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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 13 Dec 2010 10:21:05 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/13/t1292235549s7vi096cpll0cka.htm/, Retrieved Mon, 06 May 2024 15:46:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108774, Retrieved Mon, 06 May 2024 15:46:18 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Faillissementen B...] [2010-12-13 10:21:05] [dcc54e7e6e8c80b7c45e040080afe6ab] [Current]
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Dataseries X:
89
97
154
81
110
116
73
73
174
103
130
91
136
106
136
122
131
135
75
68
143
115
93
128
152
125
107
116
220
137
34
51
153
145
116
145
98
118
139
140
113
149
79
47
166
180
122
134
114
125
181
142
143
187
137
62
239
157
139
187
99
146
175
148
130
183
115
80
223
131
201
157




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108774&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]4 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=108774&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108774&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean128.6944444444444.8092584357095326.7597273394308
Geometric Mean121.555635908495
Harmonic Mean113.056313826520
Quadratic Mean134.923743895086
Winsorized Mean ( 1 / 24 )128.6527777777784.6946744927011427.4039825290967
Winsorized Mean ( 2 / 24 )128.6805555555564.6446422930169527.7051595015233
Winsorized Mean ( 3 / 24 )128.3472222222224.3375818700910629.5895791863239
Winsorized Mean ( 4 / 24 )127.9027777777784.0961717175337731.2249550550546
Winsorized Mean ( 5 / 24 )128.254.0268440987864431.8487621705172
Winsorized Mean ( 6 / 24 )127.9166666666673.95992987323532.3027605946383
Winsorized Mean ( 7 / 24 )127.9166666666673.8845199581369532.9298518337428
Winsorized Mean ( 8 / 24 )128.253.7796687594473733.9315448422395
Winsorized Mean ( 9 / 24 )127.753.6391815577153735.1040468781117
Winsorized Mean ( 10 / 24 )127.753.588297685768335.6018399774006
Winsorized Mean ( 11 / 24 )127.753.1542721359063640.5006272432141
Winsorized Mean ( 12 / 24 )126.5833333333332.8547759450437844.3408995207125
Winsorized Mean ( 13 / 24 )126.9444444444442.7921537231129145.4647046806996
Winsorized Mean ( 14 / 24 )127.1388888888892.5741967429667549.3897326365047
Winsorized Mean ( 15 / 24 )127.1388888888892.5095518272886950.661989725173
Winsorized Mean ( 16 / 24 )127.1388888888892.4412747090063352.0788948576124
Winsorized Mean ( 17 / 24 )127.3752.1903220674134758.1535482361348
Winsorized Mean ( 18 / 24 )127.8752.0400851400656762.6812075087631
Winsorized Mean ( 19 / 24 )127.6111111111111.9281454146524466.1833439227996
Winsorized Mean ( 20 / 24 )128.1666666666671.7677116229313672.5042846378586
Winsorized Mean ( 21 / 24 )129.0416666666671.6441480496222678.4854300051104
Winsorized Mean ( 22 / 24 )128.7361111111111.5200785869895884.6904312796517
Winsorized Mean ( 23 / 24 )129.0555555555561.4768544069456987.3854287522206
Winsorized Mean ( 24 / 24 )128.7222222222221.4329323358472689.8313332751417
Trimmed Mean ( 1 / 24 )128.4714285714294.4836358281615728.6534039550009
Trimmed Mean ( 2 / 24 )128.2794117647064.2300425170827830.3257972577479
Trimmed Mean ( 3 / 24 )128.0606060606063.9558683673504132.3723122633576
Trimmed Mean ( 4 / 24 )127.9531253.7746826372102833.8977173176512
Trimmed Mean ( 5 / 24 )127.9677419354843.6493566830141635.0658357214318
Trimmed Mean ( 6 / 24 )127.93.5199752823990936.3354824221458
Trimmed Mean ( 7 / 24 )127.8965517241383.3818927871024837.8180385291624
Trimmed Mean ( 8 / 24 )127.8928571428573.2330154164101739.5583814706535
Trimmed Mean ( 9 / 24 )127.8333333333333.0764484864868141.5522424298137
Trimmed Mean ( 10 / 24 )127.8461538461542.9175942867127243.8190307776478
Trimmed Mean ( 11 / 24 )127.862.7292833775740646.847462249834
Trimmed Mean ( 12 / 24 )127.8752.6029553920591249.1268503448466
Trimmed Mean ( 13 / 24 )128.0434782608702.5133376622688150.9455932575663
Trimmed Mean ( 14 / 24 )128.1818181818182.4121505163227553.1400579335436
Trimmed Mean ( 15 / 24 )128.3095238095242.332542116201555.0084489014387
Trimmed Mean ( 16 / 24 )128.452.2417798560690457.2982220588051
Trimmed Mean ( 17 / 24 )128.6052631578952.1363678358686360.1980899537391
Trimmed Mean ( 18 / 24 )128.752.0595788597101862.5127799273088
Trimmed Mean ( 19 / 24 )128.8529411764711.9929163113732564.6554701976835
