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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, 20 Oct 2007 08:34:47 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/20/zmmxa70nz1lzj7j1192894252.htm/, Retrieved Fri, 03 May 2024 03:19:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1182, Retrieved Fri, 03 May 2024 03:19:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS2CTOM
Estimated Impact228
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS2 Central tende...] [2007-10-20 15:34:47] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-    D    [Central Tendency] [paper robuustheid...] [2008-12-26 17:47:42] [c29178f7f550574a75dc881e636e0923]
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Dataseries X:
96,5
97,3
122,0
91,0
107,9
114,6
98,0
95,5
98,7
115,9
110,4
109,5
92,3
102,1
112,8
110,2
98,9
119,0
104,3
98,8
109,4
170,3
118,0
116,9
111,7
116,8
116,1
114,8
110,8
122,8
104,7
86,0
127,2
126,1
114,6
127,8
105,2
113,1
161,0
126,9
117,7
144,9
119,4
107,1
142,8
126,2
126,9
179,2
105,3
114,8
125,4
113,2
134,4
150,0
100,9
101,8
137,7
138,7
135,4
153,8
119,5
123,3
166,4
137,5
142,2
167,0
112,3
120,6
154,9
153,4
156,2
175,8
131,7
130,1
161,1
128,2
140,3
168,2
110,2
126,2




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1182&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1182&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1182&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean123.70752.4352187637284650.7993375554468
Geometric Mean121.919878468889
Harmonic Mean120.235513710664
Quadratic Mean125.586776772079
Winsorized Mean ( 1 / 26 )123.72752.4117834247657251.3012481674297
Winsorized Mean ( 2 / 26 )123.62252.3703321717494352.1540826527955
Winsorized Mean ( 3 / 26 )123.663752.3317784296065753.0340912454813
Winsorized Mean ( 4 / 26 )123.653752.3098557024839253.533105928231
Winsorized Mean ( 5 / 26 )123.666252.2936214136344053.9174640003217
Winsorized Mean ( 6 / 26 )123.321252.1957321187211256.164068899182
Winsorized Mean ( 7 / 26 )123.373752.1849772930995856.4645455994574
Winsorized Mean ( 8 / 26 )122.903752.0825536932537459.0158853517853
Winsorized Mean ( 9 / 26 )122.768752.0516029498335759.8404043092056
Winsorized Mean ( 10 / 26 )122.881251.9885272950116561.7951034960676
Winsorized Mean ( 11 / 26 )122.951.9606000437737362.7103933769927
Winsorized Mean ( 12 / 26 )122.4851.8563644372942165.9811174677163
Winsorized Mean ( 13 / 26 )122.013751.6567876724595573.6447717641858
Winsorized Mean ( 14 / 26 )121.716251.5841805410213376.8323097325314
Winsorized Mean ( 15 / 26 )121.69751.5526222969014278.3819092659384
Winsorized Mean ( 16 / 26 )121.33751.4874702156362981.5730619171397
Winsorized Mean ( 17 / 26 )121.381.3818917047092787.8361159462465
Winsorized Mean ( 18 / 26 )121.3351.3230790948160491.706535516586
Winsorized Mean ( 19 / 26 )121.643751.2709707290671895.7093245485513
Winsorized Mean ( 20 / 26 )121.143751.18646219641110102.105023123741
Winsorized Mean ( 21 / 26 )121.0651.12412567994144107.697032600756
Winsorized Mean ( 22 / 26 )120.32251.01557487461505118.477231967370
Winsorized Mean ( 23 / 26 )119.920.944230314105594127.002912540032
Winsorized Mean ( 24 / 26 )119.470.852936847499734140.06898676052
Winsorized Mean ( 25 / 26 )119.626250.80104311691583149.338091138694
Winsorized Mean ( 26 / 26 )119.626250.751765314321202159.127120819634
Trimmed Mean ( 1 / 26 )123.4794871794872.3431163726069952.6988282029295
Trimmed Mean ( 2 / 26 )123.2184210526322.2624538072448954.462292515347
Trimmed Mean ( 3 / 26 )1232.1938801150642556.0650507543333
Trimmed Mean ( 4 / 26 )122.7541666666672.1301903724979557.6259137453148
Trimmed Mean ( 5 / 26 )122.4971428571432.0624403839089159.3942708903788
Trimmed Mean ( 6 / 26 )122.2220588235291.9864376035731761.5282647709036
Trimmed Mean ( 7 / 26 )1221.9237335009690463.4183476757801
Trimmed Mean ( 8 / 26 )121.75468751.8506004089078565.7919921091203
Trimmed Mean ( 9 / 26 )121.5693548387101.7881559750667767.9858784881281
Trimmed Mean ( 10 / 26 )121.3916666666671.7194653151105470.5984968698616
Trimmed Mean ( 11 / 26 )121.1862068965521.6493567799335573.4748287156124
Trimmed Mean ( 12 / 26 )120.9571428571431.5684673989111577.1180471721073
Trimmed Mean ( 13 / 26 )120.7685185185191.4925948684984980.9117872956434
Trimmed Mean ( 14 / 26 )120.6211538461541.4429062357850783.5959751608706
Trimmed Mean ( 15 / 26 )120.4961.3960935586449186.3094018691394
Trimmed Mean ( 16 / 26 )120.36251.3430528663358989.6185868903079
Trimmed Mean ( 17 / 26 )120.2565217391301.2899561920955893.2252757698456
Trimmed Mean ( 18 / 26 )120.1363636363641.2445572453216396.529399582031
