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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 computationWed, 07 Mar 2012 17:21:39 -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/2012/Mar/07/t1331158945rwyazofaruksrdx.htm/, Retrieved Sun, 28 Apr 2024 21:28:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163730, Retrieved Sun, 28 Apr 2024 21:28:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact149
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opgave 5 oef 2 st...] [2012-03-07 22:21:39] [919141dca056cde38faaf6352f12d0de] [Current]
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Dataseries X:
115,43
115,55
117,14
119,09
119,55
119,8
121,32
121,48
119,63
118,61
118,82
119,93
118,7
119,99
116,67
116,84
115,17
114,21
114,77
115,59
116,64
118,79
125,63
127,42
131,17
137,68
144,41
146,09
151,26
156,56
158,38
154,21
158,06
154,83
150,89
149,22
148,34
143,88
134,48
133,73
130,08
123,11
122,08
126,83
123,17
123,82
125,6
126,32
129,15
130,09
133,81
136,83
138,34
138,67
137,86
138,56
141,65
142,42
143,12
146,17
147,8
151,87
157,12
158,97
161,4
165,81
165,1
164,64
167,88
167,14
169,83
169,71




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163730&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163730&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163730&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean136.1793055555562.0170516678087167.5140392925574
Geometric Mean135.146815981338
Harmonic Mean134.147790870779
Quadratic Mean137.235806476177
Winsorized Mean ( 1 / 24 )136.1854166666672.0154820555335267.5696497980563
Winsorized Mean ( 2 / 24 )136.1456944444442.0022015448179967.997996903364
Winsorized Mean ( 3 / 24 )136.1256944444441.9937910451854968.2748048112435
Winsorized Mean ( 4 / 24 )136.0584722222221.9768903579788168.8244907832571
Winsorized Mean ( 5 / 24 )136.0119444444441.966121389743169.1777960170689
Winsorized Mean ( 6 / 24 )136.0611111111111.9456094743661169.9323851491012
Winsorized Mean ( 7 / 24 )135.7490277777781.8823435863680572.1170294099725
Winsorized Mean ( 8 / 24 )135.4979166666671.8293091123538174.0705415785737
Winsorized Mean ( 9 / 24 )135.4616666666671.8107051471430874.8115544269574
Winsorized Mean ( 10 / 24 )135.6213888888891.774445661698576.430285703464
Winsorized Mean ( 11 / 24 )135.4915277777781.7472770080524277.5443888710018
Winsorized Mean ( 12 / 24 )135.4131944444441.7290711617540778.3155704864531
Winsorized Mean ( 13 / 24 )135.106251.6755203152978380.6353995033383
Winsorized Mean ( 14 / 24 )135.0381944444441.6484810232850881.9167418593279
Winsorized Mean ( 15 / 24 )134.6465277777781.5574625012720686.4525005692302
Winsorized Mean ( 16 / 24 )134.528751.534063690335487.6943707406222
Winsorized Mean ( 17 / 24 )134.4815277777781.515206988082588.7545588394919
Winsorized Mean ( 18 / 24 )134.0965277777781.4481817583818592.5964762376325
Winsorized Mean ( 19 / 24 )133.8801388888891.4121665545050294.8047795508195
Winsorized Mean ( 20 / 24 )134.0995833333331.34012926871485100.064662763415
Winsorized Mean ( 21 / 24 )133.6708333333331.26653121573159105.540891272957
Winsorized Mean ( 22 / 24 )133.8297222222221.23845008220436108.062266009151
Winsorized Mean ( 23 / 24 )133.6220833333331.12088314613466119.211430552887
Winsorized Mean ( 24 / 24 )133.4654166666671.09442238889603121.950554028135
Trimmed Mean ( 1 / 24 )136.0124285714291.9928022596834268.2518438096491
Trimmed Mean ( 2 / 24 )135.8292647058821.9650223601881469.1235211658751
Trimmed Mean ( 3 / 24 )135.6566666666671.9394157476192369.9471822032976
Trimmed Mean ( 4 / 24 )135.480781251.9116018913223370.8729060506853
Trimmed Mean ( 5 / 24 )135.3130645161291.8833639973517871.8464750873407
Trimmed Mean ( 6 / 24 )135.1453333333331.8516317352169572.9871554710089
Trimmed Mean ( 7 / 24 )134.9558620689661.8176528184918274.2473263848836
Trimmed Mean ( 8 / 24 )134.8101785714291.7917300369738375.2402291581371
Trimmed Mean ( 9 / 24 )134.6955555555561.7713832389074476.0397595489462
Trimmed Mean ( 10 / 24 )134.5776923076921.7487882815392376.9548227926376
Trimmed Mean ( 11 / 24 )134.42741.7265030555479377.8610843276717
Trimmed Mean ( 12 / 24 )134.2822916666671.7025840092264878.8697009598218
Trimmed Mean ( 13 / 24 )134.1347826086961.674238906734780.1168710565336
Trimmed Mean ( 14 / 24 )134.01251.6480616176787781.3152242382487
Trimmed Mean ( 15 / 24 )133.8869047619051.617915109563382.7527377490423
Trimmed Mean ( 16 / 24 )133.795751.5969364054378783.7827665174395
Trimmed Mean ( 17 / 24 )133.7089473684211.5715207134170985.0825230789904
