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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 computationSat, 19 Apr 2008 08:21:20 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/19/t1208614972oo6modxmdoasgmc.htm/, Retrieved Mon, 13 May 2024 23:18:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10276, Retrieved Mon, 13 May 2024 23:18:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact216
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten Lede...] [2008-04-19 14:21:20] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
101.31
101.31
101.39
101.26
101.26
101.25
101.25
101.22
101.29
101.26
101.32
101.34
101.34
101.34
101.34
101.34
101.34
101.34
101.34
101.31
102.19
102.16
102.31
102.32
102.32
102.32
102.36
102.36
102.37
102.37
102.37
102.37
103.45
103.93
104
103.92
103.92
103.9
103.91
103.84
103.8
103.81
103.81
103.81
104.51
105.14
105.15
105.23
105.23
105.22
105.13
105
105.01
105.01
105.01
105.01
105.57
106.05
106.09
106.2
106.19
106.2
106.09
106.23
106.23
106.22
106.22
106.61
106.95
107.74
107.8
107.8




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10276&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10276&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10276&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean103.6793055555560.239793723820945432.368720513191
Geometric Mean103.659683051457
Harmonic Mean103.640129176699
Quadratic Mean103.698992153305
Winsorized Mean ( 1 / 24 )103.6797222222220.239733891025751432.47836915593
Winsorized Mean ( 2 / 24 )103.6780555555560.239332963801820433.195887054683
Winsorized Mean ( 3 / 24 )103.6455555555560.232027692556349446.694764808664
Winsorized Mean ( 4 / 24 )103.6266666666670.228394495081233453.717882428863
Winsorized Mean ( 5 / 24 )103.6002777777780.223780731553548462.954415505553
Winsorized Mean ( 6 / 24 )103.6027777777780.223414359051271463.724794671778
Winsorized Mean ( 7 / 24 )103.603750.222970892005063464.651457723223
Winsorized Mean ( 8 / 24 )103.603750.222970892005063464.651457723223
Winsorized Mean ( 9 / 24 )103.601250.222558738136633465.500707217334
Winsorized Mean ( 10 / 24 )103.6026388888890.222357636143121465.927955908854
Winsorized Mean ( 11 / 24 )103.6041666666670.221665762114713467.389125313141
Winsorized Mean ( 12 / 24 )103.58750.21895493976947473.099625471175
Winsorized Mean ( 13 / 24 )103.58750.21895493976947473.099625471175
Winsorized Mean ( 14 / 24 )103.5797222222220.21770741124294475.774901877996
Winsorized Mean ( 15 / 24 )103.4797222222220.202418376700885511.217034287034
Winsorized Mean ( 16 / 24 )103.4041666666670.191848428818332538.988863779456
Winsorized Mean ( 17 / 24 )103.4041666666670.191848428818332538.988863779456
Winsorized Mean ( 18 / 24 )103.4016666666670.191513717295558539.917809161886
Winsorized Mean ( 19 / 24 )103.3963888888890.187061987662668552.738641243058
Winsorized Mean ( 20 / 24 )103.60750.156392822049902662.482450549684
Winsorized Mean ( 21 / 24 )103.6133333333330.154853659020541669.104843816374
Winsorized Mean ( 22 / 24 )103.6133333333330.145144685247901713.862399827913
Winsorized Mean ( 23 / 24 )103.6165277777780.144741169847813715.874604901458
Winsorized Mean ( 24 / 24 )103.6165277777780.144741169847813715.874604901458
Trimmed Mean ( 1 / 24 )103.6555714285710.236817025900346437.703205816757
Trimmed Mean ( 2 / 24 )103.630.233249180025227444.288807312386
Trimmed Mean ( 3 / 24 )103.6037878787880.229150734193505452.120689219787
Trimmed Mean ( 4 / 24 )103.5881250.227435002379888455.462544973510
Trimmed Mean ( 5 / 24 )103.5769354838710.226486696348668457.320174445999
Trimmed Mean ( 6 / 24 )103.5713333333330.226489728214807457.289317929263
Trimmed Mean ( 7 / 24 )103.5648275862070.226308154081352457.627468204163
Trimmed Mean ( 8 / 24 )103.5576785714290.225904386030938458.413758098731
Trimmed Mean ( 9 / 24 )103.550.225115701286601459.985684730927
Trimmed Mean ( 10 / 24 )103.5421153846150.223939150951084462.367187447417
Trimmed Mean ( 11 / 24 )103.53340.222223019068866465.898629376084
Trimmed Mean ( 12 / 24 )103.523750.219924556898384470.7239221486
Trimmed Mean ( 13 / 24 )103.5154347826090.217315573765743476.33693705815
Trimmed Mean ( 14 / 24 )103.5063636363640.213687817113609484.381211032417
Trimmed Mean ( 15 / 24 )103.4973809523810.209011294429389495.176020199931
Trimmed Mean ( 16 / 24 )103.49950.206118882176630502.134976218761
Trimmed Mean ( 17 / 24 )103.5107894736840.204177000994897506.965960756136
Trimmed Mean ( 18 / 24 )103.5233333333330.201068573945735514.865805738855
