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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 21 Oct 2008 01:34:41 -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/21/t1224574508ewsye9c69coqd0h.htm/, Retrieved Sun, 19 May 2024 19:40:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18361, Retrieved Sun, 19 May 2024 19:40:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [] [2008-10-21 07:26:01] [e3dae385761e8d86216d332d70171419]
F    D    [Central Tendency] [] [2008-10-21 07:34:41] [0e4dd4b7713a9edf1ca3fab1bbbafcc9] [Current]
Feedback Forum
2008-10-24 16:21:56 [Jan Van Riet] [reply
Op enkele outliers na (maximale) is dit een goede tijdreeks om mee te werken, daar bijna alle waarden binnen het betrouwbaarheidsinterval liggen. Ook de gemiddeldes en de mediaan liggen in mekaars buurt.

Post a new message
Dataseries X:
2
3,3
3,4
2,9
4,6
3,5
3
3,1
2,6
2,7
2,8
2,7
2,4
2,8
3,8
3
3,5
5
2,7
2,9
2,5
2,3
3,1
3,2
2,2
2,4
3,2
3,7
4,6
5,2
2,7
3,1
4
4,4
3,8
3,3
2,4
2,9
4
2,9
3,7
5,6
3,7
3,1
3,3
2,5
2,4
2,5
2
2,1
3,1
2,8
3,8
3,4
1,8
1,9
1,9
2
3
3,7




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=18361&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=18361&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18361&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 Mean3.1150.1071675650822129.0666303522939
Geometric Mean3.01322738026170
Harmonic Mean2.91724429281181
Quadratic Mean3.22193006338333
Winsorized Mean ( 1 / 20 )3.110.10438682948289829.7930305519006
Winsorized Mean ( 2 / 20 )3.103333333333330.10220635674799630.3634082269954
Winsorized Mean ( 3 / 20 )3.088333333333330.095375904129461532.3806454211043
Winsorized Mean ( 4 / 20 )3.088333333333330.095375904129461532.3806454211043
Winsorized Mean ( 5 / 20 )3.071666666666670.091073065181241133.7274984711875
Winsorized Mean ( 6 / 20 )3.041666666666670.080017359227718738.0125849693501
Winsorized Mean ( 7 / 20 )3.053333333333330.077767822876514439.2621680843714
Winsorized Mean ( 8 / 20 )3.040.070116932197515343.3561467212584
Winsorized Mean ( 9 / 20 )3.0550.067540529786505345.2321000391441
Winsorized Mean ( 10 / 20 )3.0550.067540529786505345.2321000391441
Winsorized Mean ( 11 / 20 )3.036666666666670.064219198542130747.2859633194344
Winsorized Mean ( 12 / 20 )3.036666666666670.064219198542130747.2859633194344
Winsorized Mean ( 13 / 20 )3.058333333333330.060706372428963350.3791152553564
Winsorized Mean ( 14 / 20 )3.058333333333330.060706372428963350.3791152553564
Winsorized Mean ( 15 / 20 )3.008333333333330.052199728697406757.6312062994072
Winsorized Mean ( 16 / 20 )3.0350.04794211434306663.3055100215654
Winsorized Mean ( 17 / 20 )3.0350.039116297700098277.5891425939418
Winsorized Mean ( 18 / 20 )3.0350.039116297700098277.5891425939418
Winsorized Mean ( 19 / 20 )3.003333333333330.034277586248461587.617993623111
Winsorized Mean ( 20 / 20 )3.003333333333330.034277586248461587.617993623111
Trimmed Mean ( 1 / 20 )3.094827586206900.0994972970595731.1046398009585
Trimmed Mean ( 2 / 20 )3.078571428571430.093375178357043332.9699121623066
Trimmed Mean ( 3 / 20 )3.064814814814810.087201919444291735.1461852485110
Trimmed Mean ( 4 / 20 )3.055769230769230.08299691345814136.8178659114883
Trimmed Mean ( 5 / 20 )3.0460.077628629265449839.2381010565606
Trimmed Mean ( 6 / 20 )3.039583333333330.07242871179278441.9665524637449
Trimmed Mean ( 7 / 20 )3.039130434782610.069607475087893743.6609779473409
Trimmed Mean ( 8 / 20 )3.036363636363640.066638632070737245.5646153291461
Trimmed Mean ( 9 / 20 )3.035714285714290.065004371207565146.7001561482836
Trimmed Mean ( 10 / 20 )3.03250.063487077223313547.7656262129266
Trimmed Mean ( 11 / 20 )3.028947368421050.061386064039621949.3425896546487
Trimmed Mean ( 12 / 20 )3.027777777777780.059443331839461750.9355327853237
Trimmed Mean ( 13 / 20 )3.026470588235290.056692689347743253.3837893925167
Trimmed Mean ( 14 / 20 )3.0218750.053831872192128756.1354245532233
Trimmed Mean ( 15 / 20 )3.016666666666670.049615378903670560.8010405911361
Trimmed Mean ( 16 / 20 )3.017857142857140.046591087161304464.7732716004014
Trimmed Mean ( 17 / 20 )3.015384615384620.043568622333865569.210006051552
Trimmed Mean ( 18 / 20 )3.01250.042269194250762571.2693973329207
Trimmed Mean ( 19 / 20 )3.009090909090910.039972442297796775.2791357273851
Trimmed Mean ( 20 / 20 )3.010.038319982419510378.5490965796342
Median3
Midrange3.7
Midmean - Weighted Average at Xnp2.984375
Midmean - Weighted Average at X(n+1)p2.984375
Midmean - Empirical Distribution Function2.984375
Midmean - Empirical Distribution Function - Averaging2.984375
Midmean - Empirical Distribution Function - Interpolation2.984375
Midmean - Closest Observation2.984375
Midmean - True Basic - Statistics Graphics Toolkit2.984375
Midmean - MS Excel (old versions)3.06388888888889
