# Count gives different results depending on specification

I have a tremendous list of coordinates in which i wish to count how many times a certain X appears. I use count and found accidentally, that in a loop script and individually, it gives wrong results certain values... I shal post the list at the end because it is long (1000 points).

My loop script should return to me how many times any one appears:

demo2 = Reap[
Do[Clear[dummy3];
dummy3 =
Count[
tabelsav[[All, 1]], i]; If[dummy3 == 0, Continue,
Sow[{i, dummy3}]],
{i, 0, 10, 0.01}]]


This returns a correct (seemingly) list where a particular value, 0.95 appears 4 times as it should. However if i ask just:

Count[tabelsav[[All, 1]], 0.95]


I cannot explain this discrepancy.

The long source-list is:

   tabelsav = {{0.81, 0.5109462100846561}, {1.3,
0.5048072687790746}, {1.61, 0.5010869822978168}, {2.95,
0.5019252231248612}, {7.7, 0.5031009140137692}, {1.36,
0.501960184855639}, {3.63, 0.5001125487449931}, {1.35,
0.5033465830176649}, {3., 0.5028139472844518}, {2.42,
0.500744556085373}, {8.44,
0.503866318664603}, {0.9500000000000001,
0.50323521089743}, {9.53, 0.5093581725292053}, {4.75,
0.5008881290304839}, {2.33, 0.5036601072538167}, {3.22,
0.5063466060976247}, {9.05, 0.5040083800013683}, {7.72,
0.5063431323886172}, {0.88,
0.5011011047670997}, {4.0200000000000005,
0.5028218805839639}, {1.04, 0.5011978901324959}, {2.99,
0.5101814443088554}, {1.73, 0.5021968961092514}, {1.05,
0.5040744761035159}, {2.11, 0.5021756107938509}, {5.05,
0.5000857792289806}, {3.2600000000000002,
0.5084904752220928}, {1.42, 0.5025388409352449}, {9.57,
0.5052046775360528}, {1.18,
0.5010234800254477}, {4.6000000000000005,
0.5000999647189075}, {9.39, 0.5007412512678611}, {0.63,
0.5077966238805889}, {4.5200000000000005,
0.5062010476131855}, {0.89, 0.5049669240401983}, {4.28,
0.5032637763749983}, {1.41, 0.5022525486137775}, {0.89,
0.5000193756828281}, {5.82, 0.5051011473483499}, {1.32,
0.5009934059766663}, {4.94, 0.5082684668663134}, {3.95,
0.5041504627396654}, {4.64, 0.5112623897085815}, {5.64,
0.5065690511624643}, {5.22, 0.5041508418690306}, {9.74,
0.5031308760002466}, {8.9, 0.500217532478172}, {7.4,
0.5045464565085634}, {3.8000000000000003,
0.5001922739885245}, {2.02, 0.5015750517902692}, {4.21,
0.5019770775727549}, {1.36, 0.5013158499000089}, {5.66,
0.5034607143512423}, {2.32, 0.5016779867287418}, {1.07,
0.5054164430851992}, {8.620000000000001,
0.5055408077588736}, {1.96,
0.5027274565056948}, {0.8200000000000001,
0.5031947382858473}, {5.14, 0.5009631756259397}, {1.24,
0.5018812890717584}, {9.4, 0.5059872970133213}, {3.38,
0.5039103146189894}, {3.18, 0.5072475864421937}, {7.66,
0.5042209593945588}, {5.94, 0.5041780109744176}, {7.84,
0.5031076143699232}, {0.89,
0.5072574364040147}, {1.1300000000000001,
0.5070123711835102}, {7.5600000000000005,
0.5001417068696901}, {0.72, 0.5008013996326409}, {0.76,
0.5004866756883766}, {1.02,
0.5001265136641909}, {5.1000000000000005,
0.5033439301179092}, {4.3100000000000005,
0.5006210221598733}, {3.02, 0.5028748025251597}, {1.76,
0.5010330744072706}, {1.94, 0.5109598585807998}, {5.05,
0.5018754496005065}, {3.45,