Trimmed Mean ( 20 / 24 )1291.9270987720974166.9400042529212
Trimmed Mean ( 21 / 24 )129.11.8774830302124368.7622726397656
Trimmed Mean ( 22 / 24 )129.1071428571431.8382612598761970.2332936428407
Trimmed Mean ( 23 / 24 )129.1538461538461.8116650290588571.2901359148833
Trimmed Mean ( 24 / 24 )129.1666666666671.7761163734340972.724213682533
Median130.5
Midrange136.5
Midmean - Weighted Average at Xnp128.054054054054
Midmean - Weighted Average at X(n+1)p128.75
Midmean - Empirical Distribution Function128.054054054054
Midmean - Empirical Distribution Function - Averaging128.75
Midmean - Empirical Distribution Function - Interpolation128.75
Midmean - Closest Observation128.054054054054
Midmean - True Basic - Statistics Graphics Toolkit128.75
Midmean - MS Excel (old versions)128.605263157895
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 128.694444444444 & 4.80925843570953 & 26.7597273394308 \tabularnewline
Geometric Mean & 121.555635908495 &  &  \tabularnewline
Harmonic Mean & 113.056313826520 &  &  \tabularnewline
Quadratic Mean & 134.923743895086 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 128.652777777778 & 4.69467449270114 & 27.4039825290967 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 128.680555555556 & 4.64464229301695 & 27.7051595015233 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 128.347222222222 & 4.33758187009106 & 29.5895791863239 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 127.902777777778 & 4.09617171753377 & 31.2249550550546 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 128.25 & 4.02684409878644 & 31.8487621705172 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 127.916666666667 & 3.959929873235 & 32.3027605946383 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 127.916666666667 & 3.88451995813695 & 32.9298518337428 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 128.25 & 3.77966875944737 & 33.9315448422395 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 127.75 & 3.63918155771537 & 35.1040468781117 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 127.75 & 3.5882976857683 & 35.6018399774006 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 127.75 & 3.15427213590636 & 40.5006272432141 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 126.583333333333 & 2.85477594504378 & 44.3408995207125 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 126.944444444444 & 2.79215372311291 & 45.4647046806996 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 127.138888888889 & 2.57419674296675 & 49.3897326365047 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 127.138888888889 & 2.50955182728869 & 50.661989725173 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 127.138888888889 & 2.44127470900633 & 52.0788948576124 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 127.375 & 2.19032206741347 & 58.1535482361348 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 127.875 & 2.04008514006567 & 62.6812075087631 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 127.611111111111 & 1.92814541465244 & 66.1833439227996 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 128.166666666667 & 1.76771162293136 & 72.5042846378586 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 129.041666666667 & 1.64414804962226 & 78.4854300051104 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 128.736111111111 & 1.52007858698958 & 84.6904312796517 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 129.055555555556 & 1.47685440694569 & 87.3854287522206 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 128.722222222222 & 1.43293233584726 & 89.8313332751417 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 128.471428571429 & 4.48363582816157 & 28.6534039550009 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 128.279411764706 & 4.23004251708278 & 30.3257972577479 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 128.060606060606 & 3.95586836735041 & 32.3723122633576 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 127.953125 & 3.77468263721028 & 33.8977173176512 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 127.967741935484 & 3.64935668301416 & 35.0658357214318 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 127.9 & 3.51997528239909 & 36.3354824221458 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 127.896551724138 & 3.38189278710248 & 37.8180385291624 