Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 19 Oct 2011 08:56:54 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/19/t13190290289kre59bil9fq3ry.htm/, Retrieved Wed, 15 May 2024 05:10:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132775, Retrieved Wed, 15 May 2024 05:10:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-10-19 12:56:54] [ded1bbd321fb25f4a0a8bacc8426c40e] [Current]
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Dataseries X:
2.98
2.98
2.98
3.03
3.07
3.08
3.08
3.08
3.08
3.08
3.08
3.08
3.08
3.08
3.12
3.15
3.15
3.15
3.15
3.16
3.19
3.20
3.20
3.20
3.21
3.21
3.21
3.21
3.21
3.28
3.30
3.30
3.30
3.30
3.30
3.30
3.30
3.45
3.49
3.50
3.54
3.64
3.67
3.67
3.68
3.68
3.68
3.68
3.70
3.83
3.87
3.87
3.87
3.87
3.87
3.87
3.87
3.87
3.87
3.88
3.88
3.88
3.88
3.88
3.88
3.89
3.89
3.91
3.95
3.99
3.99
3.99
4.00
4.00
4.00
4.00
4.00
4.00
4.00
4.00
4.06
4.07
4.07
4.07
4.07
4.07
4.30
4.44
4.52
4.52
4.52
4.53
4.53
4.53
4.53
4.53
4.53
4.53
4.53
4.61
4.63
4.63
4.63
4.63
4.63
4.63
4.63
4.63
4.63
4.63
4.66
4.73
4.73
4.72
4.7
4.74
4.74
4.74
4.76
4.88
4.88
4.88
4.88
4.89
4.97
4.97
4.97
4.97
4.97
4.97
4.97
4.97




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132775&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132775&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132775&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.957121212121210.055021343649828371.9197487670507
Geometric Mean3.90649361723824
Harmonic Mean3.8558707986586
Quadratic Mean4.00691788150081
Winsorized Mean ( 1 / 44 )3.957121212121210.055021343649828371.9197487670507
Winsorized Mean ( 2 / 44 )3.957121212121210.055021343649828371.9197487670507
Winsorized Mean ( 3 / 44 )3.958257575757580.054870939381189372.1375945153681
Winsorized Mean ( 4 / 44 )3.95946969696970.054717463943821872.3620835394504
Winsorized Mean ( 5 / 44 )3.959848484848480.054670694693761372.4309158138493
Winsorized Mean ( 6 / 44 )3.959848484848490.054670694693761372.4309158138494
Winsorized Mean ( 7 / 44 )3.959848484848490.054670694693761372.4309158138494
Winsorized Mean ( 8 / 44 )3.9550.054008260520846573.2295386272147
Winsorized Mean ( 9 / 44 )3.954318181818180.053918530011282673.3387609230208
Winsorized Mean ( 10 / 44 )3.954318181818180.053918530011282673.3387609230208
Winsorized Mean ( 11 / 44 )3.954318181818180.053918530011282673.3387609230208
Winsorized Mean ( 12 / 44 )3.954318181818180.053918530011282673.3387609230208
Winsorized Mean ( 13 / 44 )3.94250.052439932370811575.1812563777147
Winsorized Mean ( 14 / 44 )3.944621212121210.051664230872011176.3511068594693
Winsorized Mean ( 15 / 44 )3.94803030303030.051253931811957877.0288281007391
Winsorized Mean ( 16 / 44 )3.94803030303030.051253931811957877.0288281007391
Winsorized Mean ( 17 / 44 )3.946742424242420.051102634501304177.2316821384562
Winsorized Mean ( 18 / 44 )3.946742424242420.051102634501304177.2316821384562
Winsorized Mean ( 19 / 44 )3.946742424242420.050763941428817477.7469659202223
Winsorized Mean ( 20 / 44 )3.948257575757580.049880785036393379.1538780489702
Winsorized Mean ( 21 / 44 )3.943484848484850.048974799003264880.5206949031473
Winsorized Mean ( 22 / 44 )3.938484848484850.048423024717490681.3349614457737
Winsorized Mean ( 23 / 44 )3.938484848484850.048423024717490681.3349614457737
Winsorized Mean ( 24 / 44 )3.940303030303030.048212069524752681.7285602784596
Winsorized Mean ( 25 / 44 )3.940303030303030.048212069524752681.7285602784596
Winsorized Mean ( 26 / 44 )3.940303030303030.048212069524752681.7285602784596
Winsorized Mean ( 27 / 44 )3.940303030303030.048212069524752681.7285602784596
Winsorized Mean ( 28 / 44 )3.940303030303030.048212069524752681.7285602784596
Winsorized Mean ( 29 / 44 )3.955681818181820.046468780878845585.1255777184076
Winsorized Mean ( 30 / 44 )3.960227272727270.045967315061931886.1531126495349
Winsorized Mean ( 31 / 44 )3.960227272727270.045967315061931886.1531126495349
Winsorized Mean ( 32 / 44 )3.955378787878790.04543100776572387.0634173090709
Winsorized Mean ( 33 / 44 )3.935378787878790.043281086312310990.9260631649028
Winsorized Mean ( 34 / 44 )3.935378787878790.043281086312310990.9260631649028
Winsorized Mean ( 35 / 44 )3.935378787878790.043281086312310990.9260631649028
Winsorized Mean ( 36 / 44 )3.935378787878790.043281086312310990.9260631649028
Winsorized Mean ( 37 / 44 )3.977424242424240.0387303741666905102.695218623655
Winsorized Mean ( 38 / 44 )3.988939393939390.0375476037700848106.236856507937
Winsorized Mean ( 39 / 44 )3.991893939393940.0372488323277666107.168297364807
Winsorized Mean ( 40 / 44 )4.004015151515150.0360420148086264111.092988912396
Winsorized Mean ( 41 / 44 )4.03196969696970.0327418207527918123.144333585233
Winsorized Mean ( 42 / 44 )4.041515151515150.0318809455542687126.768986341248
