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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 10 Dec 2007 13:18:37 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/10/t1197317056anb77x74b80mmbd.htm/, Retrieved Mon, 06 May 2024 21:30:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3040, Retrieved Mon, 06 May 2024 21:30:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact204
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency 3] [2007-12-10 20:18:37] [6b5c00822e2ce0f7cf73539c28d95782] [Current]
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Dataseries X:
103,7
103,75
103,85
104,02
104,13
104,17
104,18
104,2
104,5
104,78
104,88
104,89
104,9
104,95
105,24
105,35
105,44
105,46
105,47
105,48
105,75
106,1
106,19
106,23
106,24
106,25
106,35
106,48
106,52
106,55
106,55
106,56
106,89
107,09
107,24
107,28
107,3
107,31
107,47
107,35
107,31
107,32
107,32
107,34
107,53
107,72
107,75
107,79
107,81
107,9
107,8
107,86
107,8
107,74
107,75
107,83
107,8
107,81
107,86
107,83




Summary of compuational 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 compuational 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=3040&T=0

[TABLE]
[ROW][C]Summary of compuational 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=3040&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3040&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 compuational 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 Mean106.34850.174845666409399608.242126807914
Geometric Mean106.339981933457
Harmonic Mean106.331426285358
Quadratic Mean106.356979750587
Winsorized Mean ( 1 / 20 )106.3486666666670.174534484421715609.327532143756
Winsorized Mean ( 2 / 20 )106.3520.173706974512684612.249452264993
Winsorized Mean ( 3 / 20 )106.3590.171467033282858620.288331603348
Winsorized Mean ( 4 / 20 )106.3663333333330.169800641941562626.418911713774
Winsorized Mean ( 5 / 20 )106.3680.168818392710966630.073526301796
Winsorized Mean ( 6 / 20 )106.3690.168598024262773630.903004143249
Winsorized Mean ( 7 / 20 )106.3701666666670.167917031514653633.468598790614
Winsorized Mean ( 8 / 20 )106.4101666666670.159467243624129667.28542017996
Winsorized Mean ( 9 / 20 )106.4521666666670.151260259803614703.768238960298
Winsorized Mean ( 10 / 20 )106.4671666666670.147930754083681719.70948384702
Winsorized Mean ( 11 / 20 )106.4616666666670.146495052396481726.725339355036
Winsorized Mean ( 12 / 20 )106.4636666666670.146131851048196728.545254870917
Winsorized Mean ( 13 / 20 )106.4723333333330.143854400392345740.139565025078
Winsorized Mean ( 14 / 20 )106.5353333333330.131409883337574810.710204038906
Winsorized Mean ( 15 / 20 )106.5153333333330.119795604332237889.142251312723
Winsorized Mean ( 16 / 20 )106.5233333333330.113597482134374937.726183114937
Winsorized Mean ( 17 / 20 )106.4950.107993905456832986.120462534514
Winsorized Mean ( 18 / 20 )106.4950.107105075393939994.3039543953
Winsorized Mean ( 19 / 20 )106.4918333333330.1057476720815121007.03714074431
Winsorized Mean ( 20 / 20 )106.5818333333330.09148878220472251164.97160378458
Trimmed Mean ( 1 / 20 )106.3674137931030.172854501783265615.358076855139
Trimmed Mean ( 2 / 20 )106.38750.170634463488095623.481902924156
Trimmed Mean ( 3 / 20 )106.4072222222220.168283025188233632.311084871455
Trimmed Mean ( 4 / 20 )106.4257692307690.166260972183284640.112756669357
Trimmed Mean ( 5 / 20 )106.44360.164192709077735648.28457120837
Trimmed Mean ( 6 / 20 )106.46250.161712768523534658.343190658483
Trimmed Mean ( 7 / 20 )106.4828260869570.158422374061351672.145122921336
Trimmed Mean ( 8 / 20 )106.5047727272730.154195548890728690.712368116075
Trimmed Mean ( 9 / 20 )106.5216666666670.151024344695383705.32778593757
Trimmed Mean ( 10 / 20 )106.533250.148934414880838715.303108990875
Trimmed Mean ( 11 / 20 )106.5436842105260.146767648621009725.934395022224
Trimmed Mean ( 12 / 20 )106.5561111111110.143899368374899740.490471323696
Trimmed Mean ( 13 / 20 )106.5697058823530.139762011428441762.508386886785
Trimmed Mean ( 14 / 20 )106.583750.134393612739450793.071544304971
Trimmed Mean ( 15 / 20 )106.5906666666670.130511754289270816.71315543285
Trimmed Mean ( 16 / 20 )106.6014285714290.128040496947859832.560253298919
Trimmed Mean ( 17 / 20 )106.6126923076920.125805170117934847.442853165333
Trimmed Mean ( 18 / 20 )106.630.123417519250595863.977826223289
Trimmed Mean ( 19 / 20 )106.6504545454550.119061040172236895.762832167194
Trimmed Mean ( 20 / 20 )106.67550.111429645020855957.33500703547
Median106.55
Midrange105.8
Midmean - Weighted Average at Xnp106.547096774194
Midmean - Weighted Average at X(n+1)p106.590666666667
Midmean - Empirical Distribution Function106.547096774194
Midmean - Empirical Distribution Function - Averaging106.590666666667
Midmean - Empirical Distribution Function - Interpolation106.590666666667
Midmean - Closest Observation106.547096774194