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 127.892857142857 & 3.23301541641017 & 39.5583814706535 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 127.833333333333 & 3.07644848648681 & 41.5522424298137 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 127.846153846154 & 2.91759428671272 & 43.8190307776478 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 127.86 & 2.72928337757406 & 46.847462249834 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 127.875 & 2.60295539205912 & 49.1268503448466 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 128.043478260870 & 2.51333766226881 & 50.9455932575663 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 128.181818181818 & 2.41215051632275 & 53.1400579335436 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 128.309523809524 & 2.3325421162015 & 55.0084489014387 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 128.45 & 2.24177985606904 & 57.2982220588051 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 128.605263157895 & 2.13636783586863 & 60.1980899537391 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 128.75 & 2.05957885971018 & 62.5127799273088 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 128.852941176471 & 1.99291631137325 & 64.6554701976835 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 129 & 1.92709877209741 & 66.9400042529212 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 129.1 & 1.87748303021243 & 68.7622726397656 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 129.107142857143 & 1.83826125987619 & 70.2332936428407 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 129.153846153846 & 1.81166502905885 & 71.2901359148833 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 129.166666666667 & 1.77611637343409 & 72.724213682533 \tabularnewline
Median & 130.5 &  &  \tabularnewline
Midrange & 136.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 128.054054054054 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 128.75 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 128.054054054054 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 128.75 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 128.75 &  &  \tabularnewline
Midmean - Closest Observation & 128.054054054054 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 128.75 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 128.605263157895 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108774&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]128.694444444444[/C][C]4.80925843570953[/C][C]26.7597273394308[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]121.555635908495[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]113.056313826520[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]134.923743895086[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]128.652777777778[/C][C]4.69467449270114[/C][C]27.4039825290967[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]128.680555555556[/C][C]4.64464229301695[/C][C]27.7051595015233[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]128.347222222222[/C][C]4.33758187009106[/C][C]29.5895791863239[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]127.902777777778[/C][C]4.09617171753377[/C][C]31.2249550550546[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]128.25[/C][C]4.02684409878644[/C][C]31.8487621705172[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]127.916666666667[/C][C]3.959929873235[/C][C]32.3027605946383[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]127.916666666667[/C][C]3.88451995813695[/C][C]32.9298518337428[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]128.25[/C][C]3.77966875944737[/C][C]33.9315448422395[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]127.75[/C][C]3.63918155771537[/C][C]35.1040468781117[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]127.75[/C][C]3.5882976857683[/C][C]35.6018399774006[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]127.75[/C][C]3.15427213590636[/C][C]40.5006272432141[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]126.583333333333[/C][C]2.85477594504378[/C][C]44.3408995207125[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]126.944444444444[/C][C]2.79215372311291[/C][C]45.4647046806996[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]127.138888888889[/C][C]2.57419674296675[/C][C]49.3897326365047[