Winsorized Mean ( 43 / 44 )4.041515151515150.0318809455542687126.768986341248
Winsorized Mean ( 44 / 44 )4.018181818181820.0285494036704809140.744859842256
Trimmed Mean ( 1 / 44 )3.956846153846150.054803931390279572.2000421040592
Trimmed Mean ( 2 / 44 )3.95656250.054558156942176572.5200908856464
Trimmed Mean ( 3 / 44 )3.956269841269840.05428130539972572.8845743877391
Trimmed Mean ( 4 / 44 )3.955564516129030.05402805732659873.2131546432951
Trimmed Mean ( 5 / 44 )3.954508196721310.053787342442294973.521167195867
Trimmed Mean ( 6 / 44 )3.953333333333330.053525215049779373.8592704327609
Trimmed Mean ( 7 / 44 )3.95211864406780.053227683777962174.2493071942405
Trimmed Mean ( 8 / 44 )3.950862068965520.052891018184380574.6981662404878
Trimmed Mean ( 9 / 44 )3.950263157894740.052626771632649375.0618560733454
Trimmed Mean ( 10 / 44 )3.949732142857140.052339025107951575.4643812090624
Trimmed Mean ( 11 / 44 )3.949181818181820.052010477519241475.9305049010713
Trimmed Mean ( 12 / 44 )3.948611111111110.051636503159304176.4693747547006
Trimmed Mean ( 13 / 44 )3.948018867924530.051211805799183877.0919674929224
Trimmed Mean ( 14 / 44 )3.948557692307690.050922486869309777.5405510426364
Trimmed Mean ( 15 / 44 )3.948921568627450.050683908761203777.9127274345142
Trimmed Mean ( 16 / 44 )3.9490.050452798222545178.2711789855765
Trimmed Mean ( 17 / 44 )3.949081632653060.050179791778554378.698645265021
Trimmed Mean ( 18 / 44 )3.949270833333330.049876875770835579.1803971740064
Trimmed Mean ( 19 / 44 )3.949468085106380.049522396833941479.7511497343262
Trimmed Mean ( 20 / 44 )3.949673913043480.049147644379846280.3634429051722
Trimmed Mean ( 21 / 44 )3.949777777777780.048809031362200880.9230928691735
Trimmed Mean ( 22 / 44 )3.950227272727270.048509383894549981.4322293046291
Trimmed Mean ( 23 / 44 )3.951046511627910.048211239776215281.9528087219433
Trimmed Mean ( 24 / 44 )3.951904761904760.047853667565192382.583111451614
Trimmed Mean ( 25 / 44 )3.952682926829270.047451475644237483.299473265365
Trimmed Mean ( 26 / 44 )3.95350.046973295672425684.1648418192807
Trimmed Mean ( 27 / 44 )3.954358974358970.046406889489179685.2106016560534
Trimmed Mean ( 28 / 44 )3.955263157894740.045737417475637286.4776232720524
Trimmed Mean ( 29 / 44 )3.956216216216220.044946676499479588.0202169400008
Trimmed Mean ( 30 / 44 )3.956250.044232914926678789.4413132518612
Trimmed Mean ( 31 / 44 )3.9560.04344692866896491.0536169343989
Trimmed Mean ( 32 / 44 )3.955735294117650.042508748351512793.0569693891465
Trimmed Mean ( 33 / 44 )3.955757575757580.041461111954195795.4088636148425
Trimmed Mean ( 34 / 44 )3.957031250.040503820909989997.6952584002769
Trimmed Mean ( 35 / 44 )3.958387096774190.0393449762676671100.607179677654
Trimmed Mean ( 36 / 44 )3.959833333333330.037935040869892104.384580654983
Trimmed Mean ( 37 / 44 )3.961379310344830.0362057442273346109.413005999033
Trimmed Mean ( 38 / 44 )3.960357142857140.0348875413010633113.517805931954
Trimmed Mean ( 39 / 44 )3.958518518518520.0334530422869653118.330598591355
Trimmed Mean ( 40 / 44 )3.956346153846150.0317049806077198124.786266321918
Trimmed Mean ( 41 / 44 )3.95320.0297121427798708133.049979911856
Trimmed Mean ( 42 / 44 )3.947916666666670.027789351903134142.065805652036
Trimmed Mean ( 43 / 44 )3.941521739130430.0254029694930184155.159881612018
Trimmed Mean ( 44 / 44 )3.934545454545450.022114574192082177.916401209941
Median3.89
Midrange3.975
Midmean - Weighted Average at Xnp3.92724637681159
Midmean - Weighted Average at X(n+1)p3.92724637681159
Midmean - Empirical Distribution Function3.92724637681159
Midmean - Empirical Distribution Function - Averaging3.92724637681159
Midmean - Empirical Distribution Function - Interpolation3.92724637681159
Midmean - Closest Observation3.92724637681159
Midmean - True Basic - Statistics Graphics Toolkit3.92724637681159
Midmean - MS Excel (old versions)3.937
Number of observations132

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.95712121212121 & 0.0550213436498283 & 71.9197487670507 \tabularnewline
Geometric Mean & 3.90649361723824 &  &  \tabularnewline
Harmonic Mean & 3.8558707986586 &  &  \tabularnewline
Quadratic Mean & 4.00691788150081 &  &  \tabularnewline
Winsorized Mean ( 1 / 44 ) & 3.95712121212121 & 0.0550213436498283 & 71.9197487670507 \tabularnewline
Winsorized Mean ( 2 / 44 ) & 3.95712121212121 & 0.0550213436498283 & 71.9197487670507 \tabularnewline
Winsorized Mean ( 3 / 44 ) & 3.95825757575758 & 0.0548709393811893 & 72.1375945153681 \tabularnewline
Winsorized Mean ( 4 / 44 ) & 3.9594696969697 & 0.0547174639438218 & 72.3620835394504 \tabularnewline
Winsorized Mean ( 5 / 44 ) & 3.95984848484848 & 0.0546706946937613 & 72.4309158138493 \tabularnewline
Winsorized Mean ( 6 / 44 ) & 3.95984848484849 & 0.0546706946937613 & 72.4309158138494 \tabularnewline
