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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 15 Oct 2010 13:54:55 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/15/t1287150927lfdlrpx4x1wuhnt.htm/, Retrieved Sat, 04 May 2024 19:55:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=83551, Retrieved Sat, 04 May 2024 19:55:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [opdracht 5] [2010-10-15 13:29:30] [2d4109bb9a734792293d3455e890fa94]
-    D    [Central Tendency] [opdracht 5] [2010-10-15 13:54:55] [3c432a26e3310571299b8b38ea0e36f7] [Current]
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Dataseries X:
108
106,6
122,2
115,8
115,6
124,5
121,7
118,7
113,7
113,4
115,1
143,9
101
103,4
121,5
111,9
117,4
124,3
122
119,7
115
112,2
115,3
142,6
104,1
105,3
124,4
113,9
124,8
131,8
125,6
125
119,7
116,1
120
148,1
109,2
109,4
135,1
114,9
129
138,5
125,6
130,4
120,3
126,2
127,6
150,9
114,6
118,6
131,4
124,5
136,8
136,8
136,6
131
125,8
129,4
124,8
157,1
116,6
114,2
128,4
127,3
133,5
137,2
137,7
131,2
127,7
133,9
124,3
160,6





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=83551&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=83551&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=83551&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'Gwilym Jenkins' @ 72.249.127.135
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean124.1861111111111.4314272531451986.756844148555
Geometric Mean123.617297430520
Harmonic Mean123.063534373882
Quadratic Mean124.770461470476
Winsorized Mean ( 1 / 24 )124.1708333333331.4074339260724888.2249823832506
Winsorized Mean ( 2 / 24 )124.0180555555561.3507943040717691.8112070666291
Winsorized Mean ( 3 / 24 )123.9513888888891.3090571590871394.6875298977216
Winsorized Mean ( 4 / 24 )123.7902777777781.23762759529712100.022234675576
Winsorized Mean ( 5 / 24 )123.7972222222221.19877998137645103.269343954240
Winsorized Mean ( 6 / 24 )123.5555555555561.11004780890867111.306517218414
Winsorized Mean ( 7 / 24 )123.4972222222221.09200926821661113.091734490412
Winsorized Mean ( 8 / 24 )123.7194444444441.03413122097459119.636117675519
Winsorized Mean ( 9 / 24 )123.7069444444441.01901584665361121.398450132734
Winsorized Mean ( 10 / 24 )123.8736111111110.99337593461826124.699629610731
Winsorized Mean ( 11 / 24 )123.8888888888890.981032071990356126.284239247692
Winsorized Mean ( 12 / 24 )123.6722222222220.931695457201317132.738891519034
Winsorized Mean ( 13 / 24 )123.5097222222220.887083808213349139.231176444286
Winsorized Mean ( 14 / 24 )123.5097222222220.862921121982188143.129793762044
Winsorized Mean ( 15 / 24 )123.2180555555560.79801280575013154.406113119615
Winsorized Mean ( 16 / 24 )123.1513888888890.781408065213118157.601891215829
Winsorized Mean ( 17 / 24 )123.1277777777780.770949514711597159.709261667852
Winsorized Mean ( 18 / 24 )123.1277777777780.756286181307621162.805801323633
Winsorized Mean ( 19 / 24 )123.0486111111110.721793521946388170.476192110035
Winsorized Mean ( 20 / 24 )122.8263888888890.674670246514479182.053958246183
Winsorized Mean ( 21 / 24 )122.7972222222220.645966697489387190.098379219061
Winsorized Mean ( 22 / 24 )122.7666666666670.599190899429649204.887401967427
Winsorized Mean ( 23 / 24 )122.7986111111110.53312603459403230.336924372154
Winsorized Mean ( 24 / 24 )123.1652777777780.472975298209166260.405307093458
Trimmed Mean ( 1 / 24 )123.9971428571431.3350149407567692.8807154673898
Trimmed Mean ( 2 / 24 )123.8132352941181.2471211878942899.2792332420972
Trimmed Mean ( 3 / 24 )123.7015151515151.17895986005808104.924280581886
Trimmed Mean ( 4 / 24 )123.60781251.11674729783409110.685571158072
Trimmed Mean ( 5 / 24 )123.5548387096771.06965173073421115.509408492117
Trimmed Mean ( 6 / 24 )123.4966666666671.02542802601394120.434261141394
Trimmed Mean ( 7 / 24 )123.4844827586210.998004062939579123.731442931106
Trimmed Mean ( 8 / 24 )123.4821428571430.969060688404375127.424571375880
Trimmed Mean ( 9 / 24 )123.4425925925930.947605765387564130.267878374617
Trimmed Mean ( 10 / 24 )123.4019230769230.924170535870495133.527220666788
Trimmed Mean ( 11 / 24 )123.3340.900175085010394137.011123784409
Trimmed Mean ( 12 / 24 )123.2583333333330.872195776654094141.319571399641
Trimmed Mean ( 13 / 24 )123.2043478260870.8479184887093145.302112722684
Trimmed Mean ( 14 / 24 )123.1659090909090.82659253162514149.004381697904
Trimmed Mean ( 15 / 24 )123.1238095238100.803764441051791153.183946981646
