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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 11 Dec 2010 23:03:27 +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/12/t1292108517vdihwvdoa786w96.htm/, Retrieved Tue, 07 May 2024 21:48:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108318, Retrieved Tue, 07 May 2024 21:48:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact190
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [paper] [2007-12-11 21:01:08] [b3bb3ec527e23fa7d74d4348b38c8499]
- RMPD  [Univariate Explorative Data Analysis] [PAPER] [2009-12-30 15:50:30] [23722951c28e05bb35cc9a97084fe0d9]
-    D    [Univariate Explorative Data Analysis] [] [2010-12-11 20:13:12] [afdb2fc47981b6a655b732edc8065db9]
- RMPD        [Central Tendency] [] [2010-12-11 23:03:27] [297722d8c88c4886be8e106c47d8f3cc] [Current]
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Dataseries X:
100918
105017
108666
116083
117359
102191
102617
106640
108783
112534
113149
117125
107597
108745
111311
115669
114585
101628
97493
99180
100247
97657
95378
89406
82880
82662
83469
86371
86822
73899
71415
76335
76844
78192
80651
81485
78872
81632
84822
92175
92844
77443
77550
80367
83117
86622
90999
90276
91982
96279
106810
109483
110159
98305
99450
101536
99925
102850
101993
108928
107605




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108318&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108318&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108318&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean96115.19672131151654.337429622258.0989071517659
Geometric Mean95239.8784966121
Harmonic Mean94348.6911158562
Quadratic Mean96965.6690826158
Winsorized Mean ( 1 / 20 )96152.08196721311643.857225478258.4917476268309
Winsorized Mean ( 2 / 20 )96197.7868852461619.5491864330159.3978791697692
Winsorized Mean ( 3 / 20 )96202.45901639341610.3484582984359.7401503510895
Winsorized Mean ( 4 / 20 )96170.6557377051588.5250441161760.540849572323
Winsorized Mean ( 5 / 20 )96061.72131147541564.7118247802661.3925962532849
Winsorized Mean ( 6 / 20 )96064.37704918031541.4922523399262.3190787390326
Winsorized Mean ( 7 / 20 )96002.06557377051502.1130977387463.9113431061153
Winsorized Mean ( 8 / 20 )96047.04918032791440.5018009305966.6761048950301
Winsorized Mean ( 9 / 20 )95989.2131147541416.8608338390567.7478061516226
Winsorized Mean ( 10 / 20 )96034.95081967211378.1785011772769.6825198895767
Winsorized Mean ( 11 / 20 )96035.31147540981369.456205054970.1266028960449
Winsorized Mean ( 12 / 20 )96230.45901639341333.3419770021372.172376386707
Winsorized Mean ( 13 / 20 )96260.08196721311322.8535095812872.7670004804098
Winsorized Mean ( 14 / 20 )96070.96721311481276.2870015653275.2737958588367
Winsorized Mean ( 15 / 20 )96155.55737704921261.4141297940376.228381390297
Winsorized Mean ( 16 / 20 )96304.01639344261171.6252367334582.1969460660843
Winsorized Mean ( 17 / 20 )96688.32786885251095.3126767991988.2746360166332
Winsorized Mean ( 18 / 20 )96283.47540983611012.86863588395.0601805592466
Winsorized Mean ( 19 / 20 )95670.8032786885909.766526171357105.159731124982
Winsorized Mean ( 20 / 20 )96441.6229508197765.75465872389125.943240242948
Trimmed Mean ( 1 / 20 )96173.7796610171617.6991682956759.4509668706457
Trimmed Mean ( 2 / 20 )961971585.1020434329360.6882064145611
Trimmed Mean ( 3 / 20 )96196.56363636361560.2493459026561.6546091744784
Trimmed Mean ( 4 / 20 )96194.30188679251532.9478885521962.7511884814585
Trimmed Mean ( 5 / 20 )96201.37254901961506.4011529784363.8617225954801
Trimmed Mean ( 6 / 20 )96236.14285714291479.9421832106365.0269611535534
Trimmed Mean ( 7 / 20 )96273.29787234041452.3167510368366.2894632342493
Trimmed Mean ( 8 / 20 )96325.82222222221426.8493883586667.5094533509442
Trimmed Mean ( 9 / 20 )96375.25581395351408.9050904205368.4043634090268
Trimmed Mean ( 10 / 20 )96439.07317073171389.3546318916769.4128561254556
Trimmed Mean ( 11 / 20 )96502.2820512821371.0789765672870.3841891682209
Trimmed Mean ( 12 / 20 )96572.27027027031346.1730718642371.7383762078476
Trimmed Mean ( 13 / 20 )96621.91428571431319.5584685358873.2229125041511
Trimmed Mean ( 14 / 20 )96673.36363636361282.9304595532875.3535493030742
Trimmed Mean ( 15 / 20 )96758.03225806451241.9996255465677.9050414089175
Trimmed Mean ( 16 / 20 )96842.51724137931185.0334436683881.7213368608353
Trimmed Mean ( 17 / 20 )96918.55555555561129.9442821315385.7728625102893
Trimmed Mean ( 18 / 20 )96951.61072.7773114677690.374394539862
Trimmed Mean ( 19 / 20 )97050.04347826091012.3120397989895.86969201466
Trimmed Mean ( 20 / 20 )97260.9047619048950.37637382641102.339354639376
Median98305
Midrange94387
Midmean - Weighted Average at Xnp96396.7333333333
Midmean - Weighted Average at X(n+1)p96758.0322580645
Midmean - Empirical Distribution Function96758.0322580645
Midmean - Empirical Distribution Function - Averaging96758.0322580645
Midmean - Empirical Distribution Function - Interpolation96758.0322580645
