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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 computationThu, 29 Nov 2007 02:44:28 -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/Nov/29/t119632889408imweqxsh5bwoa.htm/, Retrieved Fri, 03 May 2024 06:25:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7314, Retrieved Fri, 03 May 2024 06:25:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact260
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-11-29 09:44:28] [7c5c775a3769ba2649d285a4261e023c] [Current]
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Dataseries X:
467 037
460 070
447 988
442 867
436 087
431 328
484 015
509 673
512 927
502 831
470 984
471 067
476 049
474 605
470 439
461 251
454 724
455 626
516 847
525 192
522 975
518 585
509 239
512 238
519 164
517 009
509 933
509 127
500 857
506 971
569 323
579 714
577 992
565 464
547 344
554 788
562 325
560 854
555 332
543 599
536 662
542 722
593 530
610 763
612 613
611 324
594 167
595 454
590 865
589 379
584 428
573 100
567 456
569 028
620 735
628 884
628 232
612 117
595 404
597 141
593 408
590 072
579 799
574 205
572 775
572 942
619 567
625 809
619 916
587 625
565 742
557 274
560 576
548 854
531 673
525 919
511 038
498 662
555 362
564 591
541 657




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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7314&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7314&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7314&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean542789.0123456795841.9548322091892.9122233799297
Geometric Mean540202.701838785
Harmonic Mean537548.53640707
Quadratic Mean545298.254924884
Winsorized Mean ( 1 / 27 )542839.7160493835826.7420187049293.1635061766535
Winsorized Mean ( 2 / 27 )542947.2962962965778.6052247894893.9581914969933
Winsorized Mean ( 3 / 27 )542949.0370370375705.4793471445395.1627381332599
Winsorized Mean ( 4 / 27 )543241.2345679015631.2963798468796.4682371384391
Winsorized Mean ( 5 / 27 )543275.370370375616.7336411943996.7244318630077
Winsorized Mean ( 6 / 27 )543089.4444444445468.6870867492399.3089265905091
Winsorized Mean ( 7 / 27 )543148.6419753095442.6039363068499.7957316629346
Winsorized Mean ( 8 / 27 )543641.7777777785325.02947899451102.091787458129
Winsorized Mean ( 9 / 27 )543957.4444444445248.02994786062103.649836195426
Winsorized Mean ( 10 / 27 )5423434986.34809699889108.765571406139
Winsorized Mean ( 11 / 27 )542125.1728395064953.1762471599109.450006579183
Winsorized Mean ( 12 / 27 )542641.9135802474859.30049525108111.670787618622
Winsorized Mean ( 13 / 27 )542675.1358024694792.07405516989113.244313329634
Winsorized Mean ( 14 / 27 )543941.876543214543.87765452765119.708741717817
Winsorized Mean ( 15 / 27 )546631.6913580254118.41801967285132.728559545650
Winsorized Mean ( 16 / 27 )546562.9506172843985.19585473372137.148328599224
Winsorized Mean ( 17 / 27 )546810.8148148153903.22473522551140.092065383784
Winsorized Mean ( 18 / 27 )547576.8148148153754.82111490981145.832996581508
Winsorized Mean ( 19 / 27 )547671.1111111113630.13272871481150.868067930124
Winsorized Mean ( 20 / 27 )546909.382716053519.52761892281155.392837315889
Winsorized Mean ( 21 / 27 )545821.7901234573348.24023236327163.017511362439
Winsorized Mean ( 22 / 27 )545869.3209876543335.79224647984163.640083270681
Winsorized Mean ( 23 / 27 )545694.123456793232.08536427644168.836544197821
Winsorized Mean ( 24 / 27 )544927.6049382723046.86909058263178.848381317908
Winsorized Mean ( 25 / 27 )544799.2098765432977.63863448315182.963507917779
Winsorized Mean ( 26 / 27 )546006.7654320992805.59795882541194.613331434234
Winsorized Mean ( 27 / 27 )546005.0987654322791.90882275361195.566952013468
Trimmed Mean ( 1 / 27 )543110.1012658235715.7063091958495.0206451986569
Trimmed Mean ( 2 / 27 )543394.5324675325586.0005112865197.2779238687151
Trimmed Mean ( 3 / 27 )543636.045464.0512827662199.4932170045045
Trimmed Mean ( 4 / 27 )543890.1369863015352.89102175967101.606801777838
Trimmed Mean ( 5 / 27 )544075.2112676065247.77482635593103.677316438025
Trimmed Mean ( 6 / 27 )5442635127.21418960833106.151797032996
Trimmed Mean ( 7 / 27 )544499.4626865675023.25871409155108.395663786757
Trimmed Mean ( 8 / 27 )544739.9384615384904.73416675924111.064110702144
Trimmed Mean ( 9 / 27 )544916.4285714294789.51613338638113.772751442044
Trimmed Mean ( 10 / 27 )545057.9180327874666.9887662043116.790064287231
Trimmed Mean ( 11 / 27 )545430.6440677974571.33473946838119.315402426913
Trimmed Mean ( 12 / 27 )545857.6666666674459.05906416113122.415437609674
Trimmed Mean ( 13 / 27 )546252.3272727274339.42271487271125.881335644147
Trimmed Mean ( 14 / 27 )546672.8679245284203.33833488359130.056832063143
Trimmed Mean ( 15 / 27 )546982.686274514085.683272829133.877897465060
Trimmed Mean ( 16 / 27 )547021.3673469394023.54825053703135.954966433900
Trimmed Mean ( 17 / 27 )547070.7446808513966.95768530857137.906876775343
Trimmed Mean ( 18 / 27 )547098.2666666673906.51899676953140.047512150609
Trimmed Mean ( 19 / 27 )547048.1860465123853.53368936596141.960141040449
