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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 computationMon, 19 Oct 2009 15:52:05 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/19/t1255989316hr7cknjzhorxu09.htm/, Retrieved Mon, 29 Apr 2024 23:41:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48274, Retrieved Mon, 29 Apr 2024 23:41:57 +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)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD      [Central Tendency] [central tendency ...] [2009-10-19 21:33:34] [0a7d38ad9c7f1a2c46637c75a8a0e083]
-    D          [Central Tendency] [central tendency ...] [2009-10-19 21:52:05] [30a48cc4afddc7f052994dfe2358176d] [Current]
Feedback Forum

Post a new message
Dataseries X:
3,1
2,8
2,3
1,7
1,6
1,7
1,8
1,7
1,6
1,4
1,9
2,6
2,8
2,6
1,9
1,5
1,4
1,3
1,2
1
0,8
1,1
1,7
2,9
3,4
3,1
2,4
2
1,9
1,9
2
2,2
2,2
2
1,9
1,7
1,5
1,3
1,6
1,7
1,5
1,1
0,8
0,7
0,7
0,7
0,8
1
1,4
1,4
1,8
1,7
1,6
1,2
0,7
0,3
0
-0,2
-0,2
0,1
0,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48274&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]2 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=48274&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48274&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.552459016393440.10268543288969215.1185905605632
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean1.74435858849203
Winsorized Mean ( 1 / 20 )1.547540983606560.10131934466405415.2738945236743
Winsorized Mean ( 2 / 20 )1.554098360655740.09952273459939215.6155110378693
Winsorized Mean ( 3 / 20 )1.549180327868850.095831789984807216.1656202823140
Winsorized Mean ( 4 / 20 )1.555737704918030.091153044611134217.0673147732468
Winsorized Mean ( 5 / 20 )1.563934426229510.089321448934788817.5090579573031
Winsorized Mean ( 6 / 20 )1.573770491803280.078958439622839319.9316311127817
Winsorized Mean ( 7 / 20 )1.573770491803280.078958439622839319.9316311127817
Winsorized Mean ( 8 / 20 )1.547540983606560.073574116282561221.0337692356811
Winsorized Mean ( 9 / 20 )1.532786885245900.070815750751583821.6447170153262
Winsorized Mean ( 10 / 20 )1.532786885245900.064770351422258823.6649462537754
Winsorized Mean ( 11 / 20 )1.532786885245900.064770351422258823.6649462537754
Winsorized Mean ( 12 / 20 )1.493442622950820.058527881005272225.5167724732131
Winsorized Mean ( 13 / 20 )1.536065573770490.050518231675439430.4061627421786
Winsorized Mean ( 14 / 20 )1.536065573770490.050518231675439430.4061627421786
Winsorized Mean ( 15 / 20 )1.536065573770490.042595619652501636.0615853531850
Winsorized Mean ( 16 / 20 )1.536065573770490.042595619652501636.0615853531850
Winsorized Mean ( 17 / 20 )1.563934426229510.037984235073606941.1732505129792
Winsorized Mean ( 18 / 20 )1.563934426229510.037984235073606941.1732505129792
Winsorized Mean ( 19 / 20 )1.595081967213110.033176645079533248.0784589095516
Winsorized Mean ( 20 / 20 )1.562295081967210.028357970750061955.0919209183473
Trimmed Mean ( 1 / 20 )1.550847457627120.096864124267806716.0105453835456
Trimmed Mean ( 2 / 20 )1.554385964912280.091358110517811717.0142087670391
Trimmed Mean ( 3 / 20 )1.554545454545450.085745617897794818.1297364536857
Trimmed Mean ( 4 / 20 )1.556603773584910.080614000536226619.3093477960493
Trimmed Mean ( 5 / 20 )1.556862745098040.07614510924831320.4459979172271
Trimmed Mean ( 6 / 20 )1.555102040816330.071133989245181821.8615890563407
Trimmed Mean ( 7 / 20 )1.551063829787230.068272752519518522.7186362428232
Trimmed Mean ( 8 / 20 )1.546666666666670.064557546171433523.9579531501936
Trimmed Mean ( 9 / 20 )1.546511627906980.061392915821451525.1903922010267
Trimmed Mean ( 10 / 20 )1.548780487804880.058028793443691726.6898619787389
Trimmed Mean ( 11 / 20 )1.551282051282050.055332609161293128.0355847084692
Trimmed Mean ( 12 / 20 )1.554054054054050.051638992093410830.0945853327829
Trimmed Mean ( 13 / 20 )1.562857142857140.048348474950219532.3248488078743
Trimmed Mean ( 14 / 20 )1.566666666666670.046398036356916833.7657967810337
Trimmed Mean ( 15 / 20 )1.570967741935480.043550378289802236.0724247096458
Trimmed Mean ( 16 / 20 )1.575862068965520.042010781050554937.510896716468
Trimmed Mean ( 17 / 20 )1.581481481481480.039598065018280139.9383525622124
Trimmed Mean ( 18 / 20 )1.5840.037718253759508441.995581505432
Trimmed Mean ( 19 / 20 )1.586956521739130.034609251788091345.8535345246957
Trimmed Mean ( 20 / 20 )1.585714285714290.031837170762755849.8070100993179
Median1.6
Midrange1.6
Midmean - Weighted Average at Xnp1.57096774193548
Midmean - Weighted Average at X(n+1)p1.57096774193548
Midmean - Empirical Distribution Function1.57096774193548
Midmean - Empirical Distribution Function - Averaging1.57096774193548
Midmean - Empirical Distribution Function - Interpolation1.57096774193548
Midmean - Closest Observation1.53636363636364
Midmean - True Basic - Statistics Graphics Toolkit1.57096774193548
