Statistics is the scientific methods for collecting, organizing, presenting and analyzing data as well as deriving the valid conclusion and making reasonable decision on the basis of this analysis.

2. Chapter –1
Introduction to
Statistics

3.  Statistics is concerned with scientific methods for
collecting, organizing, summarizing, presenting and
analyzing data as well as deriving the valid
conclusion and making reasonable decision on the
basis of this analysis.
 The word ‘ Statistics’ is used to refer to
- Numerical facts, such as the number of people
living in particular area.
-The study of ways of collecting, analyzing and
interpreting the facts.

4. Statistics can be classified into two parts
I. Theoretical Statistics or Mathematical Statistics
II. Applied Statistics
Theoretical or Mathematical Statistics
It is application of mathematics to Statistics. It
involves collection of facts and analysis of facts using
mathematical techniques. It is divided into two parts;
a) Descriptive Statistics
b) Inferential Statistics

5.  Statistics which deals with collection of data,
presentation of data using table, diagram, graph
etc and summarize data using measures of central
tendency and measures of variability (spread).
 Hence summarized results is obtained from
descriptive statistics which can describe the data
but can not be used to generalized.

6. Statistics which deals with sample selection from
population and statistical techniques used to draw
the valid conclusion about population on the basis of
statistical measures obtained from sample.
With the help of inferential statistics, one can
generalized the results for the whole population by
computing statistical measures from the sample.
Hence, inferential statistics possess the
generalizability capacity and it plays a vital role in
statistics.

7.  Statistics which deals with the application of
statistical methods to specific problem is called
applied statistics.
 The statistical tools and methods are used in
order to solve many more practical problems in
diversified area like computer science,
information technology, physics, biology,
astronomy, sociology, psychology, business,
economics and so on.

8. Despite its power, essential usefulness and
universal applicability statistics has its own
limitation. Some of these limitations are as
follows:
I. Statistics deal with groups and aggregates
only.
II. Statistics does not deal with qualitative
characteristics directly.
III. If sufficient care is not exercised in collecting,
analyzing and interpreting the data, statistical
results might be misleading.

9. IV. Only a person who has an expert knowledge of
statistics can handle statistical data efficiently.
V. Some errors are possible in statistical decisions.
In particular, inferential statistics involves
certain errors. We do not know whether an error
has been committed or not.

11.  Measurement is a process of assigning numbers or
symbols to any facts or objects or products or items
according to some rule.
 Scale is simply a range of levels or numbers used for
measuring something.
 Different measurements scales are used on the basis
of nature of the data. There are generally four type
of measurement scales, which are as follows;
I. Nominal Scale
II. Ordinal Scale
III. Interval Scale
IV. Ratio Scale

12. Nominal Scale
 It is the lowest level of measurement scale. It is simply a
system of assigning numbers or the symbols to objects or
events to distinguish one from another.
 The symbols or the numbers have no numerical meaning
so that the arithmetic operations can not be used for these
numbers.
 Categorical data are generally measured on nominal scale.
 For example ; gender, religion, occupation are measured in
nominal scale. If we use 1 for male and 2 for female for
measuring gender, then 1 and 2 have no numeric meaning.

13. Ordinal Scale
 When the quantification of observation is done by
ranking based on the certain criterion or priorities or
importance, then they are said to be measured on an
ordinal scale.
 It represents the qualitative values in ascending or
descending order.
 For example, symptoms of depression from
psychiatric assessment such as none is coded by ‘0’,
mild ‘1’, moderate’2’, severe’3’. These numbers are
known as ranks.

14. Interval Scale
Some measurement scales possess a constant interval
size, they are called interval scale.
 It assumes data have equal intervals.
 This scale does not have absolute zero but only
arbitrary zero.
 Scale of temperature is an example of ordinal scale.

15. Ratio Scale
Ratio scale is the ideal scale and extended form of the
interval scale. It is the most powerful scale of
measurement.
 It possesses the characteristics of nominal, ordinal
and interval scale.
 Ratio scale has an absolute zero or true zero point
that indicates the completely absence of that property
of an object what is being measured.
 For example, length, weight, age, income, sales etc
are measured in ratio scale.

