Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 15 Mar 2009 10:43:50 -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/Mar/15/t1237135474rlzonlkc8eludpw.htm/, Retrieved Fri, 07 Oct 2022 00:12:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39089, Retrieved Fri, 07 Oct 2022 00:12:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWesleyDeBondt
Estimated Impact162
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram] [Koers Euro t.o.v....] [2009-03-15 14:07:45] [bc74728c7d756fc9a12b0f66e8f52b90]
- RMPD    [Central Tendency] [Koers Euro t.o.v....] [2009-03-15 16:43:50] [52abb83916effba29fe89a1e0cad1e5e] [Current]
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Dataseries X:
0,63709
0,64218
0,65711
0,66977
0,68255
0,68902
0,71322
0,70224
0,70045
0,69919
0,69693
0,69763
0,69278
0,70196
0,69215
0,6769
0,67124
0,66533
0,67157
0,66428
0,66576
0,66942
0,68130
0,69144
0,69862
0,695
0,69867
0,68968
0,69233
0,68293
0,68399
0,66895
0,68756
0,68527
0,6776
0,68137
0,67933
0,67922
0,68598
0,68297
0,68935
0,69463
0,6833
0,68666
0,68782
0,67669
0,67511
0,67254
0,67397
0,67286
0,66341
0,668
0,68021
0,67934
0,68136
0,67562
0,6744
0,67766
0,68887
0,69614
0,70896
0,72064
0,74725
0,75094
0,77494
0,79487
0,79209
0,79152
0,79308
0,79279
0,79924
0,78668




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39089&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39089&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39089&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.6965544444444440.00447398373633177155.689981344356
Geometric Mean0.695588142695841
Harmonic Mean0.694672845412761
Quadratic Mean0.69757384393259
Winsorized Mean ( 1 / 24 )0.6965644444444450.00444199887723836156.813286922194
Winsorized Mean ( 2 / 24 )0.6969294444444440.00436404790076369159.697936478306
Winsorized Mean ( 3 / 24 )0.6971798611111110.00432899591290744161.048861014718
Winsorized Mean ( 4 / 24 )0.6971893055555550.00431166615547212161.698350571675
Winsorized Mean ( 5 / 24 )0.6972226388888890.00429167025841071162.459508048758
Winsorized Mean ( 6 / 24 )0.6968551388888890.00416421558889268167.343674700135
Winsorized Mean ( 7 / 24 )0.6959315277777780.00380072251727928183.105060844051
Winsorized Mean ( 8 / 24 )0.6933704166666670.00303940255586782228.127207213160
Winsorized Mean ( 9 / 24 )0.6929679166666670.00291060711886226238.083632853047
Winsorized Mean ( 10 / 24 )0.6893206944444440.00199655499784125345.255049417503
Winsorized Mean ( 11 / 24 )0.6884116666666670.00172450571267585399.193613338911
Winsorized Mean ( 12 / 24 )0.6877566666666670.00157732758929262436.026524442588
Winsorized Mean ( 13 / 24 )0.6867184722222220.00133621132556265513.929540249226
Winsorized Mean ( 14 / 24 )0.686726250.00131806650548872521.010318629843
Winsorized Mean ( 15 / 24 )0.6866429166666670.00123376959733474556.54063623386
Winsorized Mean ( 16 / 24 )0.6864584722222220.00117653869317853583.455925591098
Winsorized Mean ( 17 / 24 )0.6865033333333330.00113393801184654605.415222138474
Winsorized Mean ( 18 / 24 )0.6866183333333330.00111415889312236616.266079795074
Winsorized Mean ( 19 / 24 )0.6866394444444440.00103606988258501662.734682269953
Winsorized Mean ( 20 / 24 )0.6865033333333330.000999360769870829686.942447642873
Winsorized Mean ( 21 / 24 )0.6864770833333330.000938287310254437731.627802945752
Winsorized Mean ( 22 / 24 )0.6861470833333330.000886035428642587774.401407835933
Winsorized Mean ( 23 / 24 )0.6865272222222220.000803726142986208854.180529292554
Winsorized Mean ( 24 / 24 )0.6859472222222220.00071348631652899961.402070833339
Trimmed Mean ( 1 / 24 )0.6959370.00427369714676618162.841908563081
Trimmed Mean ( 2 / 24 )0.6952726470588240.00407108444531861170.783155298664
Trimmed Mean ( 3 / 24 )0.694368939393940.00387549049533484179.169305209184
Trimmed Mean ( 4 / 24 )0.693314843750.00365002539260701189.947950815434
Trimmed Mean ( 5 / 24 )0.692190.00337342190615908205.189276424696
Trimmed Mean ( 6 / 24 )0.6909821666666670.00302361826398586228.528242105465
Trimmed Mean ( 7 / 24 )0.6897670689655170.00260785256089141264.496190969378
Trimmed Mean ( 8 / 24 )0.6886348214285710.00218344822889195315.388664735155
Trimmed Mean ( 9 / 24 )0.6878455555555560.00190448621981682361.171190633091
Trimmed Mean ( 10 / 24 )0.68705750.00156314852906129439.534367481121
Trimmed Mean ( 11 / 24 )0.68673160.00143541683798662478.419635207317
Trimmed Mean ( 12 / 24 )0.68650250.00134873993926141508.995455696181
Trimmed Mean ( 13 / 24 )0.6863389130434780.00127694881766019537.483494679989
Trimmed Mean ( 14 / 24 )0.6862911363636360.00124485907809008551.300262369115
Trimmed Mean ( 15 / 24 )0.6862378571428570.00120634104421154568.858914678957
