This document provides an overview of 42 quantitative techniques concepts, definitions, and formulas. Some of the key topics covered include: - Standard deviation and how it measures variation from the mean - Different measures of central tendency like the arithmetic mean, median, and mode - The rules of addition and multiplication for determining probabilities of events - Probability distributions like the binomial and Poisson distributions - Hypothesis testing steps and types of errors - Correlation and regression analysis techniques - Sampling methods like random, stratified, systematic, and cluster sampling - ANOVA and t-tests The document serves as a reference for fundamental quantitative analysis concepts. It defines statistical techniques concisely and presents related formulas for measures like

1. Quantitative Techniques- Theory @ a glimpse. 2017
Arun Sudhakaran Page 1
Arun Sudhakaran
2017
Quantitative Techniques- Theory @ a glimpse.

2. Quantitative Techniques- Theory @ a glimpse. 2017
Arun Sudhakaran Page 2
1. Standard Deviation
The most commonlyusedmeasure of
variation.Showsvariationaboutthe mean.
It isthe square rootof variance andhas the
same unitas the original data.
𝑺 = √(
∑(𝑿 − 𝑿̅) 𝟐̅̅̅̅̅̅̅̅̅̅̅̅
(𝒏 − 𝟏)
)
2. A frequencydistributionof asetof values
that isnot symmetrical iscalled Skewed.
3. The Statistical technique toindicate the
directionandextentof skewnessinthe
distributionof numerical valueof the
datasetiscalled Measure of Skewness.
4. Kurtosis isthe degree of flatnessor
peakednessinthe regionaroundthe Mode
of a frequencycurve.
5. StratifiedRandom Sampling isa methodof
samplingthatinvolvesthe divisionof a
populationintosmallergroupsknownas
Strata. In StratifiedRandomsampling,
Strata are formedbasedonmembers
sharedattributesorcharacteristics. E.g.
‘based on the employeesalary’.
6. ArithmeticMean isthe most common
measure of central tendency.
𝑿̅ =
∑ 𝑿
𝒏
; Meanis the average.
Median: In an orderedarray,the medianis
the middle numberanditisnot affectedby
the extreme values.
𝑀𝑒𝑑𝑖𝑎𝑛 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 = (
𝒏 + 𝟏
𝟐
) 𝒕𝒉 𝒕𝒆𝒓𝒎
Mode:It is the measure of central tendency. i.e.
the value thatoccurs mostoften.
Notaffectedbyextreme values.Itisusedforeither
numerical orcategorical data.There may be cases
where there are several modesorevenno mode.
7. Rule of Addition:
If two or more than 2 eventsare likelyto
occur from a randomexperimentandwe
are interestedtoknowthe probabilityof
occurrence of at leastone of the events,
thenthe rule of additionare usedtodo so.
The rule statesthat: Of twoeventsA&B
that isMutually Exclusive,Exhaustiveand
Equi-Probablethenthe probabilityof A orB
or both occurringisequal to the sum of
theirindividual probabilities.
8. Rule of Multiplication:
Whenoccurrence of an eventdoesnot
affectthe probabilityof occurrence of any
otherevent,thenthe eventissaidtobe
StatisticallyIndependentEvent.
9. Poissondistribution:
A discrete probabilitydistributioninwhich
the probabilityof occurrence of an
outcome withinaverysmall time periodis
verysmall.Poissondistributionoccursin
businesssituations inwhichthere are only
few successes inaninterval of time against
a large numberof failuresorvice versaand
has single independentoutcomes thatare
mutuallyexclusive.Becauseof thisthe
probabilityof success,‘p’isverysmall in
relationtothe numberof trials‘n’,so only
the probabilityof successisconsidered.
10. ClusterAnalysis:
isthe taskof groupinga setof objectsin
such a way thatthe objectsinthe same
group(called“Cluster”) are more similar(in
some wayor the another) toeach other
than to those inother groups.
11. Interval Estimate:
An interval withinwhichthe value of a
parameterof a populationhasa stated
probability of occurring.
An Interval estimateisdefinedbytwo
numbers,betweenwhichapopulation
parameterissaidto lie.
12. One WayANOVA isusedto determine
whetherthere are anysignificantdifference
betweenthe meansof three ormore

