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Lecture Notes: Introduction to Statistics - Population and Samples, Study notes of Statistics
An introduction to statistics, discussing the concepts of data, populations, censuses, samples, parameters, and statistics. It also covers the differences between quantitative and qualitative data and introduces the branches of descriptive and inferential statistics.
What you will learn
- What are the two main branches of statistics?
- How does probability play a role in inferential statistics?
- What is the difference between a population parameter and a sample statistic?
Typology: Study notes
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Lecture Notes Chapter 1: Introduction to Statistics.
Definitions:
Data consist of information coming from observations, counts, measurements, or responses.
Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to make decisions.
A population is the complete collection of all elements (scores, people, measurement, and so on) to be studied. The collection is complete in the sense that it includes all subjects to be studied.
A census is the collection of data from every element in a population.
A sample is a sub collection of elements drawn from a population.
Example 1: In a recent survey, 3002 American adults were asked if they read news on the Internet at least once a week.
Responses of American adults (population)
Responses of adults in survey (sample)
The Nature of Data:
A parameter is a numerical measurement describing some characteristic of a population.
A statistic is a numerical measurement describing some characteristic of a sample.
Example 2: A sample of Americans is selected and the average (mean) amount of time watching television is 4.6 hours per day. (sample statistic)
Example 3: Currently, 42% of the governors of the 50 United States are Democrats. (population parameter)
Quantitative data consist of numerical measurements or counts.
Qualitative data consist of attributes, labels, or nonnumeric entries.
Example 4: Quantitative data: the incomes of college graduates
Qualitative data: the genders (male/female of college graduates.
Branches of Statistics
Descriptive statistics is the branch of statistics that involves the organization, summarization and display of data.
Inferential statistics is the branch of statistics that involves using a sample to draw conclusions about a population. A basic tool in the study of inferential statistics is probability.
Question 1: Does this numerical value describe a population parameter or a sample statistic?
In New York City, there are 3250 walk buttons that pedestrians can press at traffic intersections, and 2500 of them do not work.