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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 computationFri, 05 Dec 2008 05:06:04 -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/2008/Dec/05/t1228478843apwq0cjf48phlpt.htm/, Retrieved Thu, 16 May 2024 21:51:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29208, Retrieved Thu, 16 May 2024 21:51:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact194
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Simple Regression] [simple linear reg...] [2008-12-05 11:36:25] [4ddbf81f78ea7c738951638c7e93f6ee]
- RM D    [Central Tendency] [central tendency ...] [2008-12-05 12:06:04] [e8f764b122b426f433a1e1038b457077] [Current]
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Dataseries X:
9,4
9,5
9,1
9
9,3
9,9
9,8
9,4
8,3
8
8,5
10,4
11,1
10,9
9,9
9,2
9,2
9,5
9,6
9,5
9,1
8,9
9
10,1
10,3
10,2
9,6
9,2
9,3
9,4
9,4
9,2
9
9
9
9,8
10
9,9
9,3
9
9
9,1
9,1
9,1
9,2
8,8
8,3
8,4
8,1
7,8
7,9
7,9
8
7,9
7,5
7,2
6,9
6,6
6,7
7,3
7,5




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=29208&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=29208&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29208&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 Mean8.959016393442620.12497818496374671.6846415719788
Geometric Mean8.90411291550519
Harmonic Mean8.8463761135256
Quadratic Mean9.0111679343459
Winsorized Mean ( 1 / 20 )8.957377049180330.12357292522694672.4865663957518
Winsorized Mean ( 2 / 20 )8.947540983606560.11778016378067475.9681485947695
Winsorized Mean ( 3 / 20 )8.957377049180330.11272722084345879.4606394281574
Winsorized Mean ( 4 / 20 )8.957377049180330.10978018315785381.5937520918551
Winsorized Mean ( 5 / 20 )8.96557377049180.10427698628324085.9784511429904
Winsorized Mean ( 6 / 20 )8.955737704918030.10255012342802687.3303454500813
Winsorized Mean ( 7 / 20 )8.978688524590170.092892638955528696.6566202181921
Winsorized Mean ( 8 / 20 )8.991803278688520.090181816408574399.7074979943917
Winsorized Mean ( 9 / 20 )8.991803278688520.090181816408574399.7074979943917
Winsorized Mean ( 10 / 20 )8.975409836065570.0875175466467447102.555546629910
Winsorized Mean ( 11 / 20 )8.993442622950820.0838900155733136107.205160965684
Winsorized Mean ( 12 / 20 )8.954098360655740.0780070674425943114.785732295924
Winsorized Mean ( 13 / 20 )8.975409836065570.073724332857057121.742842400051
Winsorized Mean ( 14 / 20 )8.99836065573770.0616482088730937145.963050998957
Winsorized Mean ( 15 / 20 )8.99836065573770.0616482088730937145.963050998957
Winsorized Mean ( 16 / 20 )9.024590163934430.0567640951757338158.984127836364
Winsorized Mean ( 17 / 20 )9.024590163934430.0478873757109939188.454473228997
Winsorized Mean ( 18 / 20 )9.113114754098360.0325152683627217280.271860359191
Winsorized Mean ( 19 / 20 )9.144262295081970.0277108992153276329.987930886921
Winsorized Mean ( 20 / 20 )9.177049180327870.0231876925409002395.77241953423
Trimmed Mean ( 1 / 20 )8.962711864406780.11721735481793176.4623282817478
Trimmed Mean ( 2 / 20 )8.968421052631580.10931427568839582.0425419841452
Trimmed Mean ( 3 / 20 )8.980.10348799113793086.7733531326484
Trimmed Mean ( 4 / 20 )8.988679245283020.098782882580158490.9942999283207
Trimmed Mean ( 5 / 20 )8.998039215686270.09407924052974995.6431957254267
Trimmed Mean ( 6 / 20 )9.00612244897960.090134449992138299.9187596947131
Trimmed Mean ( 7 / 20 )9.017021276595750.0856125098352898105.32364129896
Trimmed Mean ( 8 / 20 )9.024444444444440.0828260655037036108.956575319166
Trimmed Mean ( 9 / 20 )9.030232558139530.0799733402229217112.915535764396
Trimmed Mean ( 10 / 20 )9.036585365853660.0761702279686255118.636711571558
Trimmed Mean ( 11 / 20 )9.046153846153850.0717852316643423126.016920701077
Trimmed Mean ( 12 / 20 )9.054054054054050.0669582132470704135.219469203058
Trimmed Mean ( 13 / 20 )9.068571428571430.0618715705028941146.570894432803
Trimmed Mean ( 14 / 20 )9.081818181818180.0561475574657205161.749123056027
Trimmed Mean ( 15 / 20 )9.093548387096770.0522474434978767174.047719434661
Trimmed Mean ( 16 / 20 )9.106896551724140.0462726537470784196.809471994010
Trimmed Mean ( 17 / 20 )9.118518518518520.0392366757600833232.397835491330
Trimmed Mean ( 18 / 20 )9.1320.032285.375
Trimmed Mean ( 19 / 20 )9.134782608695650.0292249660800217312.567774541926
Trimmed Mean ( 20 / 20 )9.133333333333330.0270214494459259338.00308719969
Median9.1
Midrange8.85
Midmean - Weighted Average at Xnp9.08181818181818
Midmean - Weighted Average at X(n+1)p9.08181818181818
Midmean - Empirical Distribution Function9.08181818181818
Midmean - Empirical Distribution Function - Averaging9.08181818181818
Midmean - Empirical Distribution Function - Interpolation9.08181818181818
Midmean - Closest Observation9.08181818181818
Midmean - True Basic - Statistics Graphics Toolkit9.08181818181818
Midmean - MS Excel (old versions)9.08181818181818