Trimmed Mean ( 18 / 24 )133.6180555555561.5387640793751786.8346599368323
Trimmed Mean ( 19 / 24 )133.5617647058821.5083044907527888.5509295535036
Trimmed Mean ( 20 / 24 )133.52406251.4721527233962690.6998712687633
Trimmed Mean ( 21 / 24 )133.4551.4371952050682892.8579496573393
Trimmed Mean ( 22 / 24 )133.4285714285711.4047913771457794.9810581124647
Trimmed Mean ( 23 / 24 )133.3780769230771.3602893379131798.0512551305399
Trimmed Mean ( 24 / 24 )133.346251.3294262700231100.303606906822
Median133.77
Midrange142.02
Midmean - Weighted Average at Xnp133.244594594595
Midmean - Weighted Average at X(n+1)p133.618055555556
Midmean - Empirical Distribution Function133.244594594595
Midmean - Empirical Distribution Function - Averaging133.618055555556
Midmean - Empirical Distribution Function - Interpolation133.618055555556
Midmean - Closest Observation133.244594594595
Midmean - True Basic - Statistics Graphics Toolkit133.618055555556
Midmean - MS Excel (old versions)133.708947368421
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 136.179305555556 & 2.01705166780871 & 67.5140392925574 \tabularnewline
Geometric Mean & 135.146815981338 &  &  \tabularnewline
Harmonic Mean & 134.147790870779 &  &  \tabularnewline
Quadratic Mean & 137.235806476177 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 136.185416666667 & 2.01548205553352 & 67.5696497980563 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 136.145694444444 & 2.00220154481799 & 67.997996903364 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 136.125694444444 & 1.99379104518549 & 68.2748048112435 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 136.058472222222 & 1.97689035797881 & 68.8244907832571 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 136.011944444444 & 1.9661213897431 & 69.1777960170689 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 136.061111111111 & 1.94560947436611 & 69.9323851491012 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 135.749027777778 & 1.88234358636805 & 72.1170294099725 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 135.497916666667 & 1.82930911235381 & 74.0705415785737 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 135.461666666667 & 1.81070514714308 & 74.8115544269574 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 135.621388888889 & 1.7744456616985 & 76.430285703464 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 135.491527777778 & 1.74727700805242 & 77.5443888710018 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 135.413194444444 & 1.72907116175407 & 78.3155704864531 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 135.10625 & 1.67552031529783 & 80.6353995033383 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 135.038194444444 & 1.64848102328508 & 81.9167418593279 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 134.646527777778 & 1.55746250127206 & 86.4525005692302 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 134.52875 & 1.5340636903354 & 87.6943707406222 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 134.481527777778 & 1.5152069880825 & 88.7545588394919 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 134.096527777778 & 1.44818175838185 & 92.5964762376325 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 133.880138888889 & 1.41216655450502 & 94.8047795508195 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 134.099583333333 & 1.34012926871485 & 100.064662763415 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 133.670833333333 & 1.26653121573159 & 105.540891272957 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 133.829722222222 & 1.23845008220436 & 108.062266009151 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 133.622083333333 & 1.12088314613466 & 119.211430552887 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 133.465416666667 & 1.09442238889603 & 121.950554028135 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 136.012428571429 & 1.99280225968342 & 68.2518438096491 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 135.829264705882 & 1.96502236018814 & 69.1235211658751 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 135.656666666667 & 1.93941574761923 & 69.9471822032976 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 135.48078125 & 1.91160189132233 & 70.8729060506853 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 135.313064516129 & 1.88336399735178 & 71.8464750873407 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 135.145333333333 & 