Stat Term Paper.docx

8/17/2019 Stat Term Paper.docx

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Table of ContentsIntroduction............................................................................................................. 2

Meaning and defnitions o statistics..................................................................3

Types o data and data sources............................................................................5Types o statistics...................................................................................................7

Scope o statistics..................................................................................................9

Importance o statistics in business..................................................................11

Limitations o statistics.......................................................................................13

Conclusion..............................................................................................................16


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Introduction‘Statistics’ means numerical information expressed in uantitati!e terms.

T"is information ma# relate to ob$ects% sub$ects% acti!ities% p"enomena% or

re&ions of space. 's a matter of fact% data "a!e no limits as to t"eir

reference% co!era&e% and scope. 't t"e macro le!el% t"ese are data on &ross

national product and s"ares of a&riculture% manufacturin&% and ser!ices in

()* +(ross )omestic *roduct,. 't t"e micro le!el% indi!idual -rms%

"osoe!er small or lar&e% produce extensi!e statistics on t"eir operations.

T"e annual reports of companies contain !ariet# of data on sales% production%

expenditure% in!entories% capital emplo#ed% and ot"er acti!ities. T"ese data

are often -eld data% collected b# emplo#in& scienti-c sur!e# tec"niues.

/nless re&ularl# updated% suc" data are t"e product of a one0time eort and

"a!e limited use be#ond t"e situation t"at ma# "a!e called for t"eir

collection. ' student nos statistics more intimatel# as a sub$ect of stud#

lie economics% mat"ematics% c"emistr#% p"#sics% and ot"ers. t is adiscipline% "ic" scienti-call# deals it" data% and is often described as t"e

science of data. n dealin& it" statistics as data% statistics "as de!eloped

appropriate met"ods of collectin&% presentin&% summari4in&% and anal#4in&

data% and t"us consists of a bod# of t"ese met"ods.


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Meaning and defnitions o statisticsn t"e be&innin&% it ma# be noted t"at t"e ord ‘statistics’ is used rat"er

curiousl# in to senses plural and sin&ular. n t"e plural sense% it refers to a

set of -&ures or data. n t"e sin&ular sense% statistics refers to t"e "ole

bod# of tools t"at are used to collect data% or&ani4e and interpret t"em and%

-nall#% to dra conclusions from t"em. t s"ould be noted t"at bot" t"e

aspects of statistics are important if t"e uantitati!e data are to ser!e t"eir

purpose. f statistics% as a sub$ect% is inadeuate and consists of poor

met"odolo% e could not no t"e ri&"t procedure to extract from t"e data

t"e information t"e# contain. Similarl#% if our data are defecti!e or t"at t"e#

are inadeuate or inaccurate% e could not reac" t"e ri&"t conclusions e!en

t"ou&" our sub$ect is ell de!eloped.

'.. ole# "as de-ned statistics as +i, statistics is t"e science of countin&%+ii, Statistics ma# ri&"tl# be called t"e science of a!era&es% and +iii, statistics

is t"e science of measurement of social or&anism re&arded as a "ole in all

its manifestations. oddin&ton de-ned as Statistics is t"e science of

estimates and probabilities. 8urt"er% .. :in& "as de-ned Statistics in a

ider context% t"e science of Statistics is t"e met"od of $ud&in& collecti!e%

natural or social p"enomena from t"e results obtained b# t"e anal#sis or

enumeration or collection of estimates.

Seli&man explored t"at statistics is a science t"at deals it" t"e met"ods of

collectin&% classif#in&% presentin&% comparin& and interpretin& numerical data

collected to t"ro some li&"t on an# sp"ere of enuir#. Spie&al de-nesstatistics "i&"li&"tin& its role in decision0main& particularl# under

uncertaint#% as follos statistics is concerned it" scienti-c met"od for

collectin&% or&ani4in&% summa risin&% presentin& and anal#4in& data as ell

as drain& !alid conclusions and main& reasonable decisions on t"e basis

of suc" anal#sis. 'ccordin& to *rof. ;orace Secrist% Statistics is t"e a&&re&ate

of facts% aected to a mared extent b# multiplicit# of causes% numericall#

expressed% enumerated or estimated accordin& to reasonable standards of

accurac#% collected in a s#stematic manner for a pre0determined purpose%

and placed in relation to eac" ot"er.