Trimmed Mean ( 20 / 27 )546983.4146341463804.19629920659143.784224475542
Trimmed Mean ( 21 / 27 )546991.1025641033755.98410866639145.631900119598
Trimmed Mean ( 22 / 27 )5471133720.49380198793147.05386680329
Trimmed Mean ( 23 / 27 )547243.8285714293665.86182524993149.281084410245
Trimmed Mean ( 24 / 27 )547409.2121212123606.42463884624151.787231660090
Trimmed Mean ( 25 / 27 )547679.3870967743558.62728176035153.901868257991
Trimmed Mean ( 26 / 27 )548001.1724137933495.32082788190156.781365545168
Trimmed Mean ( 27 / 27 )548231.2962962963443.96829883015159.185929929297
Median554788
Midrange530106
Midmean - Weighted Average at Xnp546047.3
Midmean - Weighted Average at X(n+1)p546983.414634146
Midmean - Empirical Distribution Function546983.414634146
Midmean - Empirical Distribution Function - Averaging546983.414634146
Midmean - Empirical Distribution Function - Interpolation546983.414634146
Midmean - Closest Observation546082.071428571
Midmean - True Basic - Statistics Graphics Toolkit546983.414634146
Midmean - MS Excel (old versions)546983.414634146
Number of observations81

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 542789.012345679 & 5841.95483220918 & 92.9122233799297 \tabularnewline
Geometric Mean & 540202.701838785 &  &  \tabularnewline
Harmonic Mean & 537548.53640707 &  &  \tabularnewline
Quadratic Mean & 545298.254924884 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 542839.716049383 & 5826.74201870492 & 93.1635061766535 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 542947.296296296 & 5778.60522478948 & 93.9581914969933 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 542949.037037037 & 5705.47934714453 & 95.1627381332599 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 543241.234567901 & 5631.29637984687 & 96.4682371384391 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 543275.37037037 & 5616.73364119439 & 96.7244318630077 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 543089.444444444 & 5468.68708674923 & 99.3089265905091 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 543148.641975309 & 5442.60393630684 & 99.7957316629346 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 543641.777777778 & 5325.02947899451 & 102.091787458129 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 543957.444444444 & 5248.02994786062 & 103.649836195426 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 542343 & 4986.34809699889 & 108.765571406139 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 542125.172839506 & 4953.1762471599 & 109.450006579183 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 542641.913580247 & 4859.30049525108 & 111.670787618622 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 542675.135802469 & 4792.07405516989 & 113.244313329634 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 543941.87654321 & 4543.87765452765 & 119.708741717817 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 546631.691358025 & 4118.41801967285 & 132.728559545650 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 546562.950617284 & 3985.19585473372 & 137.148328599224 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 546810.814814815 & 3903.22473522551 & 140.092065383784 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 547576.814814815 & 3754.82111490981 & 145.832996581508 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 547671.111111111 & 3630.13272871481 & 150.868067930124 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 546909.38271605 & 3519.52761892281 & 155.392837315889 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 545821.790123457 & 3348.24023236327 & 163.017511362439 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 545869.320987654 & 3335.79224647984 & 163.640083270681 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 545694.12345679 & 3232.08536427644 & 168.836544197821 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 544927.604938272 & 3046.86909058263 & 178.848381317908 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 544799.209876543 & 2977.63863448315 & 182.963507917779 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 546006.765432099 & 2805.59795882541 & 194.613331434234 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 546005.098765432 & 2791.90882275361 & 195.566952013468 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 543110.101265823 & 5715.70630919584 & 95.0206451986569 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 543394.532467532 & 5586.00051128651 & 97.2779238687151 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 543636.04 & 5464.05128276621 & 99.4932170045045 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 543890.136986301 & 5352.89102175967 & 101.606801777838 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 544075.211267606 & 5247.77482635593 & 103.677316438025 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 544263 & 5127.21418960833 & 106.151797032996 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 544499.462686567 & 