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Welcome to Math 119 Statistics!

Welcome to Math 119 Statistics!. Instructor: Mike Slawinski Email: slawinski.michael@gmail.com Website: http://math.ucsd.edu/~mslawins/info119.html Office Hours: Tuesdays 4:00pm-4:50pm in M207. What is Statistics?. Organization of data for comprehension and prediction. Organizing Data.

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Welcome to Math 119 Statistics!

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  1. Welcome to Math 119 Statistics! Instructor: Mike Slawinski Email: slawinski.michael@gmail.com Website: http://math.ucsd.edu/~mslawins/info119.html Office Hours: Tuesdays 4:00pm-4:50pm in M207

  2. What is Statistics? Organization of data for comprehension and prediction

  3. Organizing Data • Gambling • Biology • Politics • Sports • Population Studies

  4. Statistical Questions Gambling: 1. What is the expected gain/loss in a Vegas game like craps over a long period of time? 2. A bookie gives odds of 15:1 and the probability of winning is 1/16. Should you make a bet? What is the optimal strategy in a particular game of chance? How much should you be willing to pay to play a game of chance, like dice?

  5. Questions (cont.) Biology: Given the historical results of cancer patients’ responses to certain drugs and tests, what is the probability a particular patient has cancer? What can be said about the distribution of IQ’s throughout population, given the distribution of IQ’s in a particular sample? 3. In the above question, how sure can one be of the results?

  6. Questions (cont.) Politics: 1. How is polling done? How many people must be polled in order to give accurate results? 3. What is the error, and how sure can one be of the results? Given the results of previous elections, what is the likelihood of a particular result?

  7. Questions (cont.) Legitimate Sports: 1. How are statistics compiled? 2. How useful are these stats in predicting outcomes? Which stats are the most useful in terms of predicting outcomes (gambling).

  8. Questions (cont.) Population Statistics: What is the probability that there are two people in this room with the same birthday? How is a certain characteristic distributed throughout a population (income, height, weight, blood type)? How spread-out is the above characteristic? How can this notion be quantified?

  9. Probability P(E or F)= P(E)+P(F)-P(E and F) • Example: Consider rolling a die once. • Let E be the event a 1 is rolled • Let F be the event a 2 is rolled What is the probability a 1 or 2 is rolled? P(1 or 2) = P(1) + P(2) – P(1 and 2) = 1/6 + 1/6 – 0 = 1/3 P(F given E) Example: Find the probability a 4 was rolled, given an even number was rolled. P(4 given even)

  10. Probability (cont.) The birthday problem: What is the probability there are at least two people in a room with the same birthday?

  11. The Normal Distribution Mean = average = μ Standard deviation = spread = σ Example: Assuming the heights of humans are normally distributed, and the average height is 5’6”, and the standard deviation is 6”, what percentage of the population lies between 5’ and 6’? Answer: 68.2%

  12. Sampling to Estimate the Mean (Average) Population Sample Assuming the dots represent numerical values, how does the mean of the sample relate to the mean of the population?

  13. Regression Given a finite set of data points, find the line that minimizes the vertical distances between the line and the points. Prediction: The value over 10 is close to 7.5.

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