Midmean - True Basic - Statistics Graphics Toolkit106.590666666667
Midmean - MS Excel (old versions)106.58375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 106.3485 & 0.174845666409399 & 608.242126807914 \tabularnewline
Geometric Mean & 106.339981933457 &  &  \tabularnewline
Harmonic Mean & 106.331426285358 &  &  \tabularnewline
Quadratic Mean & 106.356979750587 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 106.348666666667 & 0.174534484421715 & 609.327532143756 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 106.352 & 0.173706974512684 & 612.249452264993 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 106.359 & 0.171467033282858 & 620.288331603348 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 106.366333333333 & 0.169800641941562 & 626.418911713774 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 106.368 & 0.168818392710966 & 630.073526301796 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 106.369 & 0.168598024262773 & 630.903004143249 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 106.370166666667 & 0.167917031514653 & 633.468598790614 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 106.410166666667 & 0.159467243624129 & 667.28542017996 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 106.452166666667 & 0.151260259803614 & 703.768238960298 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 106.467166666667 & 0.147930754083681 & 719.70948384702 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 106.461666666667 & 0.146495052396481 & 726.725339355036 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 106.463666666667 & 0.146131851048196 & 728.545254870917 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 106.472333333333 & 0.143854400392345 & 740.139565025078 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 106.535333333333 & 0.131409883337574 & 810.710204038906 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 106.515333333333 & 0.119795604332237 & 889.142251312723 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 106.523333333333 & 0.113597482134374 & 937.726183114937 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 106.495 & 0.107993905456832 & 986.120462534514 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 106.495 & 0.107105075393939 & 994.3039543953 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 106.491833333333 & 0.105747672081512 & 1007.03714074431 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 106.581833333333 & 0.0914887822047225 & 1164.97160378458 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 106.367413793103 & 0.172854501783265 & 615.358076855139 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 106.3875 & 0.170634463488095 & 623.481902924156 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 106.407222222222 & 0.168283025188233 & 632.311084871455 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 106.425769230769 & 0.166260972183284 & 640.112756669357 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 106.4436 & 0.164192709077735 & 648.28457120837 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 106.4625 & 0.161712768523534 & 658.343190658483 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 106.482826086957 & 0.158422374061351 & 672.145122921336 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 106.504772727273 & 0.154195548890728 & 690.712368116075 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 106.521666666667 & 0.151024344695383 & 705.32778593757 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 106.53325 & 0.148934414880838 & 715.303108990875 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 106.543684210526 & 0.146767648621009 & 725.934395022224 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 106.556111111111 & 0.143899368374899 & 740.490471323696 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 106.569705882353 & 0.139762011428441 & 762.508386886785 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 106.58375 & 0.134393612739450 & 793.071544304971 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 106.590666666667 & 0.130511754289270 & 816.71315543285 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 106.601428571429 & 0.128040496947859 & 832.560253298919 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 106.612692307692 & 0.125805170117934 & 847.442853165333 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 106.63 & 0.123417519250595 & 863.977826223289 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 106.650454545455 & 0.119061040172236 & 895.762832167194 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 106.6755 & 0.111429645020855 & 957.33500703547 \tabularnewline
Median & 106.55 &  &  \tabularnewline