5023.25871409155 & 108.395663786757 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 544739.938461538 & 4904.73416675924 & 111.064110702144 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 544916.428571429 & 4789.51613338638 & 113.772751442044 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 545057.918032787 & 4666.9887662043 & 116.790064287231 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 545430.644067797 & 4571.33473946838 & 119.315402426913 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 545857.666666667 & 4459.05906416113 & 122.415437609674 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 546252.327272727 & 4339.42271487271 & 125.881335644147 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 546672.867924528 & 4203.33833488359 & 130.056832063143 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 546982.68627451 & 4085.683272829 & 133.877897465060 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 547021.367346939 & 4023.54825053703 & 135.954966433900 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 547070.744680851 & 3966.95768530857 & 137.906876775343 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 547098.266666667 & 3906.51899676953 & 140.047512150609 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 547048.186046512 & 3853.53368936596 & 141.960141040449 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 546983.414634146 & 3804.19629920659 & 143.784224475542 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 546991.102564103 & 3755.98410866639 & 145.631900119598 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 547113 & 3720.49380198793 & 147.05386680329 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 547243.828571429 & 3665.86182524993 & 149.281084410245 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 547409.212121212 & 3606.42463884624 & 151.787231660090 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 547679.387096774 & 3558.62728176035 & 153.901868257991 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 548001.172413793 & 3495.32082788190 & 156.781365545168 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 548231.296296296 & 3443.96829883015 & 159.185929929297 \tabularnewline
Median & 554788 &  &  \tabularnewline
Midrange & 530106 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 546047.3 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 546983.414634146 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 546983.414634146 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 546983.414634146 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 546983.414634146 &  &  \tabularnewline
Midmean - Closest Observation & 546082.071428571 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 546983.414634146 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 546983.414634146 &  &  \tabularnewline
Number of observations & 81 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7314&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]542789.012345679[/C][C]5841.95483220918[/C][C]92.9122233799297[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]540202.701838785[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]537548.53640707[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]545298.254924884[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]542839.716049383[/C][C]5826.74201870492[/C][C]93.1635061766535[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]542947.296296296[/C][C]5778.60522478948[/C][C]93.9581914969933[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]542949.037037037[/C][C]5705.47934714453[/C][C]95.1627381332599[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]543241.234567901[/C][C]5631.29637984687[/C][C]96.4682371384391[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]543275.37037037[/C][C]5616.73364119439[/C][C]96.7244318630077[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]543089.444444444[/C][C]5468.68708674923[/C][C]99.3089265905091[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]543148.641975309[/C][C]5442.60393630684[/C][C]99.7957316629346[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]543641.777777778[/C][C]5325.02947899451[/C][C]102.091787458129[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]543957.444444444[/C][C]5248.02994786062[/C][C]103.649836195426[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]542343[/C][C]4986.34809699889[/C][C]108.765571406139[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]542125.172839506[/C][C]4953.1762471599[/C][C]109.450006579183[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]542641.913580247[/C][C]4859.30049525108[/C][C]111.670787618622[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]542675.135802469[/C][C]4792.07405516989[/C][C]113.244313329634[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]543941.87654321[/C][C]4543.87765452765[/C][C]119.708741717817[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]546631.691358025[/C][C]4118.41801967285[/C][C]132.728559545650[