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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 computationSun, 19 Dec 2010 13:12:05 +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/19/t12927680496az3w03rng2kqtq.htm/, Retrieved Sun, 05 May 2024 03:41:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112409, Retrieved Sun, 05 May 2024 03:41:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2010-12-19 13:12:05] [020d6ac062bd52f65e15713212085515] [Current]
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Dataseries X:
5124
4742
5434
5684
6332
6334
5636
5940
6195
6022
4535
4320
4872
4662
4663
5491
6018
6393
5610
5777
6094
6478
5216
5201
4784
4205
4681
4896
5752
6452
5995
5601
6119
6569
5798
5492
5018
4773
5502
5908
5902
6125
5419
5559
5962
6023
5346
5379
4859
5156
5010
5508
6426
6043
5499
5191
5790
5949
5219
4729




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112409&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112409&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112409&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean5523.5333333333376.814187964809271.9077227746498
Geometric Mean5491.18872146356
Harmonic Mean5458.05591866923
Quadratic Mean5554.95681651382
Winsorized Mean ( 1 / 20 )5523.9333333333375.941256909150672.7395563118171
Winsorized Mean ( 2 / 20 )5530.2333333333373.975600522692874.7575321357056
Winsorized Mean ( 3 / 20 )5535.2833333333372.328074316097776.5302185309443
Winsorized Mean ( 4 / 20 )5533.1571.861707368220276.9971964574691
Winsorized Mean ( 5 / 20 )5529.7333333333370.581358539333978.3455213638556
Winsorized Mean ( 6 / 20 )5534.3333333333369.58253915443879.536237116181
Winsorized Mean ( 7 / 20 )5519.8666666666766.347903745710783.1957960242793
Winsorized Mean ( 8 / 20 )5514.6666666666763.970622082657586.206237912476
Winsorized Mean ( 9 / 20 )5515.4166666666763.502178848097486.8539751976072
Winsorized Mean ( 10 / 20 )5523.7560.446925989515191.3818181748089
Winsorized Mean ( 11 / 20 )5516.7833333333358.5420322786594.2362797908073
Winsorized Mean ( 12 / 20 )5517.5833333333357.045612098553996.7223092251332
Winsorized Mean ( 13 / 20 )5542.0666666666752.6081230793874105.346215418169
Winsorized Mean ( 14 / 20 )554352.1446488796277106.300456884764
Winsorized Mean ( 15 / 20 )5563.7546.8766841505364118.689069007803
Winsorized Mean ( 16 / 20 )5563.4833333333344.1715293666784125.951793227477
Winsorized Mean ( 17 / 20 )5569.7166666666742.0763906562711132.371540899660
Winsorized Mean ( 18 / 20 )5570.0166666666741.2081768232933135.167753005713
Winsorized Mean ( 19 / 20 )5564.6333333333338.9591845431043142.83238724303
Winsorized Mean ( 20 / 20 )5563.6333333333338.5091959570439144.475447878461
Trimmed Mean ( 1 / 20 )5528.2413793103573.899812455177274.8072450476571
Trimmed Mean ( 2 / 20 )5532.8571428571471.376964473938877.5160051094258
Trimmed Mean ( 3 / 20 )5534.3148148148169.567219724160379.5534856324405
Trimmed Mean ( 4 / 20 )5533.9423076923168.088772977834681.2754007109778
Trimmed Mean ( 5 / 20 )5534.1866.388969393588783.3599323886243
Trimmed Mean ( 6 / 20 )5535.2916666666764.654962280235185.612789358301
Trimmed Mean ( 7 / 20 )5535.562.731016529166988.241834841402
Trimmed Mean ( 8 / 20 )5538.5454545454561.176074640328190.5345020436203
Trimmed Mean ( 9 / 20 )5542.8095238095259.761821471315592.7483364353271
Trimmed Mean ( 10 / 20 )5547.37557.964729411679695.7025946002645
Trimmed Mean ( 11 / 20 )5551.105263157956.373775334651698.469638235241
Trimmed Mean ( 12 / 20 )5556.3055555555654.6573281722377101.657101460327
Trimmed Mean ( 13 / 20 )556252.6418294737054105.657422160417
Trimmed Mean ( 14 / 20 )5564.87551.123225381299108.852189166367
Trimmed Mean ( 15 / 20 )556848.9896540801887113.656650665180
Trimmed Mean ( 16 / 20 )5568.6071428571447.5387989490454117.138153802032
Trimmed Mean ( 17 / 20 )5569.3461538461546.1351840475422120.717978454512
Trimmed Mean ( 18 / 20 )5569.2916666666744.5633598425763124.974680687018
Trimmed Mean ( 19 / 20 )5569.1818181818242.2102876385196131.938968667429
Trimmed Mean ( 20 / 20 )5569.939.1892775346039142.128162354660
Median5533.5
Midrange5387
Midmean - Weighted Average at Xnp5550.25806451613
Midmean - Weighted Average at X(n+1)p5568
Midmean - Empirical Distribution Function5550.25806451613
Midmean - Empirical Distribution Function - Averaging5568
Midmean - Empirical Distribution Function - Interpolation5568
Midmean - Closest Observation5550.25806451613
Midmean - True Basic - Statistics Graphics Toolkit5568
Midmean - MS Excel (old versions)5564.875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 5523.53333333333 & 76.8141879648092 & 71.9077227746498 \tabularnewline