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.95901639344262 & 0.124978184963746 & 71.6846415719788 \tabularnewline
Geometric Mean & 8.90411291550519 &  &  \tabularnewline
Harmonic Mean & 8.8463761135256 &  &  \tabularnewline
Quadratic Mean & 9.0111679343459 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8.95737704918033 & 0.123572925226946 & 72.4865663957518 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8.94754098360656 & 0.117780163780674 & 75.9681485947695 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8.95737704918033 & 0.112727220843458 & 79.4606394281574 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8.95737704918033 & 0.109780183157853 & 81.5937520918551 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8.9655737704918 & 0.104276986283240 & 85.9784511429904 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8.95573770491803 & 0.102550123428026 & 87.3303454500813 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8.97868852459017 & 0.0928926389555286 & 96.6566202181921 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8.99180327868852 & 0.0901818164085743 & 99.7074979943917 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8.99180327868852 & 0.0901818164085743 & 99.7074979943917 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8.97540983606557 & 0.0875175466467447 & 102.555546629910 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8.99344262295082 & 0.0838900155733136 & 107.205160965684 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.95409836065574 & 0.0780070674425943 & 114.785732295924 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.97540983606557 & 0.073724332857057 & 121.742842400051 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.9983606557377 & 0.0616482088730937 & 145.963050998957 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8.9983606557377 & 0.0616482088730937 & 145.963050998957 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 9.02459016393443 & 0.0567640951757338 & 158.984127836364 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 9.02459016393443 & 0.0478873757109939 & 188.454473228997 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 9.11311475409836 & 0.0325152683627217 & 280.271860359191 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 9.14426229508197 & 0.0277108992153276 & 329.987930886921 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 9.17704918032787 & 0.0231876925409002 & 395.77241953423 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8.96271186440678 & 0.117217354817931 & 76.4623282817478 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8.96842105263158 & 0.109314275688395 & 82.0425419841452 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8.98 & 0.103487991137930 & 86.7733531326484 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8.98867924528302 & 0.0987828825801584 & 90.9942999283207 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8.99803921568627 & 0.094079240529749 & 95.6431957254267 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 9.0061224489796 & 0.0901344499921382 & 99.9187596947131 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 9.01702127659575 & 0.0856125098352898 & 105.32364129896 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 9.02444444444444 & 0.0828260655037036 & 108.956575319166 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 9.03023255813953 & 0.0799733402229217 & 112.915535764396 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 9.03658536585366 & 0.0761702279686255 & 118.636711571558 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 9.04615384615385 & 0.0717852316643423 & 126.016920701077 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 9.05405405405405 & 0.0669582132470704 & 135.219469203058 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 9.06857142857143 & 0.0618715705028941 & 146.570894432803 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 9.08181818181818 & 0.0561475574657205 & 161.749123056027 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 9.09354838709677 & 0.0522474434978767 & 174.047719434661 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 9.10689655172414 & 0.0462726537470784 & 196.809471994010 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 9.11851851851852 & 0.0392366757600833 & 232.397835491330 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 9.132 & 0.032 & 285.375 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 9.13478260869565 & 0.0292249660800217 & 312.567774541926 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 9.13333333333333 & 0.0270214494459259 & 338.00308719969 \tabularnewline
Median & 9.1 &  &  \tabularnewline
Midrange & 8.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 9.08181818181818 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 9.08181818181818 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 9.08181818181818 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 9.08181818181818 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 9.08181818181818 &  &  \tabularnewline
