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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 11:39:50 -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/2009/Oct/20/t1256060499i9lpdlhmgqk15gi.htm/, Retrieved Thu, 02 May 2024 15:59:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48878, Retrieved Thu, 02 May 2024 15:59:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws3oef2
Estimated Impact126

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD      [Central Tendency] [] [2009-10-20 15:12:09] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D        [Central Tendency] [] [2009-10-20 15:25:16] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D            [Central Tendency] [] [2009-10-20 17:39:50] [2b548c9d2e9bba6e1eaf65bd4d551f41] [Current]
-   PD              [Central Tendency] [WS3 Q2 Yt-Xt Cent...] [2009-10-22 20:19:23] [1b4c3bbe3f2ba180dd536c5a6a81a8e6]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,9
1,2
1,7
2,3
2,4
2,3
2,2
2,3
2,4
2,6
2,1
1,4
1,2
1,4
2,1
2,5
2,6
2,7
2,8
3
3,2
2,9
2,3
1,1
0,6
0,9
1,6
2
2,1
2,1
2
1,8
1,8
2
2,1
2,3
2,5
2,7
2,4
2,3
2,5
2,9
3,2
3,3
3,3
3,3
3,2
3
2,6
2,6
2,2
2,3
2,4
2,8
3,3
3,7
4
4,2
4,2
3,9

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48878&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48878&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48878&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.428333333333330.10256847421148323.6752408769037
Geometric Mean2.27884254921891
Harmonic Mean2.09277592642619
Quadratic Mean2.55293948224395
Winsorized Mean ( 1 / 20 )2.433333333333330.10117017790051524.0518835078667
Winsorized Mean ( 2 / 20 )2.426666666666670.099287480411572224.4408122414579
Winsorized Mean ( 3 / 20 )2.431666666666670.09547655276590325.4687312876578
Winsorized Mean ( 4 / 20 )2.4250.090592057620714226.7683510419076
Winsorized Mean ( 5 / 20 )2.391666666666670.083506881433234828.6403542512703
Winsorized Mean ( 6 / 20 )2.411666666666670.078908216247340830.5629347786447
Winsorized Mean ( 7 / 20 )2.411666666666670.078908216247340830.5629347786447
Winsorized Mean ( 8 / 20 )2.438333333333330.073418992088196833.2112068550902
Winsorized Mean ( 9 / 20 )2.438333333333330.067651970238957636.0423107371559
Winsorized Mean ( 10 / 20 )2.4550.064677601149049137.9574992947322
Winsorized Mean ( 11 / 20 )2.4550.064677601149049137.9574992947322
Winsorized Mean ( 12 / 20 )2.4550.050557625006794848.5584518590431
Winsorized Mean ( 13 / 20 )2.4550.050557625006794848.5584518590431
Winsorized Mean ( 14 / 20 )2.431666666666670.046425425691738552.3779078045026
Winsorized Mean ( 15 / 20 )2.456666666666670.042676464270561857.5649062933566
Winsorized Mean ( 16 / 20 )2.430.038127054913593663.7342696808618
Winsorized Mean ( 17 / 20 )2.430.038127054913593663.7342696808618
Winsorized Mean ( 18 / 20 )2.40.033361569961296671.9390605053745
Winsorized Mean ( 19 / 20 )2.40.033361569961296671.9390605053745
Winsorized Mean ( 20 / 20 )2.40.0234098825044052102.520805029601
Trimmed Mean ( 1 / 20 )2.429310344827590.09645904505329325.1848890219202
Trimmed Mean ( 2 / 20 )2.4250.090605825333780726.7642835443151
Trimmed Mean ( 3 / 20 )2.424074074074070.084589491939879828.6569172894067
Trimmed Mean ( 4 / 20 )2.421153846153850.078989495572009530.6515927038253
Trimmed Mean ( 5 / 20 )2.420.074010479125649232.6980723350204
Trimmed Mean ( 6 / 20 )2.427083333333330.070317137685246134.5162418896721
Trimmed Mean ( 7 / 20 )2.430434782608700.067162616500851836.1873153434674
Trimmed Mean ( 8 / 20 )2.434090909090910.063039903284442538.6119074153405
Trimmed Mean ( 9 / 20 )2.433333333333330.059387765555191640.9736468544507
Trimmed Mean ( 10 / 20 )2.43250.05631726747086243.1927916470477
Trimmed Mean ( 11 / 20 )2.428947368421050.0530583691494345.7787792455575
Trimmed Mean ( 12 / 20 )2.4250.048529977644325549.9691143023543
Trimmed Mean ( 13 / 20 )2.420588235294120.046782275648784951.741566687917
Trimmed Mean ( 14 / 20 )2.4156250.044247602222260154.5933537339736
Trimmed Mean ( 15 / 20 )2.413333333333330.041999817551145457.46056707019
Trimmed Mean ( 16 / 20 )2.407142857142860.039817231728923660.4548019191974
Trimmed Mean ( 17 / 20 )2.403846153846150.038222333073245762.8911413973514
Trimmed Mean ( 18 / 20 )2.40.03561061558059667.3956336016765
Trimmed Mean ( 19 / 20 )2.40.033549085316013171.5369726892218
Trimmed Mean ( 20 / 20 )2.40.029912152080805980.2349491108677
Median2.4
Midrange2.4
Midmean - Weighted Average at Xnp2.39117647058824
Midmean - Weighted Average at X(n+1)p2.42903225806452
Midmean - Empirical Distribution Function2.39117647058824
Midmean - Empirical Distribution Function - Averaging2.42903225806452
Midmean - Empirical Distribution Function - Interpolation2.42903225806452
Midmean - Closest Observation2.39117647058824
