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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 computationThu, 31 Dec 2009 07:37:37 -0700
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/Dec/31/t1262270343zt3jnlh0kqdr8nm.htm/, Retrieved Thu, 02 May 2024 02:49:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71470, Retrieved Thu, 02 May 2024 02:49:46 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper Central Ten...] [2009-12-31 14:37:37] [2694a35f9be9144abd040893a0238ab5] [Current]
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Dataseries X:
61,7
57,8
51,4
50,5
48,1
58,7
54
56,1
60,4
51,2
50,7
56,4
53,3
52,6
47,7
49,5
48,5
55,3
49,8
57,4
64,6
53
41,5
55,9
58,4
53,5
50,6
58,5
49,1
61,1
52,3
58,4
65,5
61,7
45,1
52,1
59,3
57,9
45
64,9
63,8
69,4
71,1
62,9
73,5
62,7
51,9
73,3
66,7
62,5
70,3
66,1
59,6
66,3
67,7
67,6
80,5
74,7
54,9
78,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71470&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71470&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71470&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean58.731.1179867397614752.5319289677177
Geometric Mean58.1158041181335
Harmonic Mean57.5150230422096
Quadratic Mean59.3544999698141
Winsorized Mean ( 1 / 20 )58.761.0950690714226453.6587157225279
Winsorized Mean ( 2 / 20 )58.62666666666671.0554535980097855.5464179355836
Winsorized Mean ( 3 / 20 )58.69666666666671.0141734734624857.8763576474456
Winsorized Mean ( 4 / 20 )58.711.0060514639036158.3568555948396
Winsorized Mean ( 5 / 20 )58.560.95716211899233561.1808583290465
Winsorized Mean ( 6 / 20 )58.540.929182253929263.0016336972149
Winsorized Mean ( 7 / 20 )58.48166666666670.89913797910075765.0419268521558
Winsorized Mean ( 8 / 20 )58.2950.84765687347018168.7719309835228
Winsorized Mean ( 9 / 20 )58.3850.82742820194777770.5620135530321
Winsorized Mean ( 10 / 20 )58.25166666666670.79708328349591373.0810291381119
Winsorized Mean ( 11 / 20 )58.19666666666670.78106463149264374.509412307469
Winsorized Mean ( 12 / 20 )58.25666666666670.75801318752845176.8544236764747
Winsorized Mean ( 13 / 20 )58.170.72869475447387479.8276639743336
Winsorized Mean ( 14 / 20 )58.14666666666670.68690522980024784.6502023045825
Winsorized Mean ( 15 / 20 )58.12166666666670.66679981015093787.1650918039557
Winsorized Mean ( 16 / 20 )57.96166666666670.62412013396427692.8694068856691
Winsorized Mean ( 17 / 20 )57.79166666666670.571469963358281101.12809136468
Winsorized Mean ( 18 / 20 )57.85166666666670.544082141452772106.328920321103
Winsorized Mean ( 19 / 20 )57.88333333333330.520262681732763111.257899837347
Winsorized Mean ( 20 / 20 )57.68333333333330.470899887801484122.495958966231
Trimmed Mean ( 1 / 20 )58.6517241379311.0512379743719855.7930036469335
Trimmed Mean ( 2 / 20 )58.53571428571430.99681124244323458.7229675923802
Trimmed Mean ( 3 / 20 )58.48518518518520.95650484539760461.1446826083498
Trimmed Mean ( 4 / 20 )58.40384615384620.9264707908146663.0390582551348
Trimmed Mean ( 5 / 20 )58.3120.89165125423770665.3977659122482
Trimmed Mean ( 6 / 20 )58.250.86496525572824167.343745444385
Trimmed Mean ( 7 / 20 )58.18695652173910.83947078277154769.3138554859914
Trimmed Mean ( 8 / 20 )58.12954545454550.81522626559554371.3047995479885
Trimmed Mean ( 9 / 20 )58.10.79793578054392472.8128771972042
Trimmed Mean ( 10 / 20 )58.05250.77966945247855274.4578357090333
Trimmed Mean ( 11 / 20 )58.0210526315790.76272661576383376.0705755278695
Trimmed Mean ( 12 / 20 )57.99444444444440.74310528686864778.0433748343062
Trimmed Mean ( 13 / 20 )57.95588235294120.7213721226461680.3411727921306
Trimmed Mean ( 14 / 20 )57.9250.69845740166132182.9327599109438
Trimmed Mean ( 15 / 20 )57.89333333333330.67718031577758485.4917545363916
Trimmed Mean ( 16 / 20 )57.86071428571430.65099312177289288.8806845272626
Trimmed Mean ( 17 / 20 )57.84615384615380.6253425096999892.5031529903614
Trimmed Mean ( 18 / 20 )57.85416666666670.60361168913138195.846663854242
Trimmed Mean ( 19 / 20 )57.85454545454550.577489988771278100.182767804585
Trimmed Mean ( 20 / 20 )57.850.542290464021286106.677147835167
Median58.15
Midrange61
Midmean - Weighted Average at Xnp57.7
Midmean - Weighted Average at X(n+1)p57.8933333333333
Midmean - Empirical Distribution Function57.7
Midmean - Empirical Distribution Function - Averaging57.8933333333333
Midmean - Empirical Distribution Function - Interpolation57.8933333333333
Midmean - Closest Observation57.7
Midmean - True Basic - Statistics Graphics Toolkit57.8933333333333
Midmean - MS Excel (old versions)57.925
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 58.73 & 1.11798673976147 & 52.5319289677177 \tabularnewline
Geometric Mean & 58.1158041181335 &  &  \tabularnewline
