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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 06 Mar 2012 04:20:55 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/06/t13310258985qzwb7cc9vg3rb9.htm/, Retrieved Wed, 01 May 2024 18:01:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163511, Retrieved Wed, 01 May 2024 18:01:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Gem consumptiepri...] [2012-03-06 09:20:55] [5a3c3333b811c6fc66e83f7a2504093f] [Current]
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Dataseries X:
18,49
18,07
17,8
17,88
18,12
18,68
18,8
19,64
19,56
19,3
20,07
19,82
20,29
19,36
18,74
18,87
18,87
18,91
19,31
20,06
20,72
20,42
20,58
20,58
21,18
19,87
19,83
19,48
19,49
19,4
19,89
20,44
20,07
19,75
19,54
19,07
19,55
18,01
17,5
17,41
17,47
17,6
17,64
18,3
18,27
17,99
18,04
17,62
18,22
17,67
17,73
17,99
18,15
18,41
18,36
19,52
19,96
19,6
19,48
19,13




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163511&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163511&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163511&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean19.00950.127470041899738149.129157853043
Geometric Mean18.9843058424594
Harmonic Mean18.9591529847983
Quadratic Mean19.0346987980723
Winsorized Mean ( 1 / 20 )19.00283333333330.12526110394675151.705778845855
Winsorized Mean ( 2 / 20 )18.99916666666670.124008449608839153.208646076908
Winsorized Mean ( 3 / 20 )19.00416666666670.123012399280104154.489846372262
Winsorized Mean ( 4 / 20 )18.99616666666670.120795408036219157.259013198341
Winsorized Mean ( 5 / 20 )18.99616666666670.120138830160115158.118458797622
Winsorized Mean ( 6 / 20 )18.98616666666670.117031815575397162.230813675063
Winsorized Mean ( 7 / 20 )18.96750.11111546013146170.700818567999
Winsorized Mean ( 8 / 20 )18.97683333333330.109383349022209173.489233077698
Winsorized Mean ( 9 / 20 )18.98733333333330.106981667648275177.482121476721
Winsorized Mean ( 10 / 20 )18.9890.101060674285331187.897024577406
Winsorized Mean ( 11 / 20 )18.97616666666670.0990115246578191191.65614035586
Winsorized Mean ( 12 / 20 )18.97616666666670.0977157446925961194.197636484927
Winsorized Mean ( 13 / 20 )18.9740.0952994685219438199.09869692118
Winsorized Mean ( 14 / 20 )18.97866666666670.0937882778102569202.356489635756
Winsorized Mean ( 15 / 20 )18.97366666666670.0891237845034559212.891168977804
Winsorized Mean ( 16 / 20 )18.95233333333330.0836100603071033226.675274048609
Winsorized Mean ( 17 / 20 )18.96083333333330.0788480952722403240.472940631818
Winsorized Mean ( 18 / 20 )18.96383333333330.0748399768042472253.391758564216
Winsorized Mean ( 19 / 20 )18.97016666666670.0729265134594298260.127157693067
Winsorized Mean ( 20 / 20 )18.98683333333330.069387347902656273.635380328559
Trimmed Mean ( 1 / 20 )18.99965517241380.123280665701594154.117071515522
Trimmed Mean ( 2 / 20 )18.996250.120799437326676157.254457639804
Trimmed Mean ( 3 / 20 )18.99462962962960.118513007056511160.274640745317
Trimmed Mean ( 4 / 20 )18.99096153846150.116086661995107163.592967633628
Trimmed Mean ( 5 / 20 )18.98940.11385504927274166.785751895034
Trimmed Mean ( 6 / 20 )18.98770833333330.111190463224135170.767418200772
Trimmed Mean ( 7 / 20 )18.98804347826090.108701879048693174.679993063921
Trimmed Mean ( 8 / 20 )18.99204545454550.107108142949025177.316541316416
Trimmed Mean ( 9 / 20 )18.99476190476190.105378163155668180.253302353565
Trimmed Mean ( 10 / 20 )18.9960.10360353424325183.352818402888
Trimmed Mean ( 11 / 20 )18.99710526315790.102608862423769185.140979194379
Trimmed Mean ( 12 / 20 )19.00027777777780.101540894968333187.119463381757
Trimmed Mean ( 13 / 20 )19.00382352941180.100150523705835189.752612629669
Trimmed Mean ( 14 / 20 )19.0081250.0985872357070368192.805132060755
Trimmed Mean ( 15 / 20 )19.01233333333330.096501662582704197.015603923294
Trimmed Mean ( 16 / 20 )19.01785714285710.094565781733299201.107174226007
Trimmed Mean ( 17 / 20 )19.02730769230770.0929690729259471204.662766804866
Trimmed Mean ( 18 / 20 )19.03708333333330.0916445543158391207.727381899037
Trimmed Mean ( 19 / 20 )19.04818181818180.0903519725589714210.821980734835
Trimmed Mean ( 20 / 20 )19.06050.088211692147804216.07679816484
Median19.1
Midrange19.295
Midmean - Weighted Average at Xnp18.981935483871
Midmean - Weighted Average at X(n+1)p19.0123333333333
Midmean - Empirical Distribution Function18.981935483871
Midmean - Empirical Distribution Function - Averaging19.0123333333333
Midmean - Empirical Distribution Function - Interpolation19.0123333333333
Midmean - Closest Observation18.981935483871
Midmean - True Basic - Statistics Graphics Toolkit19.0123333333333
Midmean - MS Excel (old versions)19.008125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 19.0095 & 0.127470041899738 & 149.129157853043 \tabularnewline
