तथ्याङ्क १२ कक्षा with numerical

What is statistics? Explain its importance and limitation

The word statistics ha been derived from Latin word ‘status’ the Italian word statista ‘ or the German word
‘statistik ’ and all these word mean data about nations . Different writers had defined statistics in different mays .
All these definitions are grouped into two categories : singular definition and plural definition of statistics

Singular definition of statistic

In singular sense , statistics has been taken as a science . Various writers such s A.L Bowley secrists croxton and
cowden has denied statistic in singular sense . But the definition given by crotons and Cowden is more scientific .
According to croxton and cowden . “ statistica may be defined as the science of a collection, Presentation ,analysis
and interpretation of numerical data

Plural Definition of statistics

In plural dene ,statistic has been taken as numerical data . Different writers have defined statistics in plural sense
lime Webster, Bowley , Horace secrest . But the definition given by Horace secrets’ is more scientific. According to
him . “statistics may be defined as the aggregate of facts , affected to m marked extent by multiplicity of causes,
numerically expressed , enumerated or estimated according to a reasonable standard of accuracy , collected in a
systematic manner for a pre-determined purpose and place in relation each other.”

Importance of statistics

in ancient period , statistics was used only for the state affairs , But, now its importance has been extended in
multiple field of human life as described below

1) Statistics in planning
This is the age of planning . Every individuals, organization , government are planning to achieve their goal . For
efficient planning: reliable, accurate and more predictable statistical methods are needed so , statists is
important in planning

2) Statistics in economics
Statistical data and techniques are useful in various field of economics like- production , consumption ,
distribution , wage, prices ,etc . likewise , index numbers , demand analysis and forecasting technique are some
tools of statistics which are frequently sued in economics

3) Statistics in business
Business forecasting , pricing ,investment decision , production decision etc in business are possible only suing
statistics and statistical tools . so, statistics acts as the best facilitator in modern business age

4) Statistics in mathematics
Statistics is branch of applied mathematics which specializes in data, Statistics depends upon mathematics and
mathematics also depend on statistics while formulating mathematical models

5) Statistics in social science
Every social phenomenon’s affected by multiple factors. Statistical tools such as regression and correlation
analysis’s can be used to a study such phenomenon likewise, one of the important part of sociology is
demography which relies on the use of statistics

6) Other additional importance
Statistics in pure science and statistics in education etc

Thus , statistics , in modern age is important in multiple fields of human life

Limitation of statistics: The limitations of statistics are as follows
1) Statistics does not study individuals: statistics deals with aggregate objects and does not give any specific
information to the individual items of a series. Individual items do not constitute statistical data and they are
meaningless for statistical enquiry.
2) Statistical laws are not exact: unlike the law of physical and natural sciences, statistical laws are only
approximation and not exact. There are only few results which area accurately correct in statistics and
almost all re approximately correct.
3) Statistics is not suitable to study of qualitative phenomenon: statistics always studies the quantitative
characteristics of given problems instead of qualitative characteristics. The problems which are relate to the
quantitative phenomena like honesty, poverty leadership , intelligence are not directly studied in statistics
4) Statistics is liable to be misused : statistic must be analyzed and used by exports in the field of study . very
fallacious conclusion and fatal results may come from the hand of inexperienced and untrained person. The
data may be manipulated for self interest.
5) Statistics is only a means : statistics provides a method , facilitate supplements for conclusions to their
discipline . so, statics is a mean.

Explain the importance of statistics in economics

Statistics presents facts quantitatively, facilities comparison, help in testing hypothesis , simplifies the
complexities . So, the importance of statistics in economics is discussed below:
1) Economics theories: - statistics is used for formulating, testing and giving empirical support to economic law ,like
law of demand , law of consumption .
2) Economic problems: all the countries of world are facing economic problems. Inflations, over population, poverty ,
unfavorable balance of payment , income inequality ,trade cycle economic growth are burning issues of modern
economics. statistics provides statistics tools like index number, probability ,regression. correlation for solving
burning issues and problems of resources allocation.
3) Economic policy formulation:-Statistics help government to formulate various economic policies like fiscal policy,
monetary policy ,industrial policy , export policy , import policy , interest rate policy ,exchange rate policy to the
problems of an economy.
4) Budget is a detailed statistical statement of receipts and expenditure of government in the coming year. So,
statistics guide a budget.
5) Preparing national income account: the collection and classification of data regarding income, consumption ,
saving investment , export , imports , taxation etc are required for preparing national income account.
Information about this account helps to forecast and know the structure of economy.

