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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, 25 Nov 2011 05:07:53 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/25/t1322215710z8dpkbxaz5dpa5g.htm/, Retrieved Thu, 18 Apr 2024 21:21:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147278, Retrieved Thu, 18 Apr 2024 21:21:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact151
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency] [2011-11-25 10:07:53] [f59ea4acf51788e47c4ec521df29536b] [Current]
- R       [Central Tendency] [] [2011-11-28 17:53:48] [74be16979710d4c4e7c6647856088456]
- R  D      [Central Tendency] [Mean ] [2011-12-10 12:04:37] [4fa66579543b578a51dd12826fe0c6d2]
- R           [Central Tendency] [Mean] [2011-12-10 12:06:58] [4fa66579543b578a51dd12826fe0c6d2]
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Dataseries X:
0
-1.948342641
-1.359385149
1.357954964
-1.700694682
1.449969008
1.319038156
2.051491606
-0.133535063
1.037244962
0.631422616
-1.637925413
-0.867991129
-1.07958031
-0.672654982
-1.05064355
0.333390996
0.487322267
-0.570817054
-0.499534007
0.115264994
1.74691902
0.739021637
0.738226066
-0.412999274
-1.583363411
-0.181363817
0.105418964
-0.463545968
-1.216121966
1.640603862
-0.052871366
1.523685005
1.083344688
-0.469412704
0.721118803
-0.943920679
-0.52258191
0.359348877
-0.247868669
0.562507598
0.648148736
-1.270108506
-0.447026313
1.78025952
0.731000414
1.581054158
-0.098455366
-0.585819713
0.397301065
0.096307367
-1.033663768
-0.793451127
0.871673984
0.803259829
1.249946587
-0.295993913
-1.450053283
0.767875716
0.609240092
0.933296633
-0.679282808
-1.196592669
0.418815652
-0.181297827
0.432789884
-0.06594299
1.739802997
0.328406732
0.120753615
-0.369205393
0.79144574
0.866899133
0.074081225
-2.264885838




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147278&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147278&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147278&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.06531626546666670.1151531466791170.567212163543178
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean0.992735869505112
Winsorized Mean ( 1 / 25 )0.06592041361333330.1132767183143350.581941413860602
Winsorized Mean ( 2 / 25 )0.07163527918666670.1115928533158710.641934291113593
Winsorized Mean ( 3 / 25 )0.07386140902666670.1110040500497980.665393821158158
Winsorized Mean ( 4 / 25 )0.07148076193333330.1093536433351140.653666030260016
Winsorized Mean ( 5 / 25 )0.07639812353333330.1068234287673430.715181345655226
Winsorized Mean ( 6 / 25 )0.07906204201333330.1045835091243580.755970445773839
Winsorized Mean ( 7 / 25 )0.08051436897333330.1017940007548260.790953969549294
Winsorized Mean ( 8 / 25 )0.076458101880.0990188133702230.772157323216242
Winsorized Mean ( 9 / 25 )0.074131600560.09779627121336420.758020726559865
Winsorized Mean ( 10 / 25 )0.08052103922666660.0935470665853050.860754293703481
Winsorized Mean ( 11 / 25 )0.06033015217333330.08886424839180750.678902407493892
Winsorized Mean ( 12 / 25 )0.05567096113333330.08727122719871190.637907394227121
Winsorized Mean ( 13 / 25 )0.05320871953333340.08200238563136840.648867946019602
Winsorized Mean ( 14 / 25 )0.05587934105333330.07805663847776010.715881981892603
Winsorized Mean ( 15 / 25 )0.06983237125333330.07557768022091510.923981406272485
Winsorized Mean ( 16 / 25 )0.08061189445333330.06999234849357541.15172438399796
Winsorized Mean ( 17 / 25 )0.07943634150666670.06939968995353521.14462098548065
Winsorized Mean ( 18 / 25 )0.09462000030666670.06562760084699431.44177143588208
Winsorized Mean ( 19 / 25 )0.09111097390666660.06409003758722341.42160899473134
Winsorized Mean ( 20 / 25 )0.1037615267066670.06228907340148121.66580623278623
Winsorized Mean ( 21 / 25 )0.1081917569866670.06113864063205071.76961338800113
Winsorized Mean ( 22 / 25 )0.1141287333066670.05956110068148641.91616226028109
Winsorized Mean ( 23 / 25 )0.09355037846666670.05628969954311621.66194488913571
Winsorized Mean ( 24 / 25 )0.09348430966666670.05487348153762511.7036336504832
Winsorized Mean ( 25 / 25 )0.09743248133333330.05239392980299351.85961392282826
Trimmed Mean ( 1 / 25 )0.07002896084931510.1105352415662880.633544196918578
Trimmed Mean ( 2 / 25 )0.07436897553521130.1072971076398310.693112584030213
Trimmed Mean ( 3 / 25 )0.07585468007246380.1045323482563170.725657476731179
Trimmed Mean ( 4 / 25 )0.07659843792537310.1015080057177670.754604894301122
Trimmed Mean ( 5 / 25 )0.07807469061538460.09850079104732220.792630087385548
Trimmed Mean ( 6 / 25 )0.07847387325396820.095693062854510.820058120339178
Trimmed Mean ( 7 / 25 )0.07835334686885250.0929360218127770.843089098721033
Trimmed Mean ( 8 / 25 )0.0779609094406780.09031426593647240.863218104385814
Trimmed Mean ( 9 / 25 )0.07820808173684210.08778654203271910.890889194697896
Trimmed Mean ( 10 / 25 )0.07882573040.0849525065447990.927879983840523
Trimmed Mean ( 11 / 25 )0.07858582820754720.08241819973390640.953500907096584