Geometric Mean & 5491.18872146356 &  &  \tabularnewline
Harmonic Mean & 5458.05591866923 &  &  \tabularnewline
Quadratic Mean & 5554.95681651382 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 5523.93333333333 & 75.9412569091506 & 72.7395563118171 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 5530.23333333333 & 73.9756005226928 & 74.7575321357056 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 5535.28333333333 & 72.3280743160977 & 76.5302185309443 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 5533.15 & 71.8617073682202 & 76.9971964574691 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 5529.73333333333 & 70.5813585393339 & 78.3455213638556 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 5534.33333333333 & 69.582539154438 & 79.536237116181 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 5519.86666666667 & 66.3479037457107 & 83.1957960242793 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 5514.66666666667 & 63.9706220826575 & 86.206237912476 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 5515.41666666667 & 63.5021788480974 & 86.8539751976072 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 5523.75 & 60.4469259895151 & 91.3818181748089 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 5516.78333333333 & 58.54203227865 & 94.2362797908073 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 5517.58333333333 & 57.0456120985539 & 96.7223092251332 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 5542.06666666667 & 52.6081230793874 & 105.346215418169 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 5543 & 52.1446488796277 & 106.300456884764 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 5563.75 & 46.8766841505364 & 118.689069007803 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 5563.48333333333 & 44.1715293666784 & 125.951793227477 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 5569.71666666667 & 42.0763906562711 & 132.371540899660 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 5570.01666666667 & 41.2081768232933 & 135.167753005713 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 5564.63333333333 & 38.9591845431043 & 142.83238724303 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 5563.63333333333 & 38.5091959570439 & 144.475447878461 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 5528.24137931035 & 73.8998124551772 & 74.8072450476571 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 5532.85714285714 & 71.3769644739388 & 77.5160051094258 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 5534.31481481481 & 69.5672197241603 & 79.5534856324405 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 5533.94230769231 & 68.0887729778346 & 81.2754007109778 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 5534.18 & 66.3889693935887 & 83.3599323886243 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 5535.29166666667 & 64.6549622802351 & 85.612789358301 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 5535.5 & 62.7310165291669 & 88.241834841402 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 5538.54545454545 & 61.1760746403281 & 90.5345020436203 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 5542.80952380952 & 59.7618214713155 & 92.7483364353271 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 5547.375 & 57.9647294116796 & 95.7025946002645 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 5551.1052631579 & 56.3737753346516 & 98.469638235241 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 5556.30555555556 & 54.6573281722377 & 101.657101460327 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 5562 & 52.6418294737054 & 105.657422160417 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 5564.875 & 51.123225381299 & 108.852189166367 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 5568 & 48.9896540801887 & 113.656650665180 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 5568.60714285714 & 47.5387989490454 & 117.138153802032 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 5569.34615384615 & 46.1351840475422 & 120.717978454512 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 5569.29166666667 & 44.5633598425763 & 124.974680687018 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 5569.18181818182 & 42.2102876385196 & 131.938968667429 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 5569.9 & 39.1892775346039 & 142.128162354660 \tabularnewline
Median & 5533.5 &  &  \tabularnewline
Midrange & 5387 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5550.25806451613 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5568 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5550.25806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5568 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5568 &  &  \tabularnewline