Midmean - True Basic - Statistics Graphics Toolkit2.42903225806452
Midmean - MS Excel (old versions)2.39117647058824
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.42833333333333 & 0.102568474211483 & 23.6752408769037 \tabularnewline
Geometric Mean & 2.27884254921891 &  &  \tabularnewline
Harmonic Mean & 2.09277592642619 &  &  \tabularnewline
Quadratic Mean & 2.55293948224395 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.43333333333333 & 0.101170177900515 & 24.0518835078667 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.42666666666667 & 0.0992874804115722 & 24.4408122414579 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.43166666666667 & 0.095476552765903 & 25.4687312876578 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.425 & 0.0905920576207142 & 26.7683510419076 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.39166666666667 & 0.0835068814332348 & 28.6403542512703 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.41166666666667 & 0.0789082162473408 & 30.5629347786447 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.41166666666667 & 0.0789082162473408 & 30.5629347786447 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2.43833333333333 & 0.0734189920881968 & 33.2112068550902 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2.43833333333333 & 0.0676519702389576 & 36.0423107371559 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2.455 & 0.0646776011490491 & 37.9574992947322 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2.455 & 0.0646776011490491 & 37.9574992947322 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2.455 & 0.0505576250067948 & 48.5584518590431 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2.455 & 0.0505576250067948 & 48.5584518590431 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.43166666666667 & 0.0464254256917385 & 52.3779078045026 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.45666666666667 & 0.0426764642705618 & 57.5649062933566 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2.43 & 0.0381270549135936 & 63.7342696808618 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2.43 & 0.0381270549135936 & 63.7342696808618 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2.4 & 0.0333615699612966 & 71.9390605053745 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.4 & 0.0333615699612966 & 71.9390605053745 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2.4 & 0.0234098825044052 & 102.520805029601 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.42931034482759 & 0.096459045053293 & 25.1848890219202 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.425 & 0.0906058253337807 & 26.7642835443151 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.42407407407407 & 0.0845894919398798 & 28.6569172894067 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2.42115384615385 & 0.0789894955720095 & 30.6515927038253 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2.42 & 0.0740104791256492 & 32.6980723350204 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2.42708333333333 & 0.0703171376852461 & 34.5162418896721 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2.43043478260870 & 0.0671626165008518 & 36.1873153434674 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2.43409090909091 & 0.0630399032844425 & 38.6119074153405 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2.43333333333333 & 0.0593877655551916 & 40.9736468544507 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2.4325 & 0.056317267470862 & 43.1927916470477 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2.42894736842105 & 0.05305836914943 & 45.7787792455575 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2.425 & 0.0485299776443255 & 49.9691143023543 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2.42058823529412 & 0.0467822756487849 & 51.741566687917 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2.415625 & 0.0442476022222601 & 54.5933537339736 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2.41333333333333 & 0.0419998175511454 & 57.46056707019 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2.40714285714286 & 0.0398172317289236 & 60.4548019191974 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2.40384615384615 & 0.0382223330732457 & 62.8911413973514 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2.4 & 0.035610615580596 & 67.3956336016765 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2.4 & 0.0335490853160131 & 71.5369726892218 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2.4 & 0.0299121520808059 & 80.2349491108677 \tabularnewline
Median & 2.4 &  &  \tabularnewline