8rom t"e abo!e de-nitions% e can "i&"li&"t t"e ma$or c"aracteristics of

statistics as follos

+i, Statistics are t"e a&&re&ates of facts. t means a sin&le -&ure is not

statistics.8or example% national income of a countr# for a sin&le #ear is not

statistics but t"e same for to or more #ears is statistics.


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Types o data and data sourcesStatistical data are t"e basic ra material of statistics. )ata ma# relate to an

acti!it# of our interest% a p"enomenon% or a problem situation under stud#.

T"e# deri!e as a result of t"e process of measurin&% countin& andb!iousl#% a !ariable ma# be a continuous !ariable or a discrete !ariable.

+i, Continuous data represent t"e numerical !alues of a continuous!ariable. ' continuous !ariable is t"e one t"at can assume an#

!alue beteen an# to points on a line se&ment% t"us representin&

an inter!al of !alues. T"e !alues are uite precise and close to eac"

ot"er% #et distin&uis"abl# dierent. 'll c"aracteristics suc" as

ei&"t% len&t"% "ei&"t% t"icness% !elocit#% temperature% tensile

stren&t"% etc.% represent continuous !ariables. T"us% t"e data

recorded on t"ese and similar ot"er c"aracteristics are called

continuous data. t ma# be noted t"at a continuous !ariable

assumes t"e -nest unit of measurement. 8inest in t"e sense t"at it

enables measurements to t"e maximum de&ree of precision.+ii, )iscrete data are t"e !alues assumed b# a discrete !ariable. '

discrete !ariable is t"e one "ose outcomes are measured in -xed

numbers. Suc" data are essentiall# count data. T"ese are deri!ed

from a process of countin&% suc" as t"e number of items possessin&

or not possessin& a certain c"aracteristic. T"e number of customers

!isitin& a departmental store e!er# da#% t"e incomin& ?i&"ts at an


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airport% and t"e defecti!e items in a consi&nment recei!ed for sale%

are all examples of discrete data.

=ualitati!e data refer to ualitati!e c"aracteristics of a sub$ect or an ob$ect.

' c"aracteristic is ualitati!e in nature "en its obser!ations are de-ned and

noted in terms of t"e presence or absence of a certain attribute in discretenumbers. T"ese data are furt"er classi-ed as nominal and ran data.

+i, @ominal data are t"e outcome of classi-cation into to or more

cate&ories of items or units comprisin& a sample or a population

accordin& to some ualit# c"aracteristic. Classi-cation of students

accordin& to sex +as males and females,% of orers accordin& to

sill +as silled% semi0silled% and unsilled,% and of emplo#ees

accordin& to t"e le!el of education +as matriculates%

under&raduates% and post0&raduates,% all result into nominal data.

(i!en an# suc" basis of classi-cation% it is ala#s possible to assi&n

eac" item to a particular class and mae a summation of itemsbelon&in& to eac" class. T"e count data so obtained are called

nominal data.+ii, Aan data% on t"e ot"er "and% are t"e result of assi&nin& rans to

specif# order in terms of t"e inte&ers 1%2%3% ...% n. Aans ma# be

assi&ned accordin& to t"e le!el of performance in a test. a contest%

a competition% an inter!ie% or a s"o. T"e candidates appearin& in

an inter!ie% for example% ma# be assi&ned rans in inte&ers

ran&in& from 1 to n% dependin& on t"eir performance in t"e

inter!ie. Aans so assi&ned can be !ieed as t"e continuous

!alues of a !ariable in!ol!in& performance as t"e ualit#c"aracteristic.

)ata sources could be seen as of to t#pes% secondar# and primar#. T"e to

can be de-ned as under

+i, Secondar# data T"e# alread# exist in some form publis"ed or

unpublis"ed 0 in an identi-able secondar# source. T"e# are%

&enerall#% a!ailable from publis"ed source+s,% t"ou&" not

necessaril# in t"e form actuall# reuired.+ii, *rimar# data T"ose data "ic" do not alread# exist in an# form%

and t"us "a!e to be collected for t"e -rst time from t"e primar#source+s,. # t"eir !er# nature% t"ese data reuire fres" and -rst0

time collection co!erin& t"e "ole population or a sample dran

from it.


