Graphical representation of chemical periodicity of main elements through boxplot

www.educacionquimica.info

educación

Q

uímica

DIDACTIC

Graphical

representation

of

chemical

periodicity

of

main

elements

through

boxplot

João

Elias

Vidueira

Ferreira

,

Maria

Tayane

Silva

Pinheiro,

Wagner

Roberto

Santos

dos

Santos,

Rodrigo

da

Silva

Maia

FederalInstituteofEducation,ScienceandTechnologyofPará,ParáState,Amazon,Brazil Received11December2015;accepted8February2016

Availableonline1June2016

KEYWORDS Chemicalperiodicity; Representative elements; Exploratorydata analysis; Boxplot

Abstract Graphicsplayanimportantrole indata analysis.Boxplotsarepowerfulgraphical representationofdatathatgivesanoverviewandanumericalsummaryofadataset.Inthis paperboxplotsareusedtoanalyzetheperiodictrendsofmainelements.Theproperties consid-eredareatomicradius,firstionizationenergy,electronaffinityandelectronegativity.Boxplots areconstructedandmetals,nonmetalsandmetalloidsarecompared.Theresultsarepresented inamannernotexploredinchemistrytextbooks,pointingoutkeychemicalfeatures visual-izedthroughmedian,quartiles,possibleoutliersandshapeofthedistribution.Thesepictorial representationscanshowsimilarities,differences,trendsandirregularitiesamongelements, groupsandperiods,whichhelpbetterunderstandtheircharacteristics.

AllRightsReserved©2016UniversidadNacionalAutónomadeMéxico,FacultaddeQuímica. ThisisanopenaccessitemdistributedundertheCreativeCommonsCCLicenseBY-NC-ND4.0.

PALAVRAS-CHAVE Periodicidade química; Elementos representativos; Análiseexploratória dedados; Boxplot

Representac¸ãográficadaperiodicidadequímicadoselementosprincipaisusando boxplot

Resumo Osgráficosdesempenhamum papel importantenaanálisede dados. Osboxplots sãopoderosasrepresentac¸õesgráficasdosdadosquefornecemumavisãogeraleumresumo numéricodoconjuntodedados.Nesteartigo,osboxplotssãousadosparaanalisaras tendên-ciasperiódicasdoselementosprincipais.Aspropriedadesconsideradassãooraioatômico,a primeiraenergiadeionizac¸ão,aafinidadeeletrônicaeaeletronegatividade.Osboxplotssão construídosemetais,não-metaisemetalóidessãocomparados.Osresultadossãoapresentados

∗_{Correspondingauthor.}

E-mailaddress:[email protected](J.E.V.Ferreira).

PeerReviewundertheresponsibilityofUniversidadNacionalAutónomadeMéxico. http://dx.doi.org/10.1016/j.eq.2016.04.007

0187-893X/AllRightsReserved©2016UniversidadNacionalAutónomadeMéxico,FacultaddeQuímica.Thisisanopenaccessitemdistributed undertheCreativeCommonsCCLicenseBY-NC-ND4.0.

210 J.E.V.Ferreiraetal. deformanãoexploradaemlivrosdequímica,destacandocaracterísticaschavesvisualizadaspor meiodemediana,quartis,possíveisoutlierseaformadadistribuic¸ão.Estasrepresentac¸ões grá-ficaspodemmostrarsimilaridades,diferenc¸as,tendênciaseirregularidadesentreelementos, gruposeperíodos,queajudamaentendermelhorsuascaracterísticas.

DireitosReservados©2016UniversidadNacionalAutónomadeMéxico,FacultaddeQuímica. EsteéumartigodeacessoabertodistribuídosobalicençadeCreativeCommonsCCLicense BY-NC-ND4.0.