Midrange & 2.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.39117647058824 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.42903225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.39117647058824 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.42903225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.42903225806452 &  &  \tabularnewline
Midmean - Closest Observation & 2.39117647058824 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.42903225806452 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.39117647058824 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48878&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]2.42833333333333[/C][C]0.102568474211483[/C][C]23.6752408769037[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.27884254921891[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.09277592642619[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.55293948224395[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.43333333333333[/C][C]0.101170177900515[/C][C]24.0518835078667[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.42666666666667[/C][C]0.0992874804115722[/C][C]24.4408122414579[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.43166666666667[/C][C]0.095476552765903[/C][C]25.4687312876578[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.425[/C][C]0.0905920576207142[/C][C]26.7683510419076[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.39166666666667[/C][C]0.0835068814332348[/C][C]28.6403542512703[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.41166666666667[/C][C]0.0789082162473408[/C][C]30.5629347786447[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.41166666666667[/C][C]0.0789082162473408[/C][C]30.5629347786447[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2.43833333333333[/C][C]0.0734189920881968[/C][C]33.2112068550902[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2.43833333333333[/C][C]0.0676519702389576[/C][C]36.0423107371559[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2.455[/C][C]0.0646776011490491[/C][C]37.9574992947322[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2.455[/C][C]0.0646776011490491[/C][C]37.9574992947322[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2.455[/C][C]0.0505576250067948[/C][C]48.5584518590431[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2.455[/C][C]0.0505576250067948[/C][C]48.5584518590431[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.43166666666667[/C][C]0.0464254256917385[/C][C]52.3779078045026[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.45666666666667[/C][C]0.0426764642705618[/C][C]57.5649062933566[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2.43[/C][C]0.0381270549135936[/C][C]63.7342696808618[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2.43[/C][C]0.0381270549135936[/C][C]63.7342696808618[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2.4[/C][C]0.0333615699612966[/C][C]71.9390605053745[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.4[/C][C]0.0333615699612966[/C][C]71.9390605053745[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2.4[/C][C]0.0234098825044052[/C][C]102.520805029601[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.42931034482759[/C][C]0.096459045053293[/C][C]25.1848890219202[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.425[/C][C]0.0906058253337807[/C][C]26.7642835443151[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.42407407407407[/C][C]0.0845894919398798[/C][C]28.6569172894067[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2.42115384615385[/C][C]0.0789894955720095[/C][C]30.6515927038253[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2.42[/C][C]0.0740104791256492[/C][C]32.6980723350204[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2.42708333333333[/C][C]0.0703171376852461[/C][C]34.5162418896721[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2.43043478260870[/C][C]0.0671626165008518[/C][C]36.1873153434674[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2.43409090909091[/C][C]0.0630399032844425[/C][C]38.6119074153405[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2.43333333333333[/C][C]0.0593877655551916[/C][C]40.9736468544507[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2.4325[/C][C]0.056317267470862[/C][C]43.1927916470477[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2.42894736842105[/C][C]0.05305836914943[/C][C]45.7787792455575[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2.425[/C][C]0.0485299776443255[/C][C]49.9691143023543[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2.42058823529412[/C][C]0.0467822756487849[/C][C]51.741566687917[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2.415625[/C][C]0.0442476022222601[/C][C]54.5933537339736[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2.41333333333333[/C][C]0.0419998175511454[/C][C]57.46056707019[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2.40714285714286[/C][C]0.0398172317289236[/C][C]60.4548019191974[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2.40384615384615[/C][C]0.0382223330732457[/C][C]62.8911413973514[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2.4[/C][C]0.035610615580596[/C][C]67.3956336016765[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2.4[/C][C]0.0335490853160131[/C][C]71.5369726892218[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2.4[/C][C]0.0299121520808059[/C][C]80.2349491108677[/C][/ROW]
