Statistics

Prepared By
M.RajaSekhar Reddy
MSIM, Proddatur
UNIT -1
1. Define statistics? Importance limitations of statistics?
Ans:
Definitions:
According to A.l.bowley:
Statistics is the science of counting numerical facts
Or
Statistics is the science of the averages
According to Boddingtons:
Statistics is the science of estimations and probability
Importance of statistics:
The use of statistics is very wide. It used in all
departments like industry, commerce, trade, economic, physics, chemistry and all
other subjects. The usefulness of statistics is as follows:
1. Government:
Every government needs statistics relating to the various aspects of
the social and economic conditions of people.
2. Economics:
All branches of economics like production, consumption, exchange and
distribution are describe, compared and correlated with the aid of statistics.
3. Business and commerce:
The businessman should be able to take correct decisions
at the correct time. So correct decisions are possible with reliable facts and figures.
The reliable facts and figures are coming with statistical investigation only.
4. Industry:
In industries the statistics are used to find out the quality level of the
production.
5. Mathematics:

Prepared By
M.RajaSekhar Reddy
MSIM, Proddatur
Statistics is the branch of mathematics. Some statistical tools like
probabilities, mathematical averages, co-efficient, graphs are also used in
mathematics also.
6. Sciences:
In the physical science, natural science like astronomy, geology and
physics, medicines, zoology, botany, agriculture etc are also using the statistical
methods.
7. Planning:
Every plan must be depend on the accurate data, that data collecting by
deferent statistical methods.
From the above we clear that statistics has huge scope to
applicable in any where
2. Write the limitations of statistics?
Ans:
Limitations of statistics:
The statistics has some important limitations, which are
follows:
1. It doesn’t applicable for individuals:
Statistics laws are true on average. Statistics are aggregates of facts. So
single observation is not a statistics, it deals with groups and aggregates only.
2. It can applicable on quantitative measures:
Statistical methods are best applicable on quantitative data not best to
applicable on qualitative data.
3. Statistics cannot be applied to heterogeneous data:
The statistical data con not apply to the various aspects.
4. Statistics can be misused:
It sufficient care is not exercised in collecting, analyzing and
interpretation the data, statistical results might be misleading.
5. It can be used by experts only:

Prepared By
M.RajaSekhar Reddy
MSIM, Proddatur
Only a person who has an expert knowledge of statistics can handle
statistical data efficiently.
6. Sometimes wrong decisions are taken:
Some errors are possible in statistical decisions. Particularly when the
wrong data was collected.
3. What is statistical investigation? What are the steps involved in a
statistical investigation?
Ans:
Investigation:
Investigation or Inquiry means a search for truth or knowledge or
information.
Statistical investigation (or) statistical inquiry:
Statistical investigation is also known as statistical survey. Statistical
investigation is a process collecting, classifying, presenting, analyzing and
interpretation of data.
The statistical investigation or inquiry is conducted by a specialized
agency like governments, companies with the help of a person.
Steps of statistical investigation:
The statistical investigation or survey is a process. So it
contains several steps, which are follows:
1. Collection of data
2. Classification and tabulation of data
3. Presentation of data.
4. Analysis of data.
Statistical investigator:
Statistical investigator is a person, who conducts the inquiry.

Prepared By
M.RajaSekhar Reddy
MSIM, Proddatur
Q) What do you mean by primary data? What are the various methods used in
collecting primary data?
Ans:
The first step in the conduct of a statistical investigation is
collection of data. The data may be collected by the investigators from the
respondents. Initially the investigator reaches the respondents and asking some
questions according to their questionnaire.
Meaning of Primary Data:
Primary data is collected by the investigator for the
first time. It is also known as raw data. It will be collected for a specific purpose.
Definition:
According to Wessel:
Data originally collected in the process of investigation
are known as primary data.
Respondents:
The persons from whom the information is collected
are known as “respondents”.
Statistical investigator:
Statistical investigator is a person, who conducts the inquiry.
Questionnaire:
Questionnaire is a form, it contains list of questions related
to survey

