1.1 Meaning | unit 1 introduction to statistics

UNIT – 1

Introduction to Statistics

1.1 Meaning

Concept of Statistics

The word statistics is derived from the Latin word “Status” that means a group of numbers that represent some information of our human interest. In ancient periods, the use of statistics was made to meet the administrative needs of the state. In modern time, the statistics is not only used for administrative of the state alone, also evaluate all those activities in our lives which can be expressed in quantitative terms.

The term “statistics” is defined in two senses: - in singular and in Plural senses.

Firstly, in plural sense, statistics means systematic collection of numerical facts. Secondly in singular sense, the term statistics means the various methods used for collection, analysis and interpretation of numerical facts. It is described as statistical method. In our study we are more concerned with the second meaning of statistics.

Definition

“Statistics is a body of methods for making wise decisions on the face of uncertainty.” —Wallis and Roberts

“Statistics is a body of methods for obtaining and analyzing numerical data in order to make better decisions in an uncertain world.” —Edward N. Dubois

Statistics are numerical statement of facts in any department of enquiry placed interrelation to each other.- Bouly.

The science of Statistics is essentially a branch of applied mathematics and can be regarded as a mathematics applied to observation data.- R.A fisher.

After analyzing the various definitions of statistics, the most proper definition of statistics are as follows:

“Statistics in the plural sense are numerical statements of facts capable of some meaningful analysis and interpretation, and in singular sense, it relates to the collection, classification, presentation and interpretation of numerical data.”

Nature of Statistics

Statistics are numerical statements of facts capable of some meaningful analysis and interpretation, and in singular sense, it relates to the collection, classification, presentation and interpretation of numerical data. It is the science of data collection and analysis.

The nature of statistics can be enumerated as under:

Aggregate of facts: Statistics are aggregate of facts as the data collected are facts and figures gathered from various authentic sources and field survey. When the data collected are presented, they are presented in an understandable manner. A single figure like 40 years or 50 years is not statistics. It needs collection of facts and figures to be statistics.

Numerically expressed: The facts and figures collected are expressed numerically so that it can be measured. Qualitative descriptions don’t have any room in statistics.

Enumerated or Estimated: The data collected are estimated or enumerated where actual enumeration is not possible. In that case, facts are expressed in terms like ‘good’, ‘average’, ‘excellent’, etc.

Statistics are affected by a marked extent by multiplicity of causes: Statistics is affected by a number of causes in case of any field of enquiry. For example, In production statistics is affected by soil, climate, raw material, soil fertility and so on.

Collected on a systematic manner: The data collected in statistics are presented in a systematic manner after going through a series of procedures. The data collected is in a raw form. Hence it needs to be tabulated, organized, analyzed and then presented in an understandable form.

Pre-determined purpose: The reason behind which statistics are used have a purpose or objective which is pre-determined. Whenever a sort of problem is identified, the reason to investigate crops us. Data is collected and accordingly reason is determined.

Capable of being placed in relation to each other: The data collected in statistics should be comparable and connected with the same department as regards the inquiry. For example, heights and weights of students should be compared with the heights and weights of students in the same class.

Key Takeaways:

Statistics means systematic collection of numerical facts.

Statistics are numerical statements of facts capable of some meaningful analysis and interpretation.

1.2 Scope

Statistics has become indispensable in every area to day. There is hardly any field where statistics didn’t enter. Statistics is used right from the education till in aeronautical engineering. However, a few identified areas can be depicted as regards use of statistics:

Statistics is used by Government, Banks, Financial Institutions in order to have knowledge about the economy, industrial performance and so on.

In industry, statistics is used widely for quality control for the products manufactured.

In education, statistics is so essential for the academicians for conducting research.

In the field of Medical Science also Statistics plays an important role to test the efficiency of a new drug or medicine.

In space research even statistics is used to conduct research and quality control.

Key Takeaways:

Statistics is used by Government, Banks, Financial Institutions in order to have knowledge about the economy, industrial performance and so on.

