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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 computationTue, 20 Oct 2009 09:50:35 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t12560540468eqmmzrcco4fxfk.htm/, Retrieved Thu, 02 May 2024 15:55:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48763, Retrieved Thu, 02 May 2024 15:55:49 +0000
QR Codes:

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)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD      [Univariate Explorative Data Analysis] [SHWS] [2009-10-19 19:25:48] [a66d3a79ef9e5308cd94a469bc5ca464]
- RMPD          [Central Tendency] [SHWWS3part3] [2009-10-20 15:50:35] [db49399df1e4a3dbe31268849cebfd7f] [Current]
Feedback Forum

Post a new message
Dataseries X:
14.30
3.64
4.26
6.55
4.43
1.47
-2.65
-1.47
-2.02
-4.02
3.64
3.98
3.33
6.93
3.80
-0.57
-2.02
-2.44
-0.21
-3.28
-4.94
-3.18
4.66
6.82
10.14
8.15
2.68
0.23
3.56
1.15
-0.43
-1.22
0.72
0.12
9.51
12.56
8.41
-0.68
-6.43
-7.48
-8.97
-10.03
-13.22
-12.82
-16.23
-16.91
-13.38
-11.85
-12.47
-12.04
-7.87
-5.30
-1.48
-0.12
13.47
11.56
26.93
74.93
408.60
77.32




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48763&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48763&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48763&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9.2027.080133165302621.29969306864113
Geometric MeanNaN
Harmonic Mean-10.9014264885055
Quadratic Mean55.156555881116
Winsorized Mean ( 1 / 20 )3.6922.419248071537601.52609401385343
Winsorized Mean ( 2 / 20 )3.707333333333332.365920669408841.56697279890609
Winsorized Mean ( 3 / 20 )1.315333333333331.286136474879341.02270121330377
Winsorized Mean ( 4 / 20 )0.51.038779569663500.481334071830051
Winsorized Mean ( 5 / 20 )0.461.017180661030840.452230383080447
Winsorized Mean ( 6 / 20 )0.4120.9886125299950820.416745678918362
Winsorized Mean ( 7 / 20 )0.31750.9601315712863480.330683845313643
Winsorized Mean ( 8 / 20 )0.3708333333333340.8726980791673010.424927408671702
Winsorized Mean ( 9 / 20 )0.4353333333333330.823434226074210.528680153858579
Winsorized Mean ( 10 / 20 )0.4353333333333330.7550050498078840.576596584942189
Winsorized Mean ( 11 / 20 )0.4591666666666670.7332736092140970.626187361575428
Winsorized Mean ( 12 / 20 )0.4251666666666670.6529355914137620.651161725992113
Winsorized Mean ( 13 / 20 )0.6461666666666670.6066970917279161.06505647624969
Winsorized Mean ( 14 / 20 )0.6671666666666660.5820296210290151.14627613881082
Winsorized Mean ( 15 / 20 )0.4246666666666670.4674850652719870.908406916528108
Winsorized Mean ( 16 / 20 )0.5606666666666670.4270898016597121.31276060558660
Winsorized Mean ( 17 / 20 )0.5408333333333330.4154266945108861.30187429089047
Winsorized Mean ( 18 / 20 )0.6158333333333330.3790331359831991.62474800979045
Winsorized Mean ( 19 / 20 )0.6253333333333330.3608503349291171.73294375202997
Winsorized Mean ( 20 / 20 )0.7120.3330766356227052.13764618664674
Trimmed Mean ( 1 / 20 )2.766034482758622.119471306019271.30505870728380
Trimmed Mean ( 2 / 20 )1.773928571428571.69766971070951.04491972745817
Trimmed Mean ( 3 / 20 )0.6998148148148151.062850336560790.658432133614695
Trimmed Mean ( 4 / 20 )0.4630769230769230.9410134029970170.492104492456832
Trimmed Mean ( 5 / 20 )0.4520.8990824801554350.502734743448518
Trimmed Mean ( 6 / 20 )0.450.8536553650446430.527144815608892
Trimmed Mean ( 7 / 20 )0.4582608695652170.8049826297731550.569280444839357
Trimmed Mean ( 8 / 20 )0.4856818181818180.7508201574616010.646868379005471
Trimmed Mean ( 9 / 20 )0.5061904761904760.7078356004117980.715124353587173
Trimmed Mean ( 10 / 20 )0.5180.6659788631434530.777802462911532
Trimmed Mean ( 11 / 20 )0.5310526315789470.6306845373880530.84202576739597
Trimmed Mean ( 12 / 20 )0.5419444444444440.5889357929059710.9202097256992
Trimmed Mean ( 13 / 20 )0.5591176470588230.556600223544461.00452285753378
Trimmed Mean ( 14 / 20 )0.54656250.5256207178061.03984200295874
Trimmed Mean ( 15 / 20 )0.5293333333333330.4888579074126211.08279589080381
Trimmed Mean ( 16 / 20 )0.5442857142857140.4744103632339461.14728883782269
Trimmed Mean ( 17 / 20 )0.5419230769230770.4647997150901981.16592816073029
Trimmed Mean ( 18 / 20 )0.5420833333333330.4519450633404221.19944519213614
Trimmed Mean ( 19 / 20 )0.5309090909090910.4431708401348721.19797839304481
Trimmed Mean ( 20 / 20 )0.5160.4329193434056011.19190793356757
Median0
Midrange195.845
Midmean - Weighted Average at Xnp0.352903225806452
Midmean - Weighted Average at X(n+1)p0.529333333333333
Midmean - Empirical Distribution Function0.352903225806452
Midmean - Empirical Distribution Function - Averaging0.529333333333333
Midmean - Empirical Distribution Function - Interpolation0.529333333333333
Midmean - Closest Observation0.352903225806452