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]546562.950617284[/C][C]3985.19585473372[/C][C]137.148328599224[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]546810.814814815[/C][C]3903.22473522551[/C][C]140.092065383784[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]547576.814814815[/C][C]3754.82111490981[/C][C]145.832996581508[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]547671.111111111[/C][C]3630.13272871481[/C][C]150.868067930124[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]546909.38271605[/C][C]3519.52761892281[/C][C]155.392837315889[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]545821.790123457[/C][C]3348.24023236327[/C][C]163.017511362439[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]545869.320987654[/C][C]3335.79224647984[/C][C]163.640083270681[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]545694.12345679[/C][C]3232.08536427644[/C][C]168.836544197821[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]544927.604938272[/C][C]3046.86909058263[/C][C]178.848381317908[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]544799.209876543[/C][C]2977.63863448315[/C][C]182.963507917779[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]546006.765432099[/C][C]2805.59795882541[/C][C]194.613331434234[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]546005.098765432[/C][C]2791.90882275361[/C][C]195.566952013468[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]543110.101265823[/C][C]5715.70630919584[/C][C]95.0206451986569[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]543394.532467532[/C][C]5586.00051128651[/C][C]97.2779238687151[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]543636.04[/C][C]5464.05128276621[/C][C]99.4932170045045[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]543890.136986301[/C][C]5352.89102175967[/C][C]101.606801777838[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]544075.211267606[/C][C]5247.77482635593[/C][C]103.677316438025[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]544263[/C][C]5127.21418960833[/C][C]106.151797032996[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]544499.462686567[/C][C]5023.25871409155[/C][C]108.395663786757[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]544739.938461538[/C][C]4904.73416675924[/C][C]111.064110702144[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]544916.428571429[/C][C]4789.51613338638[/C][C]113.772751442044[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]545057.918032787[/C][C]4666.9887662043[/C][C]116.790064287231[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]545430.644067797[/C][C]4571.33473946838[/C][C]119.315402426913[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]545857.666666667[/C][C]4459.05906416113[/C][C]122.415437609674[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]546252.327272727[/C][C]4339.42271487271[/C][C]125.881335644147[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]546672.867924528[/C][C]4203.33833488359[/C][C]130.056832063143[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]546982.68627451[/C][C]4085.683272829[/C][C]133.877897465060[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]547021.367346939[/C][C]4023.54825053703[/C][C]135.954966433900[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]547070.744680851[/C][C]3966.95768530857[/C][C]137.906876775343[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]547098.266666667[/C][C]3906.51899676953[/C][C]140.047512150609[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]547048.186046512[/C][C]3853.53368936596[/C][C]141.960141040449[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]546983.414634146[/C][C]3804.19629920659[/C][C]143.784224475542[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]546991.102564103[/C][C]3755.98410866639[/C][C]145.631900119598[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]547113[/C][C]3720.49380198793[/C][C]147.05386680329[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]547243.828571429[/C][C]3665.86182524993[/C][C]149.281084410245[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]547409.212121212[/C][C]3606.42463884624[/C][C]151.787231660090[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]547679.387096774[/C][C]3558.62728176035[/C][C]153.901868257991[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]548001.172413793[/C][C]3495.32082788190[/C][C]156.781365545168[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]548231.296296296[/C][C]3443.96829883015[/C][C]159.185929929297[/C][/ROW]
[ROW][C]Median[/C][C]554788[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]530106[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]546047.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]546983.414634146[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]546983.414634146[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]546983.414634146[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]546983.414634146[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]546082.071428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]546983.414634146[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]546983.414634146[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]81[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7314&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7314&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 Mean542789.0123456795841.9548322091892.9122233799297