Trimmed Mean ( 19 / 24 )103.5376470588240.196419400506823527.125359265246
Trimmed Mean ( 20 / 24 )103.5543750.190675760031814543.091450023445
Trimmed Mean ( 21 / 24 )103.5480.190603035761185543.265219184337
Trimmed Mean ( 22 / 24 )103.540.189883004915015545.283133929447
Trimmed Mean ( 23 / 24 )103.5307692307690.190473033081749543.545548446928
Trimmed Mean ( 24 / 24 )103.5195833333330.189989014906189544.87141472073
Median103.81
Midrange104.51
Midmean - Weighted Average at Xnp103.167906976744
Midmean - Weighted Average at X(n+1)p103.167906976744
Midmean - Empirical Distribution Function103.167906976744
Midmean - Empirical Distribution Function - Averaging103.167906976744
Midmean - Empirical Distribution Function - Interpolation103.167906976744
Midmean - Closest Observation103.167906976744
Midmean - True Basic - Statistics Graphics Toolkit103.167906976744
Midmean - MS Excel (old versions)103.259555555556
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 103.679305555556 & 0.239793723820945 & 432.368720513191 \tabularnewline
Geometric Mean & 103.659683051457 &  &  \tabularnewline
Harmonic Mean & 103.640129176699 &  &  \tabularnewline
Quadratic Mean & 103.698992153305 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 103.679722222222 & 0.239733891025751 & 432.47836915593 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 103.678055555556 & 0.239332963801820 & 433.195887054683 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 103.645555555556 & 0.232027692556349 & 446.694764808664 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 103.626666666667 & 0.228394495081233 & 453.717882428863 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 103.600277777778 & 0.223780731553548 & 462.954415505553 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 103.602777777778 & 0.223414359051271 & 463.724794671778 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 103.60375 & 0.222970892005063 & 464.651457723223 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 103.60375 & 0.222970892005063 & 464.651457723223 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 103.60125 & 0.222558738136633 & 465.500707217334 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 103.602638888889 & 0.222357636143121 & 465.927955908854 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 103.604166666667 & 0.221665762114713 & 467.389125313141 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 103.5875 & 0.21895493976947 & 473.099625471175 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 103.5875 & 0.21895493976947 & 473.099625471175 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 103.579722222222 & 0.21770741124294 & 475.774901877996 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 103.479722222222 & 0.202418376700885 & 511.217034287034 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 103.404166666667 & 0.191848428818332 & 538.988863779456 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 103.404166666667 & 0.191848428818332 & 538.988863779456 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 103.401666666667 & 0.191513717295558 & 539.917809161886 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 103.396388888889 & 0.187061987662668 & 552.738641243058 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 103.6075 & 0.156392822049902 & 662.482450549684 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 103.613333333333 & 0.154853659020541 & 669.104843816374 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 103.613333333333 & 0.145144685247901 & 713.862399827913 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 103.616527777778 & 0.144741169847813 & 715.874604901458 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 103.616527777778 & 0.144741169847813 & 715.874604901458 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 103.655571428571 & 0.236817025900346 & 437.703205816757 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 103.63 & 0.233249180025227 & 444.288807312386 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 103.603787878788 & 0.229150734193505 & 452.120689219787 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 103.588125 & 0.227435002379888 & 455.462544973510 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 103.576935483871 & 0.226486696348668 & 457.320174445999 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 103.571333333333 & 0.226489728214807 & 457.289317929263 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 