3. Quantitative Techniques- Theory @ a glimpse. 2017
Arun Sudhakaran Page 3
independentgroups.( Using F
distribution).Itspecificallyteststhe null
hypothesis.
13. The three main assumptionsare:
1) There is homogeneityof variance.
2) There is independence of observances.
3) The dependentvariableisnormally
distributedineachgroupthatis being
comparedinOne Way ANOVA.
14. Developinganalgebraicequationbetween
twovariablesbasedonthe givendataand
estimatingthe value of adependant
variable giventhe value of anindependent
variable isreferredtoas Regression
Analysis.
15. Measuringthe strengthanddirectionof the
relationshipbetweenthe twovariablesis
referredtoas CorrelationAnalysis.
The directionof the relationshipisindicated
by the CorrelationCoefficientandthe
absolute value of correlationcoefficient
indicatesthe extendof the relationship.
16. CorrelationAnalysisdeterminesthe
strengthof associationof twovariablesbut
doesnotestablisha‘Cause andEffect’
relationship.Regressionanalysisestablishes
the ‘Cause and Effect’relationship
17. In ‘Linear’RegressionAnalysisOne Variable
isconsideredasDependentVariableand
the Otheras Independent.Whilein
CorrelationAnalysisbothvariablesare
consideredtobe Independent.
18. The Classical definitionofProbability:
If an experimentcanproduce outcomes
that are mutually exclusiveand equally
likely Out of which‘n’outcomesare
favourable tothe occurrence of event‘A’
thenprobabilityof event‘A’isdenotedby
P(A)=
(𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒇𝒂𝒗𝒐𝒖𝒓𝒂𝒃𝒍𝒆 𝒐𝒖𝒕𝒄𝒐𝒎𝒆𝒔)
(𝑻𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒐𝒖𝒕𝒄𝒐𝒎𝒆𝒔)
19. Limitations:
1)Limitsitsapplicationonlytosituations
where there are finite numberof possible
outcomes.
2) Mainly consideredfordiscrete events
and itsmethodswere mainlycombinatorial.
3) Each possible outcomeisEquallyLikely.
20. MutuallyExclusive Events cannothappen
at the same time.egwhenacoinistossed;
the resultcan eitherbe a heador a tail but
cannot be both.The occurrence of one
eventexcludesthe occurrence of the other.
Thisof course meansthat the mutually
exclusiveeventsare notindependentand
independenteventscannotbe Mutually
Exclusive.
21. IndependentEventsare eventswhere the
occurrence of one eventdoesnotinfluence
and isnot influencedbythe occurrence of
the other.
22. Stepsin testingHypothesis:
1)State the Null andAlternate Hypothesis
(𝐻0& 𝐻1).
2) Chose the level of Significance (LOS),α
and the sample size ‘n’
3) Determine the appropriate TestStatistic
and SamplingDistribution.
4) Determine the Critical Value thatdivides
the Rejection&Non RejectionRegion.
5) Collectthe Data and Compute the Value
of TestStatistic.
6) Make the Statistical DecisionandState
the Managerial Conclusion.
If the teststatisticfallsintothe non
rejectionregion,donotreject 𝐻0.
Expressthe Managerial conclusioninthe
contextof the problem.
23. Type I Error:
The probabilityof rejectingthe Null
Hypothesis,when itistrue and an Alternate
Hypothesisiswrong.
The probabilityof makingaTYPE I Error is
definedbythe symbol ‘α’.Itisrepresented
by the area underthe samplingdistribution
curve overthe regionof rejection.

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Arun Sudhakaran Page 4
TYPE I Error measuresthe probabilityof not
rejectingthe true null hypothesis.
24. Type II Error:
isthe probabilityof acceptingthe null
Hypothesiswhenitisfalse andanalternate
hypothesiswhenitistrue.
The probabilityof makingaType II Error is
denotedby‘β’.
25. Conditional Probability
isthe Probabilityof one eventgiventhe
probabilityanother event:
P(A/B)=
𝑷(𝑨&𝑩)
𝒑(𝑩)
P(B/A)=
𝑷(𝑨&𝑩)
𝑷(𝑨)
Thus conditional Probabilityisthe
probabilityof aneventA giventhatthe
eventBhas alreadyoccurred.
26. Binomial Distribution
it isa frequencydistribution,of the possible
numberof successful outcomesinagiven
numberof trialsineach of whichthere is
the same probabilityof success
It isa widelyusedprobabilitydistribution
for a discrete randomvariable.Itdescribes
data resultingfromanexperimentcalleda
‘Bernoulli Process’.
27. Systematic Sampling:
It isa type of probabilitysamplingmethod,
inwhichsample membersfromalarge
populationare selectedaccordingtoa
randomstartingpointand a fixedperiodic
interval.Itisa statistical methodinvolving
the selectionof elementsfromanordinary
samplingframe.
28. ANOVA:
It isa collectionof Statistical modelsused
to analyse the differencesamonggroup
meansand theirassociated procedure
(suchas variationamongand between
groups).Itcanbe usedincaseswhere there
are more than twogroups.
29. DependentVariable:
A dependentvariableis whatyoumeasure
inthe experimentandwhatisaffected
duringthe experiment.The dependent
variable respondstothe independent
variable.Itisso calledbecause itdepends
on the IndependentVariable.
30. Spearman’s Rank Correlation:
Thismethodwasdevelopedto measure the
statistical relationshipbetweentwo
variable whenonlyrankisavailable.
Thismeansthat thismethodisappliedina
situationwhere quantitative measure of
qualitative factorssuchasbeauty,
intelligence etccannotbe fixedbut
individualobservationscanbe arrangedin a
definiteorder.
𝑹 = 𝟏 −
𝟔∑ 𝒅 𝟐
𝒏( 𝒏 𝟐 − 𝟏)
31. Baye’s Theorem
A theoremdescribinghowthe conditional
probabilityof asetof possible causesfora
givenobservedoutcomefromthe
knowledge of the probabilityof eachcause
and the conditional probabilityof the
outcome of each cause.
Baye’stheoremenablesyou,knowingjusta
little more thanthe probabilityof A givenB,
to findthe probabilityof BgivenA.
Basedon the definitionof Conditional
Probabilityandthe lawof total probability.
It isusedto revise previouslycalculated
probabilityafternewinformationis
obtained.
32. Hypothesis:
A hypothesisisanassumptionabouta
populationparameter.Thisassumption
may or may notbe true.
The processthat enablesadecisionmaker
to testthe validityof hisclaimbyanalysing
the difference betweenthe valueof sample