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Types o statistics T"ere are to ma$or di!isions of statistics suc" as descripti!e statistics and

inferential statistics. T"e term descripti!e statistics deals it" collectin&%

summari4in&% and simplif#in& data% "ic" are ot"erise uite unield# and

!oluminous. t sees to ac"ie!e t"is in a manner t"at meanin&ful conclusions

can be readil# dran from t"e data. )escripti!e statistics ma# t"us be seen

as comprisin& met"ods of brin&in& out and "i&"li&"tin& t"e latent

c"aracteristics present in a set of numerical data. t not onl# facilitates an

understandin& of t"e data and s#stematic reportin& t"ereof in a mannerB and

also maes t"em amenable to furt"er discussion% anal#sis% and

interpretations.

T"e -rst step in an# scienti-c inuir# is to collect data rele!ant to t"e

problem in "and. "en t"e inuir# relates to p"#sical and


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&rap"s are also used for better presentation of t"e data. ' useful tabular and

&rap"ic presentation of data ill reuire t"at t"e ra data be properl#

classi-ed in accordance it" t"e ob$ecti!es of in!esti&ation and t"e

relational anal#sis to be carried out.

' ell t"ou&"t0out and s"arp data classi-cation facilitates eas# description of t"e "idden data c"aracteristics b# means of a !ariet# of summar# measures.

T"ese include measures of central tendenc#% dispersion% seness% and

urtosis% "ic" constitute t"e essential scope of descripti!e statistics. T"ese

form a lar&e part of t"e sub$ect matter of an# basic textboo on t"e sub$ect%

and t"us t"e# are bein& discussed in t"at order "ere as ell.

nferential statistics% also non as inducti!e statistics% &oes be#ond

describin& a &i!en problem situation b# means of collectin&% summari4in&%

and meanin&full# presentin& t"e related data. nstead% it consists of met"ods

t"at are used for drain& inferences% or main& broad &enerali4ations% about

a totalit# of obser!ations on t"e basis of noled&e about a part of t"attotalit#. T"e totalit# of obser!ations about "ic" an inference ma# be dran%

or a &enerali4ation made% is called a population or a uni!erse. T"e part of

totalit#% "ic" is obser!ed for data collection and anal#sis to &ain noled&e

about t"e population% is called a sample.

T"e desired information about a &i!en population of our interestB ma# also be

collected e!en b# obser!in& all t"e units comprisin& t"e population. T"is

total co!era&e is called census. (ettin& t"e desired !alue for t"e population

t"rou&" census is not ala#s feasible and practical for !arious reasons. 'part

from time and mone# considerations main& t"e census operations

pro"ibiti!e% obser!in& eac" indi!idual unit of t"e population it" reference to

an# data c"aracteristic ma# at times in!ol!e e!en destructi!e testin&. n

suc" cases% ob!iousl#% t"e onl# recourse a!ailable is to emplo# t"e partial or

incomplete information &at"ered t"rou&" a sample for t"e purpose. T"is is

precisel# "at inferential statistics does. T"us% obtainin& a particular !alue

from t"e sample information and usin& it for drain& an inference about t"e

entire population underlies t"e sub$ect matter of inferential statistics.

Consider a situation in "ic" one is reuired to no t"e a!era&e bod#

ei&"t of all t"e colle&e students in a &i!en cosmopolitan cit# durin& a

certain #ear. ' uic and eas# a# to do t"is is to record t"e ei&"t of onl#

5 students% from out of a total stren&t" of% sa#% 1% or an unnon total

stren&t"% tae t"e a!era&e% and use t"is a!era&e based on incomplete

ei&"t data to represent t"e a!era&e bod# ei&"t of all t"e colle&e students.

n a dierent situation% one ma# "a!e to repeat t"is exercise for some future

#ear and use t"e uic estimate of a!era&e bod# ei&"t for a comparison.

T"is ma# be needed% for example% to decide "et"er t"e ei&"t of t"e


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under t"e pur!ie of "at e call re&ression and correlation

anal#sis.+ii, Situations occur uite often "en e reuire a!era&in& +or totalin&,

of data on prices and


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to -nd e!en "istorians’ statistical data% for "istor# is essentiall# past data

presented in certain actual format.