Trimmed Mean ( 19 / 26 )120.0095238095241.19806177928755100.169729044265
Trimmed Mean ( 20 / 26 )119.83751.14690602469739104.487636667196
Trimmed Mean ( 21 / 26 )119.71.10031677838806108.786853341779
Trimmed Mean ( 22 / 26 )119.5555555555561.05226471143324113.617376175919
Trimmed Mean ( 23 / 26 )119.4735294117651.01675192205752117.505093248308
Trimmed Mean ( 24 / 26 )119.4250.986082588309794121.110545319233
Trimmed Mean ( 25 / 26 )119.420.966798247089181123.521117626710
Trimmed Mean ( 26 / 26 )119.3964285714290.950737421158403125.582969507977
Median118.5
Midrange132.6
Midmean - Weighted Average at Xnp119.582926829268
Midmean - Weighted Average at X(n+1)p119.8375
Midmean - Empirical Distribution Function119.582926829268
Midmean - Empirical Distribution Function - Averaging119.8375
Midmean - Empirical Distribution Function - Interpolation119.8375
Midmean - Closest Observation119.582926829268
Midmean - True Basic - Statistics Graphics Toolkit119.8375
Midmean - MS Excel (old versions)120.009523809524
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 123.7075 & 2.43521876372846 & 50.7993375554468 \tabularnewline
Geometric Mean & 121.919878468889 &  &  \tabularnewline
Harmonic Mean & 120.235513710664 &  &  \tabularnewline
Quadratic Mean & 125.586776772079 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 123.7275 & 2.41178342476572 & 51.3012481674297 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 123.6225 & 2.37033217174943 & 52.1540826527955 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 123.66375 & 2.33177842960657 & 53.0340912454813 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 123.65375 & 2.30985570248392 & 53.533105928231 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 123.66625 & 2.29362141363440 & 53.9174640003217 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 123.32125 & 2.19573211872112 & 56.164068899182 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 123.37375 & 2.18497729309958 & 56.4645455994574 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 122.90375 & 2.08255369325374 & 59.0158853517853 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 122.76875 & 2.05160294983357 & 59.8404043092056 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 122.88125 & 1.98852729501165 & 61.7951034960676 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 122.95 & 1.96060004377373 & 62.7103933769927 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 122.485 & 1.85636443729421 & 65.9811174677163 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 122.01375 & 1.65678767245955 & 73.6447717641858 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 121.71625 & 1.58418054102133 & 76.8323097325314 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 121.6975 & 1.55262229690142 & 78.3819092659384 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 121.3375 & 1.48747021563629 & 81.5730619171397 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 121.38 & 1.38189170470927 & 87.8361159462465 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 121.335 & 1.32307909481604 & 91.706535516586 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 121.64375 & 1.27097072906718 & 95.7093245485513 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 121.14375 & 1.18646219641110 & 102.105023123741 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 121.065 & 1.12412567994144 & 107.697032600756 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 120.3225 & 1.01557487461505 & 118.477231967370 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 119.92 & 0.944230314105594 & 127.002912540032 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 119.47 & 0.852936847499734 & 140.06898676052 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 119.62625 & 0.80104311691583 & 149.338091138694 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 119.62625 & 0.751765314321202 & 159.127120819634 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 123.479487179487 & 2.34311637260699 & 52.6988282029295 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 123.218421052632 & 2.26245380724489 & 54.462292515347 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 123 & 2.19388011506425 & 56.0650507543333 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 122.754166666667 & 2.13019037249795 & 57.6259137453148 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 122.497142857143 & 2.06244038390891 & 59.3942708903788 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 122.222058823529 & 1.98643760357317 & 61.5282647709036 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 122 & 1.92373350096904 & 63.4183476757801 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 121.7546875 & 1.85060040890785 & 65.7919921091203 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 121.569354838710 & 1.78815597506677 & 67.9858784881281 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 121.391666666667 & 1.71946531511054 & 70.5984968698616 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 121.186206896552 & 1.64935677993355 & 73.4748287156124 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 120.957142857143 & 1.56846739891115 & 77.1180471721073 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 120.768518518519 & 1.49259486849849 & 80.9117872956434 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 120.621153846154 & 1.44290623578507 & 83.5959751608706 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 120.496 & 1.39609355864491 & 86.3094018691394 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 120.3625 & 1.34305286633589 & 89.6185868903079 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 120.256521739130 & 1.28995619209558 & 93.2252757698456 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 120.136363636364 & 1.24455724532163 & 96.529399582031 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 120.009523809524 & 1.19806177928755 & 100.169729044265 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 119.8375 & 1.14690602469739 & 104.487636667196 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 119.7 & 1.10031677838806 & 108.786853341779 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 119.555555555556 & 1.05226471143324 & 113.617376175919 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 119.473529411765 & 1.01675192205752 & 117.505093248308 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 119.425 & 0.986082588309794 & 121.110545319233 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 119.42 & 0.966798247089181 & 123.521117626710 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 119.396428571429 & 0.950737421158403 & 125.582969507977 \tabularnewline
Median & 118.5 &  &  \tabularnewline
Midrange & 132.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 119.582926829268 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 119.8375 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 119.582926829268 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 119.8375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 119.8375 &  &  \tabularnewline
Midmean - Closest Observation & 119.582926829268 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 119.8375 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 120.009523809524 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1182&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]123.7075[/C][C]2.43521876372846[/C][C]50.7993375554468[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]121.919878468889[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]120.235513710664[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]125.586776772079[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]123.7275[/C][C]2.41178342476572[/C][C]51.3012481674297[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]123.6225[/C][C]2.37033217174943[/C][C]52.1540826527955[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]123.66375[/C][C]2.33177842960657[/C][C]53.0340912454813[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]123.65375[/C][C]2.30985570248392[/C][C]53.533105928231[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]123.66625[/C][C]2.29362141363440[/C][C]53.9174640003217[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]123.32125[/C][C]2.19573211872112[/C][C]56.164068899182[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]123.37375[/C][C]2.18497729309958[/C][C]56.4645455994574[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]122.90375[/C][C]2.08255369325374[/C][C]59.0158853517853[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]122.76875[/C][C]2.05160294983357[/C][C]59.8404043092056[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]122.88125[/C][C]1.98852729501165[/C][C]61.7951034960676[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]122.95[/C][C]1.96060004377373[/C][C]62.7103933769927[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]122.485[/C][C]1.85636443729421[/C][C]65.9811174677163[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]122.01375[/C][C]1.65678767245955[/C][C]73.6447717641858[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]121.71625[/C][C]1.58418054102133[/C][C]76.8323097325314[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]121.6975[/