: When Should You Use the Mean and When Should You Use the Median by navigating to the MSL Tool for Success link under Course Home.

This video focuses more on when to use a mean and when to use a median. House prices are used to demonstrate that when data are non-symmetric – especially when there are extreme outliers – the median gives a better description of a typical value than the mean. Specifically, the prices of properties on two blocks are compared: in one, all houses are similar and there isn’t much difference between the median and mean; in the other, there is a big expensive block of apartments, so that the mean is nearly twice the median, and far from the cost of any individual property.

But we want to get away from the idea that the data, and only the data, drives the choice of descriptive statistic. The example is given that, if you wanted to buy all the houses in Brooklyn, if you took the median, and multiplied by the number of houses, you wouldn’t have enough cash. So the median is a useful descriptive statistic, but the mean is essential for planning and making decisions.

Respond to one of the following questions in your initial post:

• Should you use the median or mean to describe a data set if the data are not skewed? Are the  standard deviation or the interquartile range factors?
• You may read in the newspaper that a study of a new drug for cancer “increased survival by an average of eight weeks.” It turns out that this is a median, and it is used for complicated statistical reasons. But in a perfect world, would you prefer to know the increase in mean or median survival?
• If the median house price is \$1.9m, does that necessarily mean that half of the houses on the block are worth less than \$1.9m and half worth more? How do ties figure in?

Your initial post should be 150 to 250 words in length. Respond to at least two of your classmates’ posts by Day 7 in at least one paragraph.

# Week 4 – Discussion

Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Refer to the Discussion Forum Grading Rubric under the Settings icon above for guidance on how your discussion will be evaluated.

 Video 6: The Normal Distribution

You will find Video 6: The Normal Distribution by navigating to the MSL Tool for Success link under Course Home.

This video explains the normal distribution via the binomial distribution: The distribution of the number of heads thrown on 20 coins approximates the normal. This is used to explain that the normal distribution is the mathematical consequence of adding up a large number of random events. Some examples are given of normal distributions in the natural world (mass of ants) and social world (age of marathon runners) and explained in terms of these phenomena resulting from the aggregation of random events.

Respond to one of the following questions in your initial post:

• What is the link between the normal distribution and Video 5: Variation 2 (and Egg Roulette), where we relied on statements such as “about two-thirds of observations are within one standard deviation of the
mean”?
• Do natural phenomena such as hemoglobin levels or the weight of ants really follow a normal distribution? If you add up a large number of random events, you get a normal distribution.
• How large a number makes a normal distribution?

Your initial post should be 150 to 250 words in length. Respond to at least two of your classmates’ posts by Day 7 in at least one paragraph.

# Week 5 – Discussion

Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Refer to the Discussion Forum Grading Rubric under the Settings icon above for guidance on how your discussion will be evaluated.

 Video 24: Statistics is About People, Even if You Can’t See the Tears.

You will find Video 24: Statistics is About People, Even if You Can’t See the Tears by navigating to the MSL Tools for Success link under Course Home.

The video makes the point that though nobody wants to think that they are a statistic, acting as if you are a statistic can help you make better decisions. That said, statisticians should never forget that the numbers they analyze correspond to real people, who have friends, relatives, and stories to tell.

Respond to one of the following questions in your initial post:

• Why do you think people often feel that “the statistics don’t apply to me”?
• The reason why so many of us now live long, healthy lives is due to statistical analysis of health data. What other statistical analyses have had a large impact on how we live our lives?
• Why do you think statistics often has a bad name?

Your initial post should be 150 to 250 words in length. Respond to at least two of your classmates’ posts by Day 7 in at least one paragraph.

Date Details Due

# Course Syllabus

Course Syllabus
Prerequisites
MAT 221

Course Description
This course is designed to meet general education quantitative reasoning (mathematics) requirements. It will cover such topics as sampling, bias, probability, distributions, graphical methods of portraying data, measures of center, dispersion and position, and the Central Limit Theorem. It will also cover computational techniques such as correlation, regression, and confidence intervals.

Course Design
To accomplish the learning objectives set forth in this course, students will participate in a combination of interactive discussions, problem solving, and short answer homework. Students are required to write out the mathematical justifications for the steps they take in solving problems, which underscores their clarity of understanding. In the required writing, students are also encouraged to use specific mathematical vocabulary and proper notation. The homework is designed so that guessing is not a viable option, but rather proper algorithms and procedures must be followed in order to achieve success. Plenty of practice and step-by-step guidance are available through the MyStatLab associated with this course.

Course Learning Outcomes
Upon successful completion of this course, students will be able to
1. Apply sampling methods.
2. Identify situations when graphs can miscommunicate information.
3. Use measures of center, dispersion, and position to interpret real-world situations.
4. Utilize properties of the Normal curve to solve real-world problems.
5. Analyze scatterplots and regression models.

Course Map
The course map illustrates the careful design of the course through which each learning objective is supported by one or more specific learning activities in order to create integrity and pedagogical depth in the learning experience.
LEARNING OUTCOME
WEEK
ASSIGNMENT
1. Apply sampling methods 1
• Post Your Introduction – Discussion
• Sampling Video Discussion
• Week One MyStatLab Homework
• Midterm
2. Identify situations when graphs can miscommunicate information 2
• Variation: Quartiles Discussion
• Week Two MyStatLab Homework
• Midterm
3. Use measures of center, dispersion and position to interpret real world situations 3
• Video 2: Mean or Median Discussion
• Week Three MyStatLab Homework
• Midterm
4. Utilize properties of the Normal curve to solve real world problems. 4
• Video 6: The normal distribution – Discussion
• Week Four MyStatLab Homework
• Final
5. Analyze scatterplots and regression models. 5
• Video 24: Statistics is about people, even if you can’t see the tears – Discussion
• Week Five MyStatLab Homework
• Final

1. Synthesize theories and approaches from the subject areas of the general education curriculum to address complex problems.
1. Utilize interdisciplinary approaches and informed decision-making when solving problems.
2. Frame problems and construct solutions through reasoned analysis, including consideration of diverse views.
3. Analyze and present a reasoned response to problems within a wider societal and systems context.
4. Articulate commonalities and differences across varying cultural, economic, and geographic populations as part of global citizenship.
5. Demonstrate critical thinking and problem solving skills using adaptable, flexible, creative, and innovative approaches.
2. Integrate skills from the general education competencies when interpreting ideas and arguments in order to respond to civic, societal, environmental, and economic challenges.
1. Apply the principles of critical thinking to contemporary issues.
2. Exhibit clear, sustained, and coherent arguments and narratives in written and oral communication.
3. Utilize information, media, and technology literacy skills appropriate for an associates or bachelor degree level, by recognizing when information is needed and effectively locating, evaluating, and using the information.
4. Construct solutions to problems through qualitative or quantitative analysis and/or computational skills and practices.
5. Display leadership and interdisciplinary teamwork skills.
6. Employ the skills necessary to engage in lifelong learning through intellectual inquiry.
3. Synthesize proficiencies appropriate to the degree level and discipline or major.
1. Explain field specific concepts, theories, and practices.
2. Evaluate complex problems or challenges related to the field by applying field specific concepts, theories, and practices.
4. Construct ethical responses to contemporary issues.
1. Identify and address key ethical issues, including the application of academic knowledge to the concerns of society.
2. Articulate the constraints that ethical theories and principles place on responses to specific challenges.

Mission Statement
The mission of Ashford University is to provide high-quality, accessible, affordable, innovative, educational programs that meet the diverse needs of individuals pursuing advancement in their lives, professions, and communities.
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