Midmean - Closest Observation96331.75
Midmean - True Basic - Statistics Graphics Toolkit96758.0322580645
Midmean - MS Excel (old versions)96758.0322580645
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 96115.1967213115 & 1654.3374296222 & 58.0989071517659 \tabularnewline
Geometric Mean & 95239.8784966121 &  &  \tabularnewline
Harmonic Mean & 94348.6911158562 &  &  \tabularnewline
Quadratic Mean & 96965.6690826158 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 96152.0819672131 & 1643.8572254782 & 58.4917476268309 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 96197.786885246 & 1619.54918643301 & 59.3978791697692 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 96202.4590163934 & 1610.34845829843 & 59.7401503510895 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 96170.655737705 & 1588.52504411617 & 60.540849572323 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 96061.7213114754 & 1564.71182478026 & 61.3925962532849 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 96064.3770491803 & 1541.49225233992 & 62.3190787390326 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 96002.0655737705 & 1502.11309773874 & 63.9113431061153 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 96047.0491803279 & 1440.50180093059 & 66.6761048950301 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 95989.213114754 & 1416.86083383905 & 67.7478061516226 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 96034.9508196721 & 1378.17850117727 & 69.6825198895767 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 96035.3114754098 & 1369.4562050549 & 70.1266028960449 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 96230.4590163934 & 1333.34197700213 & 72.172376386707 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 96260.0819672131 & 1322.85350958128 & 72.7670004804098 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 96070.9672131148 & 1276.28700156532 & 75.2737958588367 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 96155.5573770492 & 1261.41412979403 & 76.228381390297 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 96304.0163934426 & 1171.62523673345 & 82.1969460660843 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 96688.3278688525 & 1095.31267679919 & 88.2746360166332 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 96283.4754098361 & 1012.868635883 & 95.0601805592466 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 95670.8032786885 & 909.766526171357 & 105.159731124982 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 96441.6229508197 & 765.75465872389 & 125.943240242948 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 96173.779661017 & 1617.69916829567 & 59.4509668706457 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 96197 & 1585.10204343293 & 60.6882064145611 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 96196.5636363636 & 1560.24934590265 & 61.6546091744784 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 96194.3018867925 & 1532.94788855219 & 62.7511884814585 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 96201.3725490196 & 1506.40115297843 & 63.8617225954801 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 96236.1428571429 & 1479.94218321063 & 65.0269611535534 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 96273.2978723404 & 1452.31675103683 & 66.2894632342493 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 96325.8222222222 & 1426.84938835866 & 67.5094533509442 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 96375.2558139535 & 1408.90509042053 & 68.4043634090268 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 96439.0731707317 & 1389.35463189167 & 69.4128561254556 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 96502.282051282 & 1371.07897656728 & 70.3841891682209 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 96572.2702702703 & 1346.17307186423 & 71.7383762078476 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 96621.9142857143 & 1319.55846853588 & 73.2229125041511 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 96673.3636363636 & 1282.93045955328 & 75.3535493030742 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 96758.0322580645 & 1241.99962554656 & 77.9050414089175 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 96842.5172413793 & 1185.03344366838 & 81.7213368608353 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 96918.5555555556 & 1129.94428213153 & 85.7728625102893 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 96951.6 & 1072.77731146776 & 90.374394539862 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 97050.0434782609 & 1012.31203979898 & 95.86969201466 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 97260.9047619048 & 950.37637382641 & 102.339354639376 \tabularnewline
Median & 98305 &  &  \tabularnewline