Introduction

Graphics arevery useful tools whenwe wanttovisualize a set of data and extract information fromit. Nowadays it is much easier to deal with spreadsheets, graphs and, mainly,calculations(Hibbert, 2006)than insomedecades agowhenitwouldbedifficultorevenimpossibletoperform some tasks due tolimitations relatedto data processing. Infact, ourabilitytostatistically analyzedatahas grown significantlywiththematuring ofcomputerhardwareand software(Schlotter,2013).

Data analysis should always start by (literally) looking at the data. An efficient way to do this is to use box and whiskers plot (Fig. 1) which, for short, are called boxplots (Massart,Smeyers-Verbeke,Capron, & Schlesier, 2005).Theywerefirstproposedbytheeminentstatistician JohnTukey (1977)and arepowerfulgraphical representa-tionsofdatathatgiveanoverviewandanumericalsummary ofadataset.Thegraphicshowsarectangle(thebox)with twolines(thewhiskers) extendingfromopposite edgesof theboxandafurtherlineinthebox,crossingitparallelto thesameedges.Therangeofthedateisrepresentedbythe endsofthewhiskerswhiletheupperandlowerquartilesare indicatedbytheedgesofthebox.Crossingtheboxthereis alinemarkingthemedianofthedate.

According toLarsen (1985) the construction and inter-pretationofthesegraphicalformatsprovidesconsiderable motivationforthe‘‘explanations’’thatwetraditionallygive forchemicalandphysicaltrends.Accordingtohim,tables of data that appear in introductory textbooks, especially alphabetically arrangeddata, seemsrather uninformative anduninteresting,andshouldbeaccompaniedbyaboxplot showing the content of the table of data. He continuous emphasizing that simply seeking highs and lows and par-ticular groupings in a table does not produce the same results and give the clues that numerical detective work ofexploratorydataanalysisachievesandstates ‘‘box-and-whiskersplotsareabletoberapidlyconstructedandthus provideameansforquicklyassessingrelativedatavaluesin alarge(orsmall)datasetconsistingofchemicalandphysical properties’’.

In this work boxplotsare usedto analyzethe periodic trendsoftherepresentativeelementsoftheperiodictable. Thepropertiesconsideredareatomicradius(size),first ion-izationenergy(theenergyrequiredtoremoveanelectron fromagaseousatom),electronaffinity(theenergychange involvedinaddinganelectrontoagaseousatom)and elec-tronegativity (a measure of the tendency of an atom to

attract electron in a chemicalbond). These atomic prop-erties generallyvaryregularlyaswemoveacrossaperiod or uptodown inagroup.The knowledgeof periodicityis importanttounderstandchemicalandphysicalpropertiesof theelementsandtheircompounds.Glasser(2011)believes thattheimportanceof theperiodictableof thechemical elements is that it is theprincipal featurerelated tothe organizationofChemistry.

Therepresentativeelements,whicharealsocalled main-groupelements,comprisebothmetalsandnonmetals.They arefound,inthelong-formperiodictable,ingroups num-bered 1, 2 and 13 through 18. The disposition of these columns is into two blocks of columns separated by the transitionmetals.Onecommonaspectaboutthe represen-tativeelementsisthateveryelementinthegrouphasthe samevalenceelectronconfigurationandshowsdistinctand fairlyregularvariationsintheirpropertieswithchangesin atomicnumber.Forthetransitionelements,thevariations are not so regular because electrons are being added to an innershell.Inthis discussionthenoble gaseswerenot included becausetheyaregenerallynotlisted inelectron affinity/electronegativity tables.They havenoaffinityfor electronssincetheyhaveeightelectronsintheiroutermost shells (except for He, which has two), as a consequence any additionalelectronmust beadded tothe nexthigher electronshell.

Themainpedagogicalobjectiveofthispaperistoshow how boxplots can be used in exploratory data analysis in Chemistry,particularly in making comparisons, as it is describedinthisexamplewiththerepresentativeelements. The results are presented in a manner not explored in chemistrytextbooks.Sothiswork isaguidetotheuse of boxplots intended to teachers and advanced college stu-dents. Authors believe that this technique is important toanyonewhodealswithchemicalinformationespecially whenanalyzingdata.