Midmean - Closest Observation & 9.08181818181818 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 9.08181818181818 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 9.08181818181818 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29208&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]8.95901639344262[/C][C]0.124978184963746[/C][C]71.6846415719788[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.90411291550519[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.8463761135256[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9.0111679343459[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8.95737704918033[/C][C]0.123572925226946[/C][C]72.4865663957518[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8.94754098360656[/C][C]0.117780163780674[/C][C]75.9681485947695[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8.95737704918033[/C][C]0.112727220843458[/C][C]79.4606394281574[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8.95737704918033[/C][C]0.109780183157853[/C][C]81.5937520918551[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8.9655737704918[/C][C]0.104276986283240[/C][C]85.9784511429904[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8.95573770491803[/C][C]0.102550123428026[/C][C]87.3303454500813[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8.97868852459017[/C][C]0.0928926389555286[/C][C]96.6566202181921[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8.99180327868852[/C][C]0.0901818164085743[/C][C]99.7074979943917[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8.99180327868852[/C][C]0.0901818164085743[/C][C]99.7074979943917[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8.97540983606557[/C][C]0.0875175466467447[/C][C]102.555546629910[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8.99344262295082[/C][C]0.0838900155733136[/C][C]107.205160965684[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.95409836065574[/C][C]0.0780070674425943[/C][C]114.785732295924[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.97540983606557[/C][C]0.073724332857057[/C][C]121.742842400051[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.9983606557377[/C][C]0.0616482088730937[/C][C]145.963050998957[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8.9983606557377[/C][C]0.0616482088730937[/C][C]145.963050998957[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]9.02459016393443[/C][C]0.0567640951757338[/C][C]158.984127836364[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]9.02459016393443[/C][C]0.0478873757109939[/C][C]188.454473228997[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]9.11311475409836[/C][C]0.0325152683627217[/C][C]280.271860359191[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]9.14426229508197[/C][C]0.0277108992153276[/C][C]329.987930886921[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]9.17704918032787[/C][C]0.0231876925409002[/C][C]395.77241953423[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8.96271186440678[/C][C]0.117217354817931[/C][C]76.4623282817478[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8.96842105263158[/C][C]0.109314275688395[/C][C]82.0425419841452[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8.98[/C][C]0.103487991137930[/C][C]86.7733531326484[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8.98867924528302[/C][C]0.0987828825801584[/C][C]90.9942999283207[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8.99803921568627[/C][C]0.094079240529749[/C][C]95.6431957254267[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]9.0061224489796[/C][C]0.0901344499921382[/C][C]99.9187596947131[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]9.01702127659575[/C][C]0.0856125098352898[/C][C]105.32364129896[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]9.02444444444444[/C][C]0.0828260655037036[/C][C]108.956575319166[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]9.03023255813953[/C][C]0.0799733402229217[/C][C]112.915535764396[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]9.03658536585366[/C][C]0.0761702279686255[/C][C]118.636711571558[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]9.04615384615385[/C][C]0.0717852316643423[/C][C]126.016920701077[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]9.05405405405405[/C][C]0.0669582132470704[/C][C]135.219469203058[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]9.06857142857143[/C][C]0.0618715705028941[/C][C]146.570894432803[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]9.08181818181818[/C][C]0.0561475574657205[/C][C]161.749123056027[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]9.09354838709677[/C][C]0.0522474434978767[/C][C]174.047719434661[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]9.10689655172414[/C][C]0.0462726537470784[/C][C]196.809471994010[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]9.11851851851852[/C][C]0.0392366757600833[/C][C]232.397835491330[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]9.132[/C][C]0.032[/C][C]285.375[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]9.13478260869565[/C][C]0.0292249660800217[/C][C]312.567774541926[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]9.13333333333333[/C][C]0.0270214494459259[/C][C]338.00308719969[/C][/ROW]