Trimmed Mean ( 16 / 24 )123.11250.788362368685222156.162324446458
Trimmed Mean ( 17 / 24 )123.1078947368420.770669487627473159.741493225368
Trimmed Mean ( 18 / 24 )123.1055555555560.748256645179095164.523170423819
Trimmed Mean ( 19 / 24 )123.1029411764710.720349554854147170.893339694499
Trimmed Mean ( 20 / 24 )123.1093750.69027459728521178.348407263107
Trimmed Mean ( 21 / 24 )123.1433333333330.660575912668989186.418140552212
Trimmed Mean ( 22 / 24 )123.1857142857140.625382724843055196.976522363372
Trimmed Mean ( 23 / 24 )123.2384615384620.588402711991787209.445774172743
Trimmed Mean ( 24 / 24 )123.2958333333330.556531675683107221.543244923113
Median124.35
Midrange130.8
Midmean - Weighted Average at Xnp122.889189189189
Midmean - Weighted Average at X(n+1)p123.105555555556
Midmean - Empirical Distribution Function122.889189189189
Midmean - Empirical Distribution Function - Averaging123.105555555556
Midmean - Empirical Distribution Function - Interpolation123.105555555556
Midmean - Closest Observation122.889189189189
Midmean - True Basic - Statistics Graphics Toolkit123.105555555556
Midmean - MS Excel (old versions)123.107894736842
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 124.186111111111 & 1.43142725314519 & 86.756844148555 \tabularnewline
Geometric Mean & 123.617297430520 &  &  \tabularnewline
Harmonic Mean & 123.063534373882 &  &  \tabularnewline
Quadratic Mean & 124.770461470476 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 124.170833333333 & 1.40743392607248 & 88.2249823832506 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 124.018055555556 & 1.35079430407176 & 91.8112070666291 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 123.951388888889 & 1.30905715908713 & 94.6875298977216 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 123.790277777778 & 1.23762759529712 & 100.022234675576 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 123.797222222222 & 1.19877998137645 & 103.269343954240 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 123.555555555556 & 1.11004780890867 & 111.306517218414 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 123.497222222222 & 1.09200926821661 & 113.091734490412 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 123.719444444444 & 1.03413122097459 & 119.636117675519 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 123.706944444444 & 1.01901584665361 & 121.398450132734 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 123.873611111111 & 0.99337593461826 & 124.699629610731 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 123.888888888889 & 0.981032071990356 & 126.284239247692 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 123.672222222222 & 0.931695457201317 & 132.738891519034 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 123.509722222222 & 0.887083808213349 & 139.231176444286 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 123.509722222222 & 0.862921121982188 & 143.129793762044 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 123.218055555556 & 0.79801280575013 & 154.406113119615 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 123.151388888889 & 0.781408065213118 & 157.601891215829 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 123.127777777778 & 0.770949514711597 & 159.709261667852 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 123.127777777778 & 0.756286181307621 & 162.805801323633 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 123.048611111111 & 0.721793521946388 & 170.476192110035 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 122.826388888889 & 0.674670246514479 & 182.053958246183 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 122.797222222222 & 0.645966697489387 & 190.098379219061 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 122.766666666667 & 0.599190899429649 & 204.887401967427 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 122.798611111111 & 0.53312603459403 & 230.336924372154 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 123.165277777778 & 0.472975298209166 & 260.405307093458 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 123.997142857143 & 1.33501494075676 & 92.8807154673898 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 123.813235294118 & 1.24712118789428 & 99.2792332420972 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 123.701515151515 & 1.17895986005808 & 104.924280581886 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 