Methodology

MostpeopleonlythinkofStatisticswhen facedwithalot ofquantitativeinformationtoprocess(Bruns,Scarminio,& BarrrosNeto,2006).Infact,itisnotaneasytasktoextract informationby lookingsomany values.Atypical example wherestatisticsisnecessaryistheanalysisofperiodic prop-erties ofchemicalelements.Table1isadatamatrixwith 38 lines for chemical elements, 4 columns for their peri-odicpropertiesandonecolumnforthecorrespondinggroup

Figure1 Themaincomponentsofaboxplot:median,quartiles,whiskers,fencesandoutliers.

in the periodic table. Values were extracted from Atkins andJones(2009),Lee(1996)andPeriodictable(2015).This matrixwasthestartingpointtoconstructtheboxplots.The strategyadoptedinthisworkcanbeperfectlyreproduced byanyone;itisonlynecessarysoftwarecapabletoconstruct boxplots.AuthorsemployedMinitab16StatisticalSoftware (2010),whichhascommonstatistical,plottingandmodeling functionsavailable.

Forthosenotfamiliarizedwithboxplots,abrief descrip-tionofthemaincomponentsofthegraphicsisdone(Fig.1). Median

Medianisacommonmeasureofcentraltendencyofasetof observationsusedin robustStatistics.Sothemedian indi-catesthemidpointofthedistribution.RobustStatisticsare moreresistant(robust)tothepresenceofoutliersthanthe classicalStatisticsbasedonthenormaldistribution,which usesthemeanasarepresentativemeasureof thecentral tendency(Massartetal.,2005).

Thewaythemedianiscomputeddependsonthenumber ofdata.Whenthisnumberisodd,themedianisthemiddle observationinarankedseriesofdata.Forexample,given thefollowingserieswithfiverankeddata:1,2,4,4,8.The medianis thethird observation:4. Incase thenumberof data is even, the median is the meanof the twomiddle observations.Forexample,intheseries:1,2,4,4,8,100. Themedianiscomputedas(4+4)/2=4.

The difference between median and mean as an ade-quatemeasureofrobuststatisticsisclearwhenwecompare them using these two examples. For the first series, the mean is computed as (1+2+4+4+8)/5=3.8. How-ever,whenwe computethemedianfor thesecondseries, (1+2+4+4+8+100)/6=19.8,itisevidentthattheaddition oftheobservation100causedasignificantincrease inthe meanbutnochangeinthemedian

Quartileandpercentile

Quartilesarevaluesthatdivideupasetofordered obser-vationsintofourequal-sizesets.Therearethreequartiles:

Q1,Q2andQ3.Percentilesdividethetotalobservationsinto 100 equal parts. Quartiles andpercentiles are correspon-dent;theonlydifferenceisthatquartilesrefertofractions andpercentilestopercentagesoftheobservations.Thefirst quartile(Q1) isthe value suchthat 25% or 0.25or 1/4 of thedataliesatorbelowit.Thesecondquartile(Q2)isthe value suchthat 50% or 0.50 or 2/4 of thedata lies at or belowit.Thethirdquartile(Q3)isthevaluesuchthat75% or0.75or3/4ofthedataliesatorbelowit.Consequently,

Q1correspondstothe25thpercentile,Q2correspondstothe 50%percentile,andQ3 correspondstothe75thpercentile (Mickey,Dunn,&Clark,2004).

Interquartilerange

The difference between the third and first quartile is the interquartile range (IQR), which is computed as IQR=Q3−Q1.TheadvantageoftheIQRasameasureof vari-abilityisthatitisnotaffectedbyoutliersasmuchasthe varianceor standard deviationis (Mickeyetal., 2004).In theboxplot,theIQRisrepresentedbytheheightofthebox, whichstartsatthefirstquartile(Q1)andstopsatthethird quartile(Q3).IQRcomprisesthemiddle50%oftheranked samplesandis particularlyuseful for comparingtwodata sets.