C][C]1.55262229690142[/C][C]78.3819092659384[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]121.3375[/C][C]1.48747021563629[/C][C]81.5730619171397[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]121.38[/C][C]1.38189170470927[/C][C]87.8361159462465[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]121.335[/C][C]1.32307909481604[/C][C]91.706535516586[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]121.64375[/C][C]1.27097072906718[/C][C]95.7093245485513[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]121.14375[/C][C]1.18646219641110[/C][C]102.105023123741[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]121.065[/C][C]1.12412567994144[/C][C]107.697032600756[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]120.3225[/C][C]1.01557487461505[/C][C]118.477231967370[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]119.92[/C][C]0.944230314105594[/C][C]127.002912540032[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]119.47[/C][C]0.852936847499734[/C][C]140.06898676052[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]119.62625[/C][C]0.80104311691583[/C][C]149.338091138694[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]119.62625[/C][C]0.751765314321202[/C][C]159.127120819634[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]123.479487179487[/C][C]2.34311637260699[/C][C]52.6988282029295[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]123.218421052632[/C][C]2.26245380724489[/C][C]54.462292515347[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]123[/C][C]2.19388011506425[/C][C]56.0650507543333[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]122.754166666667[/C][C]2.13019037249795[/C][C]57.6259137453148[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]122.497142857143[/C][C]2.06244038390891[/C][C]59.3942708903788[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]122.222058823529[/C][C]1.98643760357317[/C][C]61.5282647709036[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]122[/C][C]1.92373350096904[/C][C]63.4183476757801[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]121.7546875[/C][C]1.85060040890785[/C][C]65.7919921091203[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]121.569354838710[/C][C]1.78815597506677[/C][C]67.9858784881281[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]121.391666666667[/C][C]1.71946531511054[/C][C]70.5984968698616[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]121.186206896552[/C][C]1.64935677993355[/C][C]73.4748287156124[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]120.957142857143[/C][C]1.56846739891115[/C][C]77.1180471721073[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]120.768518518519[/C][C]1.49259486849849[/C][C]80.9117872956434[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]120.621153846154[/C][C]1.44290623578507[/C][C]83.5959751608706[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]120.496[/C][C]1.39609355864491[/C][C]86.3094018691394[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]120.3625[/C][C]1.34305286633589[/C][C]89.6185868903079[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]120.256521739130[/C][C]1.28995619209558[/C][C]93.2252757698456[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]120.136363636364[/C][C]1.24455724532163[/C][C]96.529399582031[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]120.009523809524[/C][C]1.19806177928755[/C][C]100.169729044265[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]119.8375[/C][C]1.14690602469739[/C][C]104.487636667196[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]119.7[/C][C]1.10031677838806[/C][C]108.786853341779[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]119.555555555556[/C][C]1.05226471143324[/C][C]113.617376175919[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]119.473529411765[/C][C]1.01675192205752[/C][C]117.505093248308[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]119.425[/C][C]0.986082588309794[/C][C]121.110545319233[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]119.42[/C][C]0.966798247089181[/C][C]123.521117626710[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]119.396428571429[/C][C]0.950737421158403[/C][C]125.582969507977[/C][/ROW]
