# Introduction to Probability and Statistics Fourteenth Edition Introduction Train Your Brain for Statistics.

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Introduction to Probability and Statistics Fourteenth Edition Introduction Train Your Brain for Statistics

What is Statistics? What does a statistician do? Player Games Minutes Points Rebounds FG% Bob 34 32.724 7.6.552 Andy 36 31.521 8.4.465 Larry 30 33.018 5.6.493 Michael 31 35.129 6.1.422 Player Games Minutes Points Rebounds FG% Bob 34 32.724 7.6.552 Andy 36 31.521 8.4.465 Larry 30 33.018 5.6.493 Michael 31 35.129 6.1.422

Job of a Statistician Collects numbers or data Organizes or arranges the data Analyzes the data Infers general conclusions

Uses of Statistics a theoretical discipline in its own right a tool for researchers in other fields used to draw general conclusions in a large variety of applications

POLITICS Forecasting and predicting winners Where to concentrate What should a statistician DO? (Cannot survey on every voter) If the election for mayor of Los Angeles were held today, who would you be more likely to vote for? James Hahn32% Magic Johnson36% Someone else11% No opinion yet21% If the election for mayor of Los Angeles were held today, who would you be more likely to vote for? James Hahn32% Magic Johnson36% Someone else11% No opinion yet21%

To market product Average length of life of a light bulb? What should statistician do? (cannot test all the bulbs) INDUSTRY

Solution Collect a smaller set of measurements that will (hopefully) be representative of the whole set. POPULATION:POPULATION: set of all measurements SAMPLE:SAMPLE: A subset of population

Definitions Variable is a characteristic that changes or varies over time and/or for different individuals or objects under consideration Experimental Units are items or objects on which measurements are taken Measurement results when a variable is actually measured on an experimental unit Population is the WHOLE set of all possible measurements Sample is a subset of population

Examples Light bulbsLight bulbs –Variable=lifetime –Experimental unit = bulb –Typical measurements: 1503.1 hrs, 1010.5 hrs

Examples Opinion pollsOpinion polls –Variable = opinion –Experimental unit = person –Typical Measurements = Magic Johnson, someone else

Hair colorHair color –Variable = Hair color –Experimental unit = Person –Typical Measurements = Brown, black, blonde Examples

Descriptive Statistics When we can enumerate whole population, We use DESCRIPTIVE STATISTICS:DESCRIPTIVE STATISTICS: Procedures used to summarize and describe the set of measurements.

Inferential Statistics When we cannot enumerate the whole population, we use INFERENTIAL STATISTICS:INFERENTIAL STATISTICS: Procedures used to draw conclusions or inferences about the population from information contained in the sample.

Objective of Inferential Statistics To make inferences about a population from information contained in a sample. The statistician’s job is to find the best way to do this.