Geometric Mean & 18.9843058424594 &  &  \tabularnewline
Harmonic Mean & 18.9591529847983 &  &  \tabularnewline
Quadratic Mean & 19.0346987980723 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 19.0028333333333 & 0.12526110394675 & 151.705778845855 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 18.9991666666667 & 0.124008449608839 & 153.208646076908 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 19.0041666666667 & 0.123012399280104 & 154.489846372262 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 18.9961666666667 & 0.120795408036219 & 157.259013198341 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 18.9961666666667 & 0.120138830160115 & 158.118458797622 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 18.9861666666667 & 0.117031815575397 & 162.230813675063 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 18.9675 & 0.11111546013146 & 170.700818567999 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 18.9768333333333 & 0.109383349022209 & 173.489233077698 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 18.9873333333333 & 0.106981667648275 & 177.482121476721 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 18.989 & 0.101060674285331 & 187.897024577406 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 18.9761666666667 & 0.0990115246578191 & 191.65614035586 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 18.9761666666667 & 0.0977157446925961 & 194.197636484927 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 18.974 & 0.0952994685219438 & 199.09869692118 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 18.9786666666667 & 0.0937882778102569 & 202.356489635756 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 18.9736666666667 & 0.0891237845034559 & 212.891168977804 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 18.9523333333333 & 0.0836100603071033 & 226.675274048609 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 18.9608333333333 & 0.0788480952722403 & 240.472940631818 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 18.9638333333333 & 0.0748399768042472 & 253.391758564216 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 18.9701666666667 & 0.0729265134594298 & 260.127157693067 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 18.9868333333333 & 0.069387347902656 & 273.635380328559 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 18.9996551724138 & 0.123280665701594 & 154.117071515522 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 18.99625 & 0.120799437326676 & 157.254457639804 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 18.9946296296296 & 0.118513007056511 & 160.274640745317 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 18.9909615384615 & 0.116086661995107 & 163.592967633628 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 18.9894 & 0.11385504927274 & 166.785751895034 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 18.9877083333333 & 0.111190463224135 & 170.767418200772 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 18.9880434782609 & 0.108701879048693 & 174.679993063921 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 18.9920454545455 & 0.107108142949025 & 177.316541316416 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 18.9947619047619 & 0.105378163155668 & 180.253302353565 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 18.996 & 0.10360353424325 & 183.352818402888 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 18.9971052631579 & 0.102608862423769 & 185.140979194379 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 19.0002777777778 & 0.101540894968333 & 187.119463381757 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 19.0038235294118 & 0.100150523705835 & 189.752612629669 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 19.008125 & 0.0985872357070368 & 192.805132060755 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 19.0123333333333 & 0.096501662582704 & 197.015603923294 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 19.0178571428571 & 0.094565781733299 & 201.107174226007 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 19.0273076923077 & 0.0929690729259471 & 204.662766804866 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 19.0370833333333 & 0.0916445543158391 & 207.727381899037 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 19.0481818181818 & 0.0903519725589714 & 210.821980734835 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 19.0605 & 0.088211692147804 & 216.07679816484 \tabularnewline
Median & 19.1 &  &  \tabularnewline
Midrange & 19.295 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18.981935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 19.0123333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18.981935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 19.0123333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 19.0123333333333 &  &  \tabularnewline