Winsorized Mean ( 7 / 44 ) & 3.95984848484849 & 0.0546706946937613 & 72.4309158138494 \tabularnewline
Winsorized Mean ( 8 / 44 ) & 3.955 & 0.0540082605208465 & 73.2295386272147 \tabularnewline
Winsorized Mean ( 9 / 44 ) & 3.95431818181818 & 0.0539185300112826 & 73.3387609230208 \tabularnewline
Winsorized Mean ( 10 / 44 ) & 3.95431818181818 & 0.0539185300112826 & 73.3387609230208 \tabularnewline
Winsorized Mean ( 11 / 44 ) & 3.95431818181818 & 0.0539185300112826 & 73.3387609230208 \tabularnewline
Winsorized Mean ( 12 / 44 ) & 3.95431818181818 & 0.0539185300112826 & 73.3387609230208 \tabularnewline
Winsorized Mean ( 13 / 44 ) & 3.9425 & 0.0524399323708115 & 75.1812563777147 \tabularnewline
Winsorized Mean ( 14 / 44 ) & 3.94462121212121 & 0.0516642308720111 & 76.3511068594693 \tabularnewline
Winsorized Mean ( 15 / 44 ) & 3.9480303030303 & 0.0512539318119578 & 77.0288281007391 \tabularnewline
Winsorized Mean ( 16 / 44 ) & 3.9480303030303 & 0.0512539318119578 & 77.0288281007391 \tabularnewline
Winsorized Mean ( 17 / 44 ) & 3.94674242424242 & 0.0511026345013041 & 77.2316821384562 \tabularnewline
Winsorized Mean ( 18 / 44 ) & 3.94674242424242 & 0.0511026345013041 & 77.2316821384562 \tabularnewline
Winsorized Mean ( 19 / 44 ) & 3.94674242424242 & 0.0507639414288174 & 77.7469659202223 \tabularnewline
Winsorized Mean ( 20 / 44 ) & 3.94825757575758 & 0.0498807850363933 & 79.1538780489702 \tabularnewline
Winsorized Mean ( 21 / 44 ) & 3.94348484848485 & 0.0489747990032648 & 80.5206949031473 \tabularnewline
Winsorized Mean ( 22 / 44 ) & 3.93848484848485 & 0.0484230247174906 & 81.3349614457737 \tabularnewline
Winsorized Mean ( 23 / 44 ) & 3.93848484848485 & 0.0484230247174906 & 81.3349614457737 \tabularnewline
Winsorized Mean ( 24 / 44 ) & 3.94030303030303 & 0.0482120695247526 & 81.7285602784596 \tabularnewline
Winsorized Mean ( 25 / 44 ) & 3.94030303030303 & 0.0482120695247526 & 81.7285602784596 \tabularnewline
Winsorized Mean ( 26 / 44 ) & 3.94030303030303 & 0.0482120695247526 & 81.7285602784596 \tabularnewline
Winsorized Mean ( 27 / 44 ) & 3.94030303030303 & 0.0482120695247526 & 81.7285602784596 \tabularnewline
Winsorized Mean ( 28 / 44 ) & 3.94030303030303 & 0.0482120695247526 & 81.7285602784596 \tabularnewline
Winsorized Mean ( 29 / 44 ) & 3.95568181818182 & 0.0464687808788455 & 85.1255777184076 \tabularnewline
Winsorized Mean ( 30 / 44 ) & 3.96022727272727 & 0.0459673150619318 & 86.1531126495349 \tabularnewline
Winsorized Mean ( 31 / 44 ) & 3.96022727272727 & 0.0459673150619318 & 86.1531126495349 \tabularnewline
Winsorized Mean ( 32 / 44 ) & 3.95537878787879 & 0.045431007765723 & 87.0634173090709 \tabularnewline
Winsorized Mean ( 33 / 44 ) & 3.93537878787879 & 0.0432810863123109 & 90.9260631649028 \tabularnewline
Winsorized Mean ( 34 / 44 ) & 3.93537878787879 & 0.0432810863123109 & 90.9260631649028 \tabularnewline
Winsorized Mean ( 35 / 44 ) & 3.93537878787879 & 0.0432810863123109 & 90.9260631649028 \tabularnewline
Winsorized Mean ( 36 / 44 ) & 3.93537878787879 & 0.0432810863123109 & 90.9260631649028 \tabularnewline
Winsorized Mean ( 37 / 44 ) & 3.97742424242424 & 0.0387303741666905 & 102.695218623655 \tabularnewline
Winsorized Mean ( 38 / 44 ) & 3.98893939393939 & 0.0375476037700848 & 106.236856507937 \tabularnewline
Winsorized Mean ( 39 / 44 ) & 3.99189393939394 & 0.0372488323277666 & 107.168297364807 \tabularnewline
Winsorized Mean ( 40 / 44 ) & 4.00401515151515 & 0.0360420148086264 & 111.092988912396 \tabularnewline
Winsorized Mean ( 41 / 44 ) & 4.0319696969697 & 0.0327418207527918 & 123.144333585233 \tabularnewline
Winsorized Mean ( 42 / 44 ) & 4.04151515151515 & 0.0318809455542687 & 126.768986341248 \tabularnewline
Winsorized Mean ( 43 / 44 ) & 4.04151515151515 & 0.0318809455542687 & 126.768986341248 \tabularnewline
Winsorized Mean ( 44 / 44 ) & 4.01818181818182 & 0.0285494036704809 & 140.744859842256 \tabularnewline
Trimmed Mean ( 1 / 44 ) & 3.95684615384615 & 0.0548039313902795 & 72.2000421040592 \tabularnewline
Trimmed Mean ( 2 / 44 ) & 3.9565625 & 0.0545581569421765 & 72.5200908856464 \tabularnewline
Trimmed Mean ( 3 / 44 ) & 3.95626984126984 & 0.054281305399725 & 72.8845743877391 \tabularnewline
Trimmed Mean ( 4 / 44 ) & 3.95556451612903 & 0.054028057326598 & 73.2131546432951 \tabularnewline
Trimmed Mean ( 5 / 44 ) & 3.95450819672131 & 0.0537873424422949 & 73.521167195867 \tabularnewline
Trimmed Mean ( 6 / 44 ) & 3.95333333333333 & 0.0535252150497793 & 73.8592704327609 \tabularnewline
Trimmed Mean ( 7 / 44 ) & 3.9521186440678 & 0.0532276837779621 & 74.2493071942405 \tabularnewline
Trimmed Mean ( 8 / 44 ) & 3.95086206896552 & 0.0528910181843805 & 74.6981662404878 \tabularnewline
Trimmed Mean ( 9 / 44 ) & 3.95026315789474 & 0.0526267716326493 & 75.0618560733454 \tabularnewline