103.564827586207 & 0.226308154081352 & 457.627468204163 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 103.557678571429 & 0.225904386030938 & 458.413758098731 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 103.55 & 0.225115701286601 & 459.985684730927 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 103.542115384615 & 0.223939150951084 & 462.367187447417 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 103.5334 & 0.222223019068866 & 465.898629376084 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 103.52375 & 0.219924556898384 & 470.7239221486 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 103.515434782609 & 0.217315573765743 & 476.33693705815 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 103.506363636364 & 0.213687817113609 & 484.381211032417 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 103.497380952381 & 0.209011294429389 & 495.176020199931 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 103.4995 & 0.206118882176630 & 502.134976218761 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 103.510789473684 & 0.204177000994897 & 506.965960756136 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 103.523333333333 & 0.201068573945735 & 514.865805738855 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 103.537647058824 & 0.196419400506823 & 527.125359265246 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 103.554375 & 0.190675760031814 & 543.091450023445 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 103.548 & 0.190603035761185 & 543.265219184337 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 103.54 & 0.189883004915015 & 545.283133929447 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 103.530769230769 & 0.190473033081749 & 543.545548446928 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 103.519583333333 & 0.189989014906189 & 544.87141472073 \tabularnewline
Median & 103.81 &  &  \tabularnewline
Midrange & 104.51 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 103.167906976744 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 103.167906976744 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 103.167906976744 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 103.167906976744 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 103.167906976744 &  &  \tabularnewline
Midmean - Closest Observation & 103.167906976744 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 103.167906976744 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 103.259555555556 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10276&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]103.679305555556[/C][C]0.239793723820945[/C][C]432.368720513191[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]103.659683051457[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]103.640129176699[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]103.698992153305[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]103.679722222222[/C][C]0.239733891025751[/C][C]432.47836915593[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]103.678055555556[/C][C]0.239332963801820[/C][C]433.195887054683[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]103.645555555556[/C][C]0.232027692556349[/C][C]446.694764808664[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]103.626666666667[/C][C]0.228394495081233[/C][C]453.717882428863[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]103.600277777778[/C][C]0.223780731553548[/C][C]462.954415505553[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]103.602777777778[/C][C]0.223414359051271[/C][C]463.724794671778[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]103.60375[/C][C]0.222970892005063[/C][C]464.651457723223[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]103.60375[/C][C]0.222970892005063[/C][C]464.651457723223[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]103.60125[/C][C]0.222558738136633[/C][C]465.500707217334[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]103.602638888889[/C][C]0.222357636143121[/C][C]465.927955908854[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]103.604166666667[/C][C]0.221665762114713[/C][C]467.389125313141[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]103.5875[/C][C]0.21895493976947[/C][C]473.099625471175[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]103.5875[/C][C]0.21895493976947[/C][C]473.099625471175[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]103.579722222222[/C][C]0.21770741124