Midrange & 105.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 106.547096774194 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 106.590666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 106.547096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 106.590666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 106.590666666667 &  &  \tabularnewline
Midmean - Closest Observation & 106.547096774194 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 106.590666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 106.58375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3040&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]106.3485[/C][C]0.174845666409399[/C][C]608.242126807914[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]106.339981933457[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]106.331426285358[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]106.356979750587[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]106.348666666667[/C][C]0.174534484421715[/C][C]609.327532143756[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]106.352[/C][C]0.173706974512684[/C][C]612.249452264993[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]106.359[/C][C]0.171467033282858[/C][C]620.288331603348[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]106.366333333333[/C][C]0.169800641941562[/C][C]626.418911713774[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]106.368[/C][C]0.168818392710966[/C][C]630.073526301796[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]106.369[/C][C]0.168598024262773[/C][C]630.903004143249[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]106.370166666667[/C][C]0.167917031514653[/C][C]633.468598790614[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]106.410166666667[/C][C]0.159467243624129[/C][C]667.28542017996[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]106.452166666667[/C][C]0.151260259803614[/C][C]703.768238960298[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]106.467166666667[/C][C]0.147930754083681[/C][C]719.70948384702[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]106.461666666667[/C][C]0.146495052396481[/C][C]726.725339355036[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]106.463666666667[/C][C]0.146131851048196[/C][C]728.545254870917[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]106.472333333333[/C][C]0.143854400392345[/C][C]740.139565025078[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]106.535333333333[/C][C]0.131409883337574[/C][C]810.710204038906[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]106.515333333333[/C][C]0.119795604332237[/C][C]889.142251312723[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]106.523333333333[/C][C]0.113597482134374[/C][C]937.726183114937[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]106.495[/C][C]0.107993905456832[/C][C]986.120462534514[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]106.495[/C][C]0.107105075393939[/C][C]994.3039543953[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]106.491833333333[/C][C]0.105747672081512[/C][C]1007.03714074431[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]106.581833333333[/C][C]0.0914887822047225[/C][C]1164.97160378458[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]106.367413793103[/C][C]0.172854501783265[/C][C]615.358076855139[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]106.3875[/C][C]0.170634463488095[/C][C]623.481902924156[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]106.407222222222[/C][C]0.168283025188233[/C][C]632.311084871455[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]106.425769230769[/C][C]0.166260972183284[/C][C]640.112756669357[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]106.4436[/C][C]0.164192709077735[/C][C]648.28457120837[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]106.4625[/C][C]0.161712768523534[/C][C]658.343190658483[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]106.482826086957[/C][C]0.158422374061351[/C][C]672.145122921336[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]106.504772727273[/C][C]0.154195548890728[/C][C]690.712368116075[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]106.521666666667[/C][C]0.151024344695383[/C][C]705.32778593757[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]106.53325[/C][C]0.148934414880838[/C][C]715.303108990875[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]106.543684210526[/C][C]0.146767648621009[/C][C]725.934395022224[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]106.556111111111[/C][C]0.143899368374899[/C][C]740.490471323696[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]106.569705882353[/C][C]0.139762011428441[/C][C]762.508386886785[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]106.58375[/C][C]0.134393612739450[/C][C]793.071544304971[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]106.590666666667[/C][C]0.130511754289270[/C][C]816.71315543285[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]106.601428571429[/C][C]0.128040496947859[/C][C]832.560253298919[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]106.612692307692[/C][C]0.125805170117934[/C][C]847.442853165333[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]106.63[/C][C]0.123417519250595[/C][C]863.977826223289[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]106.650454545455[/C][C]0.119061040172236[/C][C]895.762832167194[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]106.6755[/C][C]0.111429645020855[/C][C]957.33500703547[/C][/ROW]
