The document provides an introduction to statistics, including definitions of key concepts. It describes statistics as the collection, organization, analysis, and interpretation of data. Descriptive statistics describes characteristics of a data set, while inferential statistics is used to draw inferences about a population based on a sample. Key terms are also defined, such as population, sample, parameter, statistic, variable, and scale of measurement. Summation notation is introduced as a way to write expressions involving sums.

1. Introduction to
Statistics
CHAPTER 1

2. 1.1 What is Statistics
 Statistics is a scientific body of knowledge that deals with the
collection, organization or presentation, analysis, and
interpretation of data.
 Collection refers to the gathering of information or data
 Organization or presentation involves summarizing data or
information in textual, graphical, or tabular forms.
 Analysis involves describing the data by using statistical
methods and procedures.

3.  Interpretation refers to the process of making conclusions
based on the analysed data.
 1.1.1 History of Statistics
 Statistics is said to have developed from government records.
 In ancient Egypt(no date) and Judea(2030 BC), a census of the
population was taken.
 The most famous Roman census on Luke 2:1-4

4.  In the Middle Ages, taxes, military service, and custom duties
were also recorded.
 The registration of deaths was started by Henry VIII in 1532.
 The study of statistics in the modern times is particularly
concerned with drawing inferences about the properties of a
large collection of persons, objects or things by studying its
representative or small sample.
 The theory of probability emerged during the seventeenth
century.

5.  Several people who were involved in the development of
modern statistics are Abraham De Moivre (1667-1754) who
discovered the equation of the normal curve, Karl Pearson,
Marguis de Laplace, and Carl Friedrich Gauss who
independently worked on the methods of finding the
correlation among several variables.
 In 20th century, Sir Ronald Fisher made significant contribution
to the science of statistics. He discovered a unified theory for
drawing rigorous conclusions from statistical data.

6.  1.1.2 Application of Statistics
 In Business
 Summarize and describe data such as amount of sales,
expenditures, and production.
 In Education
 Analysing test scores.
 In Psychology
 Interpretation of aptitude tests, IQ tests, and other psychological
tests.

7.  In Politics and Government
 Public opinion and election polls.
 In Medicine
 Effectiveness of new drug products.
 In Agriculture
 Effectiveness of a new fertilizer.
 In Entertainment
 Surveys, ratings, and top grosser movies.
 Others
 No. of cars and pedestrian, costumers, video games, etc.

8.  1.1.3 Descriptive and Inferential Statistics
 Descriptive Statistics is a statistical procedure concerned with
describing the characteristics and properties of a group of
persons, places, or things.
 Inferential Statistics is a statistical procedure that is used to
draw inferences or information about the properties or
characteristics by a large group of people, places, or things on
the basis of the information obtained from a small portion of a
large group.

9.  1.2 Terminologies in Statistics
 Population refers to a large collection of objects, persons,
places, or things.
 Sample is a small portion or part of a population.
 Parameter is any numerical or nominal characteristic of a
population.
 Statistic is an estimate of a parameter. It is any value or
measurement obtained from a sample.
 Data are facts, or a set of information or observation under
study. Data may be classified into 2 categories.

10.  Qualitative data are data which can assume values that manifest
the concept of attributes. Sometimes called categorical data and
cannot be subject to operations.
 Quantitative data are data which are numerical in nature.
Obtained from counting or measuring.
 A variable is a characteristic or property of a sample which
makes the members different from each other.
 Discrete variable is one that can assume a finite number of
values.
 Continuous variable is one that can assume infinite values within
specified interval.

11.  Dependent variable is a variable which is affected or influenced
by another variable.
 Independent variable is one which affects or influences the
dependent variable.
 Constant is a property or characteristic of a population or
sample, which makes the group similar to each other.

12.  1.3 Scales of Measurement
 Nominal scale
 Used when we want to distinguish one object from another for
identification. The amount of difference cannot be determined.
 Ordinal scale
 Data are arranged in some specified order or rank. In this level we
can say that one is better than the other, but we cannot tell how
much more or less of the characteristic one object has than the
other.

13.  Interval scale
 Not only that one object is greater or less than another, but we
can also specify the amount of difference.
 Ratio scale
 It is like the interval. Starts from an absolute or true zero point.
There is the presence of units.

14.  1.4 Summation Notation
Σ X 𝑖
read as “The summation of X sub i, from i=m to i=n”
i=index
m=lower limit/bound
n=upper limit/bound
i = m
n

15.  𝑋1 + 𝑋2 + 𝑋3 + ⋯ + 𝑋44
𝑖=1
44
𝑋𝑖
 𝐴1
2
+ 𝐴2
2
+ 𝐴3
2
+ ⋯ + 𝐴11
2
𝑖=1
11
𝐴𝑖
2

16. (𝑌4+5) + (𝑌5+5) + ⋯ + (𝑌20+5)
𝑖=4
20
(𝑌𝑖+5)
 𝑋7 𝑌7 + 𝑋8 𝑌8 + ⋯ + 𝑋70 𝑌70
𝑖=7
70
𝑋𝑖 𝑌𝑖

17. 𝑖=7
10
𝑋𝑖
3
𝑋7
3
+ 𝑋8
3
+ 𝑋9
3
+ 𝑋10
3
𝑖=2
5
(𝐴𝑖 + 𝐵𝑖)
𝐴2 + 𝐵2 + 𝐴3 + 𝐵3 + 𝐴4 + 𝐵4 + (𝐴5 + 𝐵5)

18.  𝑋1 = 2, 𝑋2 = 4, 𝑋3 = 5
𝑌1 = 1, 𝑌2 = 3, 𝑌3 = 7
𝑖=1
3
𝑋𝑖 =
𝑖=1
3
𝑋𝑖 + 𝑌𝑖 =
𝑋1 + 𝑋2 + 𝑋311
(𝑋1+𝑌1) + 𝑋2 + 𝑌2 + (𝑋3 + 𝑌3)3+7 + 1222