0.5006893194185126}, {5.0200000000000005,
0.5003116980927497}, {4.73, 0.5026952432619735}, {2.31,
0.5019835103454474}, {1.1400000000000001,
0.5026526911993401}, {5.0600000000000005,
0.5033990031948213}, {8.56, 0.5003628830728191}, {5.4,
0.501827007325571}, {2.97, 0.5013909391635281}, {1.03,
0.5063933382277723}, {1.33, 0.5029672522568759}, {4.49,
0.5031500004292724}, {5.21, 0.5036030658004264}, {5.03,
0.5045007462822559}, {3.34, 0.5009009067256426}, {2.33,
0.502683252130243}, {2.05,
0.5028873973041389}, {1.4000000000000001,
0.5059338026247351}, {6.42,
0.5022032303965346}, {0.7000000000000001,
0.5024043005413459}, {2.08, 0.5037600808508966}, {9.07,
0.5013947967013694}, {1.6400000000000001,
0.5024621241310729}, {1.78, 0.5039479519862525}, {3.54,
0.5070104903057179}, {0.9, 0.5057995693100946}, {1.2,
0.5005837436594683}, {7.19,
0.5076759763851902}, {0.9500000000000001,
0.5057819262070574}, {5.65, 0.5096431980239409}, {6.32,
0.5014264793833055}, {4.98, 0.5036648306874812}, {1.54,
0.5039311805939243}, {1.6500000000000001,
0.5008706573615119}, {7.21, 0.5015512501592116}, {1.,
0.5008625411142199}, {2.59, 0.5003932303291205}, {0.9,
0.5042075673417277}, {1.37, 0.5032638234391172}, {8.51,
0.5004540503043337}, {5.57, 0.5053402244041116}, {6.8,
0.5006723513383826}, {1.06, 0.5025698211769374}, {1.21,
0.5023855529207454}, {3.8000000000000003,
0.505914578919494}, {3.44,
0.5017239835562792}, {3.0300000000000002,
0.5022346213766277}, {5.1000000000000005,
0.5011655501234785}, {5.1000000000000005,
0.5061064362225602}, {6.46, 0.5020053134452778}, {1.87,
0.5036316344435962}, {8.85, 0.5071278559381912}, {7.49,
0.501531568693161}, {2.06, 0.5058045753619874}, {5.59,
0.5017009176358966}, {4.48, 0.5057065740138614}, {0.72,
0.5082500569165581}, {0.9500000000000001,
0.5039844166432038}, {6.69,
0.5038784676602129}, {1.3900000000000001,
0.5009486184443135}, {4.68, 0.5005596940476884}, {2.13,
0.5019978689344542}, {4.15, 0.5154384705795821}, {6.75,
0.5059854595934982}, {0.99, 0.5067948432930836}, {4.18,
0.5060636823095165}, {7.12, 0.5016927529829089}, {1.59,
0.5017673618057692}, {0.88, 0.5017205659974725}, {1.49,
0.5070437931065557}, {0.71, 0.5053672223303575}, {0.98,
0.5038250885415472}, {3.18, 0.5017874096084308}, {0.87,
0.5089700052509033}, {1.77, 0.501416753797174}, {1.19,
0.5037659967971813}, {0.8300000000000001,
0.5101486883056678}, {4.24, 0.5017325256509887}, {5.79,
0.5054443661367897}, {9.23, 0.5093651148490717}, {1.33,
0.5009917503061815}, {6.0600000000000005,
0.5092699934378212}, {2.12, 0.5073881728088648}, {9.24,
0.5029793903961434}, {0.87, 0.5050296353749212}, {5.71,
0.5032880878265164}, {4.68, 0.50051683895868}, {2.92,
0.5031438215969047}, {4.5200000000000005,
0.507039907981513}, {7.5200000000000005,
0.5057058632368994}, {5.3500000000000005,
0.5006420640899709}, {6.03, 0.5028173959063368}, {1.21,
0.5077444901612066}, {0.87, 0.509370820189887}, {3.38,
0.5017678147904528}, {8.21, 0.5023072108120711}, {1.72,
0.5033980577659639}, {1.26, 0.5058064721029873}, {1.21,
0.5044717093814677}, {1.57,
0.5012283991549582}, {3.2600000000000002,
0.5008714353301591}, {3.9, 0.5046836821554793}, {3.71,