123.6078125 & 1.11674729783409 & 110.685571158072 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 123.554838709677 & 1.06965173073421 & 115.509408492117 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 123.496666666667 & 1.02542802601394 & 120.434261141394 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 123.484482758621 & 0.998004062939579 & 123.731442931106 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 123.482142857143 & 0.969060688404375 & 127.424571375880 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 123.442592592593 & 0.947605765387564 & 130.267878374617 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 123.401923076923 & 0.924170535870495 & 133.527220666788 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 123.334 & 0.900175085010394 & 137.011123784409 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 123.258333333333 & 0.872195776654094 & 141.319571399641 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 123.204347826087 & 0.8479184887093 & 145.302112722684 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 123.165909090909 & 0.82659253162514 & 149.004381697904 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 123.123809523810 & 0.803764441051791 & 153.183946981646 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 123.1125 & 0.788362368685222 & 156.162324446458 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 123.107894736842 & 0.770669487627473 & 159.741493225368 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 123.105555555556 & 0.748256645179095 & 164.523170423819 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 123.102941176471 & 0.720349554854147 & 170.893339694499 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 123.109375 & 0.69027459728521 & 178.348407263107 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 123.143333333333 & 0.660575912668989 & 186.418140552212 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 123.185714285714 & 0.625382724843055 & 196.976522363372 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 123.238461538462 & 0.588402711991787 & 209.445774172743 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 123.295833333333 & 0.556531675683107 & 221.543244923113 \tabularnewline
Median & 124.35 &  &  \tabularnewline
Midrange & 130.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 122.889189189189 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 123.105555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 122.889189189189 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 123.105555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 123.105555555556 &  &  \tabularnewline
Midmean - Closest Observation & 122.889189189189 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 123.105555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 123.107894736842 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=83551&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]124.186111111111[/C][C]1.43142725314519[/C][C]86.756844148555[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]123.617297430520[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]123.063534373882[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]124.770461470476[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]124.170833333333[/C][C]1.40743392607248[/C][C]88.2249823832506[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]124.018055555556[/C][C]1.35079430407176[/C][C]91.8112070666291[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]123.951388888889[/C][C]1.30905715908713[/C][C]94.6875298977216[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]123.790277777778[/C][C]1.23762759529712[/C][C]100.022234675576[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]123.797222222222[/C][C]1.19877998137645[/C][C]103.269343954240[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]123.555555555556[/C][C]1.11004780890867[/C][C]111.306517218414[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]123.497222222222[/C][C]1.09200926821661[/C][C]113.091734490412[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]123.719444444444[/C][C]1.03413122097459[/C][C]119.636117675519[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]123.706944444444[/C][C]1.01901584665361[/C][C]121.398450132734[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]123.873611111111[/C][C]0.99337593461826[/C][C]124.699629610731[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