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]127.138888888889[/C][C]2.50955182728869[/C][C]50.661989725173[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]127.138888888889[/C][C]2.44127470900633[/C][C]52.0788948576124[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]127.375[/C][C]2.19032206741347[/C][C]58.1535482361348[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]127.875[/C][C]2.04008514006567[/C][C]62.6812075087631[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]127.611111111111[/C][C]1.92814541465244[/C][C]66.1833439227996[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]128.166666666667[/C][C]1.76771162293136[/C][C]72.5042846378586[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]129.041666666667[/C][C]1.64414804962226[/C][C]78.4854300051104[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]128.736111111111[/C][C]1.52007858698958[/C][C]84.6904312796517[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]129.055555555556[/C][C]1.47685440694569[/C][C]87.3854287522206[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]128.722222222222[/C][C]1.43293233584726[/C][C]89.8313332751417[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]128.471428571429[/C][C]4.48363582816157[/C][C]28.6534039550009[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]128.279411764706[/C][C]4.23004251708278[/C][C]30.3257972577479[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]128.060606060606[/C][C]3.95586836735041[/C][C]32.3723122633576[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]127.953125[/C][C]3.77468263721028[/C][C]33.8977173176512[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]127.967741935484[/C][C]3.64935668301416[/C][C]35.0658357214318[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]127.9[/C][C]3.51997528239909[/C][C]36.3354824221458[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]127.896551724138[/C][C]3.38189278710248[/C][C]37.8180385291624[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]127.892857142857[/C][C]3.23301541641017[/C][C]39.5583814706535[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]127.833333333333[/C][C]3.07644848648681[/C][C]41.5522424298137[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]127.846153846154[/C][C]2.91759428671272[/C][C]43.8190307776478[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]127.86[/C][C]2.72928337757406[/C][C]46.847462249834[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]127.875[/C][C]2.60295539205912[/C][C]49.1268503448466[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]128.043478260870[/C][C]2.51333766226881[/C][C]50.9455932575663[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]128.181818181818[/C][C]2.41215051632275[/C][C]53.1400579335436[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]128.309523809524[/C][C]2.3325421162015[/C][C]55.0084489014387[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]128.45[/C][C]2.24177985606904[/C][C]57.2982220588051[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]128.605263157895[/C][C]2.13636783586863[/C][C]60.1980899537391[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]128.75[/C][C]2.05957885971018[/C][C]62.5127799273088[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]128.852941176471[/C][C]1.99291631137325[/C][C]64.6554701976835[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]129[/C][C]1.92709877209741[/C][C]66.9400042529212[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]129.1[/C][C]1.87748303021243[/C][C]68.7622726397656[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]129.107142857143[/C][C]1.83826125987619[/C][C]70.2332936428407[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]129.153846153846[/C][C]1.81166502905885[/C][C]71.2901359148833[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]129.166666666667[/C][C]1.77611637343409[/C][C]72.724213682533[/C][/ROW]
[ROW][C]Median[/C][C]130.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]136.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]128.054054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]128.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]128.054054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]128.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]128.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]128.054054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]128.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]128.605263157895[/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=108774&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108774&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 Mean128.6944444444444.8092584357095326.7597273394308
