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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 10:03:46 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224518663j9zphzsq8xvowi0.htm/, Retrieved Fri, 17 May 2024 09:48:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17564, Retrieved Fri, 17 May 2024 09:48:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact191
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Pearson Correlation] [Q3 Clothing produ...] [2007-10-20 14:22:11] [b731da8b544846036771bbf9bf2f34ce]
- RMPD  [Harrell-Davis Quantiles] [Compute the 95% C...] [2008-10-19 19:58:52] [988ab43f527fc78aae41c84649095267]
- RMPD      [Central Tendency] [Duitsland.Uitvoer] [2008-10-20 16:03:46] [5d823194959040fa9b19b8c8302177e6] [Current]
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Dataseries X:
3134.5
3510.5
4047.4
3580.8
3567.3
3920.1
3764.8
3139.3
4126.1
3920
3868.3
3414
3423.4
3819
4482.7
4040.4
3720.3
4405
3916.6
3540.5
4486.4
4213.6
4521.7
4102.3
3854.1
4106.5
4870.9
4559.7
4072.1
4687.7
4096.1
4107.2
4888
4256.2
4593.8
3888.2
4232.7
4386.2
5203.6
4456.6
4828.4
5244.6
4407.6
4809.3
5226.8
5290.2
5068.8
4425.2
4971
4806.9
5565.8
4754.9
5220
5684.3
4815.3
5114.4
5273.9
5602.6
5609.7
4168.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17564&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17564&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17564&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4396.8866666666783.367807924382752.7408213810154
Geometric Mean4350.03380671331
Harmonic Mean4303.05582405076
Quadratic Mean4443.27285365191
Winsorized Mean ( 1 / 20 )4395.7233333333383.030495329209852.9410708186747
Winsorized Mean ( 2 / 20 )4404.6433333333380.84335779299854.4836762546598
Winsorized Mean ( 3 / 20 )4403.2733333333380.289078271220654.8427435978136
Winsorized Mean ( 4 / 20 )4390.7066666666774.974208441637458.5628945997416
Winsorized Mean ( 5 / 20 )4391.8483333333374.207446802661759.1833909204892
Winsorized Mean ( 6 / 20 )4391.5983333333373.10585837127960.0717703228371
Winsorized Mean ( 7 / 20 )4391.0966666666772.39746234146660.6526323527177
Winsorized Mean ( 8 / 20 )4408.7968.873690240502164.0126873499128
Winsorized Mean ( 9 / 20 )4413.00567.272359121976465.5990819646812
Winsorized Mean ( 10 / 20 )4407.1716666666762.919427226825570.044688276941
Winsorized Mean ( 11 / 20 )4405.2466666666760.335384230210773.0126562194147
Winsorized Mean ( 12 / 20 )4388.5266666666756.353330696620277.87519588314
Winsorized Mean ( 13 / 20 )4374.85552.613391209886183.150979235453
Winsorized Mean ( 14 / 20 )4377.4916666666750.928122068922285.9543114655299
Winsorized Mean ( 15 / 20 )4367.7166666666749.079182370782888.9932646731866
Winsorized Mean ( 16 / 20 )4364.2548.521955686223389.9438190047877
Winsorized Mean ( 17 / 20 )4396.63543.2099707201101101.750473946834
Winsorized Mean ( 18 / 20 )4398.01542.8008972677081102.755205632527
Winsorized Mean ( 19 / 20 )4389.3739.079901657493112.317836377114
Winsorized Mean ( 20 / 20 )4374.9734.4803899315322126.882845834615
Trimmed Mean ( 1 / 20 )4396.4551724137980.366322452051554.7051929001333
Trimmed Mean ( 2 / 20 )4397.2392857142977.081877941657.046343487451
Trimmed Mean ( 3 / 20 )4393.1259259259374.487790621540458.9777987676751
Trimmed Mean ( 4 / 20 )4389.2230769230871.514758289516961.3750669358897
Trimmed Mean ( 5 / 20 )4388.77869.925210442504762.7638869046898
Trimmed Mean ( 6 / 20 )4388.0104166666768.145118165452964.3921462725004
Trimmed Mean ( 7 / 20 )4387.2304347826166.190242568675866.2821326002942
Trimmed Mean ( 8 / 20 )4386.4772727272763.851641342667268.6979563953061
Trimmed Mean ( 9 / 20 )4382.4928571428661.789636321242970.9260179871973
Trimmed Mean ( 10 / 20 )4377.407559.472735768919773.6036007660442
Trimmed Mean ( 11 / 20 )4372.7078947368457.582359024806575.9383250146642
Trimmed Mean ( 12 / 20 )4367.7777777777855.68862043728678.4321418537665
Trimmed Mean ( 13 / 20 )4364.7264705882454.182209146878480.5564508962017
Trimmed Mean ( 14 / 20 )4363.26562553.060636267922382.231686837834
Trimmed Mean ( 15 / 20 )4361.2333333333351.812892003610284.1727447491148
Trimmed Mean ( 16 / 20 )4360.3071428571450.429705890532386.4630690554106
Trimmed Mean ( 17 / 20 )4359.7384615384648.386522623532690.1023306729242
Trimmed Mean ( 18 / 20 )4354.312546.954860111963492.734010699152
Trimmed Mean ( 19 / 20 )4347.6909090909144.552405500616797.585996990235
Trimmed Mean ( 20 / 20 )4341.1142.1274950221599103.046953010534
Median4395.6
Midrange4409.4
Midmean - Weighted Average at Xnp4346.89032258064
Midmean - Weighted Average at X(n+1)p4361.23333333333
Midmean - Empirical Distribution Function4346.89032258064
Midmean - Empirical Distribution Function - Averaging4361.23333333333
Midmean - Empirical Distribution Function - Interpolation4361.23333333333
Midmean - Closest Observation4346.89032258064