Trimmed Mean ( 16 / 24 )0.686189250.00117489106900957584.04499625523
Trimmed Mean ( 17 / 24 )0.6861573684210530.00114563030811641598.934371376051
Trimmed Mean ( 18 / 24 )0.6861166666666670.00111507035865989615.312443145965
Trimmed Mean ( 19 / 24 )0.6860576470588240.00107641603945053637.35360856294
Trimmed Mean ( 20 / 24 )0.685988750.00104254522896394657.994234630683
Trimmed Mean ( 21 / 24 )0.6859270.00100331326401435683.661847801697
Trimmed Mean ( 22 / 24 )0.6858596428571430.00096362637413402711.748517129892
Trimmed Mean ( 23 / 24 )0.6858234615384620.000920859956329732744.76412707959
Trimmed Mean ( 24 / 24 )0.6857316666666670.000882422896961612777.100944487955
Median0.685625
Midrange0.718165
Midmean - Weighted Average at Xnp0.685819189189189
Midmean - Weighted Average at X(n+1)p0.686116666666667
Midmean - Empirical Distribution Function0.685819189189189
Midmean - Empirical Distribution Function - Averaging0.686116666666667
Midmean - Empirical Distribution Function - Interpolation0.686116666666667
Midmean - Closest Observation0.685819189189189
Midmean - True Basic - Statistics Graphics Toolkit0.686116666666667
Midmean - MS Excel (old versions)0.686157368421053
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.696554444444444 & 0.00447398373633177 & 155.689981344356 \tabularnewline
Geometric Mean & 0.695588142695841 &  &  \tabularnewline
Harmonic Mean & 0.694672845412761 &  &  \tabularnewline
Quadratic Mean & 0.69757384393259 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 0.696564444444445 & 0.00444199887723836 & 156.813286922194 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 0.696929444444444 & 0.00436404790076369 & 159.697936478306 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 0.697179861111111 & 0.00432899591290744 & 161.048861014718 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 0.697189305555555 & 0.00431166615547212 & 161.698350571675 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 0.697222638888889 & 0.00429167025841071 & 162.459508048758 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 0.696855138888889 & 0.00416421558889268 & 167.343674700135 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 0.695931527777778 & 0.00380072251727928 & 183.105060844051 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 0.693370416666667 & 0.00303940255586782 & 228.127207213160 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 0.692967916666667 & 0.00291060711886226 & 238.083632853047 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 0.689320694444444 & 0.00199655499784125 & 345.255049417503 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 0.688411666666667 & 0.00172450571267585 & 399.193613338911 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 0.687756666666667 & 0.00157732758929262 & 436.026524442588 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 0.686718472222222 & 0.00133621132556265 & 513.929540249226 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 0.68672625 & 0.00131806650548872 & 521.010318629843 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 0.686642916666667 & 0.00123376959733474 & 556.54063623386 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 0.686458472222222 & 0.00117653869317853 & 583.455925591098 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 0.686503333333333 & 0.00113393801184654 & 605.415222138474 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 0.686618333333333 & 0.00111415889312236 & 616.266079795074 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 0.686639444444444 & 0.00103606988258501 & 662.734682269953 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 0.686503333333333 & 0.000999360769870829 & 686.942447642873 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 0.686477083333333 & 0.000938287310254437 & 731.627802945752 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 0.686147083333333 & 0.000886035428642587 & 774.401407835933 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 0.686527222222222 & 0.000803726142986208 & 854.180529292554 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 0.685947222222222 & 0.00071348631652899 & 961.402070833339 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 0.695937 & 0.00427369714676618 & 162.841908563081 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 0.695272647058824 & 0.00407108444531861 & 170.783155298664 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 0.69436893939394 & 0.00387549049533484 & 179.169305209184 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 0.69331484375 & 0.00365002539260701 & 189.947950815434 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 0.69219 & 0.00337342190615908 & 