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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 04 Mar 2013 06:24:35 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/04/t1362396309gtqn9vib73b7err.htm/, Retrieved Sun, 28 Apr 2024 16:19:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207311, Retrieved Sun, 28 Apr 2024 16:19:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten cons...] [2013-03-04 11:24:35] [f2eb9e6f8a572d38d7977956fe5c285e] [Current]
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Dataseries X:
67,66
68
68,02
68,11
68,41
68,4
68,4
68,55
68,54
68,99
68,97
68,98
68,98
68,94
69,21
69,21
69,67
69,66
69,66
69,66
69,77
70,32
70,34
70,38
70,38
70,29
70,42
70,29
70,59
70,64
70,64
70,68
70,78
70,9
71,04
71,15
71,15
71,15
71,07
71,17
71,24
71,23
71,23
71,23
71,24
71,28
71,52
71,52
71,52
71,6
71,61
71,78
71,66
71,86
71,86
71,82
71,8
72,22
72,51
72,56
72,56
72,78
72,88
73,05
73,02
73,08
73,08
73,24
73,82
74
74,37
74,38




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207311&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207311&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207311&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean70.87111111111110.193080370727002367.054977387196
Geometric Mean70.8524385739074
Harmonic Mean70.8337679192593
Quadratic Mean70.8897825657705
Winsorized Mean ( 1 / 24 )70.87569444444440.191993477897352369.156781889944
Winsorized Mean ( 2 / 24 )70.86597222222220.189360039498233374.239318971432
Winsorized Mean ( 3 / 24 )70.86222222222220.186863706181485379.218756120569
Winsorized Mean ( 4 / 24 )70.84611111111110.176945430209787400.383954686571
Winsorized Mean ( 5 / 24 )70.8350.174882030436635405.044473826976
Winsorized Mean ( 6 / 24 )70.83583333333330.174718838524102405.427565405671
Winsorized Mean ( 7 / 24 )70.84555555555560.171760525060471412.467041135401
Winsorized Mean ( 8 / 24 )70.84333333333330.170950349251568414.408824804921
Winsorized Mean ( 9 / 24 )70.87458333333330.15902910353371445.670520417099
Winsorized Mean ( 10 / 24 )70.86486111111110.155880054136518454.611473569596
Winsorized Mean ( 11 / 24 )70.83277777777780.149978900735974472.284950951023
Winsorized Mean ( 12 / 24 )70.83277777777780.149978900735974472.284950951023
Winsorized Mean ( 13 / 24 )70.82555555555560.14820956603788477.874387254152
Winsorized Mean ( 14 / 24 )70.81194444444440.132056331771374536.225287304205
Winsorized Mean ( 15 / 24 )70.73694444444440.121511998752071582.139584328404
Winsorized Mean ( 16 / 24 )70.83694444444440.104675076455767676.731719172693
Winsorized Mean ( 17 / 24 )70.82750.103386467862526685.075150204182
Winsorized Mean ( 18 / 24 )70.82250.102713335758912689.516112749312
Winsorized Mean ( 19 / 24 )70.81986111111110.101587649785926697.130618341388
Winsorized Mean ( 20 / 24 )70.81430555555560.0928105804815947762.998196844581
Winsorized Mean ( 21 / 24 )70.95138888888890.06827299109322161039.23070826075
Winsorized Mean ( 22 / 24 )70.94833333333330.06785876661546911045.52936741942
Winsorized Mean ( 23 / 24 )70.93236111111110.06314448402587061123.33424218099
Winsorized Mean ( 24 / 24 )70.93902777777780.06223729129161191139.81547566706
Trimmed Mean ( 1 / 24 )70.86685714285710.186473599822971380.036944694234
Trimmed Mean ( 2 / 24 )70.85750.179902101828516393.866993658261
Trimmed Mean ( 3 / 24 )70.85287878787880.173759843530796407.763251555422
Trimmed Mean ( 4 / 24 )70.8493750.16755549823888422.841242123799
Trimmed Mean ( 5 / 24 )70.85032258064520.163808449830759432.51933983775
Trimmed Mean ( 6 / 24 )70.8540.159896541409757443.124031172298
Trimmed Mean ( 7 / 24 )70.85775862068970.155147421863192456.712446586263
Trimmed Mean ( 8 / 24 )70.860.150107753505066472.060891895291
Trimmed Mean ( 9 / 24 )70.86277777777780.144061922945219491.891100223091
Trimmed Mean ( 10 / 24 )70.86096153846150.139530363880408507.853341507778
Trimmed Mean ( 11 / 24 )70.86040.13457808900715526.537421676684
Trimmed Mean ( 12 / 24 )70.86416666666670.129694414887285546.393356477637
Trimmed Mean ( 13 / 24 )70.86826086956520.123399239871063574.300627326503
Trimmed Mean ( 14 / 24 )70.87363636363640.115629123392148612.939320860136
Trimmed Mean ( 15 / 24 )70.88119047619050.109675480750836646.281101217328
Trimmed Mean ( 16 / 24 )70.89850.104238723795246680.155103771844
Trimmed Mean ( 17 / 24 )70.90578947368420.10151808700163698.454744055076
Trimmed Mean ( 18 / 24 )70.9150.0979929540712955723.67447917128
Trimmed Mean ( 19 / 24 )70.92588235294120.0931572546309991761.356510922122