Harmonic Mean & 57.5150230422096 &  &  \tabularnewline
Quadratic Mean & 59.3544999698141 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 58.76 & 1.09506907142264 & 53.6587157225279 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 58.6266666666667 & 1.05545359800978 & 55.5464179355836 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 58.6966666666667 & 1.01417347346248 & 57.8763576474456 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 58.71 & 1.00605146390361 & 58.3568555948396 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 58.56 & 0.957162118992335 & 61.1808583290465 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 58.54 & 0.9291822539292 & 63.0016336972149 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 58.4816666666667 & 0.899137979100757 & 65.0419268521558 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 58.295 & 0.847656873470181 & 68.7719309835228 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 58.385 & 0.827428201947777 & 70.5620135530321 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 58.2516666666667 & 0.797083283495913 & 73.0810291381119 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 58.1966666666667 & 0.781064631492643 & 74.509412307469 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 58.2566666666667 & 0.758013187528451 & 76.8544236764747 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 58.17 & 0.728694754473874 & 79.8276639743336 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 58.1466666666667 & 0.686905229800247 & 84.6502023045825 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 58.1216666666667 & 0.666799810150937 & 87.1650918039557 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 57.9616666666667 & 0.624120133964276 & 92.8694068856691 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 57.7916666666667 & 0.571469963358281 & 101.12809136468 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 57.8516666666667 & 0.544082141452772 & 106.328920321103 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 57.8833333333333 & 0.520262681732763 & 111.257899837347 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 57.6833333333333 & 0.470899887801484 & 122.495958966231 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 58.651724137931 & 1.05123797437198 & 55.7930036469335 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 58.5357142857143 & 0.996811242443234 & 58.7229675923802 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 58.4851851851852 & 0.956504845397604 & 61.1446826083498 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 58.4038461538462 & 0.92647079081466 & 63.0390582551348 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 58.312 & 0.891651254237706 & 65.3977659122482 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 58.25 & 0.864965255728241 & 67.343745444385 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 58.1869565217391 & 0.839470782771547 & 69.3138554859914 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 58.1295454545455 & 0.815226265595543 & 71.3047995479885 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 58.1 & 0.797935780543924 & 72.8128771972042 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 58.0525 & 0.779669452478552 & 74.4578357090333 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 58.021052631579 & 0.762726615763833 & 76.0705755278695 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 57.9944444444444 & 0.743105286868647 & 78.0433748343062 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 57.9558823529412 & 0.72137212264616 & 80.3411727921306 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 57.925 & 0.698457401661321 & 82.9327599109438 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 57.8933333333333 & 0.677180315777584 & 85.4917545363916 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 57.8607142857143 & 0.650993121772892 & 88.8806845272626 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 57.8461538461538 & 0.62534250969998 & 92.5031529903614 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 57.8541666666667 & 0.603611689131381 & 95.846663854242 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 57.8545454545455 & 0.577489988771278 & 100.182767804585 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 57.85 & 0.542290464021286 & 106.677147835167 \tabularnewline
Median & 58.15 &  &  \tabularnewline
Midrange & 61 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 57.7 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 57.8933333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 57.7 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 57.8933333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 57.8933333333333 &  &  \tabularnewline