Prepared By
M.RajaSekhar Reddy
MSIM, Proddatur
Methods of collecting primary data:
There are various methods to collect the primary data
.which are follows:
1. Direct personal investigation.
2. Indirect personal investigation
3. Investigation through questionnaire.
4. Investigation through questionnaire sent to enumerator
1. Direct personal investigation:
In this method, the investigator collects the data
personally, by meeting the concerned persons. The investigator contact directly
and get information directly. This method is accurate.
Advantages:
 It will be more accurate
 The response will be more
 Supplementary information is useful for final results obtained.
 The communication gap can be filled by choosing the right words for the
questions
 There is uniformity in the collection of data.
Disadvantages:
 This method is very costly
 It is very time consuming
 It requires extra personal qualities of the investigator
 It can be used in only small area.
2. Indirect personal investigation:
Investigator appoints local agents to different parts of the
investigation and these local agents collect the data and pass it to the investigator
time to time. This method is suitable when the area of the investigation is large
and large amount of data can be collected.
Advantages:
 The investigator take the help of local agents

Prepared By
M.RajaSekhar Reddy
MSIM, Proddatur
 It is simple and convenient method of investigation
 It is economical
Disadvantages:
 Passing information may not be reliable
 Some time the enumerators (local agents) will collect the un-useful data or
wrong data.
3. Investigation through questionnaire:
Under this method a questionnaire is prepared and sent to
respondent through post or e-mail. The questionnaire contains questions, which
are related to the enquiry. The respondent has to answer the questions and
return to surveyor or investigator.
Advantages:
 Wide coverage is possible
 It saves time
 It is economical and cheapest cost
 Information gathered directly with less error.
Disadvantages:
 Information can get literates only
 It involves uncertainty response
 It is not possible to get reply within time
 If the questionnaire is complex, it may not be responded.
4. Investigation through questionnaire sent to enumerator:
Under this method the enumerators are appointed by the
investigators and the enumerators can make the survey based on the
investigators questionnaire.
Advantages:
 Information can be collected even from illiterates
 It will be more reliable and accurate
 It covers wide area
 Personal contact is there
Disadvantages:

Prepared By
M.RajaSekhar Reddy
MSIM, Proddatur
 It is costly, because enumerates has to paid
 It is suitable for the big organization
 Lack of training to enumerators.
Q) What do you mean by secondary data? What are the various methods
used in collecting secondary data?
Ans:
Secondary data:
Secondary data are collected from already existing sources. The
investigator can gather information from the other persons. Whenever there is
no possibility to collect the information in primary source than we has approach
the secondary data gathering methods. The secondary data can be classified into
two categories. There are
1. Published data
2. Unpublished data.
1. Published data:
The published data may be obtained from various
international, national, local publications. Which collect statistical data relating to
business, price, consumption, production, agriculture etc and publish their
findings in statistical reports on regular basis , i.e. , monthly, quarterly, annually
etc. the following are some of important published sources of secondary data.
Which are
1. Government publications
2. International publication
3. Semi-official publications
4. Private publications
Government publications:
The following are various government organizations which collect and publish
statistical data on various fields.
 Central statistical organization (CSO)
 National sample survey organization (NSSO)
 Census commissioner of India
 Directorate of economics and statistics ,etc
International publications:

Prepared By
M.RajaSekhar Reddy
MSIM, Proddatur
Various foreign governments and international agencies like UNO, World
Bank, international monitory fund (IMF) regularly publish reports on the data
collected by them on various aspects.
Semi-official publications:
Various local bodies such as district boards, municipal corporations,
banking organizations, etc. This type of publications providing information about
various events in local areas.
Private publications:
The following private publications may also used as secondary sources of
data .such as
 Annual reports of private banks
 Information published in news papers, books, magazines, etc.
 Reports prepared by the research scholars of the university.
2. Unpublished data:
Unpublished data collected by private institutions may not have
been published for various reasons. Such unpublished data may be given on
request.
Example:
Annual reports of organizations, diaries, letters, autobiographics, etc
Q) What is the meaning of questionnaire? What are the features of good
questionnaire?
Ans:
Questionnaire:
Questionnaire is a form, it contains list of questions related
to survey