0.50749085777909}, {4.86, 0.5025110408732278}, {5.86,
0.504195370319043}, {1.03, 0.5009897144061476}, {3.23,
0.5020818305488777}, {1.06, 0.5037426774713709}, {2.99,
0.5028930101703603}, {9.58, 0.5001418570249581}, {8.6,
0.5032008473213024}, {1.05, 0.5031112828622336}, {5.79,
0.5036122947579244}, {7.63,
0.5028723174583136}, {1.6500000000000001,
0.5025748394625876}, {8.39, 0.5126932395095996}, {1.8,
0.5027458364819463}, {4.63, 0.5016982616830904}, {5.47,
0.5004066478872781}, {6.4, 0.5008329010607683}, {3.4,
0.5064779705236596}, {2.47, 0.5012878133541617}, {2.67,
0.5033263252802949}, {9.86, 0.503900737442421}, {4.79,
0.5103801481318953}, {1.04, 0.508046923457422}, {0.84,
0.5094401342091538}, {7.25, 0.5008265212688686}, {4.04,
0.5032506361276915}, {1.45, 0.5002579933952799}, {1.18,
0.5005671576943244}, {1.6400000000000001,
0.5028579181703327}, {0.74, 0.507588931964315}, {3.84,
0.5020519751581894}, {4.7700000000000005,
0.5088310521898424}, {1.48, 0.5002018342287672}, {0.89,
0.5112377017968762}, {2.27,
0.5034614169222869}, {4.0200000000000005,
0.5039010521110797}, {3.86, 0.5022777899515114}, {0.87,
0.5009916597355644}, {1.33,
0.5004231294167313}, {8.120000000000001,
0.5007312935604318}, {5.03, 0.5025158180571903}, {5.8,
0.5022372577051709}, {5.9, 0.5005237589894902}, {8.07,
0.5092973099237901}, {9.120000000000001,
0.5018064400737199}, {3.62, 0.5014996810167306}, {4.41,
0.5013437649995602}, {1.17, 0.5056746389026118}, {3.84,
0.5034965981253541}, {2.77,
0.5122030052133616}, {6.1000000000000005,
0.501659971135687}, {3.5100000000000002,
0.5043663274858946}, {8.77, 0.5011189361653974}, {5.21,
0.5012379833159547}, {8.39, 0.5017612953951748}, {2.27,
0.5094715558734839}, {8.01, 0.5068175002427142}, {3.64,
0.5019872086788807}, {3.5, 0.5003063452767259}, {5.45,
0.5041167357214407}, {6.2, 0.5012274271254351}, {7.32,
0.5030277100739914}, {3.18,
0.5015713801171047}, {5.8500000000000005,
0.5087080700527293}, {1.54, 0.5019921455670423}, {3.93,
0.5003463520296838}, {5.3100000000000005,
0.5000460318009461}, {0.8200000000000001,
0.5084306384161053}, {0.87, 0.5032408112284076}, {1.03,
0.5006433241835044}, {2.5, 0.502739540042087}, {4.18,
0.5023724970546544}, {3., 0.5062418050883324}, {0.88,
0.5046989551933203}, {3.93, 0.5019258493392756}, {6.7,
0.5011817479922397}, {7.84, 0.5045093237303065}, {2.68,
0.5022300283961209}, {6.63, 0.5005368434047653}, {7.58,
0.504998173761705}, {3.49, 0.505626758641359}, {2.13,
0.502538829740494}, {1.46, 0.5057436402499756}, {3.85,
0.5000824763551935}, {3.5500000000000003,
0.5018664353073353}, {3.87, 0.5001919876430388}, {3.13,
0.5020499033634109}, {2.37, 0.5016400757328934}, {2.59,
0.5015239999780767}, {6.53, 0.5006370028352829}, {2.54,
0.5002220569112746}, {2.98,
0.5024630480954935}, {0.8200000000000001,
0.5031855589823996}, {7.21, 0.503005467629622}, {2.7,
0.5027968593586135}, {1.27, 0.5003124488131474}, {1.18,
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0.501638426184796}, {3.49, 0.5004662739476854}, {0.91,
0.5034400062583759}, {3.24, 0.503344295854238}, {2.92,
0.5011596358547996}, {8.51, 0.5002193235795764}, {6.26,
0.5070106765591609}, {3.48, 0.502403540043892}, {0.74,