16.  In statistics, variable may be defined as an attributes that
describe person, place, thing or idea under study. And is
denoted by capital letters like X, Y, Z etc.
 It is called a variable because the value may vary
between data units in a population, and may change in
value over time.
 For example, age, height, weight of persons life time of
any electronic appliance, time to download any image
file through internet etc.
 Generally, variables is classified into two types;
I. Qualitative variables
II. Quantitative Variable

17. Qualitative Variable
The variable which varies in kind rather than in
magnitude is called qualitative variable.
 It can be divided into different categories. It is
also called categorical variable.
 Qualitative variable are presented in nominal and
ordinal scales.
 For example, hair color, eye color, gender,
smoking habit, etc.

18. Quantitative Variable
The variable which varies in magnitude and can be
expressed numerically is called quantitative data.
 Quantitative variables are presents in interval and
ratio scale.
 Quantitative variable can be further divided into
two types;
I. Discrete Variable
II. Continuous Variable

19. I. Discrete Variable : A variable is said to be
discrete if it takes only whole number. For
example no. of girls in a class, family size, etc.
II. Continuous Variable : A variable is said to be
continuous if it takes all possible real values(
whole number as well as fractional values) within
a certain range. For example, height, weight, age,
temperature etc.

20. In any statistical investigation first approach is to
collect data. It is a set of values obtained on one or
more characters under study. It is the collected
information which is ready to use for statistical
analysis.
There are mainly two types of data on the basis of
collection procedures;
I. Primary data
II. Secondary data

21. Primary Data :
The data which are originally collected by
investigator or researcher for the first time with the
purpose of statistical inquiry is called primary data.
It is collected by government, an individual,
institution and research bodies. It needs more fund,
time and manpower.

22. Following are the method of collecting primary
data;
Direct personal interview method.
Indirect personal interview method.
Information through correspondence.
Mailed questionnaire method.
Schedule through enumerators.

23. Secondary Data :
The data that has been already collected for a
particular purpose and used for next purpose is called
secondary data.
When investigators find impracticable to collect
firsthand information on related issues, secondary
data is used. It saves time, money and manpower.
Source of Secondary data :
I. Published Source
II. Unpublished Source

24. Published Sources :
Different published source of secondary data are national organizations
and international agencies.
– International agencies such as WHO, World bank, International Labor
Organization.
– Governmental organizations such as Central Bureau of Statistics,
Ministry of Commerce and Industry, Nepal Rastra Bank, Ministry of
Finance.
– Semi-governmental organizations such as Nepal Food Corporation,
Nepal Electricity Authority.
– Private organizations such as Nepal Chamber of Commerce,
Federation of Nepal Chamber of Commerce and Industry,
Publications.

25. Unpublished Sources :
– Records maintained by government offices.
– Records maintained by research institutions,
research scholars etc.
– Records updated by the departments, institutions for
their internal purpose.

26. Cross- Sectional data refers to data collected by
observing many subjects at the one point or period
of time.
It is a snapshot of observation at a particular point.
For example; Population of women in census year
2068.
The data which can be recorded over different periods
of time is called time series data. In this case same
measurements are recorded on regular basis.
For example; population of Nepal in census year
2048, 2058, 2068.

27. The data of each unit is recorded for each follow up
time till the occurrence of an event or till the unit fails
is called failure time data.
It is also called time to event data.
Time to event data is mostly found in life time
analysis of different parts of computers, different
software, different industrial products, life time of
infrastructure, clinical studies, etc.

28. It is a dataset in which the behaviors of entities are
observed across time.
These entities could be individuals, states,
companies, institutions, Countries, etc.
Panel data is also known as longitudinal or cross-
sectional data.
Data of individual is recorded repeatedly over
number of years.
Income of persons X and Y in years 2014, 2015&
2016 according to age and qualification.

29. A population can be defined as an aggregate
observation of subjects grouped together by a
common feature.
 Population is the entire pool from which a
statistical sample is drawn.
 Census survey is conducted to enumerate all the
population units.
 Based on the number of individuals belonging to the
group, population can be divided into two types;
I. Finite population
II. Infinite Population

30. Based on the type of individuals in population,
population can be divided into two types
I. Homogeneous Population
Population consisting of individuals of same type
is called homogeneous population.
II. Heterogeneous Population
Population consisting of individuals of different
type is called heterogeneous population.