Midrange & 94387 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 96396.7333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 96758.0322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 96758.0322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 96758.0322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 96758.0322580645 &  &  \tabularnewline
Midmean - Closest Observation & 96331.75 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 96758.0322580645 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 96758.0322580645 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108318&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]96115.1967213115[/C][C]1654.3374296222[/C][C]58.0989071517659[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]95239.8784966121[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]94348.6911158562[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]96965.6690826158[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]96152.0819672131[/C][C]1643.8572254782[/C][C]58.4917476268309[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]96197.786885246[/C][C]1619.54918643301[/C][C]59.3978791697692[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]96202.4590163934[/C][C]1610.34845829843[/C][C]59.7401503510895[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]96170.655737705[/C][C]1588.52504411617[/C][C]60.540849572323[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]96061.7213114754[/C][C]1564.71182478026[/C][C]61.3925962532849[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]96064.3770491803[/C][C]1541.49225233992[/C][C]62.3190787390326[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]96002.0655737705[/C][C]1502.11309773874[/C][C]63.9113431061153[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]96047.0491803279[/C][C]1440.50180093059[/C][C]66.6761048950301[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]95989.213114754[/C][C]1416.86083383905[/C][C]67.7478061516226[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]96034.9508196721[/C][C]1378.17850117727[/C][C]69.6825198895767[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]96035.3114754098[/C][C]1369.4562050549[/C][C]70.1266028960449[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]96230.4590163934[/C][C]1333.34197700213[/C][C]72.172376386707[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]96260.0819672131[/C][C]1322.85350958128[/C][C]72.7670004804098[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]96070.9672131148[/C][C]1276.28700156532[/C][C]75.2737958588367[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]96155.5573770492[/C][C]1261.41412979403[/C][C]76.228381390297[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]96304.0163934426[/C][C]1171.62523673345[/C][C]82.1969460660843[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]96688.3278688525[/C][C]1095.31267679919[/C][C]88.2746360166332[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]96283.4754098361[/C][C]1012.868635883[/C][C]95.0601805592466[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]95670.8032786885[/C][C]909.766526171357[/C][C]105.159731124982[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]96441.6229508197[/C][C]765.75465872389[/C][C]125.943240242948[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]96173.779661017[/C][C]1617.69916829567[/C][C]59.4509668706457[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]96197[/C][C]1585.10204343293[/C][C]60.6882064145611[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]96196.5636363636[/C][C]1560.24934590265[/C][C]61.6546091744784[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]96194.3018867925[/C][C]1532.94788855219[/C][C]62.7511884814585[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]96201.3725490196[/C][C]1506.40115297843[/C][C]63.8617225954801[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]96236.1428571429[/C][C]1479.94218321063[/C][C]65.0269611535534[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]96273.2978723404[/C][C]1452.31675103683[/C][C]66.2894632342493[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]96325.8222222222[/C][C]1426.84938835866[/C][C]67.5094533509442[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]96375.2558139535[/C][C]1408.90509042053[/C][C]68.4043634090268[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]96439.0731707317[/C][C]1389.35463189167[/C][C]69.4128561254556[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]96502.282051282[/C][C]1371.07897656728[/C][C]70.3841891682209[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]96572.2702702703[/C][C]1346.17307186423[/C][C]71.7383762078476[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]96621.9142857143[/C][C]1319.55846853588[/C][C]73.2229125041511[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]96673.3636363636[/C][C]1282.93045955328[/C][C]75.3535493030742[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]96758.0322580645[/C][C]1241.99962554656[/C][C]77.9050414089175[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]96842.5172413793[/C][C]1185.03344366838[/C][C]81.7213368608353[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]96918.5555555556[/C][C]1129.94428213153[/C][C]85.7728625102893[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]96951.6[/C][C]1072.77731146776[/C][C]90.374394539862[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]97050.0434782609[/C][C]1012.31203979898[/C][C]95.86969201466[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]97260.9047619048[/C][C]950.37637382641[/C][C]102.339354639376[/C][/ROW]