0.503763104586026}, {2.36, 0.5023821090492947}, {1.31,
0.5061012784481049}, {2.47, 0.5021948467830896}, {1.83,
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0.505159948394197}, {2.57, 0.5017976786426525}, {7.43,
0.5011997680779028}, {7.67, 0.5005309669549508}, {1.25,
0.5047793616284166}, {3.19, 0.5010006683685084}, {9.43,
0.5008618019224559}, {4.76, 0.5007625124991477}, {9.01,
0.5041063160032132}, {5.67, 0.5002854120655155}, {0.93,
0.500257600075891}, {0.9, 0.5064687392974402}, {1.26,
0.5065946381018079}, {3.49, 0.501497039242547}, {3.88,
0.5017394902940288}, {6.12, 0.5014136584433144}, {1.94,
0.5089918218244472}, {6.69, 0.5005444002434879}, {2.47,
0.5033671288673328}, {1.9000000000000001,
0.5004675627088869}, {5.25,
0.5028701949011372}, {1.6400000000000001,
0.5042329315477915}, {5.9, 0.5005602457136121}, {1.18,
0.5028041884273412}, {2.23, 0.5048398044728458}, {3.35,
0.5057278578876744}, {5.04, 0.5071007057125294}, {2.64,
0.5029458704151538}, {4.78, 0.5013207931197564}, {0.75,
0.5000817041493955}, {0.88, 0.5017168883186924}, {1.25,
0.5060153097998106}, {2.2800000000000002,
0.5014708508791023}, {0.8300000000000001,
0.5011748831260362}, {0.63, 0.5040830855164764}, {4.96,
0.5004888697129709}, {9.89, 0.5020337081874794}, {3.04,
0.5029412425581916}, {6.04, 0.5055105956871854}, {9.84,
0.5012223857558749}, {5.59, 0.5036566134207263}, {1.42,
0.509785076498579}, {4.82, 0.5162990704393645}, {9.91,
0.500080075846436}, {0.97, 0.505998632027506}, {2.37,
0.5022308389113287}, {5.04, 0.5012231837259915}, {2.08,
0.5003527112362756}, {7.8, 0.5004431915871477}, {8.9,
0.5051826496589197}, {9.93, 0.5064385454179643}, {7.15,
0.502738559523307}, {3.37, 0.5009242739426236}, {4.66,
0.5008532069295164}, {2.67, 0.50051267354687}, {9.85,
0.5043266824689545}, {1.03,
0.5025006675871861}, {0.9500000000000001,
0.5056520506364827}, {3.41, 0.5004143481728401}, {1.35,
0.5020466036800005}, {3.39, 0.5027192313237163}, {2.41,
0.5101925844197512}, {9.13, 0.5002216690576016}, {3.18,
0.5021529878310833}, {0.88, 0.5018548355264083}, {2.92,
0.5018645227226244}, {5.36, 0.5074683846278654}, {0.8,
0.5022530550884748}, {6.29, 0.5003193989130776}, {1.,
0.5005060489124801}, {4.2700000000000005,
0.5038813436903959}, {9.92, 0.5028624052059641}, {7.17,
0.5017759977306311}, {5.48, 0.5008863974643626}, {4.83,
0.5015365478812477}, {0.65, 0.5086793365224469}, {2.77,
0.5004031827924348}, {1.86, 0.5018055949396782}, {5.55,
0.5038992912562512}, {3.66, 0.5057939678089606}, {8.25,
0.5129646657679212}, {1.18, 0.5034658252678281}, {0.71,
0.5040046067290045}, {3.27, 0.5093106554628457}, {1.45,
0.5005018998272578}, {8.59, 0.500215754936234}, {3.74,
0.5021207903645754}, {1.44, 0.501660438319052}, {5.01,
0.5079123602372846}, {0.79, 0.5054434721907501}, {0.65,
0.5036054711414452}, {6.140000000000001,
0.5039809222996585}, {1.1,
0.5049976513196622}, {3.3200000000000003,
0.5070530373996325}, {7.140000000000001,
0.5024051710238404}, {1.27, 0.5070039228079133}, {6.21,
0.5028698955886769}, {6.6000000000000005,
0.5004591989022191}, {0.9400000000000001,
0.5001516853579012}, {1.42, 0.5006411020404911}, {4.39,