Midmean - True Basic - Statistics Graphics Toolkit4361.23333333333
Midmean - MS Excel (old versions)4363.265625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4396.88666666667 & 83.3678079243827 & 52.7408213810154 \tabularnewline
Geometric Mean & 4350.03380671331 &  &  \tabularnewline
Harmonic Mean & 4303.05582405076 &  &  \tabularnewline
Quadratic Mean & 4443.27285365191 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 4395.72333333333 & 83.0304953292098 & 52.9410708186747 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 4404.64333333333 & 80.843357792998 & 54.4836762546598 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 4403.27333333333 & 80.2890782712206 & 54.8427435978136 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 4390.70666666667 & 74.9742084416374 & 58.5628945997416 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 4391.84833333333 & 74.2074468026617 & 59.1833909204892 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 4391.59833333333 & 73.105858371279 & 60.0717703228371 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 4391.09666666667 & 72.397462341466 & 60.6526323527177 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 4408.79 & 68.8736902405021 & 64.0126873499128 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 4413.005 & 67.2723591219764 & 65.5990819646812 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 4407.17166666667 & 62.9194272268255 & 70.044688276941 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 4405.24666666667 & 60.3353842302107 & 73.0126562194147 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 4388.52666666667 & 56.3533306966202 & 77.87519588314 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 4374.855 & 52.6133912098861 & 83.150979235453 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 4377.49166666667 & 50.9281220689222 & 85.9543114655299 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 4367.71666666667 & 49.0791823707828 & 88.9932646731866 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 4364.25 & 48.5219556862233 & 89.9438190047877 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 4396.635 & 43.2099707201101 & 101.750473946834 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 4398.015 & 42.8008972677081 & 102.755205632527 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 4389.37 & 39.079901657493 & 112.317836377114 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 4374.97 & 34.4803899315322 & 126.882845834615 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 4396.45517241379 & 80.3663224520515 & 54.7051929001333 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 4397.23928571429 & 77.0818779416 & 57.046343487451 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 4393.12592592593 & 74.4877906215404 & 58.9777987676751 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 4389.22307692308 & 71.5147582895169 & 61.3750669358897 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 4388.778 & 69.9252104425047 & 62.7638869046898 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 4388.01041666667 & 68.1451181654529 & 64.3921462725004 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 4387.23043478261 & 66.1902425686758 & 66.2821326002942 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 4386.47727272727 & 63.8516413426672 & 68.6979563953061 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 4382.49285714286 & 61.7896363212429 & 70.9260179871973 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 4377.4075 & 59.4727357689197 & 73.6036007660442 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 4372.70789473684 & 57.5823590248065 & 75.9383250146642 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 4367.77777777778 & 55.688620437286 & 78.4321418537665 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 4364.72647058824 & 54.1822091468784 & 80.5564508962017 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 4363.265625 & 53.0606362679223 & 82.231686837834 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 4361.23333333333 & 51.8128920036102 & 84.1727447491148 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 4360.30714285714 & 50.4297058905323 & 86.4630690554106 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 4359.73846153846 & 48.3865226235326 & 90.1023306729242 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 4354.3125 & 46.9548601119634 & 92.734010699152 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 4347.69090909091 & 44.5524055006167 & 97.585996990235 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 4341.11 & 42.1274950221599 & 103.046953010534 \tabularnewline
Median & 4395.6 &  &  \tabularnewline