Functions of statistics

Statistics specialize in the numerical data. So, statistics is very useful tools for natural and social science.

The major function of statistics is discuss below

1) Presents facts quantitatively: statistics helps to present facts, analyze the facts ,and interpret the available data
. It gives the more precious and concrete results.

2) Simplifies the complexities: The raw, crude, initial data can be present, analyze and interpret by means of
statistical tools. These presented analyzed and interpreted data are simple to understand. So statistics simplifies
the complex data

3) Facilities comparison: statistics presents facts numerically. Statistical tools like mean median mode dispersion
help to compare. So, statistics help to compare different countries and different time of same countries.

4) Helps to formulate the policy: Any policy or plan are formulate by evaluation of past, condition of present and
future expectation Any plan and policy are formulate by analyzing the different variable and comparing
different variable . Policies can be tested by empirically with statistics

5) Help in forecasting: Forecasting tools and idea are very useful in different field of natural and social science.
Numerical facts about different time, place, situation can be analysis zed with the help of time series
,probability ,regression ,correlation .Trend patterns relation can be find and forecast for future.

6) Formulating or testing hypothesis: hypothesis is a tentative statement it may be true and false . the trueth value
of statement can be empirically tested by statistical tools .If it is false it is rejected and new hypothesis is
formulated. It formulates principles and test principles.

 Explain the singular and plural definitions of statistics .

In singular sense , statistics has been taken as a science. Various writers such as A.L. Bowley , secrits ,Croxton and
Cowden have defined statistics in singular senses, But the definition given by croxton and cowden is more scientific.
According to croxton and cowddden "statistics may be defined as the science of collection, Presentation ,analysis and
interpretation of numerical data

This definition divides the statistics following parts

Singular definition

1) Collection of data : the initial stage of any statistical enquiry is collection of data .The methods of data collection like
primary and secondary , census and sampling etc are related with this . The accuracy of result generally depends on
the accuracy of the collected data .

2) Presentation of data :- the collected data are scrutinizes and edited from the raw data . They are organized and
presented in suitable form of tables or diagrams or graphs .

3) Analysis of data : the process of data presented in the above step leads to analysis of a data . Average . dispersion
,correlation regression, index numbers etc are tools of a analysis in statistics . These methods' help to give better
picture of the collected data .

4) Interpretation of data :-the final step consists of drawing conclusion from the collected and analyzed data. It need a
high degree of skill, care , judgments etc.

Plural definition of statistics

In plural senses , statistics has been taken as numerical data .different writers has defined statistics in plural sense like
Webster, bowley Horace secrist . But the definition given by Horace secrets is more scientific according to him "
statistics may be defined as the aggregate of facts, affected to marked extent by multiplicity of causes, numerically
expressed , enumerated or estimated according to reasonable standards of accuracy , collected in systematic manner for
a predetermine purpose and placed in relation to each other

Features of plural definitions :

1) Statistic are aggregate of facts: - in statistic the single numerical figure has no meaning. The figure of births, deaths,
sales, production etc over different times and place will constitutes statistics.

2) Statistics are numerically expressed: -the values of statistics are countable as well as numerically expressed. All
numerical data are not statistics. But all statistics are numerical data.

3) Statistics are affected by multiplicity of causes: - statistical data are generally affected by a number of factors
related with it. For example, the production of crops is affected by types of seeds used, fertilizer, and irrigation.
Methods of farming.

4) Enumerated or estimated according to reasonable standard of accuracy: - enumeration is the study of all the
elements in the study area and gives more accurate result. Estimination is the process of approximating the data on
the basis of samples. These two methods can be used on the requirements of reasonable standard of accuracy.

5) Collected in systematic manner: - the collections of data should be in a systematic manner according to
predetermined planned in respect of choice of field, choice of manpower , choice of method of data collection etc.
Unsystematic manner of data collections may mislead to the result.

6) Statics are collected for pre- determined purposes: the purpose of collecting data should be decided in advance. The
purpose should be specific and well defined.