Importance o statistics in business

T"ere are t"ree ma$or functions in an# business enterprise in "ic" t"estatistical met"ods are useful. T"ese are as follos

+i, T"e plannin& of operations T"is ma# relate to eit"er special

pro$ects or to t"e recurrin& acti!ities of a -rm o!er a speci-ed

period.


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+ii, T"e settin& up of standards T"is ma# relate to t"e si4e of

emplo#ment% !olume of sales% -xation of ualit# norms for t"e

manufactured product% norms for t"e dail# output% and so fort".+iii, T"e function of control T"is in!ol!es comparison of actual

production ac"ie!ed a&ainst t"e norm or tar&et set earlier. n case

t"e production "as fallen s"ort of t"e tar&et% it &i!es remedialmeasures so t"at suc" a de-cienc# does not occur a&ain.

' ort" notin& point is t"at alt"ou&" t"ese t"ree functions0plannin& of

operations% settin& standards% and control0are separate% but in practice t"e#

are !er# muc" interrelated.

)ierent aut"ors "a!e "i&"li&"ted t"e importance of Statistics in business.

8or instance% Croxton and Coden &i!e numerous uses of Statistics in

business suc" as pro$ect plannin&% bud&etar# plannin& and control% in!entor#

plannin& and control% ualit# control% maretin&% production and personnel

administration. it"in t"ese also t"e# "a!e speci-ed certain areas "ereStatistics is !er# rele!ant. 'not"er aut"or% rin& . urr% dealin& it" t"e

place of statistics in an industrial or&ani4ation% speci-es a number of areas

"ere statistics is extremel# useful. T"ese are customer ants and maret

researc"% de!elopment desi&n and speci-cation% purc"asin&% production%

inspection% paca&in& and s"ippin&% sales and complaints% in!entor# and

maintenance% costs% mana&ement control% industrial en&ineerin& and

researc". Statistical problems arisin& in t"e course of business operations are

multitudinous. 's suc"% one ma# do no more t"an "i&"li&"t some of t"e more

important ones to emp"asis t"e rele!ance of statistics to t"e business orld.

n t"e sp"ere of production% for example% statistics can be useful in !ariousa#s.

Statistical ualit# control met"ods are used to ensure t"e production of

ualit# &oods. dentif#in& and re$ectin& defecti!e or substandard &oods

ac"ie!e t"is. T"e sale tar&ets can be -xed on t"e basis of sale forecasts%

"ic" are done b# usin& !ar#in& met"ods of forecastin&. 'nal#sis of sales

aected a&ainst t"e tar&ets set earlier ould indicate t"e de-cienc# in

ac"ie!ement% "ic" ma# be on account of se!eral causes +i, tar&ets ere

too "i&" and unrealistic +ii, salesmenFs performance "as been poor +iii,

emer&ence of increase in competition +i!, poor ualit# of compan#Fs product%

and so on. T"ese factors can be furt"er in!esti&ated.

'not"er sp"ere in business "ere statistical met"ods can be used is

personnel mana&ement. ;ere% one is concerned it" t"e -xation of a&e

rates% incenti!e norms and performance appraisal of indi!idual emplo#ee.

T"e concept of producti!it# is !er# rele!ant "ere. >n t"e basis of

measurement of producti!it#% t"e producti!it# bonus is aarded to t"e


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orers. Comparisons of a&es and producti!it# are undertaen in order to

ensure increases in industrial producti!it#.

Statistical met"ods could also be used to ascertain t"e eGcac# of a certain

product% sa#% medicine. 8or example% a p"armaceutical compan# "as

de!eloped a ne medicine in t"e treatment of bronc"ial ast"ma. eforelaunc"in& it on commercial basis% it ants to ascertain t"e eecti!eness of

t"is medicine. t undertaes an experimentation in!ol!in& t"e formation of

to comparable &roups of ast"ma patients. >ne &roup is &i!en t"is ne

medicine for a speci-ed period and t"e ot"er one is treated it" t"e usual

medicines. Aecords are maintained for t"e to &roups for t"e speci-ed

period. T"is record is t"en anal#4ed to ascertain if t"ere is an# si&ni-cant

dierence in t"e reco!er# of t"e to &roups. f t"e dierence is reall#

si&ni-cant statisticall#% t"e ne medicine is commerciall# launc"ed.