Fence

Fencesarelimitsaboveandbelowthe boxof theboxplot thatareusedtoidentifypossibleoutliers.Theupperfence isthe upperlimitcomputed asQ3+1.5timesIQR,soit is

212 J.E.V.Ferreiraetal.

Table1 Chemicalelementsandthefourperiodicpropertiesa_{selectedtoconstructtheboxplots.}

Element Atomicradius(pm) Electronaffinityb_(kJmol−1_{) Ionizationenergy(kJmol−}1_{) Electronegativity}c _Group Metals Li 1.82 59.63 520.22 0.98 1 Na 2.27 52.87 495.85 0.93 1 K 2.75 48.39 418.81 0.82 1 Rb 3.03 46.88 403.03 0.82 1 Cs 3.43 45.51 375.71 0.79 1 Fr 3.48 44.38 392.96 0.70 1 Be 1.53 −66.00d _{899.51 1.57 1} Mg 1.73 −67.00d _{737.75 1.31 2} Ca 2.31 2.37 589.83 1.00 2 Sr 2.49 4.63 549.47 0.95 2 Ba 2.68 13.95 502.85 0.89 2 Ra 2.83 9.65 509.29 0.90 2 Al 1.84 41.76 577.54 1.61 13 Ga 1.87 41.49 578.85 1.81 13 In 1.93 28.90 558.30 1.78 13 Tl 1.96 36.38 589.35 1.80 13 Ge 2.11 118.94 762.18 2.01 14 Sn 2.17 107.30 708.58 1.96 14 Pb 2.02 35.12 715.60 1.80 14 Sb 2.06 100.92 830.58 2.05 15 Bi 2.07 90.92 702.94 1.90 15 Po 1.97 183.30 811.83 2.00 16 Nonmetals H 1.10 72.77 1312.05 2.20 1 B 1.92 26.99 800.64 2.04 13 C 1.70 121.78 1086.45 2.55 14 Si 2.10 134.07 786.52 1.90 14 N 1.55 −7e _{1402.33 3.04 15} P 1.80 72.04 1011.81 2.19 15 As 1.85 77.57 944.46 2.18 15 O 1.52 140.98 1313.94 3.44 16 S 1.80 200.41 999.59 2.58 16 Se 1.90 194.97 940.96 2.55 16 Te 2.06 190.16 869.29 2.10 16 F 1.47 328.17 1681.05 3.98 17 Cl 1.75 348.58 1251.19 3.16 17 Br 1.85 324.54 1139.86 2.96 17 I 1.98 295.15 1008.39 2.66 17 At 2.02 270.20 1037.00e _{2.20 17}

a_{ExtractedvaluesfromRoyalChemistrySociety:Homepage(http://www.rsc.org/periodic-table/element).}

b _{Theconventionadoptedinthisworkisthesameinref.a:positiveelectronaffinitycorrespondstoanexothermicprocesswhile} negativeelectronaffinitycorrespondstoanendothermicprocess.

c _{Paulingscale.}

d _{Lee,J.D.ConciseInorganicChemistry,4thed.,Chapman&Hall,NewYork,USA,1997.}

e _{Atkins,P.,Jones,L.(2009).Chemicalprinciples:thequestforinsight,5thed.,W.H.FreemanandCompany,NewYork,USA.}

fixedatavalue1.5timesIQRabovethetopofthebox.The lowerfenceis thelowerlimitcomputedasQ1−1.5times IQR,soitisfixedatavalue1.5timesIQRbelowthebottom ofthebox.Usuallythefencesarenotshowninthedrawing.

Massartetal.(2005)advisethat,dependingonthe soft-ware,someboxplotsmaybemoreconservativeinthesense thatinadditiontotheextreme level ascomputed above, theyusea second extremelevel, evenmoredistant from thebox thanthefirstone. Inthiswork, weusedthefirst extremeleveldiscussedinthepreviousparagraph.