1.85163173521695 & 72.9871554710089 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 134.955862068966 & 1.81765281849182 & 74.2473263848836 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 134.810178571429 & 1.79173003697383 & 75.2402291581371 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 134.695555555556 & 1.77138323890744 & 76.0397595489462 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 134.577692307692 & 1.74878828153923 & 76.9548227926376 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 134.4274 & 1.72650305554793 & 77.8610843276717 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 134.282291666667 & 1.70258400922648 & 78.8697009598218 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 134.134782608696 & 1.6742389067347 & 80.1168710565336 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 134.0125 & 1.64806161767877 & 81.3152242382487 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 133.886904761905 & 1.6179151095633 & 82.7527377490423 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 133.79575 & 1.59693640543787 & 83.7827665174395 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 133.708947368421 & 1.57152071341709 & 85.0825230789904 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 133.618055555556 & 1.53876407937517 & 86.8346599368323 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 133.561764705882 & 1.50830449075278 & 88.5509295535036 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 133.5240625 & 1.47215272339626 & 90.6998712687633 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 133.455 & 1.43719520506828 & 92.8579496573393 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 133.428571428571 & 1.40479137714577 & 94.9810581124647 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 133.378076923077 & 1.36028933791317 & 98.0512551305399 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 133.34625 & 1.3294262700231 & 100.303606906822 \tabularnewline
Median & 133.77 &  &  \tabularnewline
Midrange & 142.02 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 133.244594594595 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 133.618055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 133.244594594595 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 133.618055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 133.618055555556 &  &  \tabularnewline
Midmean - Closest Observation & 133.244594594595 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 133.618055555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 133.708947368421 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163730&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]136.179305555556[/C][C]2.01705166780871[/C][C]67.5140392925574[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]135.146815981338[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]134.147790870779[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]137.235806476177[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]136.185416666667[/C][C]2.01548205553352[/C][C]67.5696497980563[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]136.145694444444[/C][C]2.00220154481799[/C][C]67.997996903364[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]136.125694444444[/C][C]1.99379104518549[/C][C]68.2748048112435[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]136.058472222222[/C][C]1.97689035797881[/C][C]68.8244907832571[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]136.011944444444[/C][C]1.9661213897431[/C][C]69.1777960170689[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]136.061111111111[/C][C]1.94560947436611[/C][C]69.9323851491012[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]135.749027777778[/C][C]1.88234358636805[/C][C]72.1170294099725[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]135.497916666667[/C][C]1.82930911235381[/C][C]74.0705415785737[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]135.461666666667[/C][C]1.81070514714308[/C][C]74.8115544269574[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]135.621388888889[/C][C]1.7744456616985[/C][C]76.430285703464[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]135.491527777778[/C][C]1.74727700805242[/C][C]77.5443888710018[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]135.413194444444[/C][C]1.72907116175407[/C][C]78.3155704864531[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]135.10625[/C][C]1.67552031529783[/C][C]80.6353995033383[