Trimmed Mean ( 10 / 44 ) & 3.94973214285714 & 0.0523390251079515 & 75.4643812090624 \tabularnewline
Trimmed Mean ( 11 / 44 ) & 3.94918181818182 & 0.0520104775192414 & 75.9305049010713 \tabularnewline
Trimmed Mean ( 12 / 44 ) & 3.94861111111111 & 0.0516365031593041 & 76.4693747547006 \tabularnewline
Trimmed Mean ( 13 / 44 ) & 3.94801886792453 & 0.0512118057991838 & 77.0919674929224 \tabularnewline
Trimmed Mean ( 14 / 44 ) & 3.94855769230769 & 0.0509224868693097 & 77.5405510426364 \tabularnewline
Trimmed Mean ( 15 / 44 ) & 3.94892156862745 & 0.0506839087612037 & 77.9127274345142 \tabularnewline
Trimmed Mean ( 16 / 44 ) & 3.949 & 0.0504527982225451 & 78.2711789855765 \tabularnewline
Trimmed Mean ( 17 / 44 ) & 3.94908163265306 & 0.0501797917785543 & 78.698645265021 \tabularnewline
Trimmed Mean ( 18 / 44 ) & 3.94927083333333 & 0.0498768757708355 & 79.1803971740064 \tabularnewline
Trimmed Mean ( 19 / 44 ) & 3.94946808510638 & 0.0495223968339414 & 79.7511497343262 \tabularnewline
Trimmed Mean ( 20 / 44 ) & 3.94967391304348 & 0.0491476443798462 & 80.3634429051722 \tabularnewline
Trimmed Mean ( 21 / 44 ) & 3.94977777777778 & 0.0488090313622008 & 80.9230928691735 \tabularnewline
Trimmed Mean ( 22 / 44 ) & 3.95022727272727 & 0.0485093838945499 & 81.4322293046291 \tabularnewline
Trimmed Mean ( 23 / 44 ) & 3.95104651162791 & 0.0482112397762152 & 81.9528087219433 \tabularnewline
Trimmed Mean ( 24 / 44 ) & 3.95190476190476 & 0.0478536675651923 & 82.583111451614 \tabularnewline
Trimmed Mean ( 25 / 44 ) & 3.95268292682927 & 0.0474514756442374 & 83.299473265365 \tabularnewline
Trimmed Mean ( 26 / 44 ) & 3.9535 & 0.0469732956724256 & 84.1648418192807 \tabularnewline
Trimmed Mean ( 27 / 44 ) & 3.95435897435897 & 0.0464068894891796 & 85.2106016560534 \tabularnewline
Trimmed Mean ( 28 / 44 ) & 3.95526315789474 & 0.0457374174756372 & 86.4776232720524 \tabularnewline
Trimmed Mean ( 29 / 44 ) & 3.95621621621622 & 0.0449466764994795 & 88.0202169400008 \tabularnewline
Trimmed Mean ( 30 / 44 ) & 3.95625 & 0.0442329149266787 & 89.4413132518612 \tabularnewline
Trimmed Mean ( 31 / 44 ) & 3.956 & 0.043446928668964 & 91.0536169343989 \tabularnewline
Trimmed Mean ( 32 / 44 ) & 3.95573529411765 & 0.0425087483515127 & 93.0569693891465 \tabularnewline
Trimmed Mean ( 33 / 44 ) & 3.95575757575758 & 0.0414611119541957 & 95.4088636148425 \tabularnewline
Trimmed Mean ( 34 / 44 ) & 3.95703125 & 0.0405038209099899 & 97.6952584002769 \tabularnewline
Trimmed Mean ( 35 / 44 ) & 3.95838709677419 & 0.0393449762676671 & 100.607179677654 \tabularnewline
Trimmed Mean ( 36 / 44 ) & 3.95983333333333 & 0.037935040869892 & 104.384580654983 \tabularnewline
Trimmed Mean ( 37 / 44 ) & 3.96137931034483 & 0.0362057442273346 & 109.413005999033 \tabularnewline
Trimmed Mean ( 38 / 44 ) & 3.96035714285714 & 0.0348875413010633 & 113.517805931954 \tabularnewline
Trimmed Mean ( 39 / 44 ) & 3.95851851851852 & 0.0334530422869653 & 118.330598591355 \tabularnewline
Trimmed Mean ( 40 / 44 ) & 3.95634615384615 & 0.0317049806077198 & 124.786266321918 \tabularnewline
Trimmed Mean ( 41 / 44 ) & 3.9532 & 0.0297121427798708 & 133.049979911856 \tabularnewline
Trimmed Mean ( 42 / 44 ) & 3.94791666666667 & 0.027789351903134 & 142.065805652036 \tabularnewline
Trimmed Mean ( 43 / 44 ) & 3.94152173913043 & 0.0254029694930184 & 155.159881612018 \tabularnewline
Trimmed Mean ( 44 / 44 ) & 3.93454545454545 & 0.022114574192082 & 177.916401209941 \tabularnewline
Median & 3.89 &  &  \tabularnewline
Midrange & 3.975 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.92724637681159 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.92724637681159 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.92724637681159 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.92724637681159 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.92724637681159 &  &  \tabularnewline
Midmean - Closest Observation & 3.92724637681159 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.92724637681159 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.937 &  &  \tabularnewline
Number of observations & 132 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132775&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]3.95712121212121[/C][C]0.0550213436498283[/C][C]71.9197487670507[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.90649361723824[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.8558707986586[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.00691788150081[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 44 )[/C][C]3.95712121212121[/C][C]0.0550213436498283[/C][C]71.9197487670507[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 44 )[/C][C]3.95712121212121[/C][C]0.0550213436498283[/C][C]71.9197487670507[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 44 )[/C][C]3.95825757575758[/C][C]0.0548709393811893[/C][C]72.1375945153681[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 44 )[/C][C]3.9594696969697[/C][C]0.0547174639438218[/C][C]72.3620835394504[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 44 )[/C][C]3.95984848484848[/C][C]0.0546706946937613[/C][C]72.4309158138493[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 44 )[/C][C]3.95984848484849[/C][C]0.0546706946937613[/C][C]72.4309158138494[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 44 )[/C][C]3.95984848484849[/C][C]0.0546706946937613[/C][C]72.4309158138494[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 44 )[/C][C]3.955[/C][C]0.0540082605208465[/C][C]73.2295386272147[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 44 )[/C][C]3.95431818181818[/C][C]0.0539185300112826[/C][C]73.3387609230208[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 44 )[/C][C]3.95431818181818[/C][C]0.0539185300112826[/C][C]73.3387609230208[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 44 )[/C][C]3.95431818181818[/C][C]0.0539185300112826[/C][C]73.3387609230208[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 44 )[/C][C]3.95431818181818[/C][C]0.0539185300112826[/C][C]73.3387609230208[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 44 )[/C][C]3.9425[/C][C]0.0524399323708115[/C][C]75.1812563777147[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 44 )[/C][C]3.94462121212121[/C][C]0.0516642308720111[/C][C]76.3511068594693[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 44 )[/C][C]3.9480303030303[/C][C]0.0512539318119578[/C][C]77.0288281007391[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 44 )[/C][C]3.9480303030303[/C][C]0.0512539318119578[/C][C]77.0288281007391[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 44 )[/C][C]3.94674242424242[/C][C]0.0511026345013041[/C][C]77.2316821384562[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 44 )[/C][C]3.94674242424242[/C][C]0.0511026345013041[/C][C]77.2316821384562[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 44 )[/C][C]3.94674242424242[/C][C]0.0507639414288174[/C][C]77.7469659202223[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 44 )[/C][C]3.94825757575758[/C][C]0.0498807850363933[/C][C]79.1538780489702[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 44 )[/C][C]3.94348484848485[/C][C]0.0489747990032648[/C][C]80.5206949031473[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 44 )[/C][C]3.93848484848485[/C][C]0.0484230247174906[/C][C]81.3349614457737[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 44 )[/C][C]3.93848484848485[/C][C]0.0484230247174906[/C][C]81.3349614457737[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 44 )[/C][C]3.94030303030303[/C][C]0.0482120695247526[/C][C]81.7285602784596[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 44 )[/C][C]3.94030303030303[/C][C]0.0482120695247526[/C][C]81.7285602784596[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 44 )[/C][C]3.94030303030303[/C][C]0.0482120695247526[/C][C]81.7285602784596[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 44 )[/C][C]3.94030303030303[/C][C]0.0482120695247526[/C][C]81.7285602784596[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 44 )[/C][C]3.94030303030303[/C][C]0.0482120695247526[/C][C]81.7285602784596[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 44 )[/C][C]3.95568181818182[/C][C]0.0464687808788455[/C][C]85.1255777184076[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 44 )[/C][C]3.96022727272727[/C][C]0.0459673150619318[/C][C]86.1531126495349[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 44 )[/C][C]3.96022727272727[/C][C]0.0459673150619318[/C][C]86.1531126495349[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 44 )[/C][C]3.95537878787879[/C][C]0.045431007765723[/C][C]87.0634173090709[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 44 )[/C][C]3.93537878787879[/C][C]0.0432810863123109[/C][C]90.9260631649028[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 44 )[/C][C]3.93537878787879[/C][C]0.0432810863123109[/C][C]90.9260631649028[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 44 )[/C][C]3.93537878787879[/C][C]0.0432810863123109[/C][C]90.9260631649028[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 44 )[/C][C]3.93537878787879[/C][C]0.0432810863123109[/C][C]90.9260631649028[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 44 )[/C][C]3.97742424242424[/C][C]0.0387303741666905[/C][C]102.695218623655[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 44 )[/C][C]3.98893939393939[/C][C]0.0375476037700848[/C][C]106.236856507937[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 44 )[/C][C]3.99189393939394[/C][C]0.0372488323277666[/C][C]107.168297364807[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 44 )[/C][C]4.00401515151515[/C][C]0.0360420148086264[/C][C]111.092988912396[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 44 )[/C][C]4.0319696969697[/C][C]0.0327418207527918[/C][C]123.144333585233[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 44 )[/C][C]4.04151515151515[/C][C]0.0318809455542687[/C][C]126.768986341248[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 44 )[/C][C]4.04151515151515[/C][C]0.0318809455542687[/C][C]126.768986341248[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 44 )[/C][C]4.01818181818182[/C][C]0.0285494036704809[/C][C]140.744859842256[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 44 )[/C][C]3.95684615384615[/C][C]0.0548039313902795[/C][C]72.2000421040592[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 44 )[/C][C]3.9565625[/C][C]0.0545581569421765[/C][C]72.5200908856464[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 44 )[/C][C]3.95626984126984[/C][C]0.054281305399725[/C][C]72.8845743877391[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 44 )[/C][C]3.95556451612903[/C][C]0.054028057326598[/C][C]73.2131546432951[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 44 )[/C][C]3.95450819672131[/C][C]0.0537873424422949[/C][C]73.521167195867[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 44 )[/C][C]3.95333333333333[/C][C]0.0535252150497793[/C][C]73.8592704327609[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 44 )[/C][C]3.9521186440678[/C][C]0.0532276837779621[/C][C]74.2493071942405[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 44 )[/C][C]3.95086206896552[/C][C]0.0528910181843805[/C][C]74.6981662404878[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 44 )[/C][C]3.95026315789474[/C][C]0.0526267716326493[/C][C]75.0618560733454[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 44 )[/C][C]3.94973214285714[/C][C]0.0523390251079515[/C][C]75.4643812090624[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 44 )[/C][C]3.94918181818182[/C][C]0.0520104775192414[/C][C]75.9305049010713[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 44 )[/C][C]3.94861111111111[/C][C]0.0516365031593041[/C][C]76.4693747547006[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 44 )[/C][C]3.94801886792453[/C][C]0.0512118057991838[/C][C]77.0919674929224[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 44 )[/C][C]3.94855769230769[/C][C]0.0509224868693097[/C][C]77.5405510426364[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 44 )[/C][C]3.94892156862745[/C][C]0.0506839087612037[/C][C]77.9127274345142[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 44 )[/C][C]3.949[/C][C]0.0504527982225451[/C][C]78.2711789855765[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 44 )[/C][C]3.94908163265306[/C][C]0.0501797917785543[/C][C]78.698645265021[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 44 )[/C][C]3.94927083333333[/C][C]0.0498768757708355[/C][C]79.1803971740064[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 44 )[/C][C]3.94946808510638[/C][C]0.0495223968339414[/C][C]79.7511497343262[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 44 )[/C][C]3.94967391304348[/C][C]0.0491476443798462[/C][C]80.3634429051722[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 44 )[/C][C]3.94977777777778[/C][C]0.0488090313622008[/C][C]80.9230928691735[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 44 )[/C][C]3.95022727272727[/C][C]0.0485093838945499[/C][C]81.4322293046291[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 44 )[/C][C]3.95104651162791[/C][C]0.0482112397762152[/C][C]81.9528087219433[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 44 )[/C][C]3.95190476190476[/C][C]0.0478536675651923[/C][C]82.583111451614[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 44 )[/C][C]3.95268292682927[/C][C]0.0474514756442374[/C][C]83.299473265365[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 44 )[/C][C]3.9535[/C][C]0.0469732956724256[/C][C]84.1648418192807[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 44 )[/C][C]3.95435897435897[/C][C]0.0464068894891796[/C][C]85.2106016560534[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 44 )[/C][C]3.95526315789474[/C][C]0.0457374174756372[/C][C]86.4776232720524[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 44 )[/C][C]3.95621621621622[/C][C]0.0449466764994795[/C][C]88.0202169400008[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 44 )[/C][C]3.95625[/C][C]0.0442329149266787[/C][C]89.4413132518612[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 44 )[/C][C]3.956[/C][C]0.043446928668964[/C][C]91.0536169343989[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 44 )[/C][C]3.95573529411765[/C][C]0.0425087483515127[/C][C]93.0569693891465[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 44 )[/C][C]3.95575757575758[/C][C]0.0414611119541957[/C][C]95.4088636148425[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 44 )[/C][C]3.95703125[/C][C]0.0405038209099899[/C][C]97.6952584002769[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 44 )[/C][C]3.95838709677419[/C][C]0.0393449762676671[/C][C]100.607179677654[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 44 )[/C][C]3.95983333333333[/C][C]0.037935040869892[/C][C]104.384580654983[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 44 )[/C][C]3.96137931034483[/C][C]0.0362057442273346[/C][C]109.413005999033[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 44 )[/C][C]3.96035714285714[/C][C]0.0348875413010633[/C][C]113.517805931954[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 44 )[/C][C]3.95851851851852[/C][C]0.0334530422869653[/C][C]118.330598591355[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 44 )[/C][C]3.95634615384615[/C][C]0.0317049806077198[/C][C]124.786266321918[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 44 )[/C][C]3.9532[/C][C]0.0297121427798708[/C][C]133.049979911856[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 44 )[/C][C]3.94791666666667[/C][C]0.027789351903134[/C][C]142.065805652036[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 44 )[/C][C]3.94152173913043[/C][C]0.0254029694930184[/C][C]155.159881612018[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 44 )[/C][C]3.93454545454545[/C][C]0.022114574192082[/C][C]177.916401209941[/C][/ROW]
[ROW][C]Median[/C][C]3.89[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.92724637681159[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.92724637681159[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.92724637681159[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.92724637681159[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.92724637681159[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.92724637681159[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.92724637681159[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.937[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]132[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132775&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132775&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.957121212121210.055021343649828371.9197487670507
Geometric Mean3.90649361723824
Harmonic Mean3.8558707986586
Quadratic Mean4.00691788150081
Winsorized Mean ( 1 / 44 )3.957121212121210.055021343649828371.9197487670507
Winsorized Mean ( 2 / 44 )3.957121212121210.055021343649828371.9197487670507
Winsorized Mean ( 3 / 44 )3.958257575757580.054870939381189372.1375945153681
Winsorized Mean ( 4 / 44 )3.95946969696970.054717463943821872.3620835394504
Winsorized Mean ( 5 / 44 )3.959848484848480.054670694693761372.4309158138493
Winsorized Mean ( 6 / 44 )3.959848484848490.054670694693761372.4309158138494
Winsorized Mean ( 7 / 44 )3.959848484848490.054670694693761372.4309158138494
Winsorized Mean ( 8 / 44 )3.9550.054008260520846573.2295386272147
Winsorized Mean ( 9 / 44 )3.954318181818180.053918530011282673.3387609230208
Winsorized Mean ( 10 / 44 )3.954318181818180.053918530011282673.3387609230208
Winsorized Mean ( 11 / 44 )3.954318181818180.053918530011282673.3387609230208
Winsorized Mean ( 12 / 44 )3.954318181818180.053918530011282673.3387609230208
Winsorized Mean ( 13 / 44 )3.94250.052439932370811575.1812563777147
Winsorized Mean ( 14 / 44 )3.944621212121210.051664230872011176.3511068594693
Winsorized Mean ( 15 / 44 )3.94803030303030.051253931811957877.0288281007391
Winsorized Mean ( 16 / 44 )3.94803030303030.051253931811957877.0288281007391
Winsorized Mean ( 17 / 44 )3.946742424242420.051102634501304177.2316821384562
Winsorized Mean ( 18 / 44 )3.946742424242420.051102634501304177.2316821384562
Winsorized Mean ( 19 / 44 )3.946742424242420.050763941428817477.7469659202223
Winsorized Mean ( 20 / 44 )3.948257575757580.049880785036393379.1538780489702
Winsorized Mean ( 21 / 44 )3.943484848484850.048974799003264880.5206949031473
Winsorized Mean ( 22 / 44 )3.938484848484850.048423024717490681.3349614457737
Winsorized Mean ( 23 / 44 )3.938484848484850.048423024717490681.3349614457737
Winsorized Mean ( 24 / 44 )3.940303030303030.048212069524752681.7285602784596
Winsorized Mean ( 25 / 44 )3.940303030303030.048212069524752681.7285602784596
Winsorized Mean ( 26 / 44 )3.940303030303030.048212069524752681.7285602784596
Winsorized Mean ( 27 / 44 )3.940303030303030.048212069524752681.7285602784596
Winsorized Mean ( 28 / 44 )3.940303030303030.048212069524752681.7285602784596
Winsorized Mean ( 29 / 44 )3.955681818181820.046468780878845585.1255777184076
Winsorized Mean ( 30 / 44 )3.960227272727270.045967315061931886.1531126495349
Winsorized Mean ( 31 / 44 )3.960227272727270.045967315061931886.1531126495349