Midmean - Closest Observation & 57.7 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 57.8933333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 57.925 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71470&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]58.73[/C][C]1.11798673976147[/C][C]52.5319289677177[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]58.1158041181335[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]57.5150230422096[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]59.3544999698141[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]58.76[/C][C]1.09506907142264[/C][C]53.6587157225279[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]58.6266666666667[/C][C]1.05545359800978[/C][C]55.5464179355836[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]58.6966666666667[/C][C]1.01417347346248[/C][C]57.8763576474456[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]58.71[/C][C]1.00605146390361[/C][C]58.3568555948396[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]58.56[/C][C]0.957162118992335[/C][C]61.1808583290465[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]58.54[/C][C]0.9291822539292[/C][C]63.0016336972149[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]58.4816666666667[/C][C]0.899137979100757[/C][C]65.0419268521558[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]58.295[/C][C]0.847656873470181[/C][C]68.7719309835228[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]58.385[/C][C]0.827428201947777[/C][C]70.5620135530321[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]58.2516666666667[/C][C]0.797083283495913[/C][C]73.0810291381119[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]58.1966666666667[/C][C]0.781064631492643[/C][C]74.509412307469[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]58.2566666666667[/C][C]0.758013187528451[/C][C]76.8544236764747[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]58.17[/C][C]0.728694754473874[/C][C]79.8276639743336[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]58.1466666666667[/C][C]0.686905229800247[/C][C]84.6502023045825[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]58.1216666666667[/C][C]0.666799810150937[/C][C]87.1650918039557[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]57.9616666666667[/C][C]0.624120133964276[/C][C]92.8694068856691[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]57.7916666666667[/C][C]0.571469963358281[/C][C]101.12809136468[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]57.8516666666667[/C][C]0.544082141452772[/C][C]106.328920321103[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]57.8833333333333[/C][C]0.520262681732763[/C][C]111.257899837347[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]57.6833333333333[/C][C]0.470899887801484[/C][C]122.495958966231[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]58.651724137931[/C][C]1.05123797437198[/C][C]55.7930036469335[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]58.5357142857143[/C][C]0.996811242443234[/C][C]58.7229675923802[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]58.4851851851852[/C][C]0.956504845397604[/C][C]61.1446826083498[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]58.4038461538462[/C][C]0.92647079081466[/C][C]63.0390582551348[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]58.312[/C][C]0.891651254237706[/C][C]65.3977659122482[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]58.25[/C][C]0.864965255728241[/C][C]67.343745444385[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]58.1869565217391[/C][C]0.839470782771547[/C][C]69.3138554859914[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]58.1295454545455[/C][C]0.815226265595543[/C][C]71.3047995479885[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]58.1[/C][C]0.797935780543924[/C][C]72.8128771972042[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]58.0525[/C][C]0.779669452478552[/C][C]74.4578357090333[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]58.021052631579[/C][C]0.762726615763833[/C][C]76.0705755278695[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]57.9944444444444[/C][C]0.743105286868647[/C][C]78.0433748343062[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]57.9558823529412[/C][C]0.72137212264616[/C][C]80.3411727921306[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]57.925[/C][C]0.698457401661321[/C][C]82.9327599109438[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]57.8933333333333[/C][C]0.677180315777584[/C][C]85.4917545363916[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]57.8607142857143[/C][C]0.650993121772892[/C][C]88.8806845272626[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]57.8461538461538[/C][C]0.62534250969998[/C][C]92.5031529903614[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]57.8541666666667[/C][C]0.603611689131381[/C][C]95.846663854242[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]57.8545454545455[/C][C]0.577489988771278[/C][C]100.182767804585[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]57.85[/C][C]0.542290464021286[/C][C]106.677147835167[/C][/ROW]