205.189276424696 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 0.690982166666667 & 0.00302361826398586 & 228.528242105465 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 0.689767068965517 & 0.00260785256089141 & 264.496190969378 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 0.688634821428571 & 0.00218344822889195 & 315.388664735155 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 0.687845555555556 & 0.00190448621981682 & 361.171190633091 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 0.6870575 & 0.00156314852906129 & 439.534367481121 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 0.6867316 & 0.00143541683798662 & 478.419635207317 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 0.6865025 & 0.00134873993926141 & 508.995455696181 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 0.686338913043478 & 0.00127694881766019 & 537.483494679989 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 0.686291136363636 & 0.00124485907809008 & 551.300262369115 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 0.686237857142857 & 0.00120634104421154 & 568.858914678957 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 0.68618925 & 0.00117489106900957 & 584.04499625523 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 0.686157368421053 & 0.00114563030811641 & 598.934371376051 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 0.686116666666667 & 0.00111507035865989 & 615.312443145965 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 0.686057647058824 & 0.00107641603945053 & 637.35360856294 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 0.68598875 & 0.00104254522896394 & 657.994234630683 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 0.685927 & 0.00100331326401435 & 683.661847801697 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 0.685859642857143 & 0.00096362637413402 & 711.748517129892 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 0.685823461538462 & 0.000920859956329732 & 744.76412707959 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 0.685731666666667 & 0.000882422896961612 & 777.100944487955 \tabularnewline
Median & 0.685625 &  &  \tabularnewline
Midrange & 0.718165 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.685819189189189 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.686116666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.685819189189189 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.686116666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.686116666666667 &  &  \tabularnewline
Midmean - Closest Observation & 0.685819189189189 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.686116666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.686157368421053 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39089&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]0.696554444444444[/C][C]0.00447398373633177[/C][C]155.689981344356[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.695588142695841[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.694672845412761[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.69757384393259[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]0.696564444444445[/C][C]0.00444199887723836[/C][C]156.813286922194[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]0.696929444444444[/C][C]0.00436404790076369[/C][C]159.697936478306[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]0.697179861111111[/C][C]0.00432899591290744[/C][C]161.048861014718[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]0.697189305555555[/C][C]0.00431166615547212[/C][C]161.698350571675[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]0.697222638888889[/C][C]0.00429167025841071[/C][C]162.459508048758[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]0.696855138888889[/C][C]0.00416421558889268[/C][C]167.343674700135[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]0.695931527777778[/C][C]0.00380072251727928[/C][C]183.105060844051[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]0.693370416666667[/C][C]0.00303940255586782[/C][C]228.127207213160[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]0.692967916666667[/C][C]0.00291060711886226[/C][C]238.083632853047[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]0.689320694444444[/C][C]0.00199655499784125[/C][C]345.255049417503[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]0.688411666666667[/C][C]0.00172450571267585[/C][C]399.193613338911[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]0.687756666666667[/C][C]0.00157732758929262[/C][C]436.026524442588[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]0.686718472222222[/C][C]0.00133621132556265[/C][C]513.929