Midmean - True Basic - Statistics Graphics Toolkit0.529333333333333
Midmean - MS Excel (old versions)0.5465625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9.202 & 7.08013316530262 & 1.29969306864113 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -10.9014264885055 &  &  \tabularnewline
Quadratic Mean & 55.156555881116 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3.692 & 2.41924807153760 & 1.52609401385343 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3.70733333333333 & 2.36592066940884 & 1.56697279890609 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.31533333333333 & 1.28613647487934 & 1.02270121330377 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.5 & 1.03877956966350 & 0.481334071830051 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.46 & 1.01718066103084 & 0.452230383080447 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.412 & 0.988612529995082 & 0.416745678918362 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.3175 & 0.960131571286348 & 0.330683845313643 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.370833333333334 & 0.872698079167301 & 0.424927408671702 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.435333333333333 & 0.82343422607421 & 0.528680153858579 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.435333333333333 & 0.755005049807884 & 0.576596584942189 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.459166666666667 & 0.733273609214097 & 0.626187361575428 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.425166666666667 & 0.652935591413762 & 0.651161725992113 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.646166666666667 & 0.606697091727916 & 1.06505647624969 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.667166666666666 & 0.582029621029015 & 1.14627613881082 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.424666666666667 & 0.467485065271987 & 0.908406916528108 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.560666666666667 & 0.427089801659712 & 1.31276060558660 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.540833333333333 & 0.415426694510886 & 1.30187429089047 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.615833333333333 & 0.379033135983199 & 1.62474800979045 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.625333333333333 & 0.360850334929117 & 1.73294375202997 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.712 & 0.333076635622705 & 2.13764618664674 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.76603448275862 & 2.11947130601927 & 1.30505870728380 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.77392857142857 & 1.6976697107095 & 1.04491972745817 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.699814814814815 & 1.06285033656079 & 0.658432133614695 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.463076923076923 & 0.941013402997017 & 0.492104492456832 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.452 & 0.899082480155435 & 0.502734743448518 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.45 & 0.853655365044643 & 0.527144815608892 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.458260869565217 & 0.804982629773155 & 0.569280444839357 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.485681818181818 & 0.750820157461601 & 0.646868379005471 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.506190476190476 & 0.707835600411798 & 0.715124353587173 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.518 & 0.665978863143453 & 0.777802462911532 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.531052631578947 & 0.630684537388053 & 0.84202576739597 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.541944444444444 & 0.588935792905971 & 0.9202097256992 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.559117647058823 & 0.55660022354446 & 1.00452285753378 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.5465625 & 0.525620717806 & 1.03984200295874 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.529333333333333 & 0.488857907412621 & 1.08279589080381 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.544285714285714 & 0.474410363233946 & 1.14728883782269 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.541923076923077 & 0.464799715090198 & 1.16592816073029 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.542083333333333 & 0.451945063340422 & 1.19944519213614 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.530909090909091 & 0.443170840134872 & 1.19797839304481 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.516 & 0.432919343405601 & 1.19190793356757 \tabularnewline
Median & 0 &  &  \tabularnewline