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]135.038194444444[/C][C]1.64848102328508[/C][C]81.9167418593279[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]134.646527777778[/C][C]1.55746250127206[/C][C]86.4525005692302[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]134.52875[/C][C]1.5340636903354[/C][C]87.6943707406222[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]134.481527777778[/C][C]1.5152069880825[/C][C]88.7545588394919[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]134.096527777778[/C][C]1.44818175838185[/C][C]92.5964762376325[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]133.880138888889[/C][C]1.41216655450502[/C][C]94.8047795508195[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]134.099583333333[/C][C]1.34012926871485[/C][C]100.064662763415[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]133.670833333333[/C][C]1.26653121573159[/C][C]105.540891272957[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]133.829722222222[/C][C]1.23845008220436[/C][C]108.062266009151[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]133.622083333333[/C][C]1.12088314613466[/C][C]119.211430552887[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]133.465416666667[/C][C]1.09442238889603[/C][C]121.950554028135[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]136.012428571429[/C][C]1.99280225968342[/C][C]68.2518438096491[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]135.829264705882[/C][C]1.96502236018814[/C][C]69.1235211658751[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]135.656666666667[/C][C]1.93941574761923[/C][C]69.9471822032976[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]135.48078125[/C][C]1.91160189132233[/C][C]70.8729060506853[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]135.313064516129[/C][C]1.88336399735178[/C][C]71.8464750873407[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]135.145333333333[/C][C]1.85163173521695[/C][C]72.9871554710089[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]134.955862068966[/C][C]1.81765281849182[/C][C]74.2473263848836[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]134.810178571429[/C][C]1.79173003697383[/C][C]75.2402291581371[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]134.695555555556[/C][C]1.77138323890744[/C][C]76.0397595489462[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]134.577692307692[/C][C]1.74878828153923[/C][C]76.9548227926376[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]134.4274[/C][C]1.72650305554793[/C][C]77.8610843276717[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]134.282291666667[/C][C]1.70258400922648[/C][C]78.8697009598218[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]134.134782608696[/C][C]1.6742389067347[/C][C]80.1168710565336[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]134.0125[/C][C]1.64806161767877[/C][C]81.3152242382487[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]133.886904761905[/C][C]1.6179151095633[/C][C]82.7527377490423[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]133.79575[/C][C]1.59693640543787[/C][C]83.7827665174395[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]133.708947368421[/C][C]1.57152071341709[/C][C]85.0825230789904[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]133.618055555556[/C][C]1.53876407937517[/C][C]86.8346599368323[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]133.561764705882[/C][C]1.50830449075278[/C][C]88.5509295535036[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]133.5240625[/C][C]1.47215272339626[/C][C]90.6998712687633[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]133.455[/C][C]1.43719520506828[/C][C]92.8579496573393[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]133.428571428571[/C][C]1.40479137714577[/C][C]94.9810581124647[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]133.378076923077[/C][C]1.36028933791317[/C][C]98.0512551305399[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]133.34625[/C][C]1.3294262700231[/C][C]100.303606906822[/C][/ROW]
[ROW][C]Median[/C][C]133.77[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]142.02[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]133.244594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]133.618055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]133.244594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]133.618055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]133.618055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]133.244594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]133.618055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]133.708947368421[/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=163730&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163730&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 Mean136.1793055555562.0170516678087167.5140392925574