Winsorized Mean ( 32 / 44 )3.955378787878790.04543100776572387.0634173090709
Winsorized Mean ( 33 / 44 )3.935378787878790.043281086312310990.9260631649028
Winsorized Mean ( 34 / 44 )3.935378787878790.043281086312310990.9260631649028
Winsorized Mean ( 35 / 44 )3.935378787878790.043281086312310990.9260631649028
Winsorized Mean ( 36 / 44 )3.935378787878790.043281086312310990.9260631649028
Winsorized Mean ( 37 / 44 )3.977424242424240.0387303741666905102.695218623655
Winsorized Mean ( 38 / 44 )3.988939393939390.0375476037700848106.236856507937
Winsorized Mean ( 39 / 44 )3.991893939393940.0372488323277666107.168297364807
Winsorized Mean ( 40 / 44 )4.004015151515150.0360420148086264111.092988912396
Winsorized Mean ( 41 / 44 )4.03196969696970.0327418207527918123.144333585233
Winsorized Mean ( 42 / 44 )4.041515151515150.0318809455542687126.768986341248
Winsorized Mean ( 43 / 44 )4.041515151515150.0318809455542687126.768986341248
Winsorized Mean ( 44 / 44 )4.018181818181820.0285494036704809140.744859842256
Trimmed Mean ( 1 / 44 )3.956846153846150.054803931390279572.2000421040592
Trimmed Mean ( 2 / 44 )3.95656250.054558156942176572.5200908856464
Trimmed Mean ( 3 / 44 )3.956269841269840.05428130539972572.8845743877391
Trimmed Mean ( 4 / 44 )3.955564516129030.05402805732659873.2131546432951
Trimmed Mean ( 5 / 44 )3.954508196721310.053787342442294973.521167195867
Trimmed Mean ( 6 / 44 )3.953333333333330.053525215049779373.8592704327609
Trimmed Mean ( 7 / 44 )3.95211864406780.053227683777962174.2493071942405
Trimmed Mean ( 8 / 44 )3.950862068965520.052891018184380574.6981662404878
Trimmed Mean ( 9 / 44 )3.950263157894740.052626771632649375.0618560733454
Trimmed Mean ( 10 / 44 )3.949732142857140.052339025107951575.4643812090624
Trimmed Mean ( 11 / 44 )3.949181818181820.052010477519241475.9305049010713
Trimmed Mean ( 12 / 44 )3.948611111111110.051636503159304176.4693747547006
Trimmed Mean ( 13 / 44 )3.948018867924530.051211805799183877.0919674929224
Trimmed Mean ( 14 / 44 )3.948557692307690.050922486869309777.5405510426364
Trimmed Mean ( 15 / 44 )3.948921568627450.050683908761203777.9127274345142
Trimmed Mean ( 16 / 44 )3.9490.050452798222545178.2711789855765
Trimmed Mean ( 17 / 44 )3.949081632653060.050179791778554378.698645265021
Trimmed Mean ( 18 / 44 )3.949270833333330.049876875770835579.1803971740064
Trimmed Mean ( 19 / 44 )3.949468085106380.049522396833941479.7511497343262
Trimmed Mean ( 20 / 44 )3.949673913043480.049147644379846280.3634429051722
Trimmed Mean ( 21 / 44 )3.949777777777780.048809031362200880.9230928691735
Trimmed Mean ( 22 / 44 )3.950227272727270.048509383894549981.4322293046291
Trimmed Mean ( 23 / 44 )3.951046511627910.048211239776215281.9528087219433
Trimmed Mean ( 24 / 44 )3.951904761904760.047853667565192382.583111451614
Trimmed Mean ( 25 / 44 )3.952682926829270.047451475644237483.299473265365
Trimmed Mean ( 26 / 44 )3.95350.046973295672425684.1648418192807
Trimmed Mean ( 27 / 44 )3.954358974358970.046406889489179685.2106016560534
Trimmed Mean ( 28 / 44 )3.955263157894740.045737417475637286.4776232720524
Trimmed Mean ( 29 / 44 )3.956216216216220.044946676499479588.0202169400008
Trimmed Mean ( 30 / 44 )3.956250.044232914926678789.4413132518612
Trimmed Mean ( 31 / 44 )3.9560.04344692866896491.0536169343989
Trimmed Mean ( 32 / 44 )3.955735294117650.042508748351512793.0569693891465
Trimmed Mean ( 33 / 44 )3.955757575757580.041461111954195795.4088636148425
Trimmed Mean ( 34 / 44 )3.957031250.040503820909989997.6952584002769
Trimmed Mean ( 35 / 44 )3.958387096774190.0393449762676671100.607179677654
Trimmed Mean ( 36 / 44 )3.959833333333330.037935040869892104.384580654983
Trimmed Mean ( 37 / 44 )3.961379310344830.0362057442273346109.413005999033
Trimmed Mean ( 38 / 44 )3.960357142857140.0348875413010633113.517805931954
Trimmed Mean ( 39 / 44 )3.958518518518520.0334530422869653118.330598591355
Trimmed Mean ( 40 / 44 )3.956346153846150.0317049806077198124.786266321918
Trimmed Mean ( 41 / 44 )3.95320.0297121427798708133.049979911856
Trimmed Mean ( 42 / 44 )3.947916666666670.027789351903134142.065805652036
Trimmed Mean ( 43 / 44 )3.941521739130430.0254029694930184155.159881612018
Trimmed Mean ( 44 / 44 )3.934545454545450.022114574192082177.916401209941
Median3.89
Midrange3.975
Midmean - Weighted Average at Xnp3.92724637681159
Midmean - Weighted Average at X(n+1)p3.92724637681159
Midmean - Empirical Distribution Function3.92724637681159
Midmean - Empirical Distribution Function - Averaging3.92724637681159
Midmean - Empirical Distribution Function - Interpolation3.92724637681159
Midmean - Closest Observation3.92724637681159
Midmean - True Basic - Statistics Graphics Toolkit3.92724637681159
Midmean - MS Excel (old versions)3.937
Number of observations132



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')