Midrange & 195.845 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.352903225806452 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.529333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.352903225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.529333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.529333333333333 &  &  \tabularnewline
Midmean - Closest Observation & 0.352903225806452 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.529333333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.5465625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48763&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]9.202[/C][C]7.08013316530262[/C][C]1.29969306864113[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-10.9014264885055[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]55.156555881116[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3.692[/C][C]2.41924807153760[/C][C]1.52609401385343[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3.70733333333333[/C][C]2.36592066940884[/C][C]1.56697279890609[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.31533333333333[/C][C]1.28613647487934[/C][C]1.02270121330377[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.5[/C][C]1.03877956966350[/C][C]0.481334071830051[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.46[/C][C]1.01718066103084[/C][C]0.452230383080447[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.412[/C][C]0.988612529995082[/C][C]0.416745678918362[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.3175[/C][C]0.960131571286348[/C][C]0.330683845313643[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.370833333333334[/C][C]0.872698079167301[/C][C]0.424927408671702[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.435333333333333[/C][C]0.82343422607421[/C][C]0.528680153858579[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.435333333333333[/C][C]0.755005049807884[/C][C]0.576596584942189[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.459166666666667[/C][C]0.733273609214097[/C][C]0.626187361575428[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.425166666666667[/C][C]0.652935591413762[/C][C]0.651161725992113[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.646166666666667[/C][C]0.606697091727916[/C][C]1.06505647624969[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.667166666666666[/C][C]0.582029621029015[/C][C]1.14627613881082[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.424666666666667[/C][C]0.467485065271987[/C][C]0.908406916528108[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.560666666666667[/C][C]0.427089801659712[/C][C]1.31276060558660[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.540833333333333[/C][C]0.415426694510886[/C][C]1.30187429089047[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.615833333333333[/C][C]0.379033135983199[/C][C]1.62474800979045[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.625333333333333[/C][C]0.360850334929117[/C][C]1.73294375202997[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.712[/C][C]0.333076635622705[/C][C]2.13764618664674[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.76603448275862[/C][C]2.11947130601927[/C][C]1.30505870728380[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.77392857142857[/C][C]1.6976697107095[/C][C]1.04491972745817[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.699814814814815[/C][C]1.06285033656079[/C][C]0.658432133614695[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.463076923076923[/C][C]0.941013402997017[/C][C]0.492104492456832[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.452[/C][C]0.899082480155435[/C][C]0.502734743448518[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.45[/C][C]0.853655365044643[/C][C]0.527144815608892[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.458260869565217[/C][C]0.804982629773155[/C][C]0.569280444839357[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.485681818181818[/C][C]0.750820157461601[/C][C]0.646868379005471[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.506190476190476[/C][C]0.707835600411798[/C][C]0.715124353587173[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.518[/C][C]0.665978863143453[/C][C]0.777802462911532[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.531052631578947[/C][C]0.630684537388053[/C][C]0.84202576739597[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.541944444444444[/C][C]0.588935792905971[/C][C]0.9202097256992[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.559117647058823[/C][C]0.55660022354446[/C][C]1.00452285753378[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.5465625[/C][C]0.525620717806[/C][C]1.03984200295874[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.529333333333333[/C][C]0.488857907412621[/C][C]1.08279589080381[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.544285714285714[/C][C]0.474410363233946[/C][C]1.14728883782269[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.541923076923077[/C][C]0.464799715090198[/C][C]1.16592816073029[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.542083333333333[/C][C]0.451945063340422[/C][C]1.19944519213614[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.530909090909091[/C][C]0.443170840134872[/C][C]1.19797839304481[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.516[/C][C]0.432919343405601[/C][C]1.19190793356757[/C][/ROW]