294[/C][C]475.774901877996[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]103.479722222222[/C][C]0.202418376700885[/C][C]511.217034287034[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]103.404166666667[/C][C]0.191848428818332[/C][C]538.988863779456[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]103.404166666667[/C][C]0.191848428818332[/C][C]538.988863779456[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]103.401666666667[/C][C]0.191513717295558[/C][C]539.917809161886[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]103.396388888889[/C][C]0.187061987662668[/C][C]552.738641243058[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]103.6075[/C][C]0.156392822049902[/C][C]662.482450549684[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]103.613333333333[/C][C]0.154853659020541[/C][C]669.104843816374[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]103.613333333333[/C][C]0.145144685247901[/C][C]713.862399827913[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]103.616527777778[/C][C]0.144741169847813[/C][C]715.874604901458[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]103.616527777778[/C][C]0.144741169847813[/C][C]715.874604901458[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]103.655571428571[/C][C]0.236817025900346[/C][C]437.703205816757[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]103.63[/C][C]0.233249180025227[/C][C]444.288807312386[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]103.603787878788[/C][C]0.229150734193505[/C][C]452.120689219787[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]103.588125[/C][C]0.227435002379888[/C][C]455.462544973510[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]103.576935483871[/C][C]0.226486696348668[/C][C]457.320174445999[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]103.571333333333[/C][C]0.226489728214807[/C][C]457.289317929263[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]103.564827586207[/C][C]0.226308154081352[/C][C]457.627468204163[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]103.557678571429[/C][C]0.225904386030938[/C][C]458.413758098731[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]103.55[/C][C]0.225115701286601[/C][C]459.985684730927[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]103.542115384615[/C][C]0.223939150951084[/C][C]462.367187447417[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]103.5334[/C][C]0.222223019068866[/C][C]465.898629376084[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]103.52375[/C][C]0.219924556898384[/C][C]470.7239221486[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]103.515434782609[/C][C]0.217315573765743[/C][C]476.33693705815[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]103.506363636364[/C][C]0.213687817113609[/C][C]484.381211032417[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]103.497380952381[/C][C]0.209011294429389[/C][C]495.176020199931[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]103.4995[/C][C]0.206118882176630[/C][C]502.134976218761[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]103.510789473684[/C][C]0.204177000994897[/C][C]506.965960756136[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]103.523333333333[/C][C]0.201068573945735[/C][C]514.865805738855[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]103.537647058824[/C][C]0.196419400506823[/C][C]527.125359265246[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]103.554375[/C][C]0.190675760031814[/C][C]543.091450023445[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]103.548[/C][C]0.190603035761185[/C][C]543.265219184337[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]103.54[/C][C]0.189883004915015[/C][C]545.283133929447[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]103.530769230769[/C][C]0.190473033081749[/C][C]543.545548446928[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]103.519583333333[/C][C]0.189989014906189[/C][C]544.87141472073[/C][/ROW]
[ROW][C]Median[/C][C]103.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]104.51[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]103.167906976744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]103.167906976744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]103.167906976744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]103.167906976744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]103.167906976744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]103.167906976744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]103.167906976744[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]103.259555555556[/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=10276&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10276&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 Mean103.6793055555560.239793723820945432.368720513191