5. Quantitative Techniques- Theory @ a glimpse. 2017
Arun Sudhakaran Page 5
statisticandthe hypotheticalpopulation
parametervalue iscalled Hypothesis
Testing.
33. Difference between‘ConvenientSampling’
and ‘JudgementSampling’
In convenience sampling,unitstobe
includedare selectedatthe convenience of
the investigator.
Thismethodiseasyfor the collectionof
data for a particularissue butthe samples
may nottrulyrepresentthe populationand
hence precautionsshouldbe takenin
drawinginferencesaboutapopulation
characteristicsbasedonConvenient
Sampling.
JudgementSamplingisusedwhen aspecific
numberof respondentsare inthe best
positiontoprovide the desiredinformation.
The resultof this methodcannotbe
generalisedbecausethe responseisfroma
setof respondentswhoare conveniently
available are considered.
Thismethodisuseful onlywhenthose
caseswhere desiredinformationcanonly
be obtainedfroma veryspecificsectionof
respondents.Howeverthe validityof the
sample resultsdependsonthe judgement
of the investigatorinchoosingthe sample.
34. Difference between1way ANOVA and 2
way ANOVA?
One way ANOVA teststhe difference in
populationmeansbasedonone factor.
eg:When youwanttotest if there is a
differencebetweenthe heightsof 3 types
of seeds.
Since there ismore than one Mean,youcan
use One Way ANOVA asthere isonlyone
factor that ismakingthe heightsdifferent.
Two wayANOVA isa hypothetical test
comparisonwhenpopulationbasedon
multiple characteristic.
Supposethereare morethanonevariety of
seedsandthe possibilitythat fourdifferent
fertilizers are used,then two way ANOVA is
used.
The mean heightof the stalksmaybe
differentfora combinationof several
reasons.
A one wayAnalysisOf Variance is
performedwhenthere isonlyone
independentvariable.
Two wayANOVA isusedwhenthere are
twoindependentvariable inthe
experiment.
35. Normal Distribution:
It isthe probabilitydistributionthatplotsall
of the valuesina symmetrical fashion.
Normal Distributionisaverycommon
continuousprobabilitydistribution.Itisalso
calledthe ‘Bell Curve’
The bell curve are alsoambiguousbecause
theysometimesrefertothe multiplesof
the normal distributionthatcannotbe
directlyinterpretedintermsof
probabilities.
36. Central Limit Theorem:
In probabilitytheory,the Central Limit
Theorystates that,givencertainconditions,
the arithmeticMeanof a sufficientlylarge
numberof iteratesof independentrandom
variables,each withawell definedvariance,
will be approximatelyNormallyDistributed
regardlessof the underlyingdistribution.
37. Sample Space:
It isdenotedby‘S’,Setof all probable
outcomesof an experiment.Itisthusthe
setof all distinctoutcomesfora random
experimentiscalledthe samplespace
provided:
1) 2 or more of these outcome donotoccur
simultaneously.
2) Each randomexperimentisresultingin
to exactlyone of the outcomes.