Geometric Mean135.146815981338
Harmonic Mean134.147790870779
Quadratic Mean137.235806476177
Winsorized Mean ( 1 / 24 )136.1854166666672.0154820555335267.5696497980563
Winsorized Mean ( 2 / 24 )136.1456944444442.0022015448179967.997996903364
Winsorized Mean ( 3 / 24 )136.1256944444441.9937910451854968.2748048112435
Winsorized Mean ( 4 / 24 )136.0584722222221.9768903579788168.8244907832571
Winsorized Mean ( 5 / 24 )136.0119444444441.966121389743169.1777960170689
Winsorized Mean ( 6 / 24 )136.0611111111111.9456094743661169.9323851491012
Winsorized Mean ( 7 / 24 )135.7490277777781.8823435863680572.1170294099725
Winsorized Mean ( 8 / 24 )135.4979166666671.8293091123538174.0705415785737
Winsorized Mean ( 9 / 24 )135.4616666666671.8107051471430874.8115544269574
Winsorized Mean ( 10 / 24 )135.6213888888891.774445661698576.430285703464
Winsorized Mean ( 11 / 24 )135.4915277777781.7472770080524277.5443888710018
Winsorized Mean ( 12 / 24 )135.4131944444441.7290711617540778.3155704864531
Winsorized Mean ( 13 / 24 )135.106251.6755203152978380.6353995033383
Winsorized Mean ( 14 / 24 )135.0381944444441.6484810232850881.9167418593279
Winsorized Mean ( 15 / 24 )134.6465277777781.5574625012720686.4525005692302
Winsorized Mean ( 16 / 24 )134.528751.534063690335487.6943707406222
Winsorized Mean ( 17 / 24 )134.4815277777781.515206988082588.7545588394919
Winsorized Mean ( 18 / 24 )134.0965277777781.4481817583818592.5964762376325
Winsorized Mean ( 19 / 24 )133.8801388888891.4121665545050294.8047795508195
Winsorized Mean ( 20 / 24 )134.0995833333331.34012926871485100.064662763415
Winsorized Mean ( 21 / 24 )133.6708333333331.26653121573159105.540891272957
Winsorized Mean ( 22 / 24 )133.8297222222221.23845008220436108.062266009151
Winsorized Mean ( 23 / 24 )133.6220833333331.12088314613466119.211430552887
Winsorized Mean ( 24 / 24 )133.4654166666671.09442238889603121.950554028135
Trimmed Mean ( 1 / 24 )136.0124285714291.9928022596834268.2518438096491
Trimmed Mean ( 2 / 24 )135.8292647058821.9650223601881469.1235211658751
Trimmed Mean ( 3 / 24 )135.6566666666671.9394157476192369.9471822032976
Trimmed Mean ( 4 / 24 )135.480781251.9116018913223370.8729060506853
Trimmed Mean ( 5 / 24 )135.3130645161291.8833639973517871.8464750873407
Trimmed Mean ( 6 / 24 )135.1453333333331.8516317352169572.9871554710089
Trimmed Mean ( 7 / 24 )134.9558620689661.8176528184918274.2473263848836
Trimmed Mean ( 8 / 24 )134.8101785714291.7917300369738375.2402291581371
Trimmed Mean ( 9 / 24 )134.6955555555561.7713832389074476.0397595489462
Trimmed Mean ( 10 / 24 )134.5776923076921.7487882815392376.9548227926376
Trimmed Mean ( 11 / 24 )134.42741.7265030555479377.8610843276717
Trimmed Mean ( 12 / 24 )134.2822916666671.7025840092264878.8697009598218
Trimmed Mean ( 13 / 24 )134.1347826086961.674238906734780.1168710565336
Trimmed Mean ( 14 / 24 )134.01251.6480616176787781.3152242382487
Trimmed Mean ( 15 / 24 )133.8869047619051.617915109563382.7527377490423
Trimmed Mean ( 16 / 24 )133.795751.5969364054378783.7827665174395
Trimmed Mean ( 17 / 24 )133.7089473684211.5715207134170985.0825230789904
Trimmed Mean ( 18 / 24 )133.6180555555561.5387640793751786.8346599368323
Trimmed Mean ( 19 / 24 )133.5617647058821.5083044907527888.5509295535036
Trimmed Mean ( 20 / 24 )133.52406251.4721527233962690.6998712687633
Trimmed Mean ( 21 / 24 )133.4551.4371952050682892.8579496573393
Trimmed Mean ( 22 / 24 )133.4285714285711.4047913771457794.9810581124647
Trimmed Mean ( 23 / 24 )133.3780769230771.3602893379131798.0512551305399
Trimmed Mean ( 24 / 24 )133.346251.3294262700231100.303606906822
Median133.77
Midrange142.02
Midmean - Weighted Average at Xnp133.244594594595
Midmean - Weighted Average at X(n+1)p133.618055555556
Midmean - Empirical Distribution Function133.244594594595
Midmean - Empirical Distribution Function - Averaging133.618055555556
Midmean - Empirical Distribution Function - Interpolation133.618055555556
Midmean - Closest Observation133.244594594595
Midmean - True Basic - Statistics Graphics Toolkit133.618055555556
Midmean - MS Excel (old versions)133.708947368421
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')