Midmean - Closest Observation & 5550.25806451613 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5568 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5564.875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112409&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]5523.53333333333[/C][C]76.8141879648092[/C][C]71.9077227746498[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]5491.18872146356[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]5458.05591866923[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5554.95681651382[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]5523.93333333333[/C][C]75.9412569091506[/C][C]72.7395563118171[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]5530.23333333333[/C][C]73.9756005226928[/C][C]74.7575321357056[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]5535.28333333333[/C][C]72.3280743160977[/C][C]76.5302185309443[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]5533.15[/C][C]71.8617073682202[/C][C]76.9971964574691[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]5529.73333333333[/C][C]70.5813585393339[/C][C]78.3455213638556[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]5534.33333333333[/C][C]69.582539154438[/C][C]79.536237116181[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]5519.86666666667[/C][C]66.3479037457107[/C][C]83.1957960242793[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]5514.66666666667[/C][C]63.9706220826575[/C][C]86.206237912476[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]5515.41666666667[/C][C]63.5021788480974[/C][C]86.8539751976072[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]5523.75[/C][C]60.4469259895151[/C][C]91.3818181748089[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]5516.78333333333[/C][C]58.54203227865[/C][C]94.2362797908073[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]5517.58333333333[/C][C]57.0456120985539[/C][C]96.7223092251332[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]5542.06666666667[/C][C]52.6081230793874[/C][C]105.346215418169[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]5543[/C][C]52.1446488796277[/C][C]106.300456884764[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]5563.75[/C][C]46.8766841505364[/C][C]118.689069007803[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]5563.48333333333[/C][C]44.1715293666784[/C][C]125.951793227477[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]5569.71666666667[/C][C]42.0763906562711[/C][C]132.371540899660[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]5570.01666666667[/C][C]41.2081768232933[/C][C]135.167753005713[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]5564.63333333333[/C][C]38.9591845431043[/C][C]142.83238724303[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]5563.63333333333[/C][C]38.5091959570439[/C][C]144.475447878461[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]5528.24137931035[/C][C]73.8998124551772[/C][C]74.8072450476571[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]5532.85714285714[/C][C]71.3769644739388[/C][C]77.5160051094258[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]5534.31481481481[/C][C]69.5672197241603[/C][C]79.5534856324405[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]5533.94230769231[/C][C]68.0887729778346[/C][C]81.2754007109778[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]5534.18[/C][C]66.3889693935887[/C][C]83.3599323886243[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]5535.29166666667[/C][C]64.6549622802351[/C][C]85.612789358301[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]5535.5[/C][C]62.7310165291669[/C][C]88.241834841402[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]5538.54545454545[/C][C]61.1760746403281[/C][C]90.5345020436203[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]5542.80952380952[/C][C]59.7618214713155[/C][C]92.7483364353271[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]5547.375[/C][C]57.9647294116796[/C][C]95.7025946002645[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]5551.1052631579[/C][C]56.3737753346516[/C][C]98.469638235241[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]5556.30555555556[/C][C]54.6573281722377[/C][C]101.657101460327[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]5562[/C][C]52.6418294737054[/C][C]105.657422160417[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]5564.875[/C][C]51.123225381299[/C][C]108.852189166367[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]5568[/C][C]48.9896540801887[/C][C]113.656650665180[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]5568.60714285714[/C][C]47.5387989490454[/C][C]117.138153802032[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]5569.34615384615[/C][C]46.1351840475422[/C][C]120.717978454512[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]5569.29166666667[/C][C]44.5633598425763[/C][C]124.974680687018[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]5569.18181818182[/C][C]42.2102876385196[/C][C]131.938968667429[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]5569.9[/C][C]39.1892775346039[/C][C]142.128162354660[/C][/ROW]