Trimmed Mean ( 12 / 25 )0.08102642660784310.08028342551258191.00925472587296
Trimmed Mean ( 13 / 25 )0.08426054210204080.07791512099031631.08144017529682
Trimmed Mean ( 14 / 25 )0.08807214061702130.07603659253834841.15828626292798
Trimmed Mean ( 15 / 25 )0.09190461675555560.07443725003776341.23465894708537
Trimmed Mean ( 16 / 25 )0.09447115693023260.07285597589852081.29668370734364
Trimmed Mean ( 17 / 25 )0.09605567626829270.07192923455030741.33541913616655
Trimmed Mean ( 18 / 25 )0.09793569151282050.07071275352485541.38497918170301
Trimmed Mean ( 19 / 25 )0.09830908016216220.0698243653279931.40794806655764
Trimmed Mean ( 20 / 25 )0.09912089665714290.06881850020445951.44032340668069
Trimmed Mean ( 21 / 25 )0.09859355233333330.06770622488867871.45619627287504
Trimmed Mean ( 22 / 25 )0.09748776838709680.06626041333476131.47128222540008
Trimmed Mean ( 23 / 25 )0.09553154210344830.06444828967643631.48229755332633
Trimmed Mean ( 24 / 25 )0.09577081307407410.06264304027277951.52883405174844
Trimmed Mean ( 25 / 25 )0.0960566260.06018305452178661.59607428973594
Median0.096307367
Midrange-0.106697116
Midmean - Weighted Average at Xnp0.0803056908684211
Midmean - Weighted Average at X(n+1)p0.0979356915128206
Midmean - Empirical Distribution Function0.0979356915128206
Midmean - Empirical Distribution Function - Averaging0.0979356915128206
Midmean - Empirical Distribution Function - Interpolation0.0983090801621622
Midmean - Closest Observation0.0803056908684211
Midmean - True Basic - Statistics Graphics Toolkit0.0979356915128206
Midmean - MS Excel (old versions)0.0979356915128206
Number of observations75

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.0653162654666667 & 0.115153146679117 & 0.567212163543178 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 0.992735869505112 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 0.0659204136133333 & 0.113276718314335 & 0.581941413860602 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 0.0716352791866667 & 0.111592853315871 & 0.641934291113593 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 0.0738614090266667 & 0.111004050049798 & 0.665393821158158 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 0.0714807619333333 & 0.109353643335114 & 0.653666030260016 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 0.0763981235333333 & 0.106823428767343 & 0.715181345655226 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 0.0790620420133333 & 0.104583509124358 & 0.755970445773839 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 0.0805143689733333 & 0.101794000754826 & 0.790953969549294 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 0.07645810188 & 0.099018813370223 & 0.772157323216242 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 0.07413160056 & 0.0977962712133642 & 0.758020726559865 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 0.0805210392266666 & 0.093547066585305 & 0.860754293703481 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 0.0603301521733333 & 0.0888642483918075 & 0.678902407493892 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 0.0556709611333333 & 0.0872712271987119 & 0.637907394227121 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 0.0532087195333334 & 0.0820023856313684 & 0.648867946019602 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 0.0558793410533333 & 0.0780566384777601 & 0.715881981892603 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 0.0698323712533333 & 0.0755776802209151 & 0.923981406272485 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 0.0806118944533333 & 0.0699923484935754 & 1.15172438399796 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 0.0794363415066667 & 0.0693996899535352 & 1.14462098548065 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 0.0946200003066667 & 0.0656276008469943 & 1.44177143588208 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 0.0911109739066666 & 0.0640900375872234 & 1.42160899473134 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 0.103761526706667 & 0.0622890734014812 & 1.66580623278623 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 0.108191756986667 & 0.0611386406320507 & 1.76961338800113 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 0.114128733306667 & 0.0595611006814864 & 1.91616226028109 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 0.0935503784666667 & 0.0562896995431162 & 1.66194488913571 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 0.0934843096666667 & 0.0548734815376251 & 1.7036336504832 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 0.0974324813333333 & 0.0523939298029935 & 1.85961392282826 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 0.0700289608493151 & 0.110535241566288 & 0.633544196918578 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 0.0743689755352113 & 0.107297107639831 & 0.693112584030213 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 0.0758546800724638 & 0.104532348256317 & 0.725657476731179 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 