Introduction to Probability and Statistics
– 2022 (Dr. Bundi)
DEPARTMENT OF 0
, MATHEMATICS
INTRODUCTION TO PROBABILITY AND STATISTICS
EVANSMIGEL 6/16/2022
1
,1 DEPARMENT OF
MATHEMATICS
INTRODUCTION TO PROBABILITY AND STATISTICS
Course Outline
1 Introduction to Statistics
2 Frequency distributions: - Relative and cumulative distributions
3 Measures of location: - Mean, mode, median, quartiles, deciles and percentiles
4 Measures of dispersion: - Range, MAD, standard deviation, Skewness and Kurtosis
5 Probability: - Sample space and events, definition of probability, conditional probability,
independence and Bayes theorem
6 Probability distributions: - Random variables (RVs), expected and variance of RVs
7 Univariate distributions: - Bernoulli, Binomial, Poisson, Geometric, Uniform, Exponential
and Normal
8 Bivariate frequency distribution – Joint and marginal probabilities
Reference Book
Introductory Business Statistics by Alexander Holmes, Barbara Illowsky and Susan Dean.
OpenStax, 2017
1. Introduction to Statistics
Statistics is the science of data. It involves collecting, classifying, summarizing, organizing,
analyzing and interpreting numerical information.
Or, Statistics is the branch of scientific inquiry, which provides for collecting data (sampling and
experimental design), organizing and summarizing data (graphs and tables), and statistical
inference (making generalizations to a larger population based on observations from a sample).
Statistics involves - Identifying the problem, collecting the data, analyzing the data, presenting
the summarized data, drawing conclusions and making inference
1.1. Divisions of Statistics
1. Statistical methods
It studies all tools, rules and general principles applicable to all kinds or groups of data.
2
, 2. Applied statistics
Deal with the application of statistical methods to specific problems. Example – estimating the
national income of a country.
2
Applied statistics can be further divided into two main groups:
o Descriptive Statistics - utilizes numerical and graphical method to summarize the
information, look for patterns in the data set and present the information in a convenient form.
o Inferential Statistics - utilizes sample data to make estimates, decisions, predictions, or other
generalizations about a larger set of data.
1.2 Importance of Statistics
a). Permits summarization and presentation of large quantities of information
b). To undertake and understand research in our areas of interest
c). Used in government to formulate policies and administration – the 2009 census
d). Help businesses in decision making by making future estimates and expectations
e). Enables us to formulate and test hypothesis (statistically assess a statement)
f). Can you think of other reasons?
1.4 Data
Data are the facts and figures collected, summarized, analyzed and interpreted. o Or
is a collection of observations from an experiment or a survey.
Data set – data collected in a particular study.
Data contain information needed to make a more informed decision on a particular situation.
Examples where data is needed o A market researcher assesses products characteristics to
distinguish one product from another o A quality analyst wants to check the quality of products
produced on a production line.
o A medical researcher to compare to drugs in the market, etc
These are some reasons for collecting data o
To assist in decision making
o To provide needed information in a study or survey o To satisfy our curiosity o To assist in
making informed decisions
o To measure performance of an ongoing service or production process
Further, we have primary and secondary data. o Primary data – an experiment/survey is
undertaken to obtain the data (first hand) o Secondary data – data already published. Example,
Kenya Bureau of statistics, NSE, etc
1.4.1 Types of data categories o Categorical data – that which yields response such as
Yes or No. For example, “Did you buy the books?”
o Numerical data – it yields numerical responses. As the word suggests, involves numbers.
3
– 2022 (Dr. Bundi)
DEPARTMENT OF 0
, MATHEMATICS
INTRODUCTION TO PROBABILITY AND STATISTICS
EVANSMIGEL 6/16/2022
1
,1 DEPARMENT OF
MATHEMATICS
INTRODUCTION TO PROBABILITY AND STATISTICS
Course Outline
1 Introduction to Statistics
2 Frequency distributions: - Relative and cumulative distributions
3 Measures of location: - Mean, mode, median, quartiles, deciles and percentiles
4 Measures of dispersion: - Range, MAD, standard deviation, Skewness and Kurtosis
5 Probability: - Sample space and events, definition of probability, conditional probability,
independence and Bayes theorem
6 Probability distributions: - Random variables (RVs), expected and variance of RVs
7 Univariate distributions: - Bernoulli, Binomial, Poisson, Geometric, Uniform, Exponential
and Normal
8 Bivariate frequency distribution – Joint and marginal probabilities
Reference Book
Introductory Business Statistics by Alexander Holmes, Barbara Illowsky and Susan Dean.
OpenStax, 2017
1. Introduction to Statistics
Statistics is the science of data. It involves collecting, classifying, summarizing, organizing,
analyzing and interpreting numerical information.
Or, Statistics is the branch of scientific inquiry, which provides for collecting data (sampling and
experimental design), organizing and summarizing data (graphs and tables), and statistical
inference (making generalizations to a larger population based on observations from a sample).
Statistics involves - Identifying the problem, collecting the data, analyzing the data, presenting
the summarized data, drawing conclusions and making inference
1.1. Divisions of Statistics
1. Statistical methods
It studies all tools, rules and general principles applicable to all kinds or groups of data.
2
, 2. Applied statistics
Deal with the application of statistical methods to specific problems. Example – estimating the
national income of a country.
2
Applied statistics can be further divided into two main groups:
o Descriptive Statistics - utilizes numerical and graphical method to summarize the
information, look for patterns in the data set and present the information in a convenient form.
o Inferential Statistics - utilizes sample data to make estimates, decisions, predictions, or other
generalizations about a larger set of data.
1.2 Importance of Statistics
a). Permits summarization and presentation of large quantities of information
b). To undertake and understand research in our areas of interest
c). Used in government to formulate policies and administration – the 2009 census
d). Help businesses in decision making by making future estimates and expectations
e). Enables us to formulate and test hypothesis (statistically assess a statement)
f). Can you think of other reasons?
1.4 Data
Data are the facts and figures collected, summarized, analyzed and interpreted. o Or
is a collection of observations from an experiment or a survey.
Data set – data collected in a particular study.
Data contain information needed to make a more informed decision on a particular situation.
Examples where data is needed o A market researcher assesses products characteristics to
distinguish one product from another o A quality analyst wants to check the quality of products
produced on a production line.
o A medical researcher to compare to drugs in the market, etc
These are some reasons for collecting data o
To assist in decision making
o To provide needed information in a study or survey o To satisfy our curiosity o To assist in
making informed decisions
o To measure performance of an ongoing service or production process
Further, we have primary and secondary data. o Primary data – an experiment/survey is
undertaken to obtain the data (first hand) o Secondary data – data already published. Example,
Kenya Bureau of statistics, NSE, etc
1.4.1 Types of data categories o Categorical data – that which yields response such as
Yes or No. For example, “Did you buy the books?”
o Numerical data – it yields numerical responses. As the word suggests, involves numbers.
3