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Limitations o statisticsStatistics "as a number of limitations% pertinent amon& t"em are as follos

+i, T"ere are certain p"enomena or concepts "ere statistics cannotbe used. T"is is because t"ese p"enomena or concepts are not

amenable to measurement. 8or example% beaut#% intelli&ence%

coura&e cannot be uanti-ed. Statistics "as no place in all suc"

cases "ere uanti-cation is not possible.+ii, Statistics re!eal t"e a!era&e be"a!ior% t"e normal or t"e &eneral

trend. 'n application of t"e Fa!era&eF concept if applied to an

indi!idual or a particular situation ma# lead to a ron& conclusion

and sometimes ma# be disastrous. 8or example% one ma# be

mis&uided "en told t"at t"e a!era&e dept" of a ri!er from one

ban to t"e ot"er is four feet% "en t"ere ma# be some points inbeteen "ere its dept" is far more t"an four feet. >n t"is

understandin&% one ma# enter t"ose points "a!in& &reater dept"%

"ic" ma# be "a4ardous.+iii, Since statistics are collected for a particular purpose% suc" data ma#

not be rele!ant or useful in ot"er situations or cases. 8or example%

secondar# data +i.e.% data ori&inall# collected b# someone else, ma#

not be useful for t"e ot"er person.+i!, Statistics are not 1 per cent precise as is Dat"ematics or

'ccountanc#. T"ose "o use statistics s"ould be aare of t"is

limitation.+!, n statistical sur!e#s% samplin& is &enerall# used as it is not

p"#sicall# possible to co!er all t"e units or elements comprisin& t"e

uni!erse. T"e results ma# not be appropriate as far as t"e uni!erse

is concerned. Doreo!er% dierent sur!e#s based on t"e same si4e of

sample but dierent sample units ma# #ield dierent results.+!i, 't times% association or relations"ip beteen to or more !ariables

is studied in statistics% but suc" a relations"ip does not indicate

cause and eectF relations"ip. t simpl# s"os t"e similarit# or

dissimilarit# in t"e mo!ement of t"e to !ariables. n suc" cases% it

is t"e user "o "as to interpret t"e results carefull#% pointin& out

t"e t#pe of relations"ip obtained.+!ii, ' ma$or limitation of statistics is t"at it does not re!eal all pertainin&

to a certain p"enomenon. T"ere is some bac&round information

t"at statistics does not co!er. Similarl#% t"ere are some ot"er

aspects related to t"e problem on "and% "ic" are also not co!ered.

T"e user of Statistics "as to be ell informed and s"ould interpret


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Statistics eepin& in mind all ot"er aspects "a!in& rele!ance on t"e

&i!en problem.

'part from t"e limitations of statistics mentioned abo!e% t"ere are misuses of

it. Dan# people% noin&l# or unnoin&l#% use statistical data in ron&

manner. et us see "at t"e main misuses of statistics are so t"at t"e samecould be a!oided "en one "as to use statistical data. T"e misuse of

Statistics ma# tae se!eral forms some of "ic" are explained belo.

+i, Sources of data not &i!en 't times% t"e source of data is not &i!en.

n t"e absence of t"e source% t"e reader does not no "o far t"e

data are reliable. 8urt"er% if "e ants to refer to t"e ori&inal source%

"e is unable to do so.+ii, )efecti!e data 'not"er misuse is t"at sometimes one &i!es

defecti!e data. T"is ma# be done noin&l# in order to defend oneFs

position or to pro!e a particular point. T"is apart% t"e de-nition

used to denote a certain p"enomenon ma# be defecti!e. 8orexample% in case of data relatin& to unemplo#ed persons% t"e

de-nition ma# include e!en t"ose "o are emplo#ed% t"ou&"

partiall#. T"e uestion "ere is "o far it is $usti-ed to include

partiall# emplo#ed persons amon&st unemplo#ed ones.+iii, /nrepresentati!e sample n statistics% se!eral times one "as to

conduct a sur!e#% "ic" necessitates to c"oose a sample from t"e

&i!en population or uni!erse. T"e sample ma# turn out to be

unrepresentati!e of t"e uni!erse. >ne ma# c"oose a sample $ust on

t"e basis of con!enience. ;e ma# collect t"e desired information

from eit"er "is friends or nearb# respondents in "is nei&"bor"oode!en t"ou&" suc" respondents do not constitute a representati!e