0.0765984379253731 & 0.101508005717767 & 0.754604894301122 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 0.0780746906153846 & 0.0985007910473222 & 0.792630087385548 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 0.0784738732539682 & 0.09569306285451 & 0.820058120339178 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 0.0783533468688525 & 0.092936021812777 & 0.843089098721033 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 0.077960909440678 & 0.0903142659364724 & 0.863218104385814 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 0.0782080817368421 & 0.0877865420327191 & 0.890889194697896 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 0.0788257304 & 0.084952506544799 & 0.927879983840523 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 0.0785858282075472 & 0.0824181997339064 & 0.953500907096584 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 0.0810264266078431 & 0.0802834255125819 & 1.00925472587296 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 0.0842605421020408 & 0.0779151209903163 & 1.08144017529682 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 0.0880721406170213 & 0.0760365925383484 & 1.15828626292798 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 0.0919046167555556 & 0.0744372500377634 & 1.23465894708537 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 0.0944711569302326 & 0.0728559758985208 & 1.29668370734364 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 0.0960556762682927 & 0.0719292345503074 & 1.33541913616655 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 0.0979356915128205 & 0.0707127535248554 & 1.38497918170301 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 0.0983090801621622 & 0.069824365327993 & 1.40794806655764 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 0.0991208966571429 & 0.0688185002044595 & 1.44032340668069 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 0.0985935523333333 & 0.0677062248886787 & 1.45619627287504 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 0.0974877683870968 & 0.0662604133347613 & 1.47128222540008 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 0.0955315421034483 & 0.0644482896764363 & 1.48229755332633 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 0.0957708130740741 & 0.0626430402727795 & 1.52883405174844 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 0.096056626 & 0.0601830545217866 & 1.59607428973594 \tabularnewline
Median & 0.096307367 &  &  \tabularnewline
Midrange & -0.106697116 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.0803056908684211 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.0979356915128206 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.0979356915128206 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.0979356915128206 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.0983090801621622 &  &  \tabularnewline
Midmean - Closest Observation & 0.0803056908684211 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.0979356915128206 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.0979356915128206 &  &  \tabularnewline
Number of observations & 75 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147278&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]0.0653162654666667[/C][C]0.115153146679117[/C][C]0.567212163543178[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.992735869505112[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]0.0659204136133333[/C][C]0.113276718314335[/C][C]0.581941413860602[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]0.0716352791866667[/C][C]0.111592853315871[/C][C]0.641934291113593[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]0.0738614090266667[/C][C]0.111004050049798[/C][C]0.665393821158158[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]0.0714807619333333[/C][C]0.109353643335114[/C][C]0.653666030260016[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]0.0763981235333333[/C][C]0.106823428767343[/C][C]0.715181345655226[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]0.0790620420133333[/C][C]0.104583509124358[/C][C]0.755970445773839[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]0.0805143689733333[/C][C]0.101794000754826[/C][C]0.790953969549294[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]0.07645810188[/C][C]0.099018813370223[/C][C]0.772157323216242[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]0.07413160056[/C][C]0.0977962712133642[/C][C]0.758020726559865[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]0.0805210392266666[/C][C]0.093547066585305[/C][C]0.860754293703481[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]0.0603301521733333[/C][C]0.0888642483918075[/C][C]0.678902407493892[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]0.0556709611333333[/C][C]0.0872712271987119[/C][C]0.637907394227121[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]0.0532087195333334[/C][C]0.0820023856313684[/C][C]0.648867946019602[