Copyright ©2009 Cengage Learning 1.1 Ch 1 What is Statistics?

Copyright ©2009 Cengage Learning 1.1

Ch 1

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)

65 81 72 5971 53 85 6666 70 72 7179 76 77 6865 73 64 7282 73 77 7580 85 89 7486 83 87 7767 80 78 6964 67 79 6062 78 59 9274 68 63 6967 67 84 6972 62 74 7368 83 74 65


Example 1. Histogram

Histogram

0102030

50 60 70 80 90 100

Marks

Frequency


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 = 72.67Median = 72


Example 1. Variability

Variability: Are most of the marks clustered around the mean or are they more spread out?

Range = Maximum – minimum = 92-53 = 39

VarianceStandard deviation

A graphical technique –histogram can provide us with this and other information


Descriptive StatisticsDescriptive 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’.


Example 2. Exit PollThe 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


Key Statistical ConceptsPopulation

— 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.


Key Statistical Concepts

Parameter— A descriptive measure of a

population.

Statistic— A descriptive measure of a sample.


Key Statistical Concepts

Populations have Parameters,Samples have Statistics.

Parameter

Population Sample

Statistic

Subset


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?


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.


Inferential statisticsInferential 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 2000.

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.


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 Parametersbased on a Sample’s Statistics?


Statistical InferenceWe use statistics to make inferences about parameters.

Parameter: the actual proportion of voters in Florida who voted for Bush in 2000.

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.

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Copyright ©2009 Cengage Learning 1.1 Ch 1 What is Statistics?