Count gives different results depending on specification

Question

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 get an answer 0...

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`, 
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   0.5028930101703603`}, {9.58`, 0.5001418570249581`}, {8.6`, 
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   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`, 
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   0.5020519751581894`}, {4.7700000000000005`, 
   0.5088310521898424`}, {1.48`, 0.5002018342287672`}, {0.89`, 
   0.5112377017968762`}, {2.27`, 
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   0.5039010521110797`}, {3.86`, 0.5022777899515114`}, {0.87`, 
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   0.5004231294167313`}, {8.120000000000001`, 
   0.5007312935604318`}, {5.03`, 0.5025158180571903`}, {5.8`, 
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   0.5018064400737199`}, {3.62`, 0.5014996810167306`}, {4.41`, 
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   0.501659971135687`}, {3.5100000000000002`, 
   0.5043663274858946`}, {8.77`, 0.5011189361653974`}, {5.21`, 
   0.5012379833159547`}, {8.39`, 0.5017612953951748`}, {2.27`, 
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   0.5034400062583759`}, {3.24`, 0.503344295854238`}, {2.92`, 
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   0.5070106765591609`}, {3.48`, 0.502403540043892`}, {0.74`, 
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   0.507019869215177`}, {1.53`, 0.5023948453949935`}, {0.92`, 
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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]

Gives the answer 1 and

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

Gives the answer 4

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...

Answer 1

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  *)