Midrange & 4409.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4346.89032258064 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4361.23333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4346.89032258064 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4361.23333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4361.23333333333 &  &  \tabularnewline
Midmean - Closest Observation & 4346.89032258064 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4361.23333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4363.265625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17564&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]4396.88666666667[/C][C]83.3678079243827[/C][C]52.7408213810154[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4350.03380671331[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4303.05582405076[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4443.27285365191[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]4395.72333333333[/C][C]83.0304953292098[/C][C]52.9410708186747[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]4404.64333333333[/C][C]80.843357792998[/C][C]54.4836762546598[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]4403.27333333333[/C][C]80.2890782712206[/C][C]54.8427435978136[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]4390.70666666667[/C][C]74.9742084416374[/C][C]58.5628945997416[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]4391.84833333333[/C][C]74.2074468026617[/C][C]59.1833909204892[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]4391.59833333333[/C][C]73.105858371279[/C][C]60.0717703228371[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]4391.09666666667[/C][C]72.397462341466[/C][C]60.6526323527177[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]4408.79[/C][C]68.8736902405021[/C][C]64.0126873499128[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]4413.005[/C][C]67.2723591219764[/C][C]65.5990819646812[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]4407.17166666667[/C][C]62.9194272268255[/C][C]70.044688276941[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]4405.24666666667[/C][C]60.3353842302107[/C][C]73.0126562194147[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]4388.52666666667[/C][C]56.3533306966202[/C][C]77.87519588314[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]4374.855[/C][C]52.6133912098861[/C][C]83.150979235453[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]4377.49166666667[/C][C]50.9281220689222[/C][C]85.9543114655299[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]4367.71666666667[/C][C]49.0791823707828[/C][C]88.9932646731866[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]4364.25[/C][C]48.5219556862233[/C][C]89.9438190047877[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]4396.635[/C][C]43.2099707201101[/C][C]101.750473946834[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]4398.015[/C][C]42.8008972677081[/C][C]102.755205632527[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]4389.37[/C][C]39.079901657493[/C][C]112.317836377114[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]4374.97[/C][C]34.4803899315322[/C][C]126.882845834615[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]4396.45517241379[/C][C]80.3663224520515[/C][C]54.7051929001333[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]4397.23928571429[/C][C]77.0818779416[/C][C]57.046343487451[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]4393.12592592593[/C][C]74.4877906215404[/C][C]58.9777987676751[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]4389.22307692308[/C][C]71.5147582895169[/C][C]61.3750669358897[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]4388.778[/C][C]69.9252104425047[/C][C]62.7638869046898[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]4388.01041666667[/C][C]68.1451181654529[/C][C]64.3921462725004[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]4387.23043478261[/C][C]66.1902425686758[/C][C]66.2821326002942[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]4386.47727272727[/C][C]63.8516413426672[/C][C]68.6979563953061[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]4382.49285714286[/C][C]61.7896363212429[/C][C]70.9260179871973[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]4377.4075[/C][C]59.4727357689197[/C][C]73.6036007660442[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]4372.70789473684[/C][C]57.5823590248065[/C][C]75.9383250146642[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]4367.77777777778[/C][C]55.688620437286[/C][C]78.4321418537665[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]4364.72647058824[/C][C]54.1822091468784[/C][C]80.5564508962017[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]4363.265625[/C][C]53.0606362679223[/C][C]82.231686837834[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]4361.23333333333[/C][C]51.8128920036102[/C][C]84.1727447491148[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]4360.30714285714[/C][C]50.4297058905323[/C][C]86.4630690554106[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]4359.73846153846[/C][C]48.3865226235326[/C][C]90.1023306729242[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]4354.3125[/C][C]46.9548601119634[/C][C]92.734010699152[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]4347.69090909091[/C][C]44.5524055006167[/C][C]97.585996990235[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]4341.11[/C][C]42.1274950221599[/C][C]103.046953010534[/C][/ROW]
