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KENYATTA UNIVERSITY
INSTITUTE OF OPEN LEARNING
SCHOOL OF PURE AND APPLIED SCIENCES
SMA 160: Probability & Statistics I
E. G. Njenga
S. M. Karuku
Department of Mathematics
,www.pdfeducation.com
Preface
This module introduces statistical methods as applied to collecting, tabulating, analyzing,
presenting, and interpreting data. Topics covered include frequency distributions,
measures of central tendency, measures of dispersion, elementary probability theory,
regression and correlation. This is a basic course for students in business, behavioral and
social science and is part of the foundation for all Probability and Statistics courses in
later years. The purpose of this module is to introduce the student to statistics in a way
that will make the student aware of the techniques of statistics as they apply to the
solutions of practical problems in various fields. The module will be presented with
particular attention to statistical vocabulary, problem solving, and point of view. The
module is made up of eight units. Unit one introduces the concept of statistics, justifies
the study of statistics and discusses some of the areas where statistics is applied. Unit two
explores the graphical and tabular representation of data. Various methods of data
summarization and interpretation of statistical graphs, charts and tables are considered.
Units three and four explore numerical methods for ordering and presenting quantitative
data. Whereas Unit three considers the measures of location, Unit four discusses the
spread or variation within data. The symmetry and the peakedness of the distribution of a
sample or population are considered in Unit five where description of the shape of the
distribution is looked at. Units six and seven attend to the problem of Bivariate data with
the former addressing the question of the degree and strength of relationship between two
data sets and the latter dealing with the issue of prediction of one variable given the other.
The last unit; that is, Unit eight considers the problem of chance/uncertainty
mathematically. Here the concept of probability and its application in real life is dealt
with. The revision exercises at the end of each of units 2-8 ensure that the student has
grasped the subject matter of the unit.
E. G. Njenga
S. M. Karuku
Department of Mathematics
,www.pdfeducation.com
TABLE OF CONTENTS
Unit
Page
Unit 1
Introduction to Statistics 1
Unit 2
Data Presentation 30
Unit 3
Measures of Central Tendency 54
Unit 4
Measures of Dispersion 80
Unit 5
Moment, Skewness and Kurtosis 95
Unit 6
Correlation 111
Unit 7
Regression 126
Unit 8
Probability 136
Answers to Exercises 153
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UNIT 1
INTRODUCTION TO STATISTICS
1.0 Introduction
In our everyday life, we come across different types of quantitative information in
newspapers, magazines, over radio and television. For example, we may hear or read that
the infant mortality rate had decreased at the rate of 15% per annum during the period
1997-1998, the population of Kenya had increased at the rate of 3% per year during the
period 1989-1999, the number of admission in Public Universities had gone up by, say,
4% during 1998-99 as compared to 1996-97, etc. We would like to know what these
figures mean. This quantitative information or expression is called statistical data or
statistics. The unit begins with a discussion of the meaning and scope of statistics. This is
followed by definitions of terms commonly encountered in statistics. We also outline the
stages involved in any statistical enquiry. The different types of variables and levels of
measurement are discussed. We also introduce some mathematical symbols commonly
used in statistics. At the end of the unit, a revision exercise is provided to assist the
student in reviewing the main ideas of the Unit and practice on the use of the
mathematical symbols considered.
have successfully completed SMA 102 –Basic
Mathematics.
Prerequisite
Before starting this Unit you should …
1.1 Objectives
By the end of this unit, you should be able to:
distinguish between statistical data and statistical methods.
classify statistical studies as either descriptive or inferential.
define the terms data, population, sample and variable.
identify the population and the sample in an inferential study.
explain what is meant by a representative sample.
KENYATTA UNIVERSITY
INSTITUTE OF OPEN LEARNING
SCHOOL OF PURE AND APPLIED SCIENCES
SMA 160: Probability & Statistics I
E. G. Njenga
S. M. Karuku
Department of Mathematics
,www.pdfeducation.com
Preface
This module introduces statistical methods as applied to collecting, tabulating, analyzing,
presenting, and interpreting data. Topics covered include frequency distributions,
measures of central tendency, measures of dispersion, elementary probability theory,
regression and correlation. This is a basic course for students in business, behavioral and
social science and is part of the foundation for all Probability and Statistics courses in
later years. The purpose of this module is to introduce the student to statistics in a way
that will make the student aware of the techniques of statistics as they apply to the
solutions of practical problems in various fields. The module will be presented with
particular attention to statistical vocabulary, problem solving, and point of view. The
module is made up of eight units. Unit one introduces the concept of statistics, justifies
the study of statistics and discusses some of the areas where statistics is applied. Unit two
explores the graphical and tabular representation of data. Various methods of data
summarization and interpretation of statistical graphs, charts and tables are considered.
Units three and four explore numerical methods for ordering and presenting quantitative
data. Whereas Unit three considers the measures of location, Unit four discusses the
spread or variation within data. The symmetry and the peakedness of the distribution of a
sample or population are considered in Unit five where description of the shape of the
distribution is looked at. Units six and seven attend to the problem of Bivariate data with
the former addressing the question of the degree and strength of relationship between two
data sets and the latter dealing with the issue of prediction of one variable given the other.
The last unit; that is, Unit eight considers the problem of chance/uncertainty
mathematically. Here the concept of probability and its application in real life is dealt
with. The revision exercises at the end of each of units 2-8 ensure that the student has
grasped the subject matter of the unit.
E. G. Njenga
S. M. Karuku
Department of Mathematics
,www.pdfeducation.com
TABLE OF CONTENTS
Unit
Page
Unit 1
Introduction to Statistics 1
Unit 2
Data Presentation 30
Unit 3
Measures of Central Tendency 54
Unit 4
Measures of Dispersion 80
Unit 5
Moment, Skewness and Kurtosis 95
Unit 6
Correlation 111
Unit 7
Regression 126
Unit 8
Probability 136
Answers to Exercises 153
, www.pdfeducation.com
UNIT 1
INTRODUCTION TO STATISTICS
1.0 Introduction
In our everyday life, we come across different types of quantitative information in
newspapers, magazines, over radio and television. For example, we may hear or read that
the infant mortality rate had decreased at the rate of 15% per annum during the period
1997-1998, the population of Kenya had increased at the rate of 3% per year during the
period 1989-1999, the number of admission in Public Universities had gone up by, say,
4% during 1998-99 as compared to 1996-97, etc. We would like to know what these
figures mean. This quantitative information or expression is called statistical data or
statistics. The unit begins with a discussion of the meaning and scope of statistics. This is
followed by definitions of terms commonly encountered in statistics. We also outline the
stages involved in any statistical enquiry. The different types of variables and levels of
measurement are discussed. We also introduce some mathematical symbols commonly
used in statistics. At the end of the unit, a revision exercise is provided to assist the
student in reviewing the main ideas of the Unit and practice on the use of the
mathematical symbols considered.
have successfully completed SMA 102 –Basic
Mathematics.
Prerequisite
Before starting this Unit you should …
1.1 Objectives
By the end of this unit, you should be able to:
distinguish between statistical data and statistical methods.
classify statistical studies as either descriptive or inferential.
define the terms data, population, sample and variable.
identify the population and the sample in an inferential study.
explain what is meant by a representative sample.