In space research even statistics is used to conduct research and quality control.

1.3 Importance and limitation of statistics

Importance for administrator administration – With the help of statistics, finance minister makes the use of revenue and expenditure data to prepare budget. Also, it helps in taking decision regarding taxes.

Importance for businessman – statistics helps in providing relevant data. Thus, with the help of those data a business man can estimate demand and supply of the commodity.

Importance in economics – statistics helps in measuring economics such as gross national output, consumption, saving, investment, expenditures, etc

Importance for politician – Politician use statistics in formulating economic, social and educational policies of the country

Importance in the field of education – statistics has wide application in education for determining the reliability and viability to a test, factor analysis, etc.

Limitation of statistics

Study of numerical facts only – statistical method does not study quantitative phenomena such as honesty, wisdom, etc. So, experiments are done to measure the reaction of man through data.

Study of aggregates only – statistics study only aggregates of quantitative facts. It does not study any particular unit. Prof. Horace Sacrist defined statistics, “By statistics we mean aggregates of fact and placed in relation to each other”

It does not depict the entire story of phenomena – Any phenomena happen, due to many causes. But all the cause is not expressed in numbers. So, correct conclusion cannot be drawn. Analyzing quantitative data and ignoring qualitative data cannot give 100% conclusion.

Homogeneity of data – To compare the data, it is essential that whatever statistics are collected, the same must be uniform in quality.

It is liable to be miscued – As W.I. King points out, “One of the short-comings of statistics is that do not bear on their face the label of their quality.” Thus, the data collected by inexperienced person may be dishonest or biased. So, to get correct conclusion data must be used in caution.

Too many methods to study a problem –to find a single result many statistical methods are used. All the methods result vary in each case. “It must not be assumed that the statistics is the only method to use in research, neither should this method of considered the best attack for the problem.” —Croxten and Cowden

Key Takeaways:

Statistics helps in administration, businessman, economics, etc.

Statistics suffers from various limitations like does not depict the entire story, the data must be homogenous, liable to be miscued, etc.

1.4 Planning of statistical investigation

Statistical enquiry refers to statistical investigation where the statistical investigator requires taking the help of an investigator who with the help of enumerator which supposed to gather data. The respondents give information which is inputs to data collection. Statistical investigations test statements that may be true or false after evaluation. These statements are known as hypothesis. Before landing into investigation, the statistical investigator needs to do lot of planning for the statistical inquiry. There are certain preparations to be noted in statistical enquiry which may be as follows:

Purpose of enquiry: This means why the investigation is necessary. The reason behind which the whole activity or process is going to be undertaken.

Sources of data: Wherefrom the data is going to be collected, whether from published sources like journals, magazines, published statistical reports, websites, etc or from field survey.

Methods of data collection: If it is for field survey, questionnaire can be used as a tool for collecting data. Questionnaire refers to prepared questions beforehand for the purpose of collecting data. The respondents will fill up the necessary questions and it becomes input for the survey.

Nature and type of enquiry: The type of enquiry like explorative, descriptive should be decided in advance to have a proper guidance on the conduct of the investigation and the quality of questions to be framed for the questionnaire.

Unit of Collection: The unit of data to be collected like height, weight, income in rupees, and so on needs to be decided in advance.

Key Takeaways:

Statistical enquiry refers to statistical investigation where the statistical investigator requires taking the help of an investigator who with the help of enumerator which supposed to gather data.

Statistical investigations test statements that may be true or false after evaluation. These statements are known as hypothesis.

1.5 Census data Statistical errors and approximation

Both census and sampling provide information about a population. In census, each and every unit of population is studies. While in sampling small units are studied which represents the population. Government uses both census and sampling data for various purposes like planning, development programs, etc.

census vs sample

Census method

A well-organized procedure of gathering, recording and analyzing information regarding the members of the population is called a census. Under method census each and every unit of the universe is included in the collection of data. Huge amount of finance, time and labor are required for gathering information. This method is useful to find out the ratio of male to female, the ratio of literate to illiterate people, the ratio of people living in urban areas to the people in rural areas.