Trimmed Mean ( 20 / 24 )70.93843750.0865164880041519819.941252083599
Trimmed Mean ( 21 / 24 )70.95333333333330.0797457646096647889.744222538111
Trimmed Mean ( 22 / 24 )70.95357142857140.0785234341150169903.597406662608
Trimmed Mean ( 23 / 24 )70.95423076923080.0764926805486302927.595036025984
Trimmed Mean ( 24 / 24 )70.95708333333330.0747058947644721949.819067920172
Median71.11
Midrange71.02
Midmean - Weighted Average at Xnp70.8489473684211
Midmean - Weighted Average at X(n+1)p70.8489473684211
Midmean - Empirical Distribution Function70.8489473684211
Midmean - Empirical Distribution Function - Averaging70.8489473684211
Midmean - Empirical Distribution Function - Interpolation70.8489473684211
Midmean - Closest Observation70.8489473684211
Midmean - True Basic - Statistics Graphics Toolkit70.8489473684211
Midmean - MS Excel (old versions)70.8738461538462
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 70.8711111111111 & 0.193080370727002 & 367.054977387196 \tabularnewline
Geometric Mean & 70.8524385739074 &  &  \tabularnewline
Harmonic Mean & 70.8337679192593 &  &  \tabularnewline
Quadratic Mean & 70.8897825657705 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 70.8756944444444 & 0.191993477897352 & 369.156781889944 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 70.8659722222222 & 0.189360039498233 & 374.239318971432 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 70.8622222222222 & 0.186863706181485 & 379.218756120569 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 70.8461111111111 & 0.176945430209787 & 400.383954686571 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 70.835 & 0.174882030436635 & 405.044473826976 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 70.8358333333333 & 0.174718838524102 & 405.427565405671 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 70.8455555555556 & 0.171760525060471 & 412.467041135401 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 70.8433333333333 & 0.170950349251568 & 414.408824804921 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 70.8745833333333 & 0.15902910353371 & 445.670520417099 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 70.8648611111111 & 0.155880054136518 & 454.611473569596 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 70.8327777777778 & 0.149978900735974 & 472.284950951023 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 70.8327777777778 & 0.149978900735974 & 472.284950951023 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 70.8255555555556 & 0.14820956603788 & 477.874387254152 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 70.8119444444444 & 0.132056331771374 & 536.225287304205 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 70.7369444444444 & 0.121511998752071 & 582.139584328404 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 70.8369444444444 & 0.104675076455767 & 676.731719172693 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 70.8275 & 0.103386467862526 & 685.075150204182 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 70.8225 & 0.102713335758912 & 689.516112749312 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 70.8198611111111 & 0.101587649785926 & 697.130618341388 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 70.8143055555556 & 0.0928105804815947 & 762.998196844581 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 70.9513888888889 & 0.0682729910932216 & 1039.23070826075 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 70.9483333333333 & 0.0678587666154691 & 1045.52936741942 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 70.9323611111111 & 0.0631444840258706 & 1123.33424218099 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 70.9390277777778 & 0.0622372912916119 & 1139.81547566706 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 70.8668571428571 & 0.186473599822971 & 380.036944694234 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 70.8575 & 0.179902101828516 & 393.866993658261 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 70.8528787878788 & 0.173759843530796 & 407.763251555422 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 70.849375 & 0.16755549823888 & 422.841242123799 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 70.8503225806452 & 0.163808449830759 & 432.51933983775 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 70.854 & 0.159896541409757 & 443.124031172298 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 70.8577586206897 & 0.155147421863192 & 456.712446586263 