[ROW][C]Median[/C][C]58.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]61[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]57.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]57.8933333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]57.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]57.8933333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]57.8933333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]57.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]57.8933333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]57.925[/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=71470&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71470&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 Mean58.731.1179867397614752.5319289677177
Geometric Mean58.1158041181335
Harmonic Mean57.5150230422096
Quadratic Mean59.3544999698141
Winsorized Mean ( 1 / 20 )58.761.0950690714226453.6587157225279
Winsorized Mean ( 2 / 20 )58.62666666666671.0554535980097855.5464179355836
Winsorized Mean ( 3 / 20 )58.69666666666671.0141734734624857.8763576474456
Winsorized Mean ( 4 / 20 )58.711.0060514639036158.3568555948396
Winsorized Mean ( 5 / 20 )58.560.95716211899233561.1808583290465
Winsorized Mean ( 6 / 20 )58.540.929182253929263.0016336972149
Winsorized Mean ( 7 / 20 )58.48166666666670.89913797910075765.0419268521558
Winsorized Mean ( 8 / 20 )58.2950.84765687347018168.7719309835228
Winsorized Mean ( 9 / 20 )58.3850.82742820194777770.5620135530321
Winsorized Mean ( 10 / 20 )58.25166666666670.79708328349591373.0810291381119
Winsorized Mean ( 11 / 20 )58.19666666666670.78106463149264374.509412307469
Winsorized Mean ( 12 / 20 )58.25666666666670.75801318752845176.8544236764747
Winsorized Mean ( 13 / 20 )58.170.72869475447387479.8276639743336
Winsorized Mean ( 14 / 20 )58.14666666666670.68690522980024784.6502023045825
Winsorized Mean ( 15 / 20 )58.12166666666670.66679981015093787.1650918039557
Winsorized Mean ( 16 / 20 )57.96166666666670.62412013396427692.8694068856691
Winsorized Mean ( 17 / 20 )57.79166666666670.571469963358281101.12809136468
Winsorized Mean ( 18 / 20 )57.85166666666670.544082141452772106.328920321103
Winsorized Mean ( 19 / 20 )57.88333333333330.520262681732763111.257899837347
Winsorized Mean ( 20 / 20 )57.68333333333330.470899887801484122.495958966231
Trimmed Mean ( 1 / 20 )58.6517241379311.0512379743719855.7930036469335
Trimmed Mean ( 2 / 20 )58.53571428571430.99681124244323458.7229675923802
Trimmed Mean ( 3 / 20 )58.48518518518520.95650484539760461.1446826083498
Trimmed Mean ( 4 / 20 )58.40384615384620.9264707908146663.0390582551348
Trimmed Mean ( 5 / 20 )58.3120.89165125423770665.3977659122482
Trimmed Mean ( 6 / 20 )58.250.86496525572824167.343745444385
Trimmed Mean ( 7 / 20 )58.18695652173910.83947078277154769.3138554859914
Trimmed Mean ( 8 / 20 )58.12954545454550.81522626559554371.3047995479885
Trimmed Mean ( 9 / 20 )58.10.79793578054392472.8128771972042
Trimmed Mean ( 10 / 20 )58.05250.77966945247855274.4578357090333
Trimmed Mean ( 11 / 20 )58.0210526315790.76272661576383376.0705755278695
Trimmed Mean ( 12 / 20 )57.99444444444440.74310528686864778.0433748343062
Trimmed Mean ( 13 / 20 )57.95588235294120.7213721226461680.3411727921306
Trimmed Mean ( 14 / 20 )57.9250.69845740166132182.9327599109438
Trimmed Mean ( 15 / 20 )57.89333333333330.67718031577758485.4917545363916
Trimmed Mean ( 16 / 20 )57.86071428571430.65099312177289288.8806845272626
Trimmed Mean ( 17 / 20 )57.84615384615380.6253425096999892.5031529903614
Trimmed Mean ( 18 / 20 )57.85416666666670.60361168913138195.846663854242
Trimmed Mean ( 19 / 20 )57.85454545454550.577489988771278100.182767804585
Trimmed Mean ( 20 / 20 )57.850.542290464021286106.677147835167
Median58.15
Midrange61
Midmean - Weighted Average at Xnp57.7
Midmean - Weighted Average at X(n+1)p57.8933333333333
Midmean - Empirical Distribution Function57.7
Midmean - Empirical Distribution Function - Averaging57.8933333333333
Midmean - Empirical Distribution Function - Interpolation57.8933333333333
Midmean - Closest Observation57.7
Midmean - True Basic - Statistics Graphics Toolkit57.8933333333333
Midmean - MS Excel (old versions)57.925
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')