Prepared By
M.RajaSekhar Reddy
MSIM, Proddatur
Meaning of questionnaire:
A questionnaire is a research instrument consisting of a series
of questions and it prompts for the purpose of gathering information from
respondents.
Generally the questionnaire is used in primary data collection methods. By
using the questionnaire, the investigator can easily get the required information
from the respondents.
Merits:
 The questionnaire method is very economical when the survey area is too
wide.
 The data may be collected conveniently from the rural and remote areas
 The data is more reliable.
 By using questionnaire the surveyor or investigator can get the
information very speedily and accurately
 With the help of the questionnaire the investigator can easily cover the all
aspects or the questions related to survey.
Demerits:
 Sometimes respondents may not return the questionnaire
 This method can’t be used for illiterates.
 Once the questionnaire are sent to the respondents, the investigation
agency can’t change or modify the questions
 This method is not flexible. In case of inadequate or incomplete answers
 Sometimes this is most time consuming because some of the respondents
can take their feasible and sufficient time to return the questionnaire
Features of good questionnaire:
In order to make the questionnaire more effective, we must be very
carefully prepared. The following are the qualities of a good questionnaire.
1. The size of the questionnaire should be small as much as possible.
2. It should be simple, clear
3. The questions should be brief
4. The questions should be arranged in a logical order.

Prepared By
M.RajaSekhar Reddy
MSIM, Proddatur
5. Questions may be yes or no type or multiple choice and not of lengthy
answers.
6. Appropriate answer choices should be given.
7. The case of sensitive and personal nature of questions should be avoided.
Q) What is the meaning of schedule?
Ans:
Schedule:
A schedule is also like a questionnaire it contains various questions
related to the survey but the schedule is filled by enumerators only.
In this method, a team of enumerators is selected and a special
training will be given to them. Now the enumerator’s fill up the schedule. The
only difference b/w schedule and questionnaire method is that schedules are
filled by the enumerators but questionnaire is filled by the respondents.
In schedules a special team of enumerators is appointed for
recording the answers given by respondents. The enumerators explain clearly
the objective of survey as well rules. Census is usually conducted by using this
method.
Merits:
1. This method for illiterate population or respondents.
2. The data collected by this method is more accurate and reliable.
3. In this method information given by respondents but cross verified by
enumerators
4. Non response in this method is very little
5. The identity of the respondent is known in this method.
Demerits:
1. It is more expensive method compare with other methods of collecting
primary data.
2. It is more time consuming
3. The success of this method is mainly based on the enumerator’s skills and
efficiency.
Explain about tabulation of data?
Ans:
The process of placing classified data into tabular form is known as
tabulation. A table is a symmetric arrangement of statistical data in rows and
columns. Rows are horizontal arrangements whereas columns are vertical

Prepared By
M.RajaSekhar Reddy
MSIM, Proddatur
arrangements. It may be simple, double or complex depending upon the type of
classification.
Types of Tabulation:
There are three types of statistical tables depending on the
objectives and uses of data. Which are
 Simple Tabulation (or) One-way Tabulation
 Double Tabulation (or) Two-way Tabulation
 Complex Tabulation
 Special purpose (or) summary Tabulation
Simple Tabulation (or) One-way Tabulation:
When the data are tabulated to one characteristic, it is
said to be simple tabulation or one-way tabulation.
Example:
The data of students studied in different years of a college
represented in simple tabulation
Year No. of students
1998-1999 100
1999-2000 150
2000-2001 175
2001-2003 400
Double Tabulation (or) Two-way Tabulation:
When the data are tabulated according to two characteristics
at a time. It is said to be double tabulation or two-way tabulation.
Male Female
1998-1999 60 40
1999-2000 75 75