540249226[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]0.68672625[/C][C]0.00131806650548872[/C][C]521.010318629843[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]0.686642916666667[/C][C]0.00123376959733474[/C][C]556.54063623386[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]0.686458472222222[/C][C]0.00117653869317853[/C][C]583.455925591098[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]0.686503333333333[/C][C]0.00113393801184654[/C][C]605.415222138474[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]0.686618333333333[/C][C]0.00111415889312236[/C][C]616.266079795074[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]0.686639444444444[/C][C]0.00103606988258501[/C][C]662.734682269953[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]0.686503333333333[/C][C]0.000999360769870829[/C][C]686.942447642873[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]0.686477083333333[/C][C]0.000938287310254437[/C][C]731.627802945752[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]0.686147083333333[/C][C]0.000886035428642587[/C][C]774.401407835933[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]0.686527222222222[/C][C]0.000803726142986208[/C][C]854.180529292554[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]0.685947222222222[/C][C]0.00071348631652899[/C][C]961.402070833339[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]0.695937[/C][C]0.00427369714676618[/C][C]162.841908563081[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]0.695272647058824[/C][C]0.00407108444531861[/C][C]170.783155298664[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]0.69436893939394[/C][C]0.00387549049533484[/C][C]179.169305209184[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]0.69331484375[/C][C]0.00365002539260701[/C][C]189.947950815434[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]0.69219[/C][C]0.00337342190615908[/C][C]205.189276424696[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]0.690982166666667[/C][C]0.00302361826398586[/C][C]228.528242105465[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]0.689767068965517[/C][C]0.00260785256089141[/C][C]264.496190969378[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]0.688634821428571[/C][C]0.00218344822889195[/C][C]315.388664735155[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]0.687845555555556[/C][C]0.00190448621981682[/C][C]361.171190633091[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]0.6870575[/C][C]0.00156314852906129[/C][C]439.534367481121[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]0.6867316[/C][C]0.00143541683798662[/C][C]478.419635207317[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]0.6865025[/C][C]0.00134873993926141[/C][C]508.995455696181[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]0.686338913043478[/C][C]0.00127694881766019[/C][C]537.483494679989[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]0.686291136363636[/C][C]0.00124485907809008[/C][C]551.300262369115[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]0.686237857142857[/C][C]0.00120634104421154[/C][C]568.858914678957[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]0.68618925[/C][C]0.00117489106900957[/C][C]584.04499625523[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]0.686157368421053[/C][C]0.00114563030811641[/C][C]598.934371376051[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]0.686116666666667[/C][C]0.00111507035865989[/C][C]615.312443145965[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]0.686057647058824[/C][C]0.00107641603945053[/C][C]637.35360856294[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]0.68598875[/C][C]0.00104254522896394[/C][C]657.994234630683[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]0.685927[/C][C]0.00100331326401435[/C][C]683.661847801697[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]0.685859642857143[/C][C]0.00096362637413402[/C][C]711.748517129892[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]0.685823461538462[/C][C]0.000920859956329732[/C][C]744.76412707959[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]0.685731666666667[/C][C]0.000882422896961612[/C][C]777.100944487955[/C][/ROW]
[ROW][C]Median[/C][C]0.685625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.718165[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.685819189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.686116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.685819189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.686116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.686116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.685819189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.686116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.686157368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39089&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39089&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 Mean0.6965544444444440.00447398373633177155.689981344356