[ROW][C]Median[/C][C]2.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.39117647058824[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.42903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.39117647058824[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.42903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.42903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.39117647058824[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.42903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.39117647058824[/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=48878&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48878&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.428333333333330.10256847421148323.6752408769037
Geometric Mean2.27884254921891
Harmonic Mean2.09277592642619
Quadratic Mean2.55293948224395
Winsorized Mean ( 1 / 20 )2.433333333333330.10117017790051524.0518835078667
Winsorized Mean ( 2 / 20 )2.426666666666670.099287480411572224.4408122414579
Winsorized Mean ( 3 / 20 )2.431666666666670.09547655276590325.4687312876578
Winsorized Mean ( 4 / 20 )2.4250.090592057620714226.7683510419076
Winsorized Mean ( 5 / 20 )2.391666666666670.083506881433234828.6403542512703
Winsorized Mean ( 6 / 20 )2.411666666666670.078908216247340830.5629347786447
Winsorized Mean ( 7 / 20 )2.411666666666670.078908216247340830.5629347786447
Winsorized Mean ( 8 / 20 )2.438333333333330.073418992088196833.2112068550902
Winsorized Mean ( 9 / 20 )2.438333333333330.067651970238957636.0423107371559
Winsorized Mean ( 10 / 20 )2.4550.064677601149049137.9574992947322
Winsorized Mean ( 11 / 20 )2.4550.064677601149049137.9574992947322
Winsorized Mean ( 12 / 20 )2.4550.050557625006794848.5584518590431
Winsorized Mean ( 13 / 20 )2.4550.050557625006794848.5584518590431
Winsorized Mean ( 14 / 20 )2.431666666666670.046425425691738552.3779078045026
Winsorized Mean ( 15 / 20 )2.456666666666670.042676464270561857.5649062933566
Winsorized Mean ( 16 / 20 )2.430.038127054913593663.7342696808618
Winsorized Mean ( 17 / 20 )2.430.038127054913593663.7342696808618
Winsorized Mean ( 18 / 20 )2.40.033361569961296671.9390605053745
Winsorized Mean ( 19 / 20 )2.40.033361569961296671.9390605053745
Winsorized Mean ( 20 / 20 )2.40.0234098825044052102.520805029601
Trimmed Mean ( 1 / 20 )2.429310344827590.09645904505329325.1848890219202
Trimmed Mean ( 2 / 20 )2.4250.090605825333780726.7642835443151
Trimmed Mean ( 3 / 20 )2.424074074074070.084589491939879828.6569172894067
Trimmed Mean ( 4 / 20 )2.421153846153850.078989495572009530.6515927038253
Trimmed Mean ( 5 / 20 )2.420.074010479125649232.6980723350204
Trimmed Mean ( 6 / 20 )2.427083333333330.070317137685246134.5162418896721
Trimmed Mean ( 7 / 20 )2.430434782608700.067162616500851836.1873153434674
Trimmed Mean ( 8 / 20 )2.434090909090910.063039903284442538.6119074153405
Trimmed Mean ( 9 / 20 )2.433333333333330.059387765555191640.9736468544507
Trimmed Mean ( 10 / 20 )2.43250.05631726747086243.1927916470477
Trimmed Mean ( 11 / 20 )2.428947368421050.0530583691494345.7787792455575
Trimmed Mean ( 12 / 20 )2.4250.048529977644325549.9691143023543
Trimmed Mean ( 13 / 20 )2.420588235294120.046782275648784951.741566687917
Trimmed Mean ( 14 / 20 )2.4156250.044247602222260154.5933537339736
Trimmed Mean ( 15 / 20 )2.413333333333330.041999817551145457.46056707019
Trimmed Mean ( 16 / 20 )2.407142857142860.039817231728923660.4548019191974
Trimmed Mean ( 17 / 20 )2.403846153846150.038222333073245762.8911413973514
Trimmed Mean ( 18 / 20 )2.40.03561061558059667.3956336016765
Trimmed Mean ( 19 / 20 )2.40.033549085316013171.5369726892218
Trimmed Mean ( 20 / 20 )2.40.029912152080805980.2349491108677
Median2.4
Midrange2.4
Midmean - Weighted Average at Xnp2.39117647058824
Midmean - Weighted Average at X(n+1)p2.42903225806452
Midmean - Empirical Distribution Function2.39117647058824
Midmean - Empirical Distribution Function - Averaging2.42903225806452
Midmean - Empirical Distribution Function - Interpolation2.42903225806452
Midmean - Closest Observation2.39117647058824
Midmean - True Basic - Statistics Graphics Toolkit2.42903225806452
Midmean - MS Excel (old versions)2.39117647058824
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')