Midmean - Closest Observation & 18.981935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 19.0123333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 19.008125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163511&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]19.0095[/C][C]0.127470041899738[/C][C]149.129157853043[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]18.9843058424594[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]18.9591529847983[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]19.0346987980723[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]19.0028333333333[/C][C]0.12526110394675[/C][C]151.705778845855[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]18.9991666666667[/C][C]0.124008449608839[/C][C]153.208646076908[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]19.0041666666667[/C][C]0.123012399280104[/C][C]154.489846372262[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]18.9961666666667[/C][C]0.120795408036219[/C][C]157.259013198341[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]18.9961666666667[/C][C]0.120138830160115[/C][C]158.118458797622[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]18.9861666666667[/C][C]0.117031815575397[/C][C]162.230813675063[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]18.9675[/C][C]0.11111546013146[/C][C]170.700818567999[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]18.9768333333333[/C][C]0.109383349022209[/C][C]173.489233077698[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]18.9873333333333[/C][C]0.106981667648275[/C][C]177.482121476721[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]18.989[/C][C]0.101060674285331[/C][C]187.897024577406[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]18.9761666666667[/C][C]0.0990115246578191[/C][C]191.65614035586[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]18.9761666666667[/C][C]0.0977157446925961[/C][C]194.197636484927[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]18.974[/C][C]0.0952994685219438[/C][C]199.09869692118[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]18.9786666666667[/C][C]0.0937882778102569[/C][C]202.356489635756[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]18.9736666666667[/C][C]0.0891237845034559[/C][C]212.891168977804[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]18.9523333333333[/C][C]0.0836100603071033[/C][C]226.675274048609[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]18.9608333333333[/C][C]0.0788480952722403[/C][C]240.472940631818[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]18.9638333333333[/C][C]0.0748399768042472[/C][C]253.391758564216[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]18.9701666666667[/C][C]0.0729265134594298[/C][C]260.127157693067[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]18.9868333333333[/C][C]0.069387347902656[/C][C]273.635380328559[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]18.9996551724138[/C][C]0.123280665701594[/C][C]154.117071515522[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]18.99625[/C][C]0.120799437326676[/C][C]157.254457639804[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]18.9946296296296[/C][C]0.118513007056511[/C][C]160.274640745317[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]18.9909615384615[/C][C]0.116086661995107[/C][C]163.592967633628[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]18.9894[/C][C]0.11385504927274[/C][C]166.785751895034[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]18.9877083333333[/C][C]0.111190463224135[/C][C]170.767418200772[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]18.9880434782609[/C][C]0.108701879048693[/C][C]174.679993063921[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]18.9920454545455[/C][C]0.107108142949025[/C][C]177.316541316416[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]18.9947619047619[/C][C]0.105378163155668[/C][C]180.253302353565[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]18.996[/C][C]0.10360353424325[/C][C]183.352818402888[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]18.9971052631579[/C][C]0.102608862423769[/C][C]185.140979194379[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]19.0002777777778[/C][C]0.101540894968333[/C][C]187.119463381757[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]19.0038235294118[/C][C]0.100150523705835[/C][C]189.752612629669[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]19.008125[/C][C]0.0985872357070368[/C][C]192.805132060755[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]19.0123333333333[/C][C]0.096501662582704[/C][C]197.015603923294[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]19.0178571428571[/C][C]0.094565781733299[/C][C]201.107174226007[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]19.0273076923077[/C][C]0.0929690729259471[/C][C]204.662766804866[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]19.0370833333333[/C][C]0.0916445543158391[/C][C]207.727381899037[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]19.0481818181818[/C][C]0.0903519725589714[/C][C]210.821980734835[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]19.0605[/C][C]0.088211692147804[/C][C]216.07679816484[/C][/ROW]