[ROW][C]Median[/C][C]98305[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]94387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]96396.7333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]96758.0322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]96758.0322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]96758.0322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]96758.0322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]96331.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]96758.0322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]96758.0322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108318&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108318&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 Mean96115.19672131151654.337429622258.0989071517659
Geometric Mean95239.8784966121
Harmonic Mean94348.6911158562
Quadratic Mean96965.6690826158
Winsorized Mean ( 1 / 20 )96152.08196721311643.857225478258.4917476268309
Winsorized Mean ( 2 / 20 )96197.7868852461619.5491864330159.3978791697692
Winsorized Mean ( 3 / 20 )96202.45901639341610.3484582984359.7401503510895
Winsorized Mean ( 4 / 20 )96170.6557377051588.5250441161760.540849572323
Winsorized Mean ( 5 / 20 )96061.72131147541564.7118247802661.3925962532849
Winsorized Mean ( 6 / 20 )96064.37704918031541.4922523399262.3190787390326
Winsorized Mean ( 7 / 20 )96002.06557377051502.1130977387463.9113431061153
Winsorized Mean ( 8 / 20 )96047.04918032791440.5018009305966.6761048950301
Winsorized Mean ( 9 / 20 )95989.2131147541416.8608338390567.7478061516226
Winsorized Mean ( 10 / 20 )96034.95081967211378.1785011772769.6825198895767
Winsorized Mean ( 11 / 20 )96035.31147540981369.456205054970.1266028960449
Winsorized Mean ( 12 / 20 )96230.45901639341333.3419770021372.172376386707
Winsorized Mean ( 13 / 20 )96260.08196721311322.8535095812872.7670004804098
Winsorized Mean ( 14 / 20 )96070.96721311481276.2870015653275.2737958588367
Winsorized Mean ( 15 / 20 )96155.55737704921261.4141297940376.228381390297
Winsorized Mean ( 16 / 20 )96304.01639344261171.6252367334582.1969460660843
Winsorized Mean ( 17 / 20 )96688.32786885251095.3126767991988.2746360166332
Winsorized Mean ( 18 / 20 )96283.47540983611012.86863588395.0601805592466
Winsorized Mean ( 19 / 20 )95670.8032786885909.766526171357105.159731124982
Winsorized Mean ( 20 / 20 )96441.6229508197765.75465872389125.943240242948
Trimmed Mean ( 1 / 20 )96173.7796610171617.6991682956759.4509668706457
Trimmed Mean ( 2 / 20 )961971585.1020434329360.6882064145611
Trimmed Mean ( 3 / 20 )96196.56363636361560.2493459026561.6546091744784
Trimmed Mean ( 4 / 20 )96194.30188679251532.9478885521962.7511884814585
Trimmed Mean ( 5 / 20 )96201.37254901961506.4011529784363.8617225954801
Trimmed Mean ( 6 / 20 )96236.14285714291479.9421832106365.0269611535534
Trimmed Mean ( 7 / 20 )96273.29787234041452.3167510368366.2894632342493
Trimmed Mean ( 8 / 20 )96325.82222222221426.8493883586667.5094533509442
Trimmed Mean ( 9 / 20 )96375.25581395351408.9050904205368.4043634090268
Trimmed Mean ( 10 / 20 )96439.07317073171389.3546318916769.4128561254556
Trimmed Mean ( 11 / 20 )96502.2820512821371.0789765672870.3841891682209
Trimmed Mean ( 12 / 20 )96572.27027027031346.1730718642371.7383762078476
Trimmed Mean ( 13 / 20 )96621.91428571431319.5584685358873.2229125041511
Trimmed Mean ( 14 / 20 )96673.36363636361282.9304595532875.3535493030742
Trimmed Mean ( 15 / 20 )96758.03225806451241.9996255465677.9050414089175
Trimmed Mean ( 16 / 20 )96842.51724137931185.0334436683881.7213368608353
Trimmed Mean ( 17 / 20 )96918.55555555561129.9442821315385.7728625102893
Trimmed Mean ( 18 / 20 )96951.61072.7773114677690.374394539862
Trimmed Mean ( 19 / 20 )97050.04347826091012.3120397989895.86969201466
Trimmed Mean ( 20 / 20 )97260.9047619048950.37637382641102.339354639376
Median98305
Midrange94387
Midmean - Weighted Average at Xnp96396.7333333333
Midmean - Weighted Average at X(n+1)p96758.0322580645
Midmean - Empirical Distribution Function96758.0322580645
Midmean - Empirical Distribution Function - Averaging96758.0322580645
Midmean - Empirical Distribution Function - Interpolation96758.0322580645
Midmean - Closest Observation96331.75
Midmean - True Basic - Statistics Graphics Toolkit96758.0322580645
Midmean - MS Excel (old versions)96758.0322580645
Number of observations61



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')