Geometric Mean121.555635908495
Harmonic Mean113.056313826520
Quadratic Mean134.923743895086
Winsorized Mean ( 1 / 24 )128.6527777777784.6946744927011427.4039825290967
Winsorized Mean ( 2 / 24 )128.6805555555564.6446422930169527.7051595015233
Winsorized Mean ( 3 / 24 )128.3472222222224.3375818700910629.5895791863239
Winsorized Mean ( 4 / 24 )127.9027777777784.0961717175337731.2249550550546
Winsorized Mean ( 5 / 24 )128.254.0268440987864431.8487621705172
Winsorized Mean ( 6 / 24 )127.9166666666673.95992987323532.3027605946383
Winsorized Mean ( 7 / 24 )127.9166666666673.8845199581369532.9298518337428
Winsorized Mean ( 8 / 24 )128.253.7796687594473733.9315448422395
Winsorized Mean ( 9 / 24 )127.753.6391815577153735.1040468781117
Winsorized Mean ( 10 / 24 )127.753.588297685768335.6018399774006
Winsorized Mean ( 11 / 24 )127.753.1542721359063640.5006272432141
Winsorized Mean ( 12 / 24 )126.5833333333332.8547759450437844.3408995207125
Winsorized Mean ( 13 / 24 )126.9444444444442.7921537231129145.4647046806996
Winsorized Mean ( 14 / 24 )127.1388888888892.5741967429667549.3897326365047
Winsorized Mean ( 15 / 24 )127.1388888888892.5095518272886950.661989725173
Winsorized Mean ( 16 / 24 )127.1388888888892.4412747090063352.0788948576124
Winsorized Mean ( 17 / 24 )127.3752.1903220674134758.1535482361348
Winsorized Mean ( 18 / 24 )127.8752.0400851400656762.6812075087631
Winsorized Mean ( 19 / 24 )127.6111111111111.9281454146524466.1833439227996
Winsorized Mean ( 20 / 24 )128.1666666666671.7677116229313672.5042846378586
Winsorized Mean ( 21 / 24 )129.0416666666671.6441480496222678.4854300051104
Winsorized Mean ( 22 / 24 )128.7361111111111.5200785869895884.6904312796517
Winsorized Mean ( 23 / 24 )129.0555555555561.4768544069456987.3854287522206
Winsorized Mean ( 24 / 24 )128.7222222222221.4329323358472689.8313332751417
Trimmed Mean ( 1 / 24 )128.4714285714294.4836358281615728.6534039550009
Trimmed Mean ( 2 / 24 )128.2794117647064.2300425170827830.3257972577479
Trimmed Mean ( 3 / 24 )128.0606060606063.9558683673504132.3723122633576
Trimmed Mean ( 4 / 24 )127.9531253.7746826372102833.8977173176512
Trimmed Mean ( 5 / 24 )127.9677419354843.6493566830141635.0658357214318
Trimmed Mean ( 6 / 24 )127.93.5199752823990936.3354824221458
Trimmed Mean ( 7 / 24 )127.8965517241383.3818927871024837.8180385291624
Trimmed Mean ( 8 / 24 )127.8928571428573.2330154164101739.5583814706535
Trimmed Mean ( 9 / 24 )127.8333333333333.0764484864868141.5522424298137
Trimmed Mean ( 10 / 24 )127.8461538461542.9175942867127243.8190307776478
Trimmed Mean ( 11 / 24 )127.862.7292833775740646.847462249834
Trimmed Mean ( 12 / 24 )127.8752.6029553920591249.1268503448466
Trimmed Mean ( 13 / 24 )128.0434782608702.5133376622688150.9455932575663
Trimmed Mean ( 14 / 24 )128.1818181818182.4121505163227553.1400579335436
Trimmed Mean ( 15 / 24 )128.3095238095242.332542116201555.0084489014387
Trimmed Mean ( 16 / 24 )128.452.2417798560690457.2982220588051
Trimmed Mean ( 17 / 24 )128.6052631578952.1363678358686360.1980899537391
Trimmed Mean ( 18 / 24 )128.752.0595788597101862.5127799273088
Trimmed Mean ( 19 / 24 )128.8529411764711.9929163113732564.6554701976835
Trimmed Mean ( 20 / 24 )1291.9270987720974166.9400042529212
Trimmed Mean ( 21 / 24 )129.11.8774830302124368.7622726397656
Trimmed Mean ( 22 / 24 )129.1071428571431.8382612598761970.2332936428407
Trimmed Mean ( 23 / 24 )129.1538461538461.8116650290588571.2901359148833
Trimmed Mean ( 24 / 24 )129.1666666666671.7761163734340972.724213682533
Median130.5
Midrange136.5
Midmean - Weighted Average at Xnp128.054054054054
Midmean - Weighted Average at X(n+1)p128.75
Midmean - Empirical Distribution Function128.054054054054
Midmean - Empirical Distribution Function - Averaging128.75
Midmean - Empirical Distribution Function - Interpolation128.75
Midmean - Closest Observation128.054054054054
Midmean - True Basic - Statistics Graphics Toolkit128.75
Midmean - MS Excel (old versions)128.605263157895
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')