Midmean - MS Excel (old versions)1.57096774193548
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.55245901639344 & 0.102685432889692 & 15.1185905605632 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 1.74435858849203 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.54754098360656 & 0.101319344664054 & 15.2738945236743 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.55409836065574 & 0.099522734599392 & 15.6155110378693 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.54918032786885 & 0.0958317899848072 & 16.1656202823140 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.55573770491803 & 0.0911530446111342 & 17.0673147732468 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.56393442622951 & 0.0893214489347888 & 17.5090579573031 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.57377049180328 & 0.0789584396228393 & 19.9316311127817 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.57377049180328 & 0.0789584396228393 & 19.9316311127817 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.54754098360656 & 0.0735741162825612 & 21.0337692356811 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.53278688524590 & 0.0708157507515838 & 21.6447170153262 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.53278688524590 & 0.0647703514222588 & 23.6649462537754 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.53278688524590 & 0.0647703514222588 & 23.6649462537754 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.49344262295082 & 0.0585278810052722 & 25.5167724732131 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.53606557377049 & 0.0505182316754394 & 30.4061627421786 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.53606557377049 & 0.0505182316754394 & 30.4061627421786 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.53606557377049 & 0.0425956196525016 & 36.0615853531850 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.53606557377049 & 0.0425956196525016 & 36.0615853531850 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.56393442622951 & 0.0379842350736069 & 41.1732505129792 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.56393442622951 & 0.0379842350736069 & 41.1732505129792 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.59508196721311 & 0.0331766450795332 & 48.0784589095516 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.56229508196721 & 0.0283579707500619 & 55.0919209183473 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.55084745762712 & 0.0968641242678067 & 16.0105453835456 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.55438596491228 & 0.0913581105178117 & 17.0142087670391 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.55454545454545 & 0.0857456178977948 & 18.1297364536857 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.55660377358491 & 0.0806140005362266 & 19.3093477960493 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.55686274509804 & 0.076145109248313 & 20.4459979172271 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.55510204081633 & 0.0711339892451818 & 21.8615890563407 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.55106382978723 & 0.0682727525195185 & 22.7186362428232 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.54666666666667 & 0.0645575461714335 & 23.9579531501936 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.54651162790698 & 0.0613929158214515 & 25.1903922010267 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.54878048780488 & 0.0580287934436917 & 26.6898619787389 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.55128205128205 & 0.0553326091612931 & 28.0355847084692 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.55405405405405 & 0.0516389920934108 & 30.0945853327829 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.56285714285714 & 0.0483484749502195 & 32.3248488078743 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.56666666666667 & 0.0463980363569168 & 33.7657967810337 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.57096774193548 & 0.0435503782898022 & 36.0724247096458 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.57586206896552 & 0.0420107810505549 & 37.510896716468 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.58148148148148 & 0.0395980650182801 & 39.9383525622124 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.584 & 0.0377182537595084 & 41.995581505432 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.58695652173913 & 0.0346092517880913 & 45.8535345246957 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.58571428571429 & 0.0318371707627558 & 49.8070100993179 \tabularnewline
Median & 1.6 &  &  \tabularnewline
Midrange & 1.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.57096774193548 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.57096774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.57096774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.57096774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.57096774193548 &  &  \tabularnewline