0.50225303658142}, {5.63, 0.504666226611208}, {0.9,
0.5019914369672841}, {0.85, 0.5003866401775756}, {0.99,
0.5050402628743712}, {1.43,
0.5016992188610021}, {1.1500000000000001,
0.5079240350014476}, {5.62, 0.5019499481941615}, {9.72,
0.5084674024947616}, {8.15, 0.5049303759519219}, {3.66,
0.5071942524274655}, {3.6, 0.5001416538810785}, {0.88,
0.5010537688689856}, {2.47, 0.5019405289225632}, {4.22,
0.5019929653938368}, {1.67,
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0.5010614774579043}, {9.4, 0.5013242746881199}, {3.62,
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0.501402949453368}, {6.140000000000001,
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0.5026307057896082}, {2.98, 0.5025886071719675}, {5.73,
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0.51022840062377}, {5.95, 0.5004557300514152}, {1.01,
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0.5052569443605351}, {0.85,
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0.5011435590125549}, {4.76, 0.504660914958012}, {6.19,
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0.5028681026560692}, {0.81, 0.502404213383239}, {2.49,
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0.5030901279090607}, {2.32, 0.5031953692824397}, {1.8,
0.5055503409759046}, {7.87, 0.509365706814609}, {1.45,
0.5044185877771425}, {0.84,
0.5008919585649368}, {4.5600000000000005,
0.500386262707069}, {1.6600000000000001,
0.5007464937698282}, {1.44, 0.5010127723874596}, {9.74,
0.5031551304132433}, {4.32, 0.5010416751840887}, {7.21,
0.501462901252289}, {1.09,
0.5087557702622477}, {8.040000000000001,
0.5001203493042328}, {3.15, 0.5003145130543539}, {8.73,
0.5036964915455299}, {1.1500000000000001,
0.5050953554650189}, {9.35, 0.5072877824517771}, {3.1,
0.5000278609908476}, {2.7800000000000002,
0.5004115091697551}, {6.71, 0.5002300328077767}, {2.43,
0.5013323077384152}, {6.3100000000000005,
0.5005694159556053}, {0.91, 0.5049928109696685}, {4.82,
0.5009403511151124}, {1., 0.5023532502895675}, {2.,
0.5048067395609089}, {7.24, 0.5065146690614348}, {4.16,
0.5025327294769528}, {0.96, 0.5074742744336952}, {6.69,
0.5002380238879927}, {6.0200000000000005,
0.5020107612761264}, {1.69, 0.5040332742057951}, {7.97,
0.5000617413417427}, {2.09, 0.5022823581279093}, {0.73,
0.5009663552401961}, {4.37, 0.5051543767548864}, {6.07,
0.5007999942246505}, {0.65, 0.5107966156096774}, {8.32,
0.5034165472290095}, {6.41, 0.5014854922860411}, {1.41,
0.5072954739224551}, {6.33, 0.5000001992225086}, {1.07,
0.5034706016464965}, {1.97, 0.5005196008574128}, {7.95,
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0.5035208302561678}, {7.34, 0.509467663946227}, {4.13,
0.5064034573057505}, {1.04, 0.5043103810857164}, {5.13,
0.5013125945427757}, {5.26, 0.5006947636021745}, {4.57,
0.5012116821991728}, {7.8, 0.5085483556324307}, {6.33,
0.5036915499735362}, {7.45, 0.5011122663327268}, {1.3,
0.5045147661736676}, {1.18,
0.5012468552973133}, {1.3900000000000001,
0.5029222574858631}, {3.42,
0.5028626295358313}, {5.8100000000000005,
0.5046357114157952}, {3.89, 0.5013938727271786}, {6.74,
0.5022545431999902}, {1.23, 0.5000121998018545}, {7.67,
0.5039106302399582}}