sample.+i!, nadeuate sample Earlier% e "a!e seen t"at a sample t"at is

unrepresentati!e of t"e uni!erse is a ma$or misuse of statistics. T"is

apart% at times one ma# conduct a sur!e# based on an extremel#

inadeuate sample. 8or example% in a cit# e ma# -nd t"at t"ere

are 1% % "ouse"olds. "en e "a!e to conduct a "ouse"old

sur!e#% e ma# tae a sample of merel# 1 "ouse"olds comprisin&

onl# .1 per cent of t"e uni!erse. ' sur!e# based on suc" a small

sample ma# not #ield ri&"t information.+!, /nfair Comparisons 'n important misuse of statistics is main&

unfair comparisons from t"e data collected. 8or instance% one ma#

construct an index of production c"oosin& t"e base #ear "ere t"e

production as muc" less. T"en "e ma# compare t"e subseuent

#earFs production from t"is lo base.Suc" a comparison ill undoubtedl# &i!e a ros# picture of t"e

production t"ou&" in realit# it is not so. 'not"er source of unfair


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comparisons could be "en one maes absolute comparisons

instead of relati!e ones. 'n absolute comparison of to -&ures% sa#%

of production or export% ma# s"o a &ood increase% but in relati!e

terms it ma# turn out to be !er# ne&li&ible. 'not"er example of

unfair comparison is "en t"e population in to cities is dierent%

but a comparison of o!erall deat" rates and deat"s b# a particulardisease is attempted. Suc" a comparison is ron&. ieise% "en

data are not properl# classi-ed or "en c"an&es in t"e composition

of population in t"e to #ears are not taen into consideration%

comparisons of suc" data ould be unfair as t"e# ould lead to

misleadin& conclusions.+!i, /nanted conclusions 'not"er misuse of statistics ma# be on

account of unarranted conclusions. T"is ma# be as a result of

main& false assumptions. 8or example% "ile main& pro$ections of

population in t"e next -!e #ears% one ma# assume a loer rate of

&rot" t"ou&" t"e past to #ears indicate ot"erise. Sometimesone ma# not be sure about t"e c"an&es in business en!ironment in

t"e near future. n suc" a case% one ma# use an assumption t"at

ma# turn out to be ron&. 'not"er source of unarranted

conclusion ma# be t"e use of ron& a!era&e. Suppose in a series

t"ere are extreme !alues% one is too "i&" "ile t"e ot"er is too lo%

suc" as H and 5. T"e use of an arit"metic a!era&e in suc" a

case ma# &i!e a ron& idea. nstead% "armonic mean ould be

proper in suc" a case.+!ii, Confusion of correlation and causation n statistics% se!eral times

one "as to examine t"e relations"ip beteen to !ariables. ' closerelations"ip beteen t"e to !ariables ma# not establis" a cause0

and0eect0relations"ip in t"e sense t"at one !ariable is t"e cause

and t"e ot"er is t"e eect. t s"ould be taen as somet"in& t"at

measures de&ree of association rat"er t"an tr# to -nd out causal

relations"ip.


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Conclusion

Statistics pla#s a !ital role in e!er# -elds of "uman acti!it#. Statistics "asimportant role in determinin& t"e existin& position of per capita income%

unemplo#ment% population &rot" rate% "ousin&% sc"oolin& medical facilities

etc. in a countr#. @o statistics "olds a central position in almost e!er# -eld

lie ndustr#% Commerce% Trade% *"#sics% C"emistr#% Economics%

Dat"ematics% iolo% otan#% *s#c"olo% 'stronom# etc.% so application of

statistics is !er# ide.

"et"er desi&nin& ne products% streamlinin& a production process or

e!aluatin& current !s. prospecti!e customers% toda#’s business mana&ers

face &reater complexities t"an e!er before. Aunnin& a s"op on instinct no

lon&er suGces. Statistics pro!ide mana&ers it" more con-dence in dealin&it" uncertaint# in spite of t"e ?ood of a!ailable data% enablin& mana&ers to

more uicl# mae smarter decisions and pro!ide more stable leaders"ip to

sta rel#in& on t"em.

Documents

Stat Term Paper.docx