7) Comparable: - the data or statistics should be comparable, which means the should be able to be placed in relation
to each other.

Use of statistics in economics

Economics is multidimensional and multivariable .Statistics provides the tools to collects data , analysis the relation and
interpreted the results . So statistics is useful tools for economics .

Some major uses of statistics in economics are

1) To study economics variable: Economic variable or issues are affected by different factors . Statistics quantifies
the variables and test empirical uses . Regression correlation dispersions , index numbers time series are some
examples of statistical tools .

2) To study economic problems:- Statistics helps to study empirically, collect the facts, analysis dada for modern
economic problems like inflation ,unemployment ,economic growth economic development , national income
,trade cycle .To solve these problem , we need analysis of relation ,estimation for future ,generalization of
results ,development of principle, empirical evidence. Statistics provides these facilities. so economic is very
useful for the economics .

3) Use of diagram : The uses of diagram makes the study of economics more easier , faster and interesting
.Different types of diagram like pie char , bar chars are used in economics

4) Statistics helps the government to makes various economic policies like fiscal policy export and import policy
interest rate policy employment policy etc . It helps to solve the existing problems in the nation

5) To formulate the economic planning :- Statistics takes the data from the past . Generalize for the present .
Estimate and forecast the future. Statistics study trend patterns. Statistics test the hypothesis . So statistics
help to formulate accurate , reliable , more predictable, applicable and result oriented planning .

6) Development of econometrics: Application of statistics in economics is developing separate field of study
economics. Many econometric methods and models are useful . So , they are rewarded by Nobel prize in
economics

Collection of data

The process of enumerating or counting the items in systematic way is called collection of data .Pre-requisite of data
collection

i) Objectives' of study: Data cannot be collected without objective. Data collection without objective is haphazard
Random work, aimless, word, wastage of money time and resources.

ii) Scope of enquiry: scope of inquiry means coverage of study study area subject matter and geographical area.
So scope of enquiry should be clear before the data collection

iii) Units of data collection: units of data collection help to systemize the data collection procedures. It help to
analyze the data. Kilogram hours meters are some examples of units of data .

iv) Source s of information: Data are collected from different resources like primary and secondary sources.
Specification of sources of information gives clear procedure to investigator to collect data functionally.

v) Method of data collection: According to nature of data objective scope size, census or sampling method can be
used. Method of data helps to present and analysis the data

vi) Degree of accuracy: Degree of accuracy should be determined in the beginning. Degree of accuracy helps to
choose the method and other tools of statistics .

vii) Types of enquiry : Statically enquiries may be of different types such as official, semi-official , semi-official ,
confidential, non-confidential, regular ad-hoc.

Define and distinguish between primary and secondary data

On the basis of source of data, there is two type of data i) primary data ii) secondary data

Primary data: when the data are collected for first time by investigator or an agents of investigator then it is called
primary data. Primary data are first hand data and original in nature .The sources of primary data are census and survey.

Secondary data :- the data which are collected by someone for their own purpose but uses by some other person or
organization are called secondary data .

Difference between primary and secondary data

Primary data Secondary data
Data collected for the first time from the field of study Data that are already collected and used by others can be
are called primary data useful for other investigators are called secondary data
They ae second hand in nature
They are original in nature They may not fulfill all the requirements of the investigator
They fulfill all the requirement of the investigators because such data were not collected as per the
because they are collected as per the requirements of the requirement of the investigator
investigators Sometimes secondary data may not accurate coincide as
Primary data gives more accurate information about the per the objective and they may mislead the results
investigation because these are collected from the root of
the source of data Secondary data are found in readymade form just like
Primary data are like raw materials and they have to be finished goods
processed after collection These data are used from the existing sources it saves
Collection of primary data tkes a large amount of money money time and efforts
time and efforts

There is no need to worry about while using primary Secondary data should be careful and critically examined
data by the investigator before they are sued

Describe the various s methods of primary data collection .