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]0.0558793410533333[/C][C]0.0780566384777601[/C][C]0.715881981892603[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]0.0698323712533333[/C][C]0.0755776802209151[/C][C]0.923981406272485[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]0.0806118944533333[/C][C]0.0699923484935754[/C][C]1.15172438399796[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]0.0794363415066667[/C][C]0.0693996899535352[/C][C]1.14462098548065[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]0.0946200003066667[/C][C]0.0656276008469943[/C][C]1.44177143588208[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]0.0911109739066666[/C][C]0.0640900375872234[/C][C]1.42160899473134[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]0.103761526706667[/C][C]0.0622890734014812[/C][C]1.66580623278623[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]0.108191756986667[/C][C]0.0611386406320507[/C][C]1.76961338800113[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]0.114128733306667[/C][C]0.0595611006814864[/C][C]1.91616226028109[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]0.0935503784666667[/C][C]0.0562896995431162[/C][C]1.66194488913571[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]0.0934843096666667[/C][C]0.0548734815376251[/C][C]1.7036336504832[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]0.0974324813333333[/C][C]0.0523939298029935[/C][C]1.85961392282826[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]0.0700289608493151[/C][C]0.110535241566288[/C][C]0.633544196918578[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]0.0743689755352113[/C][C]0.107297107639831[/C][C]0.693112584030213[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]0.0758546800724638[/C][C]0.104532348256317[/C][C]0.725657476731179[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]0.0765984379253731[/C][C]0.101508005717767[/C][C]0.754604894301122[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]0.0780746906153846[/C][C]0.0985007910473222[/C][C]0.792630087385548[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]0.0784738732539682[/C][C]0.09569306285451[/C][C]0.820058120339178[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]0.0783533468688525[/C][C]0.092936021812777[/C][C]0.843089098721033[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]0.077960909440678[/C][C]0.0903142659364724[/C][C]0.863218104385814[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]0.0782080817368421[/C][C]0.0877865420327191[/C][C]0.890889194697896[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]0.0788257304[/C][C]0.084952506544799[/C][C]0.927879983840523[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]0.0785858282075472[/C][C]0.0824181997339064[/C][C]0.953500907096584[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]0.0810264266078431[/C][C]0.0802834255125819[/C][C]1.00925472587296[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]0.0842605421020408[/C][C]0.0779151209903163[/C][C]1.08144017529682[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]0.0880721406170213[/C][C]0.0760365925383484[/C][C]1.15828626292798[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]0.0919046167555556[/C][C]0.0744372500377634[/C][C]1.23465894708537[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]0.0944711569302326[/C][C]0.0728559758985208[/C][C]1.29668370734364[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]0.0960556762682927[/C][C]0.0719292345503074[/C][C]1.33541913616655[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]0.0979356915128205[/C][C]0.0707127535248554[/C][C]1.38497918170301[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]0.0983090801621622[/C][C]0.069824365327993[/C][C]1.40794806655764[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]0.0991208966571429[/C][C]0.0688185002044595[/C][C]1.44032340668069[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]0.0985935523333333[/C][C]0.0677062248886787[/C][C]1.45619627287504[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]0.0974877683870968[/C][C]0.0662604133347613[/C][C]1.47128222540008[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]0.0955315421034483[/C][C]0.0644482896764363[/C][C]1.48229755332633[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]0.0957708130740741[/C][C]0.0626430402727795[/C][C]1.52883405174844[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]0.096056626[/C][C]0.0601830545217866[/C][C]1.59607428973594[/C][/ROW]
[ROW][C]Median[/C][C]0.096307367[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.106697116[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.0803056908684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.0979356915128206[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.0979356915128206[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.0979356915128206[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.0983090801621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.0803056908684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.0979356915128206[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.0979356915128206[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]75[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147278&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147278&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 Mean0.06531626546666670.1151531466791170.567212163543178