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38. Student’s‘t’test:
Amongthe most frequently used‘t’ test.
A one sample locationtestof whetherthe
meanof a populationhasavalue specified
inthe Null Hypothesis.
A twosample locationtestof Null
Hypothesissuchthatthe meansof the two
populationsare equal.
39. Standard Error:
The Standard erroris the standard
deviationof the samplingdistributionof a
statistic- mostcommonlyof the mean.
[Itis a measure of the statistical accuracy of
an estimate,equal tothe standard
deviationof the theoretical distributionof a
large populationof suchestimates].
40. Coefficientof Variation:
It measuresthe relativevariation.Itis
alwaysin%.Itshowsvariationrelativeto
Mean. Canbe usedto compare twoor
more setof data measuredindifferent
units.
𝑪. 𝑽 = (
𝑺
𝑿̅
) ∗ 𝟏𝟎𝟎 %
41. Chi Square Test:
It isa testfor establishingthe association
betweentwocategorisedvariables.Itisone
of the nonparametriccategoriesof the
testsor methodstotesta hypothesis.
The decisionof acceptinganull hypothesis
isbasedon howclose the sample statisticis
to the expectedvalue.
42. Karl Pearson coefficientofCo relation:
Quantitativelymeasuresthe degreeof
associationof betweentwovariablesinX
and Y for a set of n pairsof values.
Usedonlywhentwovariablesare linearly
relatedandare measuredon aninterval or
ratioscale.
43. Random Sampling: Everymemberof the
populationhasanequal chance of being
selectedeachtime asample isdrawnfrom
the population.
For applyingthismethod,anexhaustivelist
of membersof the populationof interestis
preparedtoidentifyeachmemberbya
distinctnumber
The disadvantage of thismethodisthat all
membersof the populationhave tobe
available forselection,thatmaynot be
possible everytime.
ESSAY QUESTIONS:
1. Non probabilisticSampling
A Samplingtechnique where the
samplesare gatheredina process
that doesnotgive all the individuals
ina populationequalchancesof
beingselected.
The typesof nonprobabilistic
Samplingare:
1) Convenience Sampling:
2) Purposive Sampling:
3) JudgementSampling:
4) Quota Sampling:
2. Baye’s TheoremApplication:
Baye’stheoremisa methodto
compute posteriorprobabilities
whichisa revisedprobabilityof an
eventobtained,aftergetting
additional information.
Baye’sTheoremisuseful inrevising
the original orprior probability

7. Quantitative Techniques- Theory @ a glimpse. 2017
Arun Sudhakaran Page 7
estimatesknownasthe outcomes
basedon additional information
aboutthese outcomes.
The newestimate of original
probabilitiesof outcomesinviewof
additional informationiscalled
Revisedor Posteriorprobability.
Baye’sTheoremisusedtorevise
previouslycalculatedprobability
afternewinformationisobtained.
3. Methodsof Sampling:
SamplingMethodsare of two
types:
(1) Probabilistic(Random)
Sampling
and
(2) Non Probabilistic(Non-
Random) Sampling.
1. ProbablisticSampling:
a) Simple Random Sampling:
In thismethod,everymemberof
the populationhasanequal chance
of beingselected-eachtime a
sample isdrawnfromthe
population.
One disadvantage isthat,all the
membersof the population have to
be available atthe time of
selection,thatmaynotbe possible
at all pointsof time.
b) StratifiedSampling:
Thismethodisuseful whenthe
populationconsistof anumberof
heterogeneoussubpopulation
(age,type of industryetc) The
populationisdividedintosmall
groupscalled‘strata’ basedon
memberssharedattributesor
characteristics.
c) ClusterSampling:
Thismethodisalsoknownas ‘Area
SamplingMethod’, helpstomeet
the cost or in adequate sampling
frames.
For thismethodthe entire
populationisdividedin tosmaller
groupsor ‘Clusters’anda sample is
drawnusingsimple random
samplingmethods.
The elementsof aclusterare called
‘Elementaryunits’.
d) Multi Stage Sampling:
Thismethodof samplingisuseful
whenthe populationisverywidely
spreadand randomsamplingisnot
possible.
The populationisfirststratifiedin
differentstatesandfurther
classifiedintorural and urban
areas- knownas clusters;anda few
clustersare chosenrandomlyfor
the study.
The essence of thistype of
samplingisthata cubsample is
takenfromsuccessive groupsor
strata.
The selectionof samplingunitsat
each stage maybe achievedwithor
withoutsatisfaction.
e) Systematic Sampling:
ThisProcedure isuseful whenthe
elementsof the populationare
alreadyarrangedinsome order.
(e.g.: bankcustomersbyaccount
numberetc).
In suchcases,one elementof
populationischosenatrandom
fromfirst‘K’ elementandthen

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Arun Sudhakaran Page 8
everykth elementisincludedinthe
sample.
The numberK=
𝑁
𝑛
;
N= Size of Population,
n = Size of desiredsamplecalled
the sampling Interval.
2. NonProbabilistic(Non-Random)
Sampling:
Essay Question1.