[ROW][C]Median[/C][C]9.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]9.08181818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]9.08181818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]9.08181818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]9.08181818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]9.08181818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]9.08181818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]9.08181818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]9.08181818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29208&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29208&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 Mean8.959016393442620.12497818496374671.6846415719788
Geometric Mean8.90411291550519
Harmonic Mean8.8463761135256
Quadratic Mean9.0111679343459
Winsorized Mean ( 1 / 20 )8.957377049180330.12357292522694672.4865663957518
Winsorized Mean ( 2 / 20 )8.947540983606560.11778016378067475.9681485947695
Winsorized Mean ( 3 / 20 )8.957377049180330.11272722084345879.4606394281574
Winsorized Mean ( 4 / 20 )8.957377049180330.10978018315785381.5937520918551
Winsorized Mean ( 5 / 20 )8.96557377049180.10427698628324085.9784511429904
Winsorized Mean ( 6 / 20 )8.955737704918030.10255012342802687.3303454500813
Winsorized Mean ( 7 / 20 )8.978688524590170.092892638955528696.6566202181921
Winsorized Mean ( 8 / 20 )8.991803278688520.090181816408574399.7074979943917
Winsorized Mean ( 9 / 20 )8.991803278688520.090181816408574399.7074979943917
Winsorized Mean ( 10 / 20 )8.975409836065570.0875175466467447102.555546629910
Winsorized Mean ( 11 / 20 )8.993442622950820.0838900155733136107.205160965684
Winsorized Mean ( 12 / 20 )8.954098360655740.0780070674425943114.785732295924
Winsorized Mean ( 13 / 20 )8.975409836065570.073724332857057121.742842400051
Winsorized Mean ( 14 / 20 )8.99836065573770.0616482088730937145.963050998957
Winsorized Mean ( 15 / 20 )8.99836065573770.0616482088730937145.963050998957
Winsorized Mean ( 16 / 20 )9.024590163934430.0567640951757338158.984127836364
Winsorized Mean ( 17 / 20 )9.024590163934430.0478873757109939188.454473228997
Winsorized Mean ( 18 / 20 )9.113114754098360.0325152683627217280.271860359191
Winsorized Mean ( 19 / 20 )9.144262295081970.0277108992153276329.987930886921
Winsorized Mean ( 20 / 20 )9.177049180327870.0231876925409002395.77241953423
Trimmed Mean ( 1 / 20 )8.962711864406780.11721735481793176.4623282817478
Trimmed Mean ( 2 / 20 )8.968421052631580.10931427568839582.0425419841452
Trimmed Mean ( 3 / 20 )8.980.10348799113793086.7733531326484
Trimmed Mean ( 4 / 20 )8.988679245283020.098782882580158490.9942999283207
Trimmed Mean ( 5 / 20 )8.998039215686270.09407924052974995.6431957254267
Trimmed Mean ( 6 / 20 )9.00612244897960.090134449992138299.9187596947131
Trimmed Mean ( 7 / 20 )9.017021276595750.0856125098352898105.32364129896
Trimmed Mean ( 8 / 20 )9.024444444444440.0828260655037036108.956575319166
Trimmed Mean ( 9 / 20 )9.030232558139530.0799733402229217112.915535764396
Trimmed Mean ( 10 / 20 )9.036585365853660.0761702279686255118.636711571558
Trimmed Mean ( 11 / 20 )9.046153846153850.0717852316643423126.016920701077
Trimmed Mean ( 12 / 20 )9.054054054054050.0669582132470704135.219469203058
Trimmed Mean ( 13 / 20 )9.068571428571430.0618715705028941146.570894432803
Trimmed Mean ( 14 / 20 )9.081818181818180.0561475574657205161.749123056027
Trimmed Mean ( 15 / 20 )9.093548387096770.0522474434978767174.047719434661
Trimmed Mean ( 16 / 20 )9.106896551724140.0462726537470784196.809471994010
Trimmed Mean ( 17 / 20 )9.118518518518520.0392366757600833232.397835491330
Trimmed Mean ( 18 / 20 )9.1320.032285.375
Trimmed Mean ( 19 / 20 )9.134782608695650.0292249660800217312.567774541926
Trimmed Mean ( 20 / 20 )9.133333333333330.0270214494459259338.00308719969
Median9.1
Midrange8.85
Midmean - Weighted Average at Xnp9.08181818181818
Midmean - Weighted Average at X(n+1)p9.08181818181818
Midmean - Empirical Distribution Function9.08181818181818
Midmean - Empirical Distribution Function - Averaging9.08181818181818
Midmean - Empirical Distribution Function - Interpolation9.08181818181818
Midmean - Closest Observation9.08181818181818
Midmean - True Basic - Statistics Graphics Toolkit9.08181818181818
Midmean - MS Excel (old versions)9.08181818181818
Number of observations61



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')