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 70.86 & 0.150107753505066 & 472.060891895291 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 70.8627777777778 & 0.144061922945219 & 491.891100223091 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 70.8609615384615 & 0.139530363880408 & 507.853341507778 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 70.8604 & 0.13457808900715 & 526.537421676684 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 70.8641666666667 & 0.129694414887285 & 546.393356477637 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 70.8682608695652 & 0.123399239871063 & 574.300627326503 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 70.8736363636364 & 0.115629123392148 & 612.939320860136 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 70.8811904761905 & 0.109675480750836 & 646.281101217328 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 70.8985 & 0.104238723795246 & 680.155103771844 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 70.9057894736842 & 0.10151808700163 & 698.454744055076 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 70.915 & 0.0979929540712955 & 723.67447917128 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 70.9258823529412 & 0.0931572546309991 & 761.356510922122 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 70.9384375 & 0.0865164880041519 & 819.941252083599 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 70.9533333333333 & 0.0797457646096647 & 889.744222538111 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 70.9535714285714 & 0.0785234341150169 & 903.597406662608 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 70.9542307692308 & 0.0764926805486302 & 927.595036025984 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 70.9570833333333 & 0.0747058947644721 & 949.819067920172 \tabularnewline
Median & 71.11 &  &  \tabularnewline
Midrange & 71.02 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 70.8489473684211 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 70.8489473684211 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 70.8489473684211 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 70.8489473684211 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 70.8489473684211 &  &  \tabularnewline
Midmean - Closest Observation & 70.8489473684211 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 70.8489473684211 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 70.8738461538462 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207311&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]70.8711111111111[/C][C]0.193080370727002[/C][C]367.054977387196[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]70.8524385739074[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]70.8337679192593[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]70.8897825657705[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]70.8756944444444[/C][C]0.191993477897352[/C][C]369.156781889944[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]70.8659722222222[/C][C]0.189360039498233[/C][C]374.239318971432[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]70.8622222222222[/C][C]0.186863706181485[/C][C]379.218756120569[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]70.8461111111111[/C][C]0.176945430209787[/C][C]400.383954686571[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]70.835[/C][C]0.174882030436635[/C][C]405.044473826976[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]70.8358333333333[/C][C]0.174718838524102[/C][C]405.427565405671[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]70.8455555555556[/C][C]0.171760525060471[/C][C]412.467041135401[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]70.8433333333333[/C][C]0.170950349251568[/C][C]414.408824804921[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]70.8745833333333[/C][C]0.15902910353371[/C][C]445.670520417099[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]70.8648611111111[/C][C]0.155880054136518[/C][C]454.611473569596[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]70.8327777777778[/C][C]0.149978900735974[/C][C]472.284950951023[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]70.8327777777778[/C][C]0.149978900735974[/C][C]472.284950951023[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]70.8255555555556[/C][C]0.14820956603788[/C][C]477.874387254152[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]70.8119444444444[/C][C]0.132056331771374[/C][C]536.225