]123.888888888889[/C][C]0.981032071990356[/C][C]126.284239247692[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]123.672222222222[/C][C]0.931695457201317[/C][C]132.738891519034[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]123.509722222222[/C][C]0.887083808213349[/C][C]139.231176444286[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]123.509722222222[/C][C]0.862921121982188[/C][C]143.129793762044[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]123.218055555556[/C][C]0.79801280575013[/C][C]154.406113119615[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]123.151388888889[/C][C]0.781408065213118[/C][C]157.601891215829[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]123.127777777778[/C][C]0.770949514711597[/C][C]159.709261667852[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]123.127777777778[/C][C]0.756286181307621[/C][C]162.805801323633[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]123.048611111111[/C][C]0.721793521946388[/C][C]170.476192110035[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]122.826388888889[/C][C]0.674670246514479[/C][C]182.053958246183[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]122.797222222222[/C][C]0.645966697489387[/C][C]190.098379219061[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]122.766666666667[/C][C]0.599190899429649[/C][C]204.887401967427[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]122.798611111111[/C][C]0.53312603459403[/C][C]230.336924372154[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]123.165277777778[/C][C]0.472975298209166[/C][C]260.405307093458[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]123.997142857143[/C][C]1.33501494075676[/C][C]92.8807154673898[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]123.813235294118[/C][C]1.24712118789428[/C][C]99.2792332420972[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]123.701515151515[/C][C]1.17895986005808[/C][C]104.924280581886[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]123.6078125[/C][C]1.11674729783409[/C][C]110.685571158072[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]123.554838709677[/C][C]1.06965173073421[/C][C]115.509408492117[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]123.496666666667[/C][C]1.02542802601394[/C][C]120.434261141394[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]123.484482758621[/C][C]0.998004062939579[/C][C]123.731442931106[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]123.482142857143[/C][C]0.969060688404375[/C][C]127.424571375880[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]123.442592592593[/C][C]0.947605765387564[/C][C]130.267878374617[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]123.401923076923[/C][C]0.924170535870495[/C][C]133.527220666788[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]123.334[/C][C]0.900175085010394[/C][C]137.011123784409[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]123.258333333333[/C][C]0.872195776654094[/C][C]141.319571399641[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]123.204347826087[/C][C]0.8479184887093[/C][C]145.302112722684[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]123.165909090909[/C][C]0.82659253162514[/C][C]149.004381697904[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]123.123809523810[/C][C]0.803764441051791[/C][C]153.183946981646[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]123.1125[/C][C]0.788362368685222[/C][C]156.162324446458[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]123.107894736842[/C][C]0.770669487627473[/C][C]159.741493225368[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]123.105555555556[/C][C]0.748256645179095[/C][C]164.523170423819[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]123.102941176471[/C][C]0.720349554854147[/C][C]170.893339694499[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]123.109375[/C][C]0.69027459728521[/C][C]178.348407263107[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]123.143333333333[/C][C]0.660575912668989[/C][C]186.418140552212[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]123.185714285714[/C][C]0.625382724843055[/C][C]196.976522363372[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]123.238461538462[/C][C]0.588402711991787[/C][C]209.445774172743[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]123.295833333333[/C][C]0.556531675683107[/C][C]221.543244923113[/C][/ROW]