[ROW][C]Median[/C][C]118.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]132.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]119.582926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]119.8375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]119.582926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]119.8375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]119.8375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]119.582926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]119.8375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]120.009523809524[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1182&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1182&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 Mean123.70752.4352187637284650.7993375554468
Geometric Mean121.919878468889
Harmonic Mean120.235513710664
Quadratic Mean125.586776772079
Winsorized Mean ( 1 / 26 )123.72752.4117834247657251.3012481674297
Winsorized Mean ( 2 / 26 )123.62252.3703321717494352.1540826527955
Winsorized Mean ( 3 / 26 )123.663752.3317784296065753.0340912454813
Winsorized Mean ( 4 / 26 )123.653752.3098557024839253.533105928231
Winsorized Mean ( 5 / 26 )123.666252.2936214136344053.9174640003217
Winsorized Mean ( 6 / 26 )123.321252.1957321187211256.164068899182
Winsorized Mean ( 7 / 26 )123.373752.1849772930995856.4645455994574
Winsorized Mean ( 8 / 26 )122.903752.0825536932537459.0158853517853
Winsorized Mean ( 9 / 26 )122.768752.0516029498335759.8404043092056
Winsorized Mean ( 10 / 26 )122.881251.9885272950116561.7951034960676
Winsorized Mean ( 11 / 26 )122.951.9606000437737362.7103933769927
Winsorized Mean ( 12 / 26 )122.4851.8563644372942165.9811174677163
Winsorized Mean ( 13 / 26 )122.013751.6567876724595573.6447717641858
Winsorized Mean ( 14 / 26 )121.716251.5841805410213376.8323097325314
Winsorized Mean ( 15 / 26 )121.69751.5526222969014278.3819092659384
Winsorized Mean ( 16 / 26 )121.33751.4874702156362981.5730619171397
Winsorized Mean ( 17 / 26 )121.381.3818917047092787.8361159462465
Winsorized Mean ( 18 / 26 )121.3351.3230790948160491.706535516586
Winsorized Mean ( 19 / 26 )121.643751.2709707290671895.7093245485513
Winsorized Mean ( 20 / 26 )121.143751.18646219641110102.105023123741
Winsorized Mean ( 21 / 26 )121.0651.12412567994144107.697032600756
Winsorized Mean ( 22 / 26 )120.32251.01557487461505118.477231967370
Winsorized Mean ( 23 / 26 )119.920.944230314105594127.002912540032
Winsorized Mean ( 24 / 26 )119.470.852936847499734140.06898676052
Winsorized Mean ( 25 / 26 )119.626250.80104311691583149.338091138694
Winsorized Mean ( 26 / 26 )119.626250.751765314321202159.127120819634
Trimmed Mean ( 1 / 26 )123.4794871794872.3431163726069952.6988282029295
Trimmed Mean ( 2 / 26 )123.2184210526322.2624538072448954.462292515347
Trimmed Mean ( 3 / 26 )1232.1938801150642556.0650507543333
Trimmed Mean ( 4 / 26 )122.7541666666672.1301903724979557.6259137453148
Trimmed Mean ( 5 / 26 )122.4971428571432.0624403839089159.3942708903788
Trimmed Mean ( 6 / 26 )122.2220588235291.9864376035731761.5282647709036
Trimmed Mean ( 7 / 26 )1221.9237335009690463.4183476757801
Trimmed Mean ( 8 / 26 )121.75468751.8506004089078565.7919921091203
Trimmed Mean ( 9 / 26 )121.5693548387101.7881559750667767.9858784881281
Trimmed Mean ( 10 / 26 )121.3916666666671.7194653151105470.5984968698616
Trimmed Mean ( 11 / 26 )121.1862068965521.6493567799335573.4748287156124
Trimmed Mean ( 12 / 26 )120.9571428571431.5684673989111577.1180471721073
Trimmed Mean ( 13 / 26 )120.7685185185191.4925948684984980.9117872956434
Trimmed Mean ( 14 / 26 )120.6211538461541.4429062357850783.5959751608706
Trimmed Mean ( 15 / 26 )120.4961.3960935586449186.3094018691394
Trimmed Mean ( 16 / 26 )120.36251.3430528663358989.6185868903079
Trimmed Mean ( 17 / 26 )120.2565217391301.2899561920955893.2252757698456
Trimmed Mean ( 18 / 26 )120.1363636363641.2445572453216396.529399582031
Trimmed Mean ( 19 / 26 )120.0095238095241.19806177928755100.169729044265
Trimmed Mean ( 20 / 26 )119.83751.14690602469739104.487636667196
Trimmed Mean ( 21 / 26 )119.71.10031677838806108.786853341779
Trimmed Mean ( 22 / 26 )119.5555555555561.05226471143324113.617376175919
Trimmed Mean ( 23 / 26 )119.4735294117651.01675192205752117.505093248308
Trimmed Mean ( 24 / 26 )119.4250.986082588309794121.110545319233
Trimmed Mean ( 25 / 26 )119.420.966798247089181123.521117626710
Trimmed Mean ( 26 / 26 )119.3964285714290.950737421158403125.582969507977
Median118.5
Midrange132.6
Midmean - Weighted Average at Xnp119.582926829268
Midmean - Weighted Average at X(n+1)p119.8375
Midmean - Empirical Distribution Function119.582926829268
Midmean - Empirical Distribution Function - Averaging119.8375
Midmean - Empirical Distribution Function - Interpolation119.8375
Midmean - Closest Observation119.582926829268
Midmean - True Basic - Statistics Graphics Toolkit119.8375
Midmean - MS Excel (old versions)120.009523809524
Number of observations80



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')