Whisker

WhiskersarethelinesthatextendfromQ1andQ3, respec-tively,inthedirectionoftheminimumandmaximumvalues of the data set. Softwaremay use three main criteriato extend the whiskers. Some of them extend the whiskers to the maximum and minimum values of the series of observations. However, some programs stop the whiskers at the fences whereas others, like Minitab 16.0, extend the whiskers to the data value just before the fences.

Figure 2 Different types of distributions (symmetric and asymmetric)andthecorrespondingboxplots.

Sometimesthewhiskersarerepresentedendinginasmall horizontallinebutMinitabdoesnotshowthisdetailinthe graphic.

Dataset thatfollowsa symmetricdistribution(suchas normaldistribution)ofobservablevaluesgeneratesboxplot withsymmetric shapeas theone presented in Figure 2a: thepositionofthelineidentifyingthemedianisinthe mid-dleofthebox; thewhiskershavethesamesizeinlength. Onthecontrary,asymmetricdistributiongeneratesboxplot withthelineofthemedianmovedfromthecenterofthebox andonewhiskerislongerthantheother,revealingthedata isskewedinthedirectionofthelongerwhisker(Fig.2b---d). Negativeorleftskeweddistribution(Fig.2c)isdepictured by boxplot withmediangenerally movedtothe right and theright-handwhiskerisshorterthantheleft-handwhisker. Positiveorrightskeweddistribution(Fig.2bandd)is depic-turedbyboxplotswithmediangenerallymovedtotheleft and the left-hand whisker is shorter than the right-hand whisker.

Outlier

Outlieristhevaluebeyondthefence.Therearemany rea-sons to appear an extreme value. Sometimes outlier is a consequenceoferrorwhilecollectingdataorwhilemaking measurements. However sometimes theyare correct and justrevealhowvaluesareindeedverydifferentfromthe restofthedata.Outliersmaybepresentornotinaseries ofvalues.Ifpresent,theyaresignalizedwithadiscrete sym-bol,suchasasterisk,belowthelowerfenceor/andabove theupperfence.

Aftertheseconsiderationsaboutthecomponentsofthe boxplot,wecallattentiontothefactthatthereisavariety ofwaystodrawboxplots,none ofthemis standard. Soft-waremay alsoemploy a particular mathematical method tocomputequartilesandpercentiles.Consequently, differ-entdrawingsof boxplotmay begeneratedfromthesame dataset.The methodologytoconstructboxplotiseasy.In general,acolumnwithdataisselected.Thentheoptionto createthegraphicischosen.Detailedexplanations involv-ingmathematicsandvariationsofboxplotsareavoided,but canbefound in amore specializedliterature (Cox,2009; Dawson,2011; Larsen, 1985;Massart etal., 2005;McGill, Tukey,&Larsen,1978;Mickeyetal.,2004).

Thisactivityhasaninterdisciplinarycharacteristicsince it involves concepts from both Chemistry and Statistics accordingtoFigure3.Themainpurposeistoanswerthree principalquestionsabouttherepresentativeelementswhen we analyze boxplots constructed based on their periodic properties.

Question1. Howdifferentaremetalsfromnonmetals?

Question2. Whatisthetendencyalongagroup?

Question3. Whatisthetendencyalongaperiod?

Results

and

discussions

Theexploratory analysis ofthe dataset presented inthis work (Table 1) can be better visualized through boxplots asalreadyexplained.Thusthevisualizationoftheperiodic trendsof the chemical elements is presented in thenext graphicsandisdiscussedhere.

Figure 3 Statistical andchemical conceptsinvolved inthisinterdisciplinary activity.Key concept areas within the areas of StatisticsandChemistry.

214 J.E.V.Ferreiraetal.

Figure4 Boxplotsforatomicradiusofmetalsandnonmetals. Unitsareinpm.

Figure5 Boxplotsforatomicradiusaccordingtothegroupsin theperiodictable.Unitsareinpm.Differentcolorsfor chemi-calelements:metals(black),metalloids(green)andnonmetals (red).