Geometric Mean540202.701838785
Harmonic Mean537548.53640707
Quadratic Mean545298.254924884
Winsorized Mean ( 1 / 27 )542839.7160493835826.7420187049293.1635061766535
Winsorized Mean ( 2 / 27 )542947.2962962965778.6052247894893.9581914969933
Winsorized Mean ( 3 / 27 )542949.0370370375705.4793471445395.1627381332599
Winsorized Mean ( 4 / 27 )543241.2345679015631.2963798468796.4682371384391
Winsorized Mean ( 5 / 27 )543275.370370375616.7336411943996.7244318630077
Winsorized Mean ( 6 / 27 )543089.4444444445468.6870867492399.3089265905091
Winsorized Mean ( 7 / 27 )543148.6419753095442.6039363068499.7957316629346
Winsorized Mean ( 8 / 27 )543641.7777777785325.02947899451102.091787458129
Winsorized Mean ( 9 / 27 )543957.4444444445248.02994786062103.649836195426
Winsorized Mean ( 10 / 27 )5423434986.34809699889108.765571406139
Winsorized Mean ( 11 / 27 )542125.1728395064953.1762471599109.450006579183
Winsorized Mean ( 12 / 27 )542641.9135802474859.30049525108111.670787618622
Winsorized Mean ( 13 / 27 )542675.1358024694792.07405516989113.244313329634
Winsorized Mean ( 14 / 27 )543941.876543214543.87765452765119.708741717817
Winsorized Mean ( 15 / 27 )546631.6913580254118.41801967285132.728559545650
Winsorized Mean ( 16 / 27 )546562.9506172843985.19585473372137.148328599224
Winsorized Mean ( 17 / 27 )546810.8148148153903.22473522551140.092065383784
Winsorized Mean ( 18 / 27 )547576.8148148153754.82111490981145.832996581508
Winsorized Mean ( 19 / 27 )547671.1111111113630.13272871481150.868067930124
Winsorized Mean ( 20 / 27 )546909.382716053519.52761892281155.392837315889
Winsorized Mean ( 21 / 27 )545821.7901234573348.24023236327163.017511362439
Winsorized Mean ( 22 / 27 )545869.3209876543335.79224647984163.640083270681
Winsorized Mean ( 23 / 27 )545694.123456793232.08536427644168.836544197821
Winsorized Mean ( 24 / 27 )544927.6049382723046.86909058263178.848381317908
Winsorized Mean ( 25 / 27 )544799.2098765432977.63863448315182.963507917779
Winsorized Mean ( 26 / 27 )546006.7654320992805.59795882541194.613331434234
Winsorized Mean ( 27 / 27 )546005.0987654322791.90882275361195.566952013468
Trimmed Mean ( 1 / 27 )543110.1012658235715.7063091958495.0206451986569
Trimmed Mean ( 2 / 27 )543394.5324675325586.0005112865197.2779238687151
Trimmed Mean ( 3 / 27 )543636.045464.0512827662199.4932170045045
Trimmed Mean ( 4 / 27 )543890.1369863015352.89102175967101.606801777838
Trimmed Mean ( 5 / 27 )544075.2112676065247.77482635593103.677316438025
Trimmed Mean ( 6 / 27 )5442635127.21418960833106.151797032996
Trimmed Mean ( 7 / 27 )544499.4626865675023.25871409155108.395663786757
Trimmed Mean ( 8 / 27 )544739.9384615384904.73416675924111.064110702144
Trimmed Mean ( 9 / 27 )544916.4285714294789.51613338638113.772751442044
Trimmed Mean ( 10 / 27 )545057.9180327874666.9887662043116.790064287231
Trimmed Mean ( 11 / 27 )545430.6440677974571.33473946838119.315402426913
Trimmed Mean ( 12 / 27 )545857.6666666674459.05906416113122.415437609674
Trimmed Mean ( 13 / 27 )546252.3272727274339.42271487271125.881335644147
Trimmed Mean ( 14 / 27 )546672.8679245284203.33833488359130.056832063143
Trimmed Mean ( 15 / 27 )546982.686274514085.683272829133.877897465060
Trimmed Mean ( 16 / 27 )547021.3673469394023.54825053703135.954966433900
Trimmed Mean ( 17 / 27 )547070.7446808513966.95768530857137.906876775343
Trimmed Mean ( 18 / 27 )547098.2666666673906.51899676953140.047512150609
Trimmed Mean ( 19 / 27 )547048.1860465123853.53368936596141.960141040449
Trimmed Mean ( 20 / 27 )546983.4146341463804.19629920659143.784224475542
Trimmed Mean ( 21 / 27 )546991.1025641033755.98410866639145.631900119598
Trimmed Mean ( 22 / 27 )5471133720.49380198793147.05386680329
Trimmed Mean ( 23 / 27 )547243.8285714293665.86182524993149.281084410245
Trimmed Mean ( 24 / 27 )547409.2121212123606.42463884624151.787231660090
Trimmed Mean ( 25 / 27 )547679.3870967743558.62728176035153.901868257991
Trimmed Mean ( 26 / 27 )548001.1724137933495.32082788190156.781365545168
Trimmed Mean ( 27 / 27 )548231.2962962963443.96829883015159.185929929297
Median554788
Midrange530106
Midmean - Weighted Average at Xnp546047.3
Midmean - Weighted Average at X(n+1)p546983.414634146
Midmean - Empirical Distribution Function546983.414634146
Midmean - Empirical Distribution Function - Averaging546983.414634146
Midmean - Empirical Distribution Function - Interpolation546983.414634146
Midmean - Closest Observation546082.071428571
Midmean - True Basic - Statistics Graphics Toolkit546983.414634146
Midmean - MS Excel (old versions)546983.414634146
Number of observations81



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')