[ROW][C]Median[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]195.845[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.352903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.529333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.352903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.529333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.529333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.352903225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.529333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.5465625[/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=48763&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48763&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 Mean9.2027.080133165302621.29969306864113
Geometric MeanNaN
Harmonic Mean-10.9014264885055
Quadratic Mean55.156555881116
Winsorized Mean ( 1 / 20 )3.6922.419248071537601.52609401385343
Winsorized Mean ( 2 / 20 )3.707333333333332.365920669408841.56697279890609
Winsorized Mean ( 3 / 20 )1.315333333333331.286136474879341.02270121330377
Winsorized Mean ( 4 / 20 )0.51.038779569663500.481334071830051
Winsorized Mean ( 5 / 20 )0.461.017180661030840.452230383080447
Winsorized Mean ( 6 / 20 )0.4120.9886125299950820.416745678918362
Winsorized Mean ( 7 / 20 )0.31750.9601315712863480.330683845313643
Winsorized Mean ( 8 / 20 )0.3708333333333340.8726980791673010.424927408671702
Winsorized Mean ( 9 / 20 )0.4353333333333330.823434226074210.528680153858579
Winsorized Mean ( 10 / 20 )0.4353333333333330.7550050498078840.576596584942189
Winsorized Mean ( 11 / 20 )0.4591666666666670.7332736092140970.626187361575428
Winsorized Mean ( 12 / 20 )0.4251666666666670.6529355914137620.651161725992113
Winsorized Mean ( 13 / 20 )0.6461666666666670.6066970917279161.06505647624969
Winsorized Mean ( 14 / 20 )0.6671666666666660.5820296210290151.14627613881082
Winsorized Mean ( 15 / 20 )0.4246666666666670.4674850652719870.908406916528108
Winsorized Mean ( 16 / 20 )0.5606666666666670.4270898016597121.31276060558660
Winsorized Mean ( 17 / 20 )0.5408333333333330.4154266945108861.30187429089047
Winsorized Mean ( 18 / 20 )0.6158333333333330.3790331359831991.62474800979045
Winsorized Mean ( 19 / 20 )0.6253333333333330.3608503349291171.73294375202997
Winsorized Mean ( 20 / 20 )0.7120.3330766356227052.13764618664674
Trimmed Mean ( 1 / 20 )2.766034482758622.119471306019271.30505870728380
Trimmed Mean ( 2 / 20 )1.773928571428571.69766971070951.04491972745817
Trimmed Mean ( 3 / 20 )0.6998148148148151.062850336560790.658432133614695
Trimmed Mean ( 4 / 20 )0.4630769230769230.9410134029970170.492104492456832
Trimmed Mean ( 5 / 20 )0.4520.8990824801554350.502734743448518
Trimmed Mean ( 6 / 20 )0.450.8536553650446430.527144815608892
Trimmed Mean ( 7 / 20 )0.4582608695652170.8049826297731550.569280444839357
Trimmed Mean ( 8 / 20 )0.4856818181818180.7508201574616010.646868379005471
Trimmed Mean ( 9 / 20 )0.5061904761904760.7078356004117980.715124353587173
Trimmed Mean ( 10 / 20 )0.5180.6659788631434530.777802462911532
Trimmed Mean ( 11 / 20 )0.5310526315789470.6306845373880530.84202576739597
Trimmed Mean ( 12 / 20 )0.5419444444444440.5889357929059710.9202097256992
Trimmed Mean ( 13 / 20 )0.5591176470588230.556600223544461.00452285753378
Trimmed Mean ( 14 / 20 )0.54656250.5256207178061.03984200295874
Trimmed Mean ( 15 / 20 )0.5293333333333330.4888579074126211.08279589080381
Trimmed Mean ( 16 / 20 )0.5442857142857140.4744103632339461.14728883782269
Trimmed Mean ( 17 / 20 )0.5419230769230770.4647997150901981.16592816073029
Trimmed Mean ( 18 / 20 )0.5420833333333330.4519450633404221.19944519213614
Trimmed Mean ( 19 / 20 )0.5309090909090910.4431708401348721.19797839304481
Trimmed Mean ( 20 / 20 )0.5160.4329193434056011.19190793356757
Median0
Midrange195.845
Midmean - Weighted Average at Xnp0.352903225806452
Midmean - Weighted Average at X(n+1)p0.529333333333333
Midmean - Empirical Distribution Function0.352903225806452
Midmean - Empirical Distribution Function - Averaging0.529333333333333
Midmean - Empirical Distribution Function - Interpolation0.529333333333333
Midmean - Closest Observation0.352903225806452
Midmean - True Basic - Statistics Graphics Toolkit0.529333333333333
Midmean - MS Excel (old versions)0.5465625
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')