InFigure4theupperpositionoftheboxplotformetals revealstheygenerallyhavelargeratomicradiiin compari-sontononmetals,suchanevidenceisalsosupportedbythe factthatmedianformetals(2.09pm)isquitesimilartothe maximumvaluefornonmetals(2.10pm).So50%of metal-licatomsarelargerinsizethanallnonmetalatoms.Among nonmetals,valuesforatomicradiiaredistributedinashort range,whilethecontraryisfoundamongmetals.

Consideringvariationsofatomicradiiingroups(Fig.5), thealkalimetalsandalkalineearthmetalscontainthe ele-ments with the largest variations. Elements that receive additionalelectronsinaporbital(Groups13---17)displayon averagesmallerradiusandvariationsinatomicsizeandare smalltoo.Itisconfirmedthetendencytofindlargerradiias wemovedownwardsalongagroupintheperiodictable.But theheaviermembersofthegrouphaveincommonatomic radiuswithsimilarsizes.Metalloids(greensymbols)tendto have intermediateradii between metals (black) and non-metals(red).Hydrogenispointedoutashavinganextreme smallatomicradius(1.10pm).

When we analyze the electron affinities, the contrary is observed. Nonmetals have generally larger values for thisproperty(Fig.6).Q1for nonmetals(73.97kJmol−1)is largerthanQ3formetals(67.45kJmol−1).Consequentlyat least75%oftheatomsclassifiedasnonmetalshavestronger

Figure 6 Boxplots for electronaffinity ofmetals and non-metals.UnitsareinkJmol−1_.

Figure7 Boxplotsforelectronaffinityofatomsaccordingto thegroupsintheperiodictable.UnitsareinkJmol−1_.Different colorsforchemicalelements:metals(black),metalloids(green) andnonmetals(red).

attractionsforelectronthan75%ofmetallicatoms.Theline markingthemediancrossestheboxesneartheircenterand whiskers inboth sidesarefairlythesamesize,suggesting afairlydistributionofelectron affinitieswithsymmetrical shape.Inthisexampleanoutlierispointed:polonium.This elementpresentsan anomalousvalue forelectron affinity (183.30kJmol−1_{)amongallmetals.Thisvalueisevenlarger} thanthe rangeforall othermetallic elements(−67.00to 118.94kJmol−1_).

Thevaluesofelectronaffinityusuallybecomelargeron moving across a period from left to right, but when we lookat Figure7wesee thatvariationsforelectron affini-tiesingroupsareratherirregular.TheelementsinGroups 2and15appearnottofollowthegeneraltrendsincethe addedelectron wouldstartap orbitalorwouldbepaired withanotherelectronintheporbital,respectively(McMurry & Fay, 2003; Zumdahl & Zumdahl, 2007). Groups 1 and 13 display shortrange and most of the boxes exhibit the line marking the media settled in the upper part of the box,indicatingthat50%oftheelementsinthegroupwith the strongest attraction for electrons exhibit small varia-tionsinvaluesforelectronaffinities.Electronaffinitiesfor metalloids(greensymbols)havefairlyintermediatevalues betweenthoseformetals(black)andnonmetals(red).

Resultsfor ionizationenergyarerathersimilartothose for electron affinity.Nonmetals alsohave generallylarger

Figure8 Boxplots forionizationenergy ofmetalsand non-metals.UnitsareinkJmol−1_.

Figure9 Boxplotsforionizationenergyofatomsaccordingto thegroupsintheperiodictable.UnitsareinkJmol−1_.Different colorsforchemicalelements:metals(black),metalloids(green) andnonmetals(red).

values (Fig. 8). Q1 for nonmetals (941.84kJmol−1) is far largerthemaximumvalueformetals(899.51kJmol−1_).Thus nowatleast75%oftheatomsclassifiedasnonmetalshave largerionizationenergiesthanallmetallicatoms.Moreover, theline markingthe median crossestheboxes toward Q1 indicatingadistributionwithasymmetricalshape.