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.115 & 0.10716756508221 & 29.0666303522939 \tabularnewline
Geometric Mean & 3.01322738026170 &  &  \tabularnewline
Harmonic Mean & 2.91724429281181 &  &  \tabularnewline
Quadratic Mean & 3.22193006338333 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3.11 & 0.104386829482898 & 29.7930305519006 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3.10333333333333 & 0.102206356747996 & 30.3634082269954 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3.08833333333333 & 0.0953759041294615 & 32.3806454211043 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3.08833333333333 & 0.0953759041294615 & 32.3806454211043 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3.07166666666667 & 0.0910730651812411 & 33.7274984711875 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3.04166666666667 & 0.0800173592277187 & 38.0125849693501 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3.05333333333333 & 0.0777678228765144 & 39.2621680843714 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3.04 & 0.0701169321975153 & 43.3561467212584 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3.055 & 0.0675405297865053 & 45.2321000391441 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3.055 & 0.0675405297865053 & 45.2321000391441 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3.03666666666667 & 0.0642191985421307 & 47.2859633194344 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3.03666666666667 & 0.0642191985421307 & 47.2859633194344 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3.05833333333333 & 0.0607063724289633 & 50.3791152553564 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3.05833333333333 & 0.0607063724289633 & 50.3791152553564 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3.00833333333333 & 0.0521997286974067 & 57.6312062994072 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3.035 & 0.047942114343066 & 63.3055100215654 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3.035 & 0.0391162977000982 & 77.5891425939418 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3.035 & 0.0391162977000982 & 77.5891425939418 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3.00333333333333 & 0.0342775862484615 & 87.617993623111 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3.00333333333333 & 0.0342775862484615 & 87.617993623111 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3.09482758620690 & 0.09949729705957 & 31.1046398009585 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3.07857142857143 & 0.0933751783570433 & 32.9699121623066 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3.06481481481481 & 0.0872019194442917 & 35.1461852485110 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3.05576923076923 & 0.082996913458141 & 36.8178659114883 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3.046 & 0.0776286292654498 & 39.2381010565606 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3.03958333333333 & 0.072428711792784 & 41.9665524637449 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3.03913043478261 & 0.0696074750878937 & 43.6609779473409 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3.03636363636364 & 0.0666386320707372 & 45.5646153291461 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3.03571428571429 & 0.0650043712075651 & 46.7001561482836 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3.0325 & 0.0634870772233135 & 47.7656262129266 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3.02894736842105 & 0.0613860640396219 & 49.3425896546487 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3.02777777777778 & 0.0594433318394617 & 50.9355327853237 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3.02647058823529 & 0.0566926893477432 & 53.3837893925167 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3.021875 & 0.0538318721921287 & 56.1354245532233 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3.01666666666667 & 0.0496153789036705 & 60.8010405911361 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3.01785714285714 & 0.0465910871613044 & 64.7732716004014 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3.01538461538462 & 0.0435686223338655 & 69.210006051552 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3.0125 & 0.0422691942507625 & 71.2693973329207 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3.00909090909091 & 0.0399724422977967 & 75.2791357273851 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3.01 & 0.0383199824195103 & 78.5490965796342 \tabularnewline
Median & 3 &  &  \tabularnewline
