Introduction to Statistics .pdf

Basic concepts of Statistics

1. ALLPPT.com _ Free PowerPoint Templates, Diagrams and Charts
Presented By
Ms. A. DALLY MARIA EVANGELINE
ASSISTANT PROFESSOR
DEPARTMENT OF MATHEMATICS
NUMERICAL
ANALYSIS &
STATISTICS

2. OBJECTIVE

3. Tolearnbasicconceptsofstatistics
Tolearnthebasicideasofnumericalanalysis

4. Statistics
•Numericalstatementoffactsinanydepartment
•Classifiedfactsrepresentingtheconditionsofthe
peopleinastate…..Speciallythosefactswhichcan
bestatedinnumberorintablesofnumbers

5. Statistics
•Branchofscientificmethodswhichdealswiththe
dataobtainedbycountingormeasuringthe
propertiesofpopulationofnaturalphenomenon
•Dealswiththemethodofcollecting,classifying,
presentingcomparingandinterpretingnumericalda
tacollectedtothrowsomelightonanysphereof
inquiry

6. Importance and Scope
•Statisticsandplanning
•Statisticsandmathematics
•Statisticsandeconomics
•Statisticsandbiology

7. Statistical data
•Dataareindividualpiecesoffactualinformation
recordedandusedforthepurposeofanalysis
•Rawinformationfromwhichstatisticsarecreated
•Statisticsdealswithcollection,analysisandinter-
pretationofnumericaldata

8. Types of data
•PrimaryData–firsthanddatagatheredbythe
researcherhimself
•SecondaryData–datacollectedbysomeoneelse
earlier–dataalreadyavailableinlibrary,internet
•Groupedandungroupeddata

9. Data collection methods
•Interviews
•Surveys
•Questionnaires
•Observations

10. FrequencyDistribution
Aclassificationaccordingtothenumberpossessing
thesamevaluesofthevariables.Itissimplyatablein
whichthedataaregroupedintoclassesandthe
numberofcaseswhichfallineachclassisrecorded

11. Frequency Distribution
Frequencydistributioncanbeoftwokinds:
➢UnivariateFrequencyDistribution
➢BivariateFrequencyDistribution

12. Frequency Distribution
Frequencydistributioncanbeoftwokinds:
➢UnivariateFrequencyDistribution
➢BivariateFrequencyDistribution

13. Frequency Distribution
Representation of data as above is called frequency distribution

14. Frequency distribution
•Prepare the frequency distribution table for the
given set of scores:
39, 16, 30, 37, 53, 15, 16, 60, 58, 26, 28, 19, 20,
12, 14, 24, 59, 21, 57, 38, 25, 36, 24, 15, 25, 41,
52, 45, 60, 63, 18, 26, 43, 36, 18, 27, 59, 63, 46,
42, 48, 35, 64, 24.

15. Frequency Distribution
Class intervalFrequency
10-20 9
20-30 12
30-40 8
40-50 7
50-60 6
60-70 5

16. Classification & Tabulation
Classificationistheprocessofarrangingthingsin
groupsorclassesaccordingtotheirresemblancesand
affinities,andgivingexpressiontotheunityofattribute
thatmaysubsistamongstadiversityofindividuals

17. Chief Characteristics of
Classification
•Allthefactsareclassifiedintohomogeneousgroup
bytheprocessofclassification
•Thebasisofclassificationisunityindiversity
•Itshouldbeflexibletoaccommodateadjustments

18. Types ofClassification
•Geographical
•ChronologicalorHistorical
•Qualitativebycharacterorbyattributes
•Quantitativeornumericalorbymagnitudes

19. Graphical Representation of Data

20. General Characteristics of
Quantitative Data
•Measure of Central Tendency
•Measure of Dispersion
•SkewnessandKurtosis

21. Averages or Measure of
Central Tendency
•Arithmetic Mean
•Median
•Mode
•Geometric Mean
•Harmonic Mean

22. Arithmetic Mean
•Average is a value which is typical or representative
of a set of data
•Arithmeticmeanofseriesisthefigureobtainedby
dividingthetotalvalueofthevariousitembytheir
number

23. Arithmetic Mean
Arithmetic Mean is given by
ത??????=
σ??????
�
Where,nisthenumber of observations
σ??????is the sum of variables

24. Arithmetic Mean
Arithmetic Mean is given by
ത??????=
σ??????
�
Where, n is the number of observations
σ??????is the sum of variables

25. Merits & Demerits of
Arithmetic Mean
It iswidelyusedbecause:
•It iseasytounderstand
•It is rigidly defined
Thedemerits are:
•The meanisundulyaffectedbytheextreme
items.
•It cannotbeaccuratelydeterminedeven if one
of the values is not known

26. Median
Medianisthevalueofitemthatgoestodivide
theseriesintoequalparts.Itmaybedefinedasthe
valueofthatitemwhichdividestheseriesintotwo
equalparts,onehalfcontainingthevaluesgreater
thanitandtheotherhalfcontainingvaluesless
thanit

27. Median
Medianisgivenby
Median =??????????????????���
??????+1
2
??????ℎ????????????��
Where, n is the number of observation

28. Merits & Demerits of
Median
Merits:
•Itiseasytounderstandandeasytocompute
•Itisquiterigidlydefined
Demerits:
•Itcannotbecomputedifthedistributionisirregular
•Itignoresextremeitems

29. Mode
Modeisthemostcommonitemsofaseries.Itisthe
valuewhichoccursthegreaternumberoffrequencyin
aseries.

30. Merits & Demerits of Mode
Merits:
•Itiseasytounderstandanditcanbeeasilycompute
dbyinspection
•Itisnotaffectedbytheextremevalues
Demerits:
•Itcannotbecomputedifthedistributionisirregular
•Itignoresextremeitems