287304205[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]70.7369444444444[/C][C]0.121511998752071[/C][C]582.139584328404[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]70.8369444444444[/C][C]0.104675076455767[/C][C]676.731719172693[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]70.8275[/C][C]0.103386467862526[/C][C]685.075150204182[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]70.8225[/C][C]0.102713335758912[/C][C]689.516112749312[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]70.8198611111111[/C][C]0.101587649785926[/C][C]697.130618341388[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]70.8143055555556[/C][C]0.0928105804815947[/C][C]762.998196844581[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]70.9513888888889[/C][C]0.0682729910932216[/C][C]1039.23070826075[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]70.9483333333333[/C][C]0.0678587666154691[/C][C]1045.52936741942[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]70.9323611111111[/C][C]0.0631444840258706[/C][C]1123.33424218099[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]70.9390277777778[/C][C]0.0622372912916119[/C][C]1139.81547566706[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]70.8668571428571[/C][C]0.186473599822971[/C][C]380.036944694234[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]70.8575[/C][C]0.179902101828516[/C][C]393.866993658261[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]70.8528787878788[/C][C]0.173759843530796[/C][C]407.763251555422[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]70.849375[/C][C]0.16755549823888[/C][C]422.841242123799[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]70.8503225806452[/C][C]0.163808449830759[/C][C]432.51933983775[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]70.854[/C][C]0.159896541409757[/C][C]443.124031172298[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]70.8577586206897[/C][C]0.155147421863192[/C][C]456.712446586263[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]70.86[/C][C]0.150107753505066[/C][C]472.060891895291[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]70.8627777777778[/C][C]0.144061922945219[/C][C]491.891100223091[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]70.8609615384615[/C][C]0.139530363880408[/C][C]507.853341507778[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]70.8604[/C][C]0.13457808900715[/C][C]526.537421676684[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]70.8641666666667[/C][C]0.129694414887285[/C][C]546.393356477637[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]70.8682608695652[/C][C]0.123399239871063[/C][C]574.300627326503[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]70.8736363636364[/C][C]0.115629123392148[/C][C]612.939320860136[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]70.8811904761905[/C][C]0.109675480750836[/C][C]646.281101217328[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]70.8985[/C][C]0.104238723795246[/C][C]680.155103771844[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]70.9057894736842[/C][C]0.10151808700163[/C][C]698.454744055076[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]70.915[/C][C]0.0979929540712955[/C][C]723.67447917128[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]70.9258823529412[/C][C]0.0931572546309991[/C][C]761.356510922122[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]70.9384375[/C][C]0.0865164880041519[/C][C]819.941252083599[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]70.9533333333333[/C][C]0.0797457646096647[/C][C]889.744222538111[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]70.9535714285714[/C][C]0.0785234341150169[/C][C]903.597406662608[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]70.9542307692308[/C][C]0.0764926805486302[/C][C]927.595036025984[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]70.9570833333333[/C][C]0.0747058947644721[/C][C]949.819067920172[/C][/ROW]
[ROW][C]Median[/C][C]71.11[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]71.02[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]70.8489473684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]70.8489473684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]70.8489473684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]70.8489473684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]70.8489473684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]70.8489473684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]70.8489473684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]70.8738461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207311&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207311&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 Mean70.87111111111110.193080370727002367.054977387196