Merits

It helps government with future plans

It gives complete information about population

It gives more reliable and accurate information

It covers wide range of the study

Demerits

It is time consuming and expensive

Sometimes we many loose information while investing all individual

It need a number of manpower

Sampling method

The sample is a small segment considered for study which represents the standard of entire population. The selection of sample should give justifiable conclusion about the whole population. When the population size is very large and it is difficult to consider all members then sampling method is used. Under this method selection of appropriate representative sample is utmost important. On the basis of data collected from sample, conclusion is drawn for the whole population.

Key Takeaways:

A well-organized procedure of gathering, recording and analyzing information regarding the members of the population is called a census.

The sample is a small segment considered for study which represents the standard of entire population.

Types of sampling method

Image result for types of sampling methods

Probability sampling

It is also called as random sampling
Random sampling is one of the simplest sampling techniques in which each sample have an equal chance of being chosen from the population
It is an unbiased representation of the population

Types of random sampling

Simple random sampling – It is one of the basic and easiest form of random sampling. Simple random sampling assures that every member have an equal chance of being included in the sample.

Stratified random sampling – It is also known as proportional random sampling. In this sampling technique, the populations are split into different groups. The overall sample selected randomly from different groups. These techniques guarantee that each group will be represented in sample.

Systematic random sampling – systematic random sampling refers to selecting sample on a system of interval in a numbered population.

Cluster random sampling – under cluster sampling, the researcher divide the population into separate groups known as cluster. Here each cluster represents the population as a whole. The researcher randomly selects the cluster for his analysis.

2. Non random sampling –

It is also called as non-probability sampling

Non random sampling is one of the sampling techniques in which each sample does not have an equal chance of being chosen from the population

It is a biased representation of the population

Types of non-random sampling

Convenience sampling – under this technique, the samples are selected because they are easily accessible to the researcher. This technique is easiest, cheapest and less time consuming

Consecutive sampling – It is similar like convenience sampling. Under this technique all subjects that are available as a part of sample are included which result a better presentation of the entire population

Quota sampling – Under quota sampling, the samples are selected on the same proportions of individuals as the entire population depending on characteristics, traits as the basis of quota.

Judgmental sampling - Judgmental sampling is more commonly known as purposive sampling. The researcher keeps a specific purpose in mind and selects the subject for sampling process. The researcher believes that some subjects are fit for the research compared to other individuals.

Snowball sampling – this technique is used when the population size is small. Under snowball sampling, the researcher ask initial subject to identify another potential subject who meets the criteria of research. Thus, this technique hardly represents the population.

Key takeaways:

There are two types of sampling methods: Probability and Non-Probability sampling methods.

1.6 Classification and tabulation of data frequency distribution.

Classification of data is the process of arranging the data into homogenous groups according to their common characteristics. Raw data cannot be easily understood and not fit for analysis and interpretation. Therefore, arrangement of data helps the user in comparison and analysis.

Example- population of a state can be grouped according to sex, age, etc

Definition

“Classification is the process of arranging data into sequences according to their common characteristics or separating them into different related parts.” - Prof. Secrist

Objectives of data classification

To consolidate the huge data in such a way that similarities and differences are easily understood.

It helps in comparison and analysis of data

Classification of data ensures prominent data are collected and optional data are separated

To allow a statistical method of the material gathered.

To study relationships

Types of classification

Geographical classification – when the data classified according to the geographical location or regions (like states, cities, regions, zones, areas, etc). It is called geographical classification. It is also known as a real or spatial classification.

Ex- production of food grains are classified in different states in India

S.No	Name of states	Total food grains (000’ tones)
1	Andhra Pradesh	1093.00
2	Bihar	12899.09
3	Karnataka	1834.70
4	Punjab	41289.00
5	Orissa	3600

2. Chronological classification – classification of data on the basis of time (like months, years, etc) of their occurrence are called chronological classification. This type of classification is suitable for data which takes place in course of time such as population, production, sales, etc.