Midrange & 3.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.984375 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.984375 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.984375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.984375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.984375 &  &  \tabularnewline
Midmean - Closest Observation & 2.984375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.984375 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.06388888888889 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18361&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]3.115[/C][C]0.10716756508221[/C][C]29.0666303522939[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.01322738026170[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.91724429281181[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.22193006338333[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3.11[/C][C]0.104386829482898[/C][C]29.7930305519006[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3.10333333333333[/C][C]0.102206356747996[/C][C]30.3634082269954[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3.08833333333333[/C][C]0.0953759041294615[/C][C]32.3806454211043[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3.08833333333333[/C][C]0.0953759041294615[/C][C]32.3806454211043[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3.07166666666667[/C][C]0.0910730651812411[/C][C]33.7274984711875[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3.04166666666667[/C][C]0.0800173592277187[/C][C]38.0125849693501[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3.05333333333333[/C][C]0.0777678228765144[/C][C]39.2621680843714[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3.04[/C][C]0.0701169321975153[/C][C]43.3561467212584[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3.055[/C][C]0.0675405297865053[/C][C]45.2321000391441[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3.055[/C][C]0.0675405297865053[/C][C]45.2321000391441[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3.03666666666667[/C][C]0.0642191985421307[/C][C]47.2859633194344[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3.03666666666667[/C][C]0.0642191985421307[/C][C]47.2859633194344[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3.05833333333333[/C][C]0.0607063724289633[/C][C]50.3791152553564[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3.05833333333333[/C][C]0.0607063724289633[/C][C]50.3791152553564[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3.00833333333333[/C][C]0.0521997286974067[/C][C]57.6312062994072[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3.035[/C][C]0.047942114343066[/C][C]63.3055100215654[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3.035[/C][C]0.0391162977000982[/C][C]77.5891425939418[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3.035[/C][C]0.0391162977000982[/C][C]77.5891425939418[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3.00333333333333[/C][C]0.0342775862484615[/C][C]87.617993623111[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3.00333333333333[/C][C]0.0342775862484615[/C][C]87.617993623111[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3.09482758620690[/C][C]0.09949729705957[/C][C]31.1046398009585[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3.07857142857143[/C][C]0.0933751783570433[/C][C]32.9699121623066[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3.06481481481481[/C][C]0.0872019194442917[/C][C]35.1461852485110[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3.05576923076923[/C][C]0.082996913458141[/C][C]36.8178659114883[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3.046[/C][C]0.0776286292654498[/C][C]39.2381010565606[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3.03958333333333[/C][C]0.072428711792784[/C][C]41.9665524637449[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3.03913043478261[/C][C]0.0696074750878937[/C][C]43.6609779473409[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3.03636363636364[/C][C]0.0666386320707372[/C][C]45.5646153291461[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3.03571428571429[/C][C]0.0650043712075651[/C][C]46.7001561482836[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3.0325[/C][C]0.0634870772233135[/C][C]47.7656262129266[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3.02894736842105[/C][C]0.0613860640396219[/C][C]49.3425896546487[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3.02777777777778[/C][C]0.0594433318394617[/C][C]50.9355327853237[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3.02647058823529[/C][C]0.0566926893477432[/C][C]53.3837893925167[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3.021875[/C][C]0.0538318721921287[/C][C]56.1354245532233[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3.01666666666667[/C][C]0.0496153789036705[/C][C]60.8010405911361[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3.01785714285714[/C][C]0.0465910871613044[/C][C]64.7732716004014[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3.01538461538462[/C][C]0.0435686223338655[/C][C]69.210006051552[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3.0125[/C][C]0.0422691942507625[/C][C]71.2693973329207[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3.00909090909091[/C][C]0.0399724422977967[/C][C]75.2791357273851[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3.01[/C][C]0.0383199824195103[/C][C]78.5490965796342[/C][/ROW]
