Probability & Statistics

Chapter 01Introduction to Statistics

1

Statistics

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

21-2

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.

31-2

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.

4

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

5

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.

6

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

7

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.

8

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.

9

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 100. The statistic 9 describes the number of problems out of every 100 pens.

10

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.

11

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.

121-14

Nominal level

131-13

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.

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.

14

Ordinal level

151-13

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.

Interval level

161-13

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.

Ratio level

171-13

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.

18Level of

data

Nominal Ordinal Interval Ratio

Data may only be classified

Data are rankedMeaningful difference

between values

Meaningful 0 point &

ratio between values

Classification of students by

district

Your rank for this course

moduleTemperature

Number of study hours