[ROW][C]Median[/C][C]5533.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5550.25806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5550.25806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]5550.25806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5564.875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112409&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112409&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 Mean5523.5333333333376.814187964809271.9077227746498
Geometric Mean5491.18872146356
Harmonic Mean5458.05591866923
Quadratic Mean5554.95681651382
Winsorized Mean ( 1 / 20 )5523.9333333333375.941256909150672.7395563118171
Winsorized Mean ( 2 / 20 )5530.2333333333373.975600522692874.7575321357056
Winsorized Mean ( 3 / 20 )5535.2833333333372.328074316097776.5302185309443
Winsorized Mean ( 4 / 20 )5533.1571.861707368220276.9971964574691
Winsorized Mean ( 5 / 20 )5529.7333333333370.581358539333978.3455213638556
Winsorized Mean ( 6 / 20 )5534.3333333333369.58253915443879.536237116181
Winsorized Mean ( 7 / 20 )5519.8666666666766.347903745710783.1957960242793
Winsorized Mean ( 8 / 20 )5514.6666666666763.970622082657586.206237912476
Winsorized Mean ( 9 / 20 )5515.4166666666763.502178848097486.8539751976072
Winsorized Mean ( 10 / 20 )5523.7560.446925989515191.3818181748089
Winsorized Mean ( 11 / 20 )5516.7833333333358.5420322786594.2362797908073
Winsorized Mean ( 12 / 20 )5517.5833333333357.045612098553996.7223092251332
Winsorized Mean ( 13 / 20 )5542.0666666666752.6081230793874105.346215418169
Winsorized Mean ( 14 / 20 )554352.1446488796277106.300456884764
Winsorized Mean ( 15 / 20 )5563.7546.8766841505364118.689069007803
Winsorized Mean ( 16 / 20 )5563.4833333333344.1715293666784125.951793227477
Winsorized Mean ( 17 / 20 )5569.7166666666742.0763906562711132.371540899660
Winsorized Mean ( 18 / 20 )5570.0166666666741.2081768232933135.167753005713
Winsorized Mean ( 19 / 20 )5564.6333333333338.9591845431043142.83238724303
Winsorized Mean ( 20 / 20 )5563.6333333333338.5091959570439144.475447878461
Trimmed Mean ( 1 / 20 )5528.2413793103573.899812455177274.8072450476571
Trimmed Mean ( 2 / 20 )5532.8571428571471.376964473938877.5160051094258
Trimmed Mean ( 3 / 20 )5534.3148148148169.567219724160379.5534856324405
Trimmed Mean ( 4 / 20 )5533.9423076923168.088772977834681.2754007109778
Trimmed Mean ( 5 / 20 )5534.1866.388969393588783.3599323886243
Trimmed Mean ( 6 / 20 )5535.2916666666764.654962280235185.612789358301
Trimmed Mean ( 7 / 20 )5535.562.731016529166988.241834841402
Trimmed Mean ( 8 / 20 )5538.5454545454561.176074640328190.5345020436203
Trimmed Mean ( 9 / 20 )5542.8095238095259.761821471315592.7483364353271
Trimmed Mean ( 10 / 20 )5547.37557.964729411679695.7025946002645
Trimmed Mean ( 11 / 20 )5551.105263157956.373775334651698.469638235241
Trimmed Mean ( 12 / 20 )5556.3055555555654.6573281722377101.657101460327
Trimmed Mean ( 13 / 20 )556252.6418294737054105.657422160417
Trimmed Mean ( 14 / 20 )5564.87551.123225381299108.852189166367
Trimmed Mean ( 15 / 20 )556848.9896540801887113.656650665180
Trimmed Mean ( 16 / 20 )5568.6071428571447.5387989490454117.138153802032
Trimmed Mean ( 17 / 20 )5569.3461538461546.1351840475422120.717978454512
Trimmed Mean ( 18 / 20 )5569.2916666666744.5633598425763124.974680687018
Trimmed Mean ( 19 / 20 )5569.1818181818242.2102876385196131.938968667429
Trimmed Mean ( 20 / 20 )5569.939.1892775346039142.128162354660
Median5533.5
Midrange5387
Midmean - Weighted Average at Xnp5550.25806451613
Midmean - Weighted Average at X(n+1)p5568
Midmean - Empirical Distribution Function5550.25806451613
Midmean - Empirical Distribution Function - Averaging5568
Midmean - Empirical Distribution Function - Interpolation5568
Midmean - Closest Observation5550.25806451613
Midmean - True Basic - Statistics Graphics Toolkit5568
Midmean - MS Excel (old versions)5564.875
Number of observations60



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')