Prepared By
M.RajaSekhar Reddy
MSIM, Proddatur
Example: The data of
students studied in different years
according to sex of a college represented in Double tabulation
Complex Tabulation:
When the data are tabulated according to many characteristics, it is said to
be complex tabulation.
Example:
The data of students studied in different years according to sex and
marital status of a college represented in complex tabulation
Special purpose (or) summary Tabulation:
When the data tabulated for a specific purpose, mostly
this type of tables are used to comparison. These tables are also called text tables.
Generally these tables indicate rates, percentages, averages etc.
Example:
The numbers of sales in two companies of same product are displayed
in the following table.
Year Avg. sales of company A Avg. sales of company B
2000-2001 75 100
2001-2003 200 200
Male Female
1998-1999 58 2 35 5
1999-2000 70 5 65 10
2000-2001 60 15 80 20
2001-2003 185 15 160 40

Prepared By
M.RajaSekhar Reddy
MSIM, Proddatur
(in lakhs of Rs) (in lakhs of Rs)
2008 152 148
2009 122 123
2010 170 165
2011 182 190
Explain about classification of data?
Ans:
Classification of data:
The process of arranging data into homogenous group or
classes according to some common characteristics present in the data is called
classification. This helps separating the characters have similarities and
dissimilarities.
Methods of classification:
There are two methods or types of classification, which
are
 Classification according to attributes
 Classification according to variables
Classification according to attributes:
An attribute is a qualitative characteristic which can be
measured quantitatively only as presence or absence of the characteristic.
Example:
Intelligence, beauty, etc
There are two types of classification of attributes.
Simple classification (one way classification):
In simple classification, the data is classified on the basis of
only one attribute.
Example:
Intelligence is one attribute, and then the classification may be
represented in the following diagram.

Prepared By
M.RajaSekhar Reddy
MSIM, Proddatur
Manifold classification (Two way classification):
In this classification, the data is classified on the basis of more
than one attribute.
Example:
Two attributes intelligence and sex of a group of persons may be
classified as shown diagram.
Classification according to variables:
Variables are quantifiable characteristics of data which can be
measured numerically.
Example:
Age, height, weight, marks, etc.
There are three types of classification of variables. Which are
 Univariate frequency distribution
 Bivariate frequency distribution
 Multivariate frequency distribution
Univariate frequency distribution:
Sex
Male
Average Good Excellent
Female
Average Good Excellent
Intelligence
average good excellent

Prepared By
M.RajaSekhar Reddy
MSIM, Proddatur
The frequency distribution is formed with one variable is
called univaiate frequency distribution.
Example:
The students in a class may be classified on the basis of variable
height of them.
If the height of the students are
151,142,184,171,132,181,121,163,165,172,182,173,191,127,133,136,
147,156,129,136,134,166,159,152,156,187,137,139
Height as class interval Tally marks No.of students (frequency)
120-130 ll 2
130-140 llll l 6
140-150 ll 2
150-160 llll 5
160-170 lll 3
170-180 lll 3
180-190 llll 4
Bivariate frequency distribution:
The frequency distribution is formed with two variable
is called bivaiate frequency distribution.
Example:
If a frequency distribution shows two variables like marks in
statistics and age groups of the students.
Mark in
statistics
Age groups
18-20 20-22 22-24
0-10 ll l lll
10-20 - ll -
20-30 - lll llll
30-40 lll lll lllll
40-50 ll ll llll
Multivariate frequency distribution:
The frequency is formed with more than two
variables is called multivariate frequency distribution.

Prepared By
M.RajaSekhar Reddy
MSIM, Proddatur
Example:
The students in a class may be classified on the basis of marks, age
and sex.
Mark in
statistics
Age groups
18-20 20-22 22-24
Male Female Male Female Male Female
0-10 l l l - l ll
10-20 - - ll - -
20-30 - - ll l lll ll
30-40 l ll - lll llll l
40-50 ll - l l ll ll

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