[ROW][C]Median[/C][C]4395.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4409.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4346.89032258064[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4361.23333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4346.89032258064[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4361.23333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4361.23333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4346.89032258064[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4361.23333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4363.265625[/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=17564&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17564&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 Mean4396.8866666666783.367807924382752.7408213810154
Geometric Mean4350.03380671331
Harmonic Mean4303.05582405076
Quadratic Mean4443.27285365191
Winsorized Mean ( 1 / 20 )4395.7233333333383.030495329209852.9410708186747
Winsorized Mean ( 2 / 20 )4404.6433333333380.84335779299854.4836762546598
Winsorized Mean ( 3 / 20 )4403.2733333333380.289078271220654.8427435978136
Winsorized Mean ( 4 / 20 )4390.7066666666774.974208441637458.5628945997416
Winsorized Mean ( 5 / 20 )4391.8483333333374.207446802661759.1833909204892
Winsorized Mean ( 6 / 20 )4391.5983333333373.10585837127960.0717703228371
Winsorized Mean ( 7 / 20 )4391.0966666666772.39746234146660.6526323527177
Winsorized Mean ( 8 / 20 )4408.7968.873690240502164.0126873499128
Winsorized Mean ( 9 / 20 )4413.00567.272359121976465.5990819646812
Winsorized Mean ( 10 / 20 )4407.1716666666762.919427226825570.044688276941
Winsorized Mean ( 11 / 20 )4405.2466666666760.335384230210773.0126562194147
Winsorized Mean ( 12 / 20 )4388.5266666666756.353330696620277.87519588314
Winsorized Mean ( 13 / 20 )4374.85552.613391209886183.150979235453
Winsorized Mean ( 14 / 20 )4377.4916666666750.928122068922285.9543114655299
Winsorized Mean ( 15 / 20 )4367.7166666666749.079182370782888.9932646731866
Winsorized Mean ( 16 / 20 )4364.2548.521955686223389.9438190047877
Winsorized Mean ( 17 / 20 )4396.63543.2099707201101101.750473946834
Winsorized Mean ( 18 / 20 )4398.01542.8008972677081102.755205632527
Winsorized Mean ( 19 / 20 )4389.3739.079901657493112.317836377114
Winsorized Mean ( 20 / 20 )4374.9734.4803899315322126.882845834615
Trimmed Mean ( 1 / 20 )4396.4551724137980.366322452051554.7051929001333
Trimmed Mean ( 2 / 20 )4397.2392857142977.081877941657.046343487451
Trimmed Mean ( 3 / 20 )4393.1259259259374.487790621540458.9777987676751
Trimmed Mean ( 4 / 20 )4389.2230769230871.514758289516961.3750669358897
Trimmed Mean ( 5 / 20 )4388.77869.925210442504762.7638869046898
Trimmed Mean ( 6 / 20 )4388.0104166666768.145118165452964.3921462725004
Trimmed Mean ( 7 / 20 )4387.2304347826166.190242568675866.2821326002942
Trimmed Mean ( 8 / 20 )4386.4772727272763.851641342667268.6979563953061
Trimmed Mean ( 9 / 20 )4382.4928571428661.789636321242970.9260179871973
Trimmed Mean ( 10 / 20 )4377.407559.472735768919773.6036007660442
Trimmed Mean ( 11 / 20 )4372.7078947368457.582359024806575.9383250146642
Trimmed Mean ( 12 / 20 )4367.7777777777855.68862043728678.4321418537665
Trimmed Mean ( 13 / 20 )4364.7264705882454.182209146878480.5564508962017
Trimmed Mean ( 14 / 20 )4363.26562553.060636267922382.231686837834
Trimmed Mean ( 15 / 20 )4361.2333333333351.812892003610284.1727447491148
Trimmed Mean ( 16 / 20 )4360.3071428571450.429705890532386.4630690554106
Trimmed Mean ( 17 / 20 )4359.7384615384648.386522623532690.1023306729242
Trimmed Mean ( 18 / 20 )4354.312546.954860111963492.734010699152
Trimmed Mean ( 19 / 20 )4347.6909090909144.552405500616797.585996990235
Trimmed Mean ( 20 / 20 )4341.1142.1274950221599103.046953010534
Median4395.6
Midrange4409.4
Midmean - Weighted Average at Xnp4346.89032258064
Midmean - Weighted Average at X(n+1)p4361.23333333333
Midmean - Empirical Distribution Function4346.89032258064
Midmean - Empirical Distribution Function - Averaging4361.23333333333
Midmean - Empirical Distribution Function - Interpolation4361.23333333333
Midmean - Closest Observation4346.89032258064
Midmean - True Basic - Statistics Graphics Toolkit4361.23333333333
Midmean - MS Excel (old versions)4363.265625
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')