Statistics and Probability: 5 sessions Anna Bargagliotti The University of Memphis Fundamentals of Statistics (purpose and vocab) Probability Problems Regression, correlation, causation Random Variables II Counting Problems

Fundamentals of Statistics (purpose and vocab)

What is statistics? Definition 1: Statistics is a collection of procedures and principles for gaining and analyzing information in order to help people make decisions when faced with uncertainty. (Seeing Through Statistics, by Jennifer Utts) Definition 2: Statistics is the science of collecting, organizing, and interpreting data OR Statistics are the data that describe or summarize something. (Our text) Definition 3: Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. (Wikipedia) Definition 4: A set of concepts, rules, and procedures that help us organize numerical information, understand, and make decisions. (http://bobhall.tamu.edu/FiniteMath/Module8/Introduction.html)

Experimental Design Observational (Descriptive) Experimental What do we need to answer before we do a study? What is your population? Once the population for your experiment has been determined, you select a representative sample.

Types of Information What types of variables exist? Categorical Ordinal Nominal Quantitative Discrete Continuous

What can be used to represent information graphically? Bar Histogram Box plot Scatterplot Pie Stem and Leaf Any others?

What types of descriptive questions do statisticians ask? Where is the center? What is the spread? What is the shape?

What types of research questions do statisticians ask? What is the relationship between or among variables? What types of relationships are there between or among variables? What is the cause of an outcome? Are samples, procedures, groups, trials, experiments, different or the same?

Examples and Problems Researchers chose two groups of 100 high school students. One group receives $5 for every week they have perfect attendance, the other group gets nothing. What may be potential research questions the researcher is trying to study? Is there a control group? What is the treatment? Is this observational or experimental?

Categorical? Quantitative? Ordinal? Nominal? Discrete? Continuous? A person’s height A person’s degree A person’s race A person’s SAT score A person’s shoe size Amount of time it takes to assemble a puzzle The state in which a person lives Rating of a newly elected politician Population in the city of Memphis

Represent the information in one graph in the most clear manner The polls for the Democratic party in the state of Tennessee are showing: Clinton has 33% support, Edwards 40%, and Obama 34%. In the state of Florida: Clinton has 43%, Edwards 35%, and Obama 34%.

Represent the information in one graph in the most clear manner These data represent the percentage of people in each of the 50 states that supports universal heath care. 57, 60 , 50, 52, 42, 51, 39, 42, 49, 56, 38, 70, 43, 58, 48, 59, 57, 43, 40, 44, 33, 47, 46, 57, 51, 59, 63, 50, 48, 41, 47, 36, 56, 61, 50, 61, 49, 47, 32, 57, 61, 51, 60, 67, 41, 53, 45, 52, 48, 70

Determine if the following statements make sense Your bar graph must be wrong because your bars are wider than those shown in the solutions manual. Your pie chart must be wrong because when I added the percentages on your wedges, they totaled 124% I was unable to make a bar chart, because the data categories were qualitative rather than quantitative. I rearranged the bars on my histogram so that the tallest bar comes first.

Find the descriptive statistics For the previous data set, find the measures of center. For the previous data set, find the shape. What does finding the “shape” mean?

Finding the spread: Why or why not is this a good measure of spread Finding the spread: Why or why not is this a good measure of spread? When would it be good? When would it be bad? Range: the difference between the highest and lowest score in a distribution. Interquartile Range: measure of the spread of the middle 50% of the scores. Defined as the 75th and 25th percentile. Variance: measure of squared deviation from the mean divided by the N-1 (where N is the sample size). Standard Deviation: square root of the variance. Measure of variability in same units as the data.

Find the measures of spread Consider the following set of 100-meter dash running times: (time in seconds) 9.92, 9.97, 9.99, 10.01, 10.06, 10.07, 10.08, 10.10, 10.13, 10.13, 9.89, 9.98

What does this all have to do with random variables? Recall: what is a random variable? What are the concepts we talked about with random variables? How do those concepts relate to what we talked about today? How do use random variables in statistics? How do probability concepts come into play?