Geometric Mean0.695588142695841
Harmonic Mean0.694672845412761
Quadratic Mean0.69757384393259
Winsorized Mean ( 1 / 24 )0.6965644444444450.00444199887723836156.813286922194
Winsorized Mean ( 2 / 24 )0.6969294444444440.00436404790076369159.697936478306
Winsorized Mean ( 3 / 24 )0.6971798611111110.00432899591290744161.048861014718
Winsorized Mean ( 4 / 24 )0.6971893055555550.00431166615547212161.698350571675
Winsorized Mean ( 5 / 24 )0.6972226388888890.00429167025841071162.459508048758
Winsorized Mean ( 6 / 24 )0.6968551388888890.00416421558889268167.343674700135
Winsorized Mean ( 7 / 24 )0.6959315277777780.00380072251727928183.105060844051
Winsorized Mean ( 8 / 24 )0.6933704166666670.00303940255586782228.127207213160
Winsorized Mean ( 9 / 24 )0.6929679166666670.00291060711886226238.083632853047
Winsorized Mean ( 10 / 24 )0.6893206944444440.00199655499784125345.255049417503
Winsorized Mean ( 11 / 24 )0.6884116666666670.00172450571267585399.193613338911
Winsorized Mean ( 12 / 24 )0.6877566666666670.00157732758929262436.026524442588
Winsorized Mean ( 13 / 24 )0.6867184722222220.00133621132556265513.929540249226
Winsorized Mean ( 14 / 24 )0.686726250.00131806650548872521.010318629843
Winsorized Mean ( 15 / 24 )0.6866429166666670.00123376959733474556.54063623386
Winsorized Mean ( 16 / 24 )0.6864584722222220.00117653869317853583.455925591098
Winsorized Mean ( 17 / 24 )0.6865033333333330.00113393801184654605.415222138474
Winsorized Mean ( 18 / 24 )0.6866183333333330.00111415889312236616.266079795074
Winsorized Mean ( 19 / 24 )0.6866394444444440.00103606988258501662.734682269953
Winsorized Mean ( 20 / 24 )0.6865033333333330.000999360769870829686.942447642873
Winsorized Mean ( 21 / 24 )0.6864770833333330.000938287310254437731.627802945752
Winsorized Mean ( 22 / 24 )0.6861470833333330.000886035428642587774.401407835933
Winsorized Mean ( 23 / 24 )0.6865272222222220.000803726142986208854.180529292554
Winsorized Mean ( 24 / 24 )0.6859472222222220.00071348631652899961.402070833339
Trimmed Mean ( 1 / 24 )0.6959370.00427369714676618162.841908563081
Trimmed Mean ( 2 / 24 )0.6952726470588240.00407108444531861170.783155298664
Trimmed Mean ( 3 / 24 )0.694368939393940.00387549049533484179.169305209184
Trimmed Mean ( 4 / 24 )0.693314843750.00365002539260701189.947950815434
Trimmed Mean ( 5 / 24 )0.692190.00337342190615908205.189276424696
Trimmed Mean ( 6 / 24 )0.6909821666666670.00302361826398586228.528242105465
Trimmed Mean ( 7 / 24 )0.6897670689655170.00260785256089141264.496190969378
Trimmed Mean ( 8 / 24 )0.6886348214285710.00218344822889195315.388664735155
Trimmed Mean ( 9 / 24 )0.6878455555555560.00190448621981682361.171190633091
Trimmed Mean ( 10 / 24 )0.68705750.00156314852906129439.534367481121
Trimmed Mean ( 11 / 24 )0.68673160.00143541683798662478.419635207317
Trimmed Mean ( 12 / 24 )0.68650250.00134873993926141508.995455696181
Trimmed Mean ( 13 / 24 )0.6863389130434780.00127694881766019537.483494679989
Trimmed Mean ( 14 / 24 )0.6862911363636360.00124485907809008551.300262369115
Trimmed Mean ( 15 / 24 )0.6862378571428570.00120634104421154568.858914678957
Trimmed Mean ( 16 / 24 )0.686189250.00117489106900957584.04499625523
Trimmed Mean ( 17 / 24 )0.6861573684210530.00114563030811641598.934371376051
Trimmed Mean ( 18 / 24 )0.6861166666666670.00111507035865989615.312443145965
Trimmed Mean ( 19 / 24 )0.6860576470588240.00107641603945053637.35360856294
Trimmed Mean ( 20 / 24 )0.685988750.00104254522896394657.994234630683
Trimmed Mean ( 21 / 24 )0.6859270.00100331326401435683.661847801697
Trimmed Mean ( 22 / 24 )0.6858596428571430.00096362637413402711.748517129892
Trimmed Mean ( 23 / 24 )0.6858234615384620.000920859956329732744.76412707959
Trimmed Mean ( 24 / 24 )0.6857316666666670.000882422896961612777.100944487955
Median0.685625
Midrange0.718165
Midmean - Weighted Average at Xnp0.685819189189189
Midmean - Weighted Average at X(n+1)p0.686116666666667
Midmean - Empirical Distribution Function0.685819189189189
Midmean - Empirical Distribution Function - Averaging0.686116666666667
Midmean - Empirical Distribution Function - Interpolation0.686116666666667
Midmean - Closest Observation0.685819189189189
Midmean - True Basic - Statistics Graphics Toolkit0.686116666666667
Midmean - MS Excel (old versions)0.686157368421053
Number of observations72



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')