Week 8 _ Measures of Deispersion or Variability_46913544.pdf

Nakakabadteio namannnnn

1. MEASURESof
VARIATION

2. WEEK7:COURSECONTENT
1.Range
2.MeanAbsolutedeviation
3.Variance
4.StandardDeviation
5.QuartileDeviation

3. WEEK7:Unitexpectedoutcomes;
1.Performefficientlyandhonestlythecomputations
ofmeasuresofdispersion.
2.Analyze,compareandinterpretdataconfidently,
accurately,andindependentlyusingmeasuresof
dispersion.

5. Eventsofnaturevaryformtime.Peoplekeeponchangingtheirlocation,motion,physicalappearance,skin
reactiontodifferentchemicals,height,weight,haircolor,eyecolor,ideas,andevenvalueinlife.Usually,the
heightsofagroupofpeoplewiththesameracetendtoconvergetoacertaincommonvalue.

6. MEASURESOFVARIATION
■Themeasureofvariationwillenableyoutoknow
howvariedtheobservationsare,whetherthereare
extremesvaluesinthedistribution,orwhetherthe
valuesareveryclosetoeachother.
■Ifthemeasureofvariationiszero,itmeansthat
thereisnovariationatallandthattheobservations
areallalike,orhomogeneous.Otherwise,theyare
heterogenous.

7. MEASURESOFVARIATION
Thecommonmeasuresofvariationarethe:
1.R

8. RANGE
The isthesimplestformofmeasuringthe
variationofadistribution.

9. ■Therangeissimpleto
computeandisusefulwhenyou
wishtoevaluatethewholeofa
dataset.
■Therangeisusefulforshowing
thespreadwithinadatasetand
forcomparingthespread
betweensimilardatasets.FORMULA:

10. IllustrativeExamples: Data3:Agroupofscientistswenton
themountainrangeinSierraMadre,
Philippinestostudythedifferentspecies
ofplantsexistinginthatarea.Theages
ofthescientistsare34,35,45,56,32,25,
and40.Whatistherangeoftheirages?
HighestAge=56and
LowestAge=25
:R=H–L=56–25=
31
therefore,therangeof
theiragesis31

11. MeanAbsoluteDeviation-MAD
ofasetofdataistheaveragedistancebetween
eachdatavalueandthemean.
Ungroupeddata: Groupeddata

23. VARIANCE

24. VARIANCE
• isanothermeasureofvariationwhichcanbe
usedinsteadoftherange.
•Thevarianceconsidersthedeviationofeachobservation
fromthemean.
•Toobtainthevarianceofadistribution,firstsquarethe
deviationfromthemeanofeachrowscoreandadd
themtogether.
•Then,dividetheresultingsumbyNorthetotalnumberof
cases.

25. (UngroupedData)(UngroupedData)

26. (UngroupedData)(GroupedData)

27. (UngroupedData)(GroupedData)Exceptwhenspecifiedthatthe
populationvarianceistobeused,youwill
alwaysusethesamplevarianceformulain
theexamplesandexercisesthroughoutthe
book.

29. (UngroupedData)(GroupedData)

30. (UngroupedData)(GroupedData)
b.)GroupedData:Computeforthepopulationand
samplevariancesforthedatainthetablebelow.

31. (UngroupedData)(GroupedData)
Step1:Completethetableif
needed.
Step2:Findthemean.
Step3:SolveforSampleor
PopulationVariance

32. The (σ)forapopulationand(s)forasample,isthe
squarerootofthevalueofthevariance.Insymbolsandformulafor
groupedandungroupeddata:

34. THEQUARTILEDEVIATION
(InterQuartileDeviation)
The isanotherwayof
determiningthespreadofadistributionintermsof
quartiles.
Thequartiledeviationformulaisshownbelow:

35. QuartileDeviation=(29-18)/2=5.5
Example:FindtheQuartiledeviationinthedatabelow

36. InterquartileRange:

37. Example