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Introduction to Statistics I

Introduction to Statistics I. MATH 1131, Summer I 2008, Department of Math. & Stat., York University. Goal of the course. Understanding the need for statistical techniques Introduction to basic concepts Able to summarize and analyze data with some basic statistical skills. TextBook.

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Introduction to Statistics I

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  1. Introduction to Statistics I MATH 1131, Summer I 2008, Department of Math. & Stat., York University

  2. Goal of the course • Understanding the need for statistical techniques • Introduction to basic concepts • Able to summarize and analyze data with some basic statistical skills

  3. TextBook Introduction to Statistics and Data Analysis, 3rd Edition, Peck, Olsen and Pevore. We will cover roughly the first 10 chapters.

  4. Timeline • 6 week course, from May 6, 2008 to June 12, 2008 • 6 hours per week, Tuesdays and Thursdays, 6 - 9 pm. CSE “B” • Tutorial: one hour before each class • Final Exam: June 18 – 20, 2008

  5. Course webpage • http://math.yorku.ca/~jnliu/Syllabus_Math1131_2008.htm Assignments, solutions, and other announcements will be posted on the webpage.

  6. Course Description • Displaying and describing distributions • relations between variables • Simpson's paradox and the need for design • Experimental design and sampling design, randomization

  7. Course Description • Probability models and random variables, mean and variance • Basic laws of probability • Probability distribution - binomial distribution and the normal distribution. • The Central Limit Theorem • Inference including confidence intervals and test of significance

  8. Evaluation • 4 Assignments, 5% each • 2 Quizzes, 5% each • Midterm, 30% • Final Exam, 40%

  9. Mean • We have a data set with n data points X_1, X_2, … X_n • The MEAN of this data set is defined as (X_1+x_2+…X_n)/n Suppose the value of the mean is m.

  10. Variance • (x_1 – m)^2 • (x_2 – m)^2 • … • (X_n - m)^2 • Sum of those numbers /(n-1) is called the variance. • Take the square root, you will get the standard deviation.

  11. What are they for? • Mean describes the center of the data • Variance or standard deviation describes the degree of spread of the data • Together they give a simple summary of the information from the data

  12. Example • Result of the final exam • The class mean is 75, with a standard deviation of 15 • Grades more than 90 or less than 60 are considered one standard deviation away from the mean, therefore extremely well or poor.

  13. display data graphically • Bar chart • Pie chart

  14. 5-number summary • 5-number: Minimum Maximum Q1: the first quartile Median Q3: the third quartile

  15. Median • Median: the “middle point” of the data set, such that half of the data points are bigger than it, and the other half are smaller than it. • How to find the median: Sort the data Take the data point in the middle

  16. Boxplot

  17. Side by side boxplot

  18. Histogram

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