Midmean - Closest Observation & 1.53636363636364 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.57096774193548 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.57096774193548 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48274&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]1.55245901639344[/C][C]0.102685432889692[/C][C]15.1185905605632[/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]1.74435858849203[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.54754098360656[/C][C]0.101319344664054[/C][C]15.2738945236743[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.55409836065574[/C][C]0.099522734599392[/C][C]15.6155110378693[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.54918032786885[/C][C]0.0958317899848072[/C][C]16.1656202823140[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.55573770491803[/C][C]0.0911530446111342[/C][C]17.0673147732468[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.56393442622951[/C][C]0.0893214489347888[/C][C]17.5090579573031[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.57377049180328[/C][C]0.0789584396228393[/C][C]19.9316311127817[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.57377049180328[/C][C]0.0789584396228393[/C][C]19.9316311127817[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.54754098360656[/C][C]0.0735741162825612[/C][C]21.0337692356811[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.53278688524590[/C][C]0.0708157507515838[/C][C]21.6447170153262[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.53278688524590[/C][C]0.0647703514222588[/C][C]23.6649462537754[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.53278688524590[/C][C]0.0647703514222588[/C][C]23.6649462537754[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.49344262295082[/C][C]0.0585278810052722[/C][C]25.5167724732131[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.53606557377049[/C][C]0.0505182316754394[/C][C]30.4061627421786[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.53606557377049[/C][C]0.0505182316754394[/C][C]30.4061627421786[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.53606557377049[/C][C]0.0425956196525016[/C][C]36.0615853531850[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.53606557377049[/C][C]0.0425956196525016[/C][C]36.0615853531850[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.56393442622951[/C][C]0.0379842350736069[/C][C]41.1732505129792[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.56393442622951[/C][C]0.0379842350736069[/C][C]41.1732505129792[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.59508196721311[/C][C]0.0331766450795332[/C][C]48.0784589095516[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.56229508196721[/C][C]0.0283579707500619[/C][C]55.0919209183473[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.55084745762712[/C][C]0.0968641242678067[/C][C]16.0105453835456[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.55438596491228[/C][C]0.0913581105178117[/C][C]17.0142087670391[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.55454545454545[/C][C]0.0857456178977948[/C][C]18.1297364536857[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.55660377358491[/C][C]0.0806140005362266[/C][C]19.3093477960493[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.55686274509804[/C][C]0.076145109248313[/C][C]20.4459979172271[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.55510204081633[/C][C]0.0711339892451818[/C][C]21.8615890563407[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.55106382978723[/C][C]0.0682727525195185[/C][C]22.7186362428232[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.54666666666667[/C][C]0.0645575461714335[/C][C]23.9579531501936[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.54651162790698[/C][C]0.0613929158214515[/C][C]25.1903922010267[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.54878048780488[/C][C]0.0580287934436917[/C][C]26.6898619787389[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.55128205128205[/C][C]0.0553326091612931[/C][C]28.0355847084692[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.55405405405405[/C][C]0.0516389920934108[/C][C]30.0945853327829[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.56285714285714[/C][C]0.0483484749502195[/C][C]32.3248488078743[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.56666666666667[/C][C]0.0463980363569168[/C][C]33.7657967810337[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.57096774193548[/C][C]0.0435503782898022[/C][C]36.0724247096458[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.57586206896552[/C][C]0.0420107810505549[/C][C]37.510896716468[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.58148148148148[/C][C]0.0395980650182801[/C][C]39.9383525622124[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.584[/C][C]0.0377182537595084[/C][C]41.995581505432[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.58695652173913[/C][C]0.0346092517880913[/C][C]45.8535345246957[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.58571428571429[/C][C]0.0318371707627558[/C][C]49.8070100993179[/C][/ROW]