Primary data can be collected from various methods. Some of them are discussed below
1) Direct personal interview: in this method the investigator collects the data by personally contacting the respondents

of informants . This method can provide accurate result only if the investigator and informants both are unbiased .If
there is small field of study , this method is more applicable. It is expensive method but researcher can collect other
supplementary information related with the study .
2) Indirect oral interview:- in this method the investigator contact the witness for collecting data. Witness is the third
person i.e. relatives fiends etc .In this method a wide area can be covered easily. It saves times money and effort. It
is likely to get inaccurate and unreliable information .This method is suitable when there is difficult to direct
interview .This method is also applicable . If the informants hesitate to give information.
3) information through correspondents : -correspondents are local agents appointed for collection of information in
different area . This method is very useful when area of enquiry is very wide and scattered. It saves money time and
effort . Data can be collected from well experience local agents .This method of data collection is suitable if
information is to be collected from wide area and information must be supplied in the regular basis.
4) Mailed Questionnaire-: a list of questions are called questionnaire. In this method , a list of questionnaire is send to
informants by post . Here informant are requested to fill up the questionnaire and send back to the related office of
enquiry within the mentioned time . To reduce the non response rate, postage expenses are usually born by the
investigator by sending a self addressed stamped envelope width it .
5) Questionnaire sent through enumerators. In this method the questionnaire is send to informants through
enumerator . The enumerators are appointed and trained properly and sent to meet the informants personally
along with questionnaire. Enumerators fill up questionnaire by asking questions and come back to the instigator for
further processing of the data. From this method , the more reliable and specific information can be obtained .

sources of secondary data

major sources of secondary data are a) published (b) unpublished

A)published sources: Many government offices as well as various international agencies collect data and published them
daily weekly, monthly, half yearly or yearly . Main sources of published data are

1) Governmental official: five year plan, annual economic survey , annual budget , report of CBS and bulletins of
NRB, department of ministry etc.

2) international official :Official publication of internal agencies like world Bank , IME, UN, UNDP , ILP ,WHO etc
3) Magazines newspaper report , financial and market report .
4) report of various committees and commissions
5) Publication of universities and research work .

B) Unpublished sources : - data which are collected for own purpose but which are not come out from any
sources of publication or media are known as unpublished sources .They are :
1. manuscript
2. record of privates office ,business houses, campus, universities hospital
3. research work conducted by students of universities
4. Treaty agreement, various record and report among different nation.

Precautions in the uses of secondary data

Secondary data are collected by someone and used by others .Before using secondary data , the investigator
should be caution whether these data are useful or not. The following pints should be considered in using the
secondary data.
1) Reliability of data: In the use of secondary data, the reliability of data should be examined on the basis of objective
of survey, method of collection data , agency of conducting survey ,technique of sample design , period of data
collection .
2) Suitability of data: the study nature should resemble the use of secondary data with primary data .The suitability of
secondary data for the preset investigation is examined in terms of nature , objectives' and scope of investigation.
3) Adequacy of data: the study area should not be too wide or too narrow otherwise, the findings cannot be
generalized.

Techniques o f Data Collection

There are two techniques of data collection a) census methods b) sampling method

Census method: a census inquiry implies complete enumeration of each and every unit related to the field of study. For
example, data about the population which are obtained by national census

Merits :

1) it gives complete information about the population 3) The data will be adequate for the purpose.
2) it gives more accurate and reliable information. 4) it cover the wide range of study

limitation 3) it is not suitable if it require s destroyable items

1) it requires more manpower time and budget
2) it is not applicable if the population is infinite .

Sampling Method : the representatives parts of the population is called sample .if only the representative parts of
population is investigated then such investigation is known as sampling method of data collection . For example, doctor
examines few drops of blood.

merits:1) it is less cost an less time consuming 2) it can test reliability of census 3)more trained and skilled man power
can be used for accurate information4) it is only method if census method is not suitable

demerits :1) the sample may provide wrong result .2)if investigator is biased it provide wrong conclusion3) all
population may not represents the population.