Geometric Mean103.659683051457
Harmonic Mean103.640129176699
Quadratic Mean103.698992153305
Winsorized Mean ( 1 / 24 )103.6797222222220.239733891025751432.47836915593
Winsorized Mean ( 2 / 24 )103.6780555555560.239332963801820433.195887054683
Winsorized Mean ( 3 / 24 )103.6455555555560.232027692556349446.694764808664
Winsorized Mean ( 4 / 24 )103.6266666666670.228394495081233453.717882428863
Winsorized Mean ( 5 / 24 )103.6002777777780.223780731553548462.954415505553
Winsorized Mean ( 6 / 24 )103.6027777777780.223414359051271463.724794671778
Winsorized Mean ( 7 / 24 )103.603750.222970892005063464.651457723223
Winsorized Mean ( 8 / 24 )103.603750.222970892005063464.651457723223
Winsorized Mean ( 9 / 24 )103.601250.222558738136633465.500707217334
Winsorized Mean ( 10 / 24 )103.6026388888890.222357636143121465.927955908854
Winsorized Mean ( 11 / 24 )103.6041666666670.221665762114713467.389125313141
Winsorized Mean ( 12 / 24 )103.58750.21895493976947473.099625471175
Winsorized Mean ( 13 / 24 )103.58750.21895493976947473.099625471175
Winsorized Mean ( 14 / 24 )103.5797222222220.21770741124294475.774901877996
Winsorized Mean ( 15 / 24 )103.4797222222220.202418376700885511.217034287034
Winsorized Mean ( 16 / 24 )103.4041666666670.191848428818332538.988863779456
Winsorized Mean ( 17 / 24 )103.4041666666670.191848428818332538.988863779456
Winsorized Mean ( 18 / 24 )103.4016666666670.191513717295558539.917809161886
Winsorized Mean ( 19 / 24 )103.3963888888890.187061987662668552.738641243058
Winsorized Mean ( 20 / 24 )103.60750.156392822049902662.482450549684
Winsorized Mean ( 21 / 24 )103.6133333333330.154853659020541669.104843816374
Winsorized Mean ( 22 / 24 )103.6133333333330.145144685247901713.862399827913
Winsorized Mean ( 23 / 24 )103.6165277777780.144741169847813715.874604901458
Winsorized Mean ( 24 / 24 )103.6165277777780.144741169847813715.874604901458
Trimmed Mean ( 1 / 24 )103.6555714285710.236817025900346437.703205816757
Trimmed Mean ( 2 / 24 )103.630.233249180025227444.288807312386
Trimmed Mean ( 3 / 24 )103.6037878787880.229150734193505452.120689219787
Trimmed Mean ( 4 / 24 )103.5881250.227435002379888455.462544973510
Trimmed Mean ( 5 / 24 )103.5769354838710.226486696348668457.320174445999
Trimmed Mean ( 6 / 24 )103.5713333333330.226489728214807457.289317929263
Trimmed Mean ( 7 / 24 )103.5648275862070.226308154081352457.627468204163
Trimmed Mean ( 8 / 24 )103.5576785714290.225904386030938458.413758098731
Trimmed Mean ( 9 / 24 )103.550.225115701286601459.985684730927
Trimmed Mean ( 10 / 24 )103.5421153846150.223939150951084462.367187447417
Trimmed Mean ( 11 / 24 )103.53340.222223019068866465.898629376084
Trimmed Mean ( 12 / 24 )103.523750.219924556898384470.7239221486
Trimmed Mean ( 13 / 24 )103.5154347826090.217315573765743476.33693705815
Trimmed Mean ( 14 / 24 )103.5063636363640.213687817113609484.381211032417
Trimmed Mean ( 15 / 24 )103.4973809523810.209011294429389495.176020199931
Trimmed Mean ( 16 / 24 )103.49950.206118882176630502.134976218761
Trimmed Mean ( 17 / 24 )103.5107894736840.204177000994897506.965960756136
Trimmed Mean ( 18 / 24 )103.5233333333330.201068573945735514.865805738855
Trimmed Mean ( 19 / 24 )103.5376470588240.196419400506823527.125359265246
Trimmed Mean ( 20 / 24 )103.5543750.190675760031814543.091450023445
Trimmed Mean ( 21 / 24 )103.5480.190603035761185543.265219184337
Trimmed Mean ( 22 / 24 )103.540.189883004915015545.283133929447
Trimmed Mean ( 23 / 24 )103.5307692307690.190473033081749543.545548446928
Trimmed Mean ( 24 / 24 )103.5195833333330.189989014906189544.87141472073
Median103.81
Midrange104.51
Midmean - Weighted Average at Xnp103.167906976744
Midmean - Weighted Average at X(n+1)p103.167906976744
Midmean - Empirical Distribution Function103.167906976744
Midmean - Empirical Distribution Function - Averaging103.167906976744
Midmean - Empirical Distribution Function - Interpolation103.167906976744
Midmean - Closest Observation103.167906976744
Midmean - True Basic - Statistics Graphics Toolkit103.167906976744
Midmean - MS Excel (old versions)103.259555555556
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')