Ex – profit of a company from 2001 to 2005

S.No	Year	Profits (in 000 Rs)
1	2001	77
2	2002	88
3	2003	89
4	2004	94
5	2005	99

3. Qualitative classification – under this classification, the data are classified on the basis of some attributes or quality such as sex, color, literacy, honesty, intelligence, religion, etc. In this the attributes cannot be measured. This sort of classification is known as descriptive classification.

For example, Population can be divided on the basis of marital status as married or unmarried etc.

4. Quantitative classification – quantitative classification states that classification of data according to some characteristics that can be measured such as height, weight, income, sales, profit, etc.

Ex – students are classified according to weights

S.No	weight	No. of students
1	30-40	77
2	40-50	60
3	50-60	50
4	60 - 70	20

5. Alphabetical classification – when data are arranged according to alphabetical order is called alphabetical classification

Ex – state wise classification of population in alphabetical order

S.No	Name of states	Population
1	Andhra Pradesh	157
2	Bihar	150
3	Karnataka	200
4	Punjab	700
5	Orissa	450

Tabulation is a systematic & logical presentation of numeric data in rows and columns, to facilitate comparison and statistical analysis. The method of placing organized data in tabular form is known as tabulation. Tabulation simplifies complex data and facilitates comparison.

Definition

“Table involves the orderly and systematic presentation of numerical data in a form designed to elucidate the problem under consideration” – According prof. L.R Connor

“Table in its broadest sense is an orderly arrangement of data in column and rows” – According to Prof M.M.Blaire

Objectives of tabulation

It simplifies the raw data in meaningful form so that common man can easily understand in less time

It brings essential facts in clear and precise manner

Data presented in rows and columns helps in detailed comparison

Tables serve as the best source of organized data for further statistical analysis

Table saves the space without sacrificing the quality and quantity of data.

Parts of table

Table number	A serial number should be allotted to a table
Title of the table	Every table should be given a title. The title is the description of the content of table.
Caption	Caption refers to the column headings. Caption should be clearly defined and placed at the top of the column.
Stub	Stub refers to row headings. Stubs heading perform for the horizontal rows of the numbers in the table
Body	Body contains the information. Data presented in the body should be arranged according to the classification of stubs and caption.
Head note	Something that is not explained in the title, caption, and stubs can be explained in the head notes on the top of the table below the title. It is generally given in brackets
Source note	It is a brief statement indicating the source of data presented in the table.
Footnote	Some exception in the data can be given in the foot notes. Footnotes are placed below the body of the table.

Types of tabulation

Kinds of Tables
According to
Purpose
According to
Originality
According to
Construction
General
Purpose
Table
Sp...

According to purpose

General purpose table – general purpose table is a table which is of general use. It does not serve any specific purpose under consideration

Special purpose table – special purpose table is prepared with some specific purpose in mind.

2. According to originality

Original table – an original table is that table in which data are presented in the same manner in which they are collected.

Derived table – a derived table is that in which data is not presented in same manner in which they are collected. Here the data are first converted into ratio or percentage and then presented.

3. According to construction

Simple table – simple table also known as one-way table. Under this data are presented based on one characteristic

Faculty wise library user

Complex tables – in complex table data are presented according to two or more characteristics simultaneously.

The complex tables are

two way,

three-way table and

manifold table

Two-way table – Under this the variable under study is divided into two characteristics

Three-way table - Under this the variable under study is divided into three characteristics

Manifold table - Under this the variable under study is divided into large number of characteristics.

Key Takeaways:

Table in its broadest sense is an orderly arrangement of data in column and rows.

It simplifies the raw data in meaningful form so that common man can easily understand in less time.

REFERENCE:

B.N Gupta – Statistics

S.P Singh – statistics

Gupta and Kapoor – Statistics

Yule and Kendall – Statistics method

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