1. Probability & Statistics
Chapter 01
Introduction to Statistics

2. Statistics Statistics is the science of data which involves
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Statistics
Statistics is the science of data which involves
collecting,
classifying
summarizing,
organizing,
analyzing, and interpreting numerical information

3. Sources of Statistical Data
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Sources of Statistical Data
For Researching problems
usually requires published data. Statistics on these problems can be found in published articles, journals, and magazines.
Published data is not always available on a given subject. In such cases, information will have to be collected and analyzed.
One way of collecting data is via questionnaires.

4. Why study Statistic? Reasons for studying statistics:
Data (specially numeric data) is everywhere
Statistical techniques are used to make many decisions that affect our lives
No matter what your future line of work
An understanding of statistical methods will help you make these decisions more effectively.

5. Definitions Populations and Parameters
A population is the entire collection of all observations of interest.
A parameter is a descriptive measure of the entire population of all observations of interest

6. Definitions Samples and Statistics
A sample is a representative portion of the population which is selected for study.
A statistic describes a sample and serves as an estimate of the corresponding population parameter.

7. Definitions Variables
A variable is a the characteristic of the population that is being examined in the statistical study.
There are two basic types of data: Qualitative & Quantitative

8. Types of Variables
Qualitative or Attribute variable: the characteristic or variable being studied is nonnumeric.
EXAMPLES: Gender, religious affiliation, type of automobile owned, state of birth, eye color.
Quantitative variable: the variable can be reported numerically.
EXAMPLE: balance in your savings account, minutes remaining in class, number of children in a family.

9. Types of Variables
Quantitative variables can be classified as either discrete or continuous.
Discrete variables: can only assume certain values and there are usually “gaps” between values.
EXAMPLE: the number of bedrooms in a house. (1,2,3,..., etc...).
Continuous variables: can assume any value within a specific range.
EXAMPLE: The time it takes to fly from Sri Lanka to New York.

10. Types of Statistics
Descriptive Statistics: Methods of organizing, summarizing, and presenting data in an informative way.
EXAMPLE: According to Consumer Report of Ceylon Pencil Company, 9 defective pens per The statistic 9 describes the number of problems out of every 100 pens.

11. Types of Statistics
Inferential Statistics: A decision, estimate, prediction, or generalization about a population, based on a sample.
EXAMPLE: TV networks constantly monitor the popularity of their programs by hiring people to sample the preferences of TV viewers.

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Levels of Measurement
Level of measurement of data often dictates the calculations that can be done to summarize and present the data and the statistical tests that can be performed.
There are four levels of measurement: nominal, ordinal, interval and ratio.

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Nominal level
Nominal level (scaled): Data that can only be classified into categories and cannot be arranged in an ordering scheme.
EXAMPLES: eye color, gender, religious affiliation
These categories are mutually exclusive and/or exhaustive.

14. Nominal level
Mutually exclusive: An individual or item that, by virtue of being included in one category, must be excluded from any other category.
EXAMPLE: eye color.
Exhaustive: each person, object, or item must be classified in at least one category.
EXAMPLE: religious affiliation.

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Ordinal level
Ordinal level: involves data that may be arranged in some order, but differences between data values cannot be determined or are meaningless.
EXAMPLE: During a taste test of 4 colas, cola C was ranked number 1, cola B was ranked number 2, cola A was ranked number 3, and cola D was ranked number 4.

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Interval level
Interval level: similar to the ordinal level, with the additional property that meaningful amounts of differences between data values can be determined. There is no natural zero point.
EXAMPLE: Temperature on the Fahrenheit scale.

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Ratio level
Ratio level: the interval level with an inherent zero starting point. Differences and ratios are meaningful for this level of measurement.
EXAMPLES: money, heights of students.