Difference between Census and Sampling Method

Census method Sampling method

A census is a technique of data collection where all the If examining only part of the whole population is used to
element of study area are enumerated collect the information , it is called sampling method
Data and information are collected from all possible Data and information are collects only from the selected
units samples
It is appropriate when the size of the population is small It is appropriate when size of population is large and
and area of study is small areas of study is large too
It requires more time money and manpower It requires less time money and manpower

It is applicable if the nature of the units of population It is applicable if the selected samples represent the
same or different of both characteristics of thee remaining population too

Methods of Sampling:

there are various methods of sampling depending upon the choice of the investigator, nature of data , objective of the

enquiry, availability of tie and financial resource. Common sampling procedures are :

a) probability sampling b) non probability sampling

Probability Sampling : under this method , each and every units of population has equal chance of selection under some
rule .Some types of probability sampling are:

1) Simple random sampling : in simple random sampling technique ,each and every units of population has an equal
and in depend chance of include in sample. generally lottery method and table of random number are used to find
sample .merits: *) it is free from persona biasness *)it save money and time *)it is more representative .Demerits :
*) difficult to get population list *)sample may not represents the population in case of heterogeneous population .

2) stratified sampling: it is used in case of heterogeneous population. The heterogeneous population is divided into
different strata and sample is taken from these strata. Merits*) it is more representative sampling *) it is more
convenient to apply *) it gives more accurate result .
Demerits :-#)the process of stratification takes more time and money .#)if the stratum are not made properly ,the
method give faulty result

3) Systematic sampling :- in this methods , a complete list of item in the population is arranged in numerical,
alphabetical or some other orders, the sampling interval is obtained by dividing the total number of items by sample
size. Then following formula is used

p,p+i,p+2i…. where p=random start , i.e. sampling interval=

merits: *) it is simple and systematic *) it takes less time and labor. Demerits: sample may not represents the

population *) it requires complete information about population.

4) Multistage Sampling : in this method sampling is done in various stage, At ,first the population is divided into large a

sample units .The sample is selected at random to get small unit of sample .Merits :*)this method is simpler and

easier to administers than other methods *) this methods is quite convenient when the area of investigator is vast.

Demerits :It is less efficient than other techniques

b) Non Probability Sampling : under this methods , selection of sample items is depend on investigator

.Judgments sampling and quota sampling are example of non probability sampling .

i) Judgment sampling: in this methods sampling is done according to the opinion, knowledge, and institution

of investigator. Merits: simple method of sampling *)quick decision for urgent need .

Demerit :*) chance of biasness *) it is not scientific

ii0) quota sampling: in this method, populations is divided into different categories on basis of certain variable

and certain number (quota) is selected as sample . It is mostly used in public opinions

Numerical part

measures of dispersion discreate continuous Coefficient
. individual
x 10 20 50 CI 0-10 10-20 20-30 30-40
E g 12,3,6,10 f6 4
f 2 15 10 19
range L-S L-S
12

L-S

QD

MD | | || ||
from | | || ||
mean
√ () √ () √ ()
MD
from
median

SD

Mean

Median ( ) () Median class=
Md=

() () Q3 class=
Q3=

Variance= coefficient of varience =

Q1) find the range and coefficient and coefficient of range

X 10 20 30 40 50 60
f 289231
solution

Largest value (L) = 60
Smallest value (S) =10
we have
Range = L-S

=60-10
=50
coefficient range =

Q 2 ) find the Quartile deviation and its coefficient from the following data
9,11,7,13,17,6,19,21,24,26,30,32

Solution
Given data is
9,11,7,13,17,6,19,21,24,26,30,32
Arranging in ascending order

6,7,9,11,13,17,19,21,24,26,30,32

N= 12

()

()

()

()

()

=( )

()
()

we have
QD =

Coefficient of quartile deviation =
Q 2 calculate the quartile deviation and coefficient of quartile deviation of the following
income distribution

Income 5000- 10000- 15000- 20000- 25000- 30000- 35000-
10000 15000 20000 25000 30000 35000 40000

No of house 7 9 13 12 8 6 3
hold

solution f Cf
Income 7
16
5000-10000 7 29
41
10000-15000 9 49
55
15000-20000 13 58

20000-25000 12

25000-30000 8

30000-35000 6

35000-40000 3

N=58

for Q1 ,

from the Cf table , Cf just greater than 14.5 is 16
Q1 class = 10000-15000
L= 10000, cf = 7 , i= 5000, f=9
we have ,