Ionization energiesexhibit aregular increase whenwe move from left to right through the groups despite two principalirregularitiesoccur(Fig.9).Oneoftheminvolves Group 13 because the 2p electrons are slightly higher in energythanthe2s electrons(thegroup before,Group 2). Thenlessenergyisrequiredtoremoveelectronin2porbital, consequently the ionization energyin Group 13 does not follow a tendency to increase. The same dip is found in Group16buttheexplanationforthisbehavioristhefourth

pelectroninthisgroup,whichispairedwithanother elec-troninthesameorbital,soitexperiencesgreaterrepulsion thanit wouldinan orbitalby itself.Thisincreased repul-sionmakesiteasiertoremovethep fourthelectroninan outershellforGroup16thanthethirdpelectroninanouter shellforGroup15.Otherobservationisthesignificant dif-ferenceinionizationenergiesinvolvingtheelementsinthe secondperiod(B,C,N,PandF)fromthoseofotherelements intheirfamilies,becausesecond-periodelementshaveno low-energydorbitals.Goingfromgroups13to15,electrons

Figure10 Boxplotsforelectronegativityofmetalsand non-metals.

Figure11 Schematicboxplotsforelectronegativityofatoms accordingtothegroupsintheperiodictable.UnitsareinPauling scale.Differentcolorsforchemicalelements:metals(black), metalloids(green)andnonmetals(red).

aregoingsinglyintoseparateporbitals,wheretheydonot shieldoneanothersignificantly.

Hydrogen is marked as an outlier among elements in Group 1. The exceedingly high ionization energy for this atomisadirectconsequenceofitssmallsize(atomicradius 1.10pm).Ionization energiesincreasedowntoupthrough the Groups even though some exceptions are observed. Clearlyweobservethatmetalloids(greensymbols)exhibit intermediatevaluesforelectronaffinitiesbetweenthosefor metals(black)andnonmetals(red).

The last periodic property investigated is electroneg-ativity. The position of the boxplots for metals and nonmetalsdiffergreatlywithrespecttothe electronegativ-ities(Fig.10),whosevaluestendtobelargerfornonmetals.

Q1for nonmetals(2.18)islargerthanthemaximum value formetals(2.05).Thenatleast75%oftheatomsclassified asnonmetals have strongerpower toattract electrons to itselfwheninchemicalcombinationthanallmetallicatoms. The line marking the median crosses the boxes near the center. However,distributionis only somewhat symmetri-calformetals;nonmetalsshowwhiskerswithdifferentsize, revealingaratherasymmetricaldistribution.

Electronegativity displays a regular increase when we movefromlefttorightacrosstheperiodictable(Fig.11). Thesamewayasoccurredwithionizationenergy,hydrogen

216 J.E.V.Ferreiraetal. ismarkedasan outlieramongelements inGroup 1.

Elec-tronegativity tends to increase down to up through the Groupseventhough some exceptionsareobserved inthis casetoo.Valuesofelectronegativitiesformetalloids(green symbols)areintermediatebetweenthoseformetals(black) andnonmetals(red).

Thisarticledescribedtheuseofboxplotstoanalyzethe periodic trends of the representative elements. A similar studywaspresentedinthisjournal(Ferreira,DaCosta,De Miranda,&Figueiredo,2015)usingtheknearestneighbor(k -NN)methodtoclassifytherepresentativeelementsasmetal ornonmetalaccordingtotheiratomicradius,firstionization energy,electronaffinityandelectronegativity.Nowwecan haveabetterideaabouthowthisclassificationisrelatedto theseproperties.Boxplotsshowaratherdistinctdistribution ofvaluesforbothclasses,whichsupportthisdistinctionin behaviorandclassification.Moreover,metalloidsarelocated in boxplots in a regionintermediate between metals and nonmetals, which allowed for the misclassifications veri-fiedwhenusingthek-NNmethod.Thisregionisnotclearly definedsincesomeirregularitiesoccuralongthegroupsand acrosstheperiods,somethingobservedevenwhenwe ana-lyzemetals andnonmetals separately.Authors agreewith

RichandLaing(2011)whentheystatethat‘‘natureisclever inthatnosingleandsimpleperiodicchartrevealallofthe importantrelationshipsamongthechemicalelements’’.So wepresentedinthisarticleanalternativewayofvisualizing theserelationshipsthroughboxplots.