[ROW][C]Median[/C][C]3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.984375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.984375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.984375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.984375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.984375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.984375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.984375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.06388888888889[/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=18361&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18361&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 Mean3.1150.1071675650822129.0666303522939
Geometric Mean3.01322738026170
Harmonic Mean2.91724429281181
Quadratic Mean3.22193006338333
Winsorized Mean ( 1 / 20 )3.110.10438682948289829.7930305519006
Winsorized Mean ( 2 / 20 )3.103333333333330.10220635674799630.3634082269954
Winsorized Mean ( 3 / 20 )3.088333333333330.095375904129461532.3806454211043
Winsorized Mean ( 4 / 20 )3.088333333333330.095375904129461532.3806454211043
Winsorized Mean ( 5 / 20 )3.071666666666670.091073065181241133.7274984711875
Winsorized Mean ( 6 / 20 )3.041666666666670.080017359227718738.0125849693501
Winsorized Mean ( 7 / 20 )3.053333333333330.077767822876514439.2621680843714
Winsorized Mean ( 8 / 20 )3.040.070116932197515343.3561467212584
Winsorized Mean ( 9 / 20 )3.0550.067540529786505345.2321000391441
Winsorized Mean ( 10 / 20 )3.0550.067540529786505345.2321000391441
Winsorized Mean ( 11 / 20 )3.036666666666670.064219198542130747.2859633194344
Winsorized Mean ( 12 / 20 )3.036666666666670.064219198542130747.2859633194344
Winsorized Mean ( 13 / 20 )3.058333333333330.060706372428963350.3791152553564
Winsorized Mean ( 14 / 20 )3.058333333333330.060706372428963350.3791152553564
Winsorized Mean ( 15 / 20 )3.008333333333330.052199728697406757.6312062994072
Winsorized Mean ( 16 / 20 )3.0350.04794211434306663.3055100215654
Winsorized Mean ( 17 / 20 )3.0350.039116297700098277.5891425939418
Winsorized Mean ( 18 / 20 )3.0350.039116297700098277.5891425939418
Winsorized Mean ( 19 / 20 )3.003333333333330.034277586248461587.617993623111
Winsorized Mean ( 20 / 20 )3.003333333333330.034277586248461587.617993623111
Trimmed Mean ( 1 / 20 )3.094827586206900.0994972970595731.1046398009585
Trimmed Mean ( 2 / 20 )3.078571428571430.093375178357043332.9699121623066
Trimmed Mean ( 3 / 20 )3.064814814814810.087201919444291735.1461852485110
Trimmed Mean ( 4 / 20 )3.055769230769230.08299691345814136.8178659114883
Trimmed Mean ( 5 / 20 )3.0460.077628629265449839.2381010565606
Trimmed Mean ( 6 / 20 )3.039583333333330.07242871179278441.9665524637449
Trimmed Mean ( 7 / 20 )3.039130434782610.069607475087893743.6609779473409
Trimmed Mean ( 8 / 20 )3.036363636363640.066638632070737245.5646153291461
Trimmed Mean ( 9 / 20 )3.035714285714290.065004371207565146.7001561482836
Trimmed Mean ( 10 / 20 )3.03250.063487077223313547.7656262129266
Trimmed Mean ( 11 / 20 )3.028947368421050.061386064039621949.3425896546487
Trimmed Mean ( 12 / 20 )3.027777777777780.059443331839461750.9355327853237
Trimmed Mean ( 13 / 20 )3.026470588235290.056692689347743253.3837893925167
Trimmed Mean ( 14 / 20 )3.0218750.053831872192128756.1354245532233
Trimmed Mean ( 15 / 20 )3.016666666666670.049615378903670560.8010405911361
Trimmed Mean ( 16 / 20 )3.017857142857140.046591087161304464.7732716004014
Trimmed Mean ( 17 / 20 )3.015384615384620.043568622333865569.210006051552
Trimmed Mean ( 18 / 20 )3.01250.042269194250762571.2693973329207
Trimmed Mean ( 19 / 20 )3.009090909090910.039972442297796775.2791357273851
Trimmed Mean ( 20 / 20 )3.010.038319982419510378.5490965796342
Median3
Midrange3.7
Midmean - Weighted Average at Xnp2.984375
Midmean - Weighted Average at X(n+1)p2.984375
Midmean - Empirical Distribution Function2.984375
Midmean - Empirical Distribution Function - Averaging2.984375
Midmean - Empirical Distribution Function - Interpolation2.984375
Midmean - Closest Observation2.984375
Midmean - True Basic - Statistics Graphics Toolkit2.984375
Midmean - MS Excel (old versions)3.06388888888889
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')