Q1=

=

for Q3

from the CF table , Cf just greater than 43.5 is 49
Q3 class = 25000-30000

L= 25000 , Cf = 41 , I = 5000, f= 8
we have ,

Q3=

=

=26562.5
Quartile deviation is given by

Coefficient of QD is given by

Questions

calculate the mean deviation from the mean

Marks 2,3,5,6,5,8,9
solution

Marks (X) ||

2 -3.42 3.42

3 -2.42 2.42

5 -0.42 0.42

6 0.58 0.58

5 -0.42 0.42

8 2.58 2.58

9 3.58 3.58

||

we have ,

we have ,
MD from mean = | |

Question 30
find the mean deviation form mean 3

X 10 15 20 25 | ||

f5 44 4
solution fx |
XF

10 5 50 9

15 4 60 4 16
4
20 4 80 1 24
33
25 4 100 6
|
30 3 90 11

|

we have ,

we have ,
MD from mean = | |

Coefficient MD=

Question
Calculate the mean deviation from the mean for the following
data

Class 2-4 4-6 6-8 8-10

f 342 1

Solution |

Class F m fm | ||

2-4 3 3 9 2.2 6.6
4-6 4 5 20 0.2 0.8
6-8 2 7 14 1.8 3.6
8-10 1 9 9 3.8 3.8

N= 10 ||
We have ,

Again we have

||

Find the mean deviation from the median

Marks : 10,15,20,25,30,40,50,20,25,20
Arranging in ascending order
10,15,20,20,20,25,25,30,40,50
N = 10
we have ,
median = ( )

()

median =
To calculate MD from median
X |X-median|
10 12.5
15 7.5
20 2.5
20 2.5
20 2.5
25 2.5
25 2.5
30 7.5

40 17.5 |

50 22.5 |

|
We have ,

|

MD from median =

Coefficient of MD from median =

Questions

find the mean deviation from median 60
X 10 20 30 40 50

F2 39 21 11 5 |
solution Cf | ||
XF

10 2 2 30 60

20 3 5 20 60

30 9 14 10 90

40 21 35 0 0

50 11 46 10 110

60 5 51 20 100

N=51 ||

Median =( )

from Cf table , Cf just greater than 26 is 35
so , median = 40
we have ,

| |

Coefficient of MD =

find the MD from median

Scores 140-150 150-160 160-170 170-180 180-190 190-200
8 10 15 8 3
frequency 4

Solution cf
Scores F

140-150 4 4

150-160 8 12

160-170 10 22

170-180 15 37

180-190 8 45

190-200 3 48

N=48
for Median ,

from above CF table , cf just greater than 24 is 37
Median class = 170-180
L= 170, cf=22, f=15, i= 10

Md=

Find the SD from the following data
Income :500,1000,1500,1200,2000,2500
solution

X

500 250000

1000 1000000

1500 2250000
1200 1440000
2000 4000000
2500 6250000

we have

√ ()

√ ()

find the standard deviation of the following data
X 5 7 8 10 12
f 7 8 10 11 9

Solution fx
XF

5 7 35 25 175
49 392
7 8 56 64 640
100 1100
8 10 80 144 1296

10 11 110

12 9 108

N=45

() √ ()

=√ ()
=

Find the standard deviation of the following data

Income 0-20 20-40 40-60 60-80 80-100 100-120
8
Families 6 7 8 9 12

solution

Income F M Fm
0-20 6 10 60 100 600
20-40 7 30 210 900 6300
40-60 8 50 400 2500 2000
60-80 9 70 630 4900 44100
80-100 12 90 1080 8100 97200
100-120 8 110 880 12100 96800

we have ()
() √

Laspeyres and paasche's Formula for price index
1. Laspeyres price index =

2) Paasche's price index =

Question
find the price index by using
a. Laspeeyres method
b. paasches method

commodity 20 03 20 04
quantity price quantity price
A 50 300 56 560
B 100 200 120 240

C 60 240 60 360
30 300 24 288
D
Solution 2003 2004

Commodity

A
B
C
D

For Paasche’s method of finding price index

Commodity 2003 2004

A 50 300 56 560 31360 16800

B 100 200 120 240 28800 24000

C 60 240 60 360 21600 14400

D 30 300 24 288 6912 7200

=8867 =62400

We have ,

Paasche's price index =

= =142.

Laspeyres and paasche's Formula for quantity index
1. Laspeyres price index =

2) Paasche's price index =