Conclusion

Applicationofboxplotstoinvestigatetheperiodic proper-tiesofchemicalelementsshowedsimilarities,differences, trends and irregularities among elements, groups and periods,whichhelpbetterunderstandtheircharacteristics. Inaddition, theypointed out thatmetals, nonmetals and metalloids display a somewhat distinct range for atomic radius, first ionization energy, electron affinity and elec-tronegativity.Finally,authorswantwiththisarticletocall attentiontotheadvantages oftheapplicationofboxplots indataanalysisofchemicalinterest.Thesepictorial repre-sentationsareeasytobeconstructedandinterpretedand, themostimportant,canbeveryusefultouncoverchemical informationhidden.

Conflict

of

interest

Theauthorsdeclarenoconflictofinterest.

References

Atkins,P.,&Jones,L.(2009).Chemicalprinciples:Thequestfor insight(5thed.).NewYork,USA:W.H.FreemanandCompany. Bruns, R., Scarminio, I., & Barrros Neto, B. (2006). Statistical

design:Chemometrics.Amsterdan,TheNetherlands:Elsevier. Cox,N.J.(2009).SpeakingStata:Creatingandvaryingboxplots.

STATAJournal,9(3),478---496.

Dawson,R.(2011).HowSignificantisaboxplotoutlier?Journalof StatisticsEducation,19(2),1---13.

Ferreira,J.E.V.,DaCosta,C.H.,DeMiranda,R.M.,&Figueiredo, A.F.(2015).Theuseoftheknearestneighbormethodtoclassify therepresentativeelements.EducaciónQuímica,25,195---201. Glasser,L.(2011).Periodictablesontheworldwideweb.Australian

JournalofEducationinChemistry,71,3---4.

Hibbert,D.B.(2006).TeachingmoderndataanalysiswiththeRoyal AustralianChemicalInstitute’stitrationcompetition.Australian JournalofEducationinChemistry,66,5---11.

Larsen,R.D.(1985).Box-and-whiskerplots.JournalofChemical Education,62,302---305.

Lee,J.D.(1996).Conciseinorganicchemistry(5thed.).Oxford, England:BlackwellPublishing.

Massart, D.L., Smeyers-Verbeke,J., Capron, X., & Schlesier, K. (2005).Visualpresentationofdatabymeansofboxplots.LC.GC, 18(4),215---218.

McGill,R.,Tukey,J.W.,&Larsen,W.A.(1978).Variationsofbox plots.TheAmericanStatistician,32(1),12---16.

McMurry,J.,&Fay,R.C.(2003).Chemistry(4thed.).UpperSaddle River,NJ:PretinceHall.

Mickey,R.M.,Dunn,O.J.,&Clark,V.A.(2004).Appliedstatistics: Analysisofvarianceandregression(3rded.).NewJersey,USA: Wiley-Interscience.

(2010).Minitab16StatisticalSoftware.Pennsylvania,USA:Minitab Inc.,StateCollege.

Periodic table. Royal Society of Chemistry. Retrieved from http://www.rsc.org/periodic-table/element.

Rich,R.L.,&Laing,M.(2011).Cantheperiodictablebeimproved? EducaciónQuímica,22(2),162---165.

Schlotter, N.E.(2013). Astatisticscurriculumforundergraduate chemistrymajor.JournalofChemicalEducation,90(1),51---55. Tukey, J. W. (1977). Exploratory data analysis. Reading, USA:

Addison-Wesley.

Zumdahl, S. S., & Zumdahl, S. A. (2007). Chemistry(7th ed.). Boston,USA:HoughtonMifflinCompany.