Edit01: I now used two steps to correct the precision issue:

1) round2[x_, n_] := Floor[10^n x]/10^n // N 2) tabelsav2 = round2[tabelsav, 2]

Count[tabelsav2[[All, 1]], 0.94]


Count[tabelsav2[[All, 1]], 0.95]


However a slightly modified code (just to see if a different module works) now gives a completely differently wrong result:

    tabelmod = {};
Do[
If[
MemberQ[tabelsav2[[All, 1]], i] == True,
AppendTo[tabelmod, {i, Count[tabelsav2[[All, 1]], i]}],
Continue],
{i, 0, k*h1, h1}]


where k=1000 and h1=0.01 (timestep). In tabelmod there is no 0.94 or 0.95 component...

• This is likely a precision issue. You are trying to mach 0.95, but 0.9500000000000001  shows up in your list. Nov 29, 2016 at 19:59
• In your demo2 you take the values to be counted from tabelsav itself, i.e. values really existing in the list. Look closely - you'll see there's no 0.95 - there's an 0.9500000000000001, which is not the same. So, Count[tabelsav[[All, 1]], 0.95] correctly says there's no 0.95. Nov 29, 2016 at 20:01
• I used round2[x_, n_] := Floor[10^n x]/10^n // N and tabelsav2 = round2[tabelsav, 2] to produce the table i want... BUT now its even worse... now the 0.95 doesnt show up in the loop! It does however if i specifically ask it through Count... what gives? Nov 29, 2016 at 20:35
• You are facing numerical artifacts; MemberQ[Table[i, {i, 0, k*h1, h1}], 0.95] gives False, because 0.01*95 =!= 0.95 -- see here. You could do round2[x_, n_] := Floor[10^n x]/10^n; tabelsav2 = round2[tabelsav, 2]; k = 1000; h1 = 1/100; then create tabelmod (run N on it afterwards) and see that there are 4. occurences of 0.95. Nov 29, 2016 at 21:47

Count[tabelsav[[All, 1]], 0.95]

(*  0  *)


The Count is 0 since the four cases are not the same as 0.95

Cases[tabelsav[[All, 1]], _?(# == 0.95 &)] // InputForm

(*  {0.9500000000000001,
0.9500000000000001,
0.9500000000000001,
0.9500000000000001}  *)


However, if you use a pattern that tests if they are numerically Equal as was used with Cases

Count[tabelsav[[All, 1]], _?(# == 0.95 &)]

(*  4  *)
`