[ROW][C]Median[/C][C]106.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]105.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]106.547096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]106.590666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]106.547096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]106.590666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]106.590666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]106.547096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]106.590666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]106.58375[/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=3040&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3040&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 Mean106.34850.174845666409399608.242126807914
Geometric Mean106.339981933457
Harmonic Mean106.331426285358
Quadratic Mean106.356979750587
Winsorized Mean ( 1 / 20 )106.3486666666670.174534484421715609.327532143756
Winsorized Mean ( 2 / 20 )106.3520.173706974512684612.249452264993
Winsorized Mean ( 3 / 20 )106.3590.171467033282858620.288331603348
Winsorized Mean ( 4 / 20 )106.3663333333330.169800641941562626.418911713774
Winsorized Mean ( 5 / 20 )106.3680.168818392710966630.073526301796
Winsorized Mean ( 6 / 20 )106.3690.168598024262773630.903004143249
Winsorized Mean ( 7 / 20 )106.3701666666670.167917031514653633.468598790614
Winsorized Mean ( 8 / 20 )106.4101666666670.159467243624129667.28542017996
Winsorized Mean ( 9 / 20 )106.4521666666670.151260259803614703.768238960298
Winsorized Mean ( 10 / 20 )106.4671666666670.147930754083681719.70948384702
Winsorized Mean ( 11 / 20 )106.4616666666670.146495052396481726.725339355036
Winsorized Mean ( 12 / 20 )106.4636666666670.146131851048196728.545254870917
Winsorized Mean ( 13 / 20 )106.4723333333330.143854400392345740.139565025078
Winsorized Mean ( 14 / 20 )106.5353333333330.131409883337574810.710204038906
Winsorized Mean ( 15 / 20 )106.5153333333330.119795604332237889.142251312723
Winsorized Mean ( 16 / 20 )106.5233333333330.113597482134374937.726183114937
Winsorized Mean ( 17 / 20 )106.4950.107993905456832986.120462534514
Winsorized Mean ( 18 / 20 )106.4950.107105075393939994.3039543953
Winsorized Mean ( 19 / 20 )106.4918333333330.1057476720815121007.03714074431
Winsorized Mean ( 20 / 20 )106.5818333333330.09148878220472251164.97160378458
Trimmed Mean ( 1 / 20 )106.3674137931030.172854501783265615.358076855139
Trimmed Mean ( 2 / 20 )106.38750.170634463488095623.481902924156
Trimmed Mean ( 3 / 20 )106.4072222222220.168283025188233632.311084871455
Trimmed Mean ( 4 / 20 )106.4257692307690.166260972183284640.112756669357
Trimmed Mean ( 5 / 20 )106.44360.164192709077735648.28457120837
Trimmed Mean ( 6 / 20 )106.46250.161712768523534658.343190658483
Trimmed Mean ( 7 / 20 )106.4828260869570.158422374061351672.145122921336
Trimmed Mean ( 8 / 20 )106.5047727272730.154195548890728690.712368116075
Trimmed Mean ( 9 / 20 )106.5216666666670.151024344695383705.32778593757
Trimmed Mean ( 10 / 20 )106.533250.148934414880838715.303108990875
Trimmed Mean ( 11 / 20 )106.5436842105260.146767648621009725.934395022224
Trimmed Mean ( 12 / 20 )106.5561111111110.143899368374899740.490471323696
Trimmed Mean ( 13 / 20 )106.5697058823530.139762011428441762.508386886785
Trimmed Mean ( 14 / 20 )106.583750.134393612739450793.071544304971
Trimmed Mean ( 15 / 20 )106.5906666666670.130511754289270816.71315543285
Trimmed Mean ( 16 / 20 )106.6014285714290.128040496947859832.560253298919
Trimmed Mean ( 17 / 20 )106.6126923076920.125805170117934847.442853165333
Trimmed Mean ( 18 / 20 )106.630.123417519250595863.977826223289
Trimmed Mean ( 19 / 20 )106.6504545454550.119061040172236895.762832167194
Trimmed Mean ( 20 / 20 )106.67550.111429645020855957.33500703547
Median106.55
Midrange105.8
Midmean - Weighted Average at Xnp106.547096774194
Midmean - Weighted Average at X(n+1)p106.590666666667
Midmean - Empirical Distribution Function106.547096774194
Midmean - Empirical Distribution Function - Averaging106.590666666667
Midmean - Empirical Distribution Function - Interpolation106.590666666667
Midmean - Closest Observation106.547096774194
Midmean - True Basic - Statistics Graphics Toolkit106.590666666667
Midmean - MS Excel (old versions)106.58375
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')