INTRODUCTION TO STATISTICS: A COMPREHENSIVE COURSE NOTES STUDY
GUIDE WITH HIGH-YIELD REVISION NOTES, WORKED EXAMPLES, PRACTICE
QUESTIONS, DETAILED EXPLANATIONS, DESCRIPTIVE AND INFERENTIAL
STATISTICS CONCEPTS, PROBABILITY FUNDAMENTALS, DATA ANALYSIS
TECHNIQUES, AND COMPLETE EXAM SUCCESS TOOLKIT | UPDATED FOR
2026/2027 | LATEST EDITION
Chapter 1 Topics
• 1.1 An Overview of Statistics
• 1.2 Data Classification
• 1.3 Experimental Design
1.1 An Overview of Statistics
What is Statistics?
Statistics is the science of data. Data are numbers with context, and the discipline can be
broken down into three main branches:
• Data Analysis
• Probability
• Statistical Inference
A Definition of Statistics
, Data A collection of facts consisting of information coming from
observations, counts, measurements or responses.
Statistics The science of collecting, organizing, analyzing and interpreting data
in order to make decisions. It uses data to gain insight and draw
conclusions.
Data Sets: Population vs. Sample
Population The collection of all outcomes, responses, measurements or counts
that are of interest. Example: All students taking Statistics classes at
NSCC.
Sample A subset of the population. Example: All students in Math 109
Section 05.
Parameter A numerical description of a population characteristic.
Statistic A numerical description of a sample characteristic.
Branches of Statistics
1. Descriptive Statistics
Descriptive statistics involves the organization, analysis, summarization and display of data. It
describes and presents data in a meaningful way.
2. Probability Theory
,Probability theory is the branch of statistics that deals with chance or random phenomena. It tries
to quantify how likely events are to occur.
3. Inferential Statistics
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.
1.2 Data Classification
Types of Data
Qualitative Data Data that cannot be measured by a numerical scale. It consists of
attributes such as gender or nationality. Can be binary (yes/no) or
categorical.
Quantitative Data Data that can be measured or identified by a numerical scale. It
consists of numerical measurements or counts.
Levels of Measurement
Data can be further classified into four levels of measurement, from lowest to highest:
Nominal Level
Data at this level is qualitative only. Categories have no meaningful order or ranking (e.g., types
of fruits, gender, nationality).
Ordinal Level
, Data at this level can be qualitative or quantitative. Values can be ranked or ordered, but
differences between measurements are not meaningful (e.g., satisfaction ratings: poor, fair, good,
excellent).
Interval Level
Data at this level can be ordered and meaningful differences can be calculated. A zero entry
measures a position on a scale — it is not an inherent zero* (e.g., temperature in °C or °F,
calendar years).
*Note: An inherent zero is a zero that implies 'none.'
Ratio Level
Data at this level are similar to those at the interval level with the added property that a zero
entry is an inherent zero. A ratio of two data values can be performed so that one data value can
be a multiple of another (e.g., weight, height, income).
1.3 Experimental Design
What is an Experiment?
An experiment deliberately imposes a treatment on a group of objects or subjects in the
interest of observing the response. This differs from an observational study, which involves
collecting and analyzing data without changing existing conditions.
It is wise to take time and effort to organize the experiment properly to ensure that the
right type of data, and enough of it, is available to answer the questions of interest as clearly and
efficiently as possible.
GUIDE WITH HIGH-YIELD REVISION NOTES, WORKED EXAMPLES, PRACTICE
QUESTIONS, DETAILED EXPLANATIONS, DESCRIPTIVE AND INFERENTIAL
STATISTICS CONCEPTS, PROBABILITY FUNDAMENTALS, DATA ANALYSIS
TECHNIQUES, AND COMPLETE EXAM SUCCESS TOOLKIT | UPDATED FOR
2026/2027 | LATEST EDITION
Chapter 1 Topics
• 1.1 An Overview of Statistics
• 1.2 Data Classification
• 1.3 Experimental Design
1.1 An Overview of Statistics
What is Statistics?
Statistics is the science of data. Data are numbers with context, and the discipline can be
broken down into three main branches:
• Data Analysis
• Probability
• Statistical Inference
A Definition of Statistics
, Data A collection of facts consisting of information coming from
observations, counts, measurements or responses.
Statistics The science of collecting, organizing, analyzing and interpreting data
in order to make decisions. It uses data to gain insight and draw
conclusions.
Data Sets: Population vs. Sample
Population The collection of all outcomes, responses, measurements or counts
that are of interest. Example: All students taking Statistics classes at
NSCC.
Sample A subset of the population. Example: All students in Math 109
Section 05.
Parameter A numerical description of a population characteristic.
Statistic A numerical description of a sample characteristic.
Branches of Statistics
1. Descriptive Statistics
Descriptive statistics involves the organization, analysis, summarization and display of data. It
describes and presents data in a meaningful way.
2. Probability Theory
,Probability theory is the branch of statistics that deals with chance or random phenomena. It tries
to quantify how likely events are to occur.
3. Inferential Statistics
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.
1.2 Data Classification
Types of Data
Qualitative Data Data that cannot be measured by a numerical scale. It consists of
attributes such as gender or nationality. Can be binary (yes/no) or
categorical.
Quantitative Data Data that can be measured or identified by a numerical scale. It
consists of numerical measurements or counts.
Levels of Measurement
Data can be further classified into four levels of measurement, from lowest to highest:
Nominal Level
Data at this level is qualitative only. Categories have no meaningful order or ranking (e.g., types
of fruits, gender, nationality).
Ordinal Level
, Data at this level can be qualitative or quantitative. Values can be ranked or ordered, but
differences between measurements are not meaningful (e.g., satisfaction ratings: poor, fair, good,
excellent).
Interval Level
Data at this level can be ordered and meaningful differences can be calculated. A zero entry
measures a position on a scale — it is not an inherent zero* (e.g., temperature in °C or °F,
calendar years).
*Note: An inherent zero is a zero that implies 'none.'
Ratio Level
Data at this level are similar to those at the interval level with the added property that a zero
entry is an inherent zero. A ratio of two data values can be performed so that one data value can
be a multiple of another (e.g., weight, height, income).
1.3 Experimental Design
What is an Experiment?
An experiment deliberately imposes a treatment on a group of objects or subjects in the
interest of observing the response. This differs from an observational study, which involves
collecting and analyzing data without changing existing conditions.
It is wise to take time and effort to organize the experiment properly to ensure that the
right type of data, and enough of it, is available to answer the questions of interest as clearly and
efficiently as possible.