[ROW][C]Median[/C][C]19.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19.295[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18.981935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]19.0123333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18.981935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]19.0123333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]19.0123333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18.981935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]19.0123333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]19.008125[/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=163511&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163511&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 Mean19.00950.127470041899738149.129157853043
Geometric Mean18.9843058424594
Harmonic Mean18.9591529847983
Quadratic Mean19.0346987980723
Winsorized Mean ( 1 / 20 )19.00283333333330.12526110394675151.705778845855
Winsorized Mean ( 2 / 20 )18.99916666666670.124008449608839153.208646076908
Winsorized Mean ( 3 / 20 )19.00416666666670.123012399280104154.489846372262
Winsorized Mean ( 4 / 20 )18.99616666666670.120795408036219157.259013198341
Winsorized Mean ( 5 / 20 )18.99616666666670.120138830160115158.118458797622
Winsorized Mean ( 6 / 20 )18.98616666666670.117031815575397162.230813675063
Winsorized Mean ( 7 / 20 )18.96750.11111546013146170.700818567999
Winsorized Mean ( 8 / 20 )18.97683333333330.109383349022209173.489233077698
Winsorized Mean ( 9 / 20 )18.98733333333330.106981667648275177.482121476721
Winsorized Mean ( 10 / 20 )18.9890.101060674285331187.897024577406
Winsorized Mean ( 11 / 20 )18.97616666666670.0990115246578191191.65614035586
Winsorized Mean ( 12 / 20 )18.97616666666670.0977157446925961194.197636484927
Winsorized Mean ( 13 / 20 )18.9740.0952994685219438199.09869692118
Winsorized Mean ( 14 / 20 )18.97866666666670.0937882778102569202.356489635756
Winsorized Mean ( 15 / 20 )18.97366666666670.0891237845034559212.891168977804
Winsorized Mean ( 16 / 20 )18.95233333333330.0836100603071033226.675274048609
Winsorized Mean ( 17 / 20 )18.96083333333330.0788480952722403240.472940631818
Winsorized Mean ( 18 / 20 )18.96383333333330.0748399768042472253.391758564216
Winsorized Mean ( 19 / 20 )18.97016666666670.0729265134594298260.127157693067
Winsorized Mean ( 20 / 20 )18.98683333333330.069387347902656273.635380328559
Trimmed Mean ( 1 / 20 )18.99965517241380.123280665701594154.117071515522
Trimmed Mean ( 2 / 20 )18.996250.120799437326676157.254457639804
Trimmed Mean ( 3 / 20 )18.99462962962960.118513007056511160.274640745317
Trimmed Mean ( 4 / 20 )18.99096153846150.116086661995107163.592967633628
Trimmed Mean ( 5 / 20 )18.98940.11385504927274166.785751895034
Trimmed Mean ( 6 / 20 )18.98770833333330.111190463224135170.767418200772
Trimmed Mean ( 7 / 20 )18.98804347826090.108701879048693174.679993063921
Trimmed Mean ( 8 / 20 )18.99204545454550.107108142949025177.316541316416
Trimmed Mean ( 9 / 20 )18.99476190476190.105378163155668180.253302353565
Trimmed Mean ( 10 / 20 )18.9960.10360353424325183.352818402888
Trimmed Mean ( 11 / 20 )18.99710526315790.102608862423769185.140979194379
Trimmed Mean ( 12 / 20 )19.00027777777780.101540894968333187.119463381757
Trimmed Mean ( 13 / 20 )19.00382352941180.100150523705835189.752612629669
Trimmed Mean ( 14 / 20 )19.0081250.0985872357070368192.805132060755
Trimmed Mean ( 15 / 20 )19.01233333333330.096501662582704197.015603923294
Trimmed Mean ( 16 / 20 )19.01785714285710.094565781733299201.107174226007
Trimmed Mean ( 17 / 20 )19.02730769230770.0929690729259471204.662766804866
Trimmed Mean ( 18 / 20 )19.03708333333330.0916445543158391207.727381899037
Trimmed Mean ( 19 / 20 )19.04818181818180.0903519725589714210.821980734835
Trimmed Mean ( 20 / 20 )19.06050.088211692147804216.07679816484
Median19.1
Midrange19.295
Midmean - Weighted Average at Xnp18.981935483871
Midmean - Weighted Average at X(n+1)p19.0123333333333
Midmean - Empirical Distribution Function18.981935483871
Midmean - Empirical Distribution Function - Averaging19.0123333333333
Midmean - Empirical Distribution Function - Interpolation19.0123333333333
Midmean - Closest Observation18.981935483871
Midmean - True Basic - Statistics Graphics Toolkit19.0123333333333
Midmean - MS Excel (old versions)19.008125
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')