Geometric Mean70.8524385739074
Harmonic Mean70.8337679192593
Quadratic Mean70.8897825657705
Winsorized Mean ( 1 / 24 )70.87569444444440.191993477897352369.156781889944
Winsorized Mean ( 2 / 24 )70.86597222222220.189360039498233374.239318971432
Winsorized Mean ( 3 / 24 )70.86222222222220.186863706181485379.218756120569
Winsorized Mean ( 4 / 24 )70.84611111111110.176945430209787400.383954686571
Winsorized Mean ( 5 / 24 )70.8350.174882030436635405.044473826976
Winsorized Mean ( 6 / 24 )70.83583333333330.174718838524102405.427565405671
Winsorized Mean ( 7 / 24 )70.84555555555560.171760525060471412.467041135401
Winsorized Mean ( 8 / 24 )70.84333333333330.170950349251568414.408824804921
Winsorized Mean ( 9 / 24 )70.87458333333330.15902910353371445.670520417099
Winsorized Mean ( 10 / 24 )70.86486111111110.155880054136518454.611473569596
Winsorized Mean ( 11 / 24 )70.83277777777780.149978900735974472.284950951023
Winsorized Mean ( 12 / 24 )70.83277777777780.149978900735974472.284950951023
Winsorized Mean ( 13 / 24 )70.82555555555560.14820956603788477.874387254152
Winsorized Mean ( 14 / 24 )70.81194444444440.132056331771374536.225287304205
Winsorized Mean ( 15 / 24 )70.73694444444440.121511998752071582.139584328404
Winsorized Mean ( 16 / 24 )70.83694444444440.104675076455767676.731719172693
Winsorized Mean ( 17 / 24 )70.82750.103386467862526685.075150204182
Winsorized Mean ( 18 / 24 )70.82250.102713335758912689.516112749312
Winsorized Mean ( 19 / 24 )70.81986111111110.101587649785926697.130618341388
Winsorized Mean ( 20 / 24 )70.81430555555560.0928105804815947762.998196844581
Winsorized Mean ( 21 / 24 )70.95138888888890.06827299109322161039.23070826075
Winsorized Mean ( 22 / 24 )70.94833333333330.06785876661546911045.52936741942
Winsorized Mean ( 23 / 24 )70.93236111111110.06314448402587061123.33424218099
Winsorized Mean ( 24 / 24 )70.93902777777780.06223729129161191139.81547566706
Trimmed Mean ( 1 / 24 )70.86685714285710.186473599822971380.036944694234
Trimmed Mean ( 2 / 24 )70.85750.179902101828516393.866993658261
Trimmed Mean ( 3 / 24 )70.85287878787880.173759843530796407.763251555422
Trimmed Mean ( 4 / 24 )70.8493750.16755549823888422.841242123799
Trimmed Mean ( 5 / 24 )70.85032258064520.163808449830759432.51933983775
Trimmed Mean ( 6 / 24 )70.8540.159896541409757443.124031172298
Trimmed Mean ( 7 / 24 )70.85775862068970.155147421863192456.712446586263
Trimmed Mean ( 8 / 24 )70.860.150107753505066472.060891895291
Trimmed Mean ( 9 / 24 )70.86277777777780.144061922945219491.891100223091
Trimmed Mean ( 10 / 24 )70.86096153846150.139530363880408507.853341507778
Trimmed Mean ( 11 / 24 )70.86040.13457808900715526.537421676684
Trimmed Mean ( 12 / 24 )70.86416666666670.129694414887285546.393356477637
Trimmed Mean ( 13 / 24 )70.86826086956520.123399239871063574.300627326503
Trimmed Mean ( 14 / 24 )70.87363636363640.115629123392148612.939320860136
Trimmed Mean ( 15 / 24 )70.88119047619050.109675480750836646.281101217328
Trimmed Mean ( 16 / 24 )70.89850.104238723795246680.155103771844
Trimmed Mean ( 17 / 24 )70.90578947368420.10151808700163698.454744055076
Trimmed Mean ( 18 / 24 )70.9150.0979929540712955723.67447917128
Trimmed Mean ( 19 / 24 )70.92588235294120.0931572546309991761.356510922122
Trimmed Mean ( 20 / 24 )70.93843750.0865164880041519819.941252083599
Trimmed Mean ( 21 / 24 )70.95333333333330.0797457646096647889.744222538111
Trimmed Mean ( 22 / 24 )70.95357142857140.0785234341150169903.597406662608
Trimmed Mean ( 23 / 24 )70.95423076923080.0764926805486302927.595036025984
Trimmed Mean ( 24 / 24 )70.95708333333330.0747058947644721949.819067920172
Median71.11
Midrange71.02
Midmean - Weighted Average at Xnp70.8489473684211
Midmean - Weighted Average at X(n+1)p70.8489473684211
Midmean - Empirical Distribution Function70.8489473684211
Midmean - Empirical Distribution Function - Averaging70.8489473684211
Midmean - Empirical Distribution Function - Interpolation70.8489473684211
Midmean - Closest Observation70.8489473684211
Midmean - True Basic - Statistics Graphics Toolkit70.8489473684211
Midmean - MS Excel (old versions)70.8738461538462
Number of observations72



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')