[ROW][C]Median[/C][C]1.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.57096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.57096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.57096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.57096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.57096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.53636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.57096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.57096774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48274&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48274&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 Mean1.552459016393440.10268543288969215.1185905605632
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean1.74435858849203
Winsorized Mean ( 1 / 20 )1.547540983606560.10131934466405415.2738945236743
Winsorized Mean ( 2 / 20 )1.554098360655740.09952273459939215.6155110378693
Winsorized Mean ( 3 / 20 )1.549180327868850.095831789984807216.1656202823140
Winsorized Mean ( 4 / 20 )1.555737704918030.091153044611134217.0673147732468
Winsorized Mean ( 5 / 20 )1.563934426229510.089321448934788817.5090579573031
Winsorized Mean ( 6 / 20 )1.573770491803280.078958439622839319.9316311127817
Winsorized Mean ( 7 / 20 )1.573770491803280.078958439622839319.9316311127817
Winsorized Mean ( 8 / 20 )1.547540983606560.073574116282561221.0337692356811
Winsorized Mean ( 9 / 20 )1.532786885245900.070815750751583821.6447170153262
Winsorized Mean ( 10 / 20 )1.532786885245900.064770351422258823.6649462537754
Winsorized Mean ( 11 / 20 )1.532786885245900.064770351422258823.6649462537754
Winsorized Mean ( 12 / 20 )1.493442622950820.058527881005272225.5167724732131
Winsorized Mean ( 13 / 20 )1.536065573770490.050518231675439430.4061627421786
Winsorized Mean ( 14 / 20 )1.536065573770490.050518231675439430.4061627421786
Winsorized Mean ( 15 / 20 )1.536065573770490.042595619652501636.0615853531850
Winsorized Mean ( 16 / 20 )1.536065573770490.042595619652501636.0615853531850
Winsorized Mean ( 17 / 20 )1.563934426229510.037984235073606941.1732505129792
Winsorized Mean ( 18 / 20 )1.563934426229510.037984235073606941.1732505129792
Winsorized Mean ( 19 / 20 )1.595081967213110.033176645079533248.0784589095516
Winsorized Mean ( 20 / 20 )1.562295081967210.028357970750061955.0919209183473
Trimmed Mean ( 1 / 20 )1.550847457627120.096864124267806716.0105453835456
Trimmed Mean ( 2 / 20 )1.554385964912280.091358110517811717.0142087670391
Trimmed Mean ( 3 / 20 )1.554545454545450.085745617897794818.1297364536857
Trimmed Mean ( 4 / 20 )1.556603773584910.080614000536226619.3093477960493
Trimmed Mean ( 5 / 20 )1.556862745098040.07614510924831320.4459979172271
Trimmed Mean ( 6 / 20 )1.555102040816330.071133989245181821.8615890563407
Trimmed Mean ( 7 / 20 )1.551063829787230.068272752519518522.7186362428232
Trimmed Mean ( 8 / 20 )1.546666666666670.064557546171433523.9579531501936
Trimmed Mean ( 9 / 20 )1.546511627906980.061392915821451525.1903922010267
Trimmed Mean ( 10 / 20 )1.548780487804880.058028793443691726.6898619787389
Trimmed Mean ( 11 / 20 )1.551282051282050.055332609161293128.0355847084692
Trimmed Mean ( 12 / 20 )1.554054054054050.051638992093410830.0945853327829
Trimmed Mean ( 13 / 20 )1.562857142857140.048348474950219532.3248488078743
Trimmed Mean ( 14 / 20 )1.566666666666670.046398036356916833.7657967810337
Trimmed Mean ( 15 / 20 )1.570967741935480.043550378289802236.0724247096458
Trimmed Mean ( 16 / 20 )1.575862068965520.042010781050554937.510896716468
Trimmed Mean ( 17 / 20 )1.581481481481480.039598065018280139.9383525622124
Trimmed Mean ( 18 / 20 )1.5840.037718253759508441.995581505432
Trimmed Mean ( 19 / 20 )1.586956521739130.034609251788091345.8535345246957
Trimmed Mean ( 20 / 20 )1.585714285714290.031837170762755849.8070100993179
Median1.6
Midrange1.6
Midmean - Weighted Average at Xnp1.57096774193548
Midmean - Weighted Average at X(n+1)p1.57096774193548
Midmean - Empirical Distribution Function1.57096774193548
Midmean - Empirical Distribution Function - Averaging1.57096774193548
Midmean - Empirical Distribution Function - Interpolation1.57096774193548
Midmean - Closest Observation1.53636363636364
Midmean - True Basic - Statistics Graphics Toolkit1.57096774193548
Midmean - MS Excel (old versions)1.57096774193548
Number of observations61



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')