Copyright ©2009 Cengage Learning 1.1 Day 3 What is Statistics?

Copyright © 2009 Cengage Learning 1.2 Example 1. Statistics Marks A list of the final marks in last year. (out of 100)

Copyright © 2009 Cengage Learning 1.3 Example 1. Histogram

Copyright ©2009 Cengage Learning 1.4 Example 1. Central Location “Typical mark” : idea of average man/woman Mean (average mark) Median (mark such that 50% of class is above the grade and 50% is below) Mean = Median = 72

Copyright ©2009 Cengage Learning 1.5 Example 1. Variability Variability: Are most of the marks clustered around the mean or are they more spread out? Range = Maximum – minimum = = 39 Variance Standard deviation A graphical technique –histogram can provide us with this and other information

Copyright © 2009 Cengage Learning 1.6 Descriptive Statistics Descriptive statistics deals with methods of organizing, summarizing, and presenting data. Graphical techniques: histogram, bar and pie charts. Numerical techniques: The mean and median to describe the location of the data. The range, variance, and standard deviation measure the variability of the data

Copyright © 2009 Cengage Learning Excel: How to do Tools -> Data Analysis -> Histogram, Descriptive Statistics If it is your first time to use ‘Data Analysis’, be sure to do the followings before you use these tools. Tools -> Add-Ins -> click ‘Analysis Toolpak’.

Copyright © 2009 Cengage Learning 1.8 Example 2. Exit Poll The exit poll results from the state of Florida during the 2000 year elections were recorded (the Republican candidate George W. Bush vs. the Democrat Albert Gore). Suppose that the results (765 people who voted for either Bush or Gore) were stored. (1 = Gore and 2 = Bush). The network analysts would like to know whether more than 50% of the electorate voted for Bush. Approximately 5 million Floridians voted for Bush or Gore for president. The sample consisted of the 765 people randomly selected by the polling company

Copyright © 2009 Cengage Learning 1.9 Key Statistical Concepts Population — a population is the group of all items of interest to a statistics practitioner. — frequently very large; sometimes infinite. E.g. All 5 million Florida voters Sample — A sample is a set of data drawn from the population. E.g. a sample of 765 voters exit polled on election day.

Copyright © 2009 Cengage Learning 1.10 Key Statistical Concepts Parameter — A descriptive measure of a population. Statistic — A descriptive measure of a sample.

Copyright © 2009 Cengage Learning 1.11 Key Statistical Concepts Populations have Parameters, Samples have Statistics. Parameter Population Sample Statistic Subset

Copyright © 2009 Cengage Learning Example 3. Lake Michigan A researcher in Shedd Aquarium in Chicago wanted to know the average size of fish in the Lake Michigan. She collected 500 samples from the Lake, measured lengths, and calculated the average (mean) of the sample. Population? Sample? Parameter? Statistics?

Copyright © 2009 Cengage Learning Idea of statistics. Because we will not ask every one of the 5 million actual voters for whom they voted, we cannot predict the outcome with 100% certainty. A sample that is only a small fraction of the size of the population can lead an inference. But inferences will be correct only a certain percentage of the time.

Copyright © 2009 Cengage Learning 1.14 Inferential statistics Inferential statistics is a body of methods used to draw conclusions or inferences about characteristics of populations based on sample data. The population is 5 million voters in Florida in the year of The sample is 765 people randomly selected at the poll station. To have a definite answer of the question (who will win in Florida), one sure way is to interview all 5 million voters. Statistical techniques make such endeavors unnecessary. Instead, we can randomly draw a much smaller number of voters infer from the data.

Copyright © 2009 Cengage Learning 1.15 Statistical Inference Statistical inference is the process of making an estimate, prediction, or decision about a population based on a sample. Parameter Population Sample Statistic Inference What can we infer about a Population’s Parameters based on a Sample’s Statistics?

Copyright © 2009 Cengage Learning 1.16 Statistical Inference We use statistics to make inferences about parameters. Parameter: the actual proportion of voters in Florida who voted for Bush in Statistics: the sample proportion among the people who were selected at the exit poll. Therefore, we can make an estimate, prediction, or decision about a population based on sample data.