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean0.992735869505112
Winsorized Mean ( 1 / 25 )0.06592041361333330.1132767183143350.581941413860602
Winsorized Mean ( 2 / 25 )0.07163527918666670.1115928533158710.641934291113593
Winsorized Mean ( 3 / 25 )0.07386140902666670.1110040500497980.665393821158158
Winsorized Mean ( 4 / 25 )0.07148076193333330.1093536433351140.653666030260016
Winsorized Mean ( 5 / 25 )0.07639812353333330.1068234287673430.715181345655226
Winsorized Mean ( 6 / 25 )0.07906204201333330.1045835091243580.755970445773839
Winsorized Mean ( 7 / 25 )0.08051436897333330.1017940007548260.790953969549294
Winsorized Mean ( 8 / 25 )0.076458101880.0990188133702230.772157323216242
Winsorized Mean ( 9 / 25 )0.074131600560.09779627121336420.758020726559865
Winsorized Mean ( 10 / 25 )0.08052103922666660.0935470665853050.860754293703481
Winsorized Mean ( 11 / 25 )0.06033015217333330.08886424839180750.678902407493892
Winsorized Mean ( 12 / 25 )0.05567096113333330.08727122719871190.637907394227121
Winsorized Mean ( 13 / 25 )0.05320871953333340.08200238563136840.648867946019602
Winsorized Mean ( 14 / 25 )0.05587934105333330.07805663847776010.715881981892603
Winsorized Mean ( 15 / 25 )0.06983237125333330.07557768022091510.923981406272485
Winsorized Mean ( 16 / 25 )0.08061189445333330.06999234849357541.15172438399796
Winsorized Mean ( 17 / 25 )0.07943634150666670.06939968995353521.14462098548065
Winsorized Mean ( 18 / 25 )0.09462000030666670.06562760084699431.44177143588208
Winsorized Mean ( 19 / 25 )0.09111097390666660.06409003758722341.42160899473134
Winsorized Mean ( 20 / 25 )0.1037615267066670.06228907340148121.66580623278623
Winsorized Mean ( 21 / 25 )0.1081917569866670.06113864063205071.76961338800113
Winsorized Mean ( 22 / 25 )0.1141287333066670.05956110068148641.91616226028109
Winsorized Mean ( 23 / 25 )0.09355037846666670.05628969954311621.66194488913571
Winsorized Mean ( 24 / 25 )0.09348430966666670.05487348153762511.7036336504832
Winsorized Mean ( 25 / 25 )0.09743248133333330.05239392980299351.85961392282826
Trimmed Mean ( 1 / 25 )0.07002896084931510.1105352415662880.633544196918578
Trimmed Mean ( 2 / 25 )0.07436897553521130.1072971076398310.693112584030213
Trimmed Mean ( 3 / 25 )0.07585468007246380.1045323482563170.725657476731179
Trimmed Mean ( 4 / 25 )0.07659843792537310.1015080057177670.754604894301122
Trimmed Mean ( 5 / 25 )0.07807469061538460.09850079104732220.792630087385548
Trimmed Mean ( 6 / 25 )0.07847387325396820.095693062854510.820058120339178
Trimmed Mean ( 7 / 25 )0.07835334686885250.0929360218127770.843089098721033
Trimmed Mean ( 8 / 25 )0.0779609094406780.09031426593647240.863218104385814
Trimmed Mean ( 9 / 25 )0.07820808173684210.08778654203271910.890889194697896
Trimmed Mean ( 10 / 25 )0.07882573040.0849525065447990.927879983840523
Trimmed Mean ( 11 / 25 )0.07858582820754720.08241819973390640.953500907096584
Trimmed Mean ( 12 / 25 )0.08102642660784310.08028342551258191.00925472587296
Trimmed Mean ( 13 / 25 )0.08426054210204080.07791512099031631.08144017529682
Trimmed Mean ( 14 / 25 )0.08807214061702130.07603659253834841.15828626292798
Trimmed Mean ( 15 / 25 )0.09190461675555560.07443725003776341.23465894708537
Trimmed Mean ( 16 / 25 )0.09447115693023260.07285597589852081.29668370734364
Trimmed Mean ( 17 / 25 )0.09605567626829270.07192923455030741.33541913616655
Trimmed Mean ( 18 / 25 )0.09793569151282050.07071275352485541.38497918170301
Trimmed Mean ( 19 / 25 )0.09830908016216220.0698243653279931.40794806655764
Trimmed Mean ( 20 / 25 )0.09912089665714290.06881850020445951.44032340668069
Trimmed Mean ( 21 / 25 )0.09859355233333330.06770622488867871.45619627287504
Trimmed Mean ( 22 / 25 )0.09748776838709680.06626041333476131.47128222540008
Trimmed Mean ( 23 / 25 )0.09553154210344830.06444828967643631.48229755332633
Trimmed Mean ( 24 / 25 )0.09577081307407410.06264304027277951.52883405174844
Trimmed Mean ( 25 / 25 )0.0960566260.06018305452178661.59607428973594
Median0.096307367
Midrange-0.106697116
Midmean - Weighted Average at Xnp0.0803056908684211
Midmean - Weighted Average at X(n+1)p0.0979356915128206
Midmean - Empirical Distribution Function0.0979356915128206
Midmean - Empirical Distribution Function - Averaging0.0979356915128206
Midmean - Empirical Distribution Function - Interpolation0.0983090801621622
Midmean - Closest Observation0.0803056908684211
Midmean - True Basic - Statistics Graphics Toolkit0.0979356915128206
Midmean - MS Excel (old versions)0.0979356915128206
Number of observations75



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')