[ROW][C]Median[/C][C]124.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]130.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]122.889189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]123.105555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]122.889189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]123.105555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]123.105555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]122.889189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]123.105555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]123.107894736842[/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=83551&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=83551&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 Mean124.1861111111111.4314272531451986.756844148555
Geometric Mean123.617297430520
Harmonic Mean123.063534373882
Quadratic Mean124.770461470476
Winsorized Mean ( 1 / 24 )124.1708333333331.4074339260724888.2249823832506
Winsorized Mean ( 2 / 24 )124.0180555555561.3507943040717691.8112070666291
Winsorized Mean ( 3 / 24 )123.9513888888891.3090571590871394.6875298977216
Winsorized Mean ( 4 / 24 )123.7902777777781.23762759529712100.022234675576
Winsorized Mean ( 5 / 24 )123.7972222222221.19877998137645103.269343954240
Winsorized Mean ( 6 / 24 )123.5555555555561.11004780890867111.306517218414
Winsorized Mean ( 7 / 24 )123.4972222222221.09200926821661113.091734490412
Winsorized Mean ( 8 / 24 )123.7194444444441.03413122097459119.636117675519
Winsorized Mean ( 9 / 24 )123.7069444444441.01901584665361121.398450132734
Winsorized Mean ( 10 / 24 )123.8736111111110.99337593461826124.699629610731
Winsorized Mean ( 11 / 24 )123.8888888888890.981032071990356126.284239247692
Winsorized Mean ( 12 / 24 )123.6722222222220.931695457201317132.738891519034
Winsorized Mean ( 13 / 24 )123.5097222222220.887083808213349139.231176444286
Winsorized Mean ( 14 / 24 )123.5097222222220.862921121982188143.129793762044
Winsorized Mean ( 15 / 24 )123.2180555555560.79801280575013154.406113119615
Winsorized Mean ( 16 / 24 )123.1513888888890.781408065213118157.601891215829
Winsorized Mean ( 17 / 24 )123.1277777777780.770949514711597159.709261667852
Winsorized Mean ( 18 / 24 )123.1277777777780.756286181307621162.805801323633
Winsorized Mean ( 19 / 24 )123.0486111111110.721793521946388170.476192110035
Winsorized Mean ( 20 / 24 )122.8263888888890.674670246514479182.053958246183
Winsorized Mean ( 21 / 24 )122.7972222222220.645966697489387190.098379219061
Winsorized Mean ( 22 / 24 )122.7666666666670.599190899429649204.887401967427
Winsorized Mean ( 23 / 24 )122.7986111111110.53312603459403230.336924372154
Winsorized Mean ( 24 / 24 )123.1652777777780.472975298209166260.405307093458
Trimmed Mean ( 1 / 24 )123.9971428571431.3350149407567692.8807154673898
Trimmed Mean ( 2 / 24 )123.8132352941181.2471211878942899.2792332420972
Trimmed Mean ( 3 / 24 )123.7015151515151.17895986005808104.924280581886
Trimmed Mean ( 4 / 24 )123.60781251.11674729783409110.685571158072
Trimmed Mean ( 5 / 24 )123.5548387096771.06965173073421115.509408492117
Trimmed Mean ( 6 / 24 )123.4966666666671.02542802601394120.434261141394
Trimmed Mean ( 7 / 24 )123.4844827586210.998004062939579123.731442931106
Trimmed Mean ( 8 / 24 )123.4821428571430.969060688404375127.424571375880
Trimmed Mean ( 9 / 24 )123.4425925925930.947605765387564130.267878374617
Trimmed Mean ( 10 / 24 )123.4019230769230.924170535870495133.527220666788
Trimmed Mean ( 11 / 24 )123.3340.900175085010394137.011123784409
Trimmed Mean ( 12 / 24 )123.2583333333330.872195776654094141.319571399641
Trimmed Mean ( 13 / 24 )123.2043478260870.8479184887093145.302112722684
Trimmed Mean ( 14 / 24 )123.1659090909090.82659253162514149.004381697904
Trimmed Mean ( 15 / 24 )123.1238095238100.803764441051791153.183946981646
Trimmed Mean ( 16 / 24 )123.11250.788362368685222156.162324446458
Trimmed Mean ( 17 / 24 )123.1078947368420.770669487627473159.741493225368
Trimmed Mean ( 18 / 24 )123.1055555555560.748256645179095164.523170423819
Trimmed Mean ( 19 / 24 )123.1029411764710.720349554854147170.893339694499
Trimmed Mean ( 20 / 24 )123.1093750.69027459728521178.348407263107
Trimmed Mean ( 21 / 24 )123.1433333333330.660575912668989186.418140552212
Trimmed Mean ( 22 / 24 )123.1857142857140.625382724843055196.976522363372
Trimmed Mean ( 23 / 24 )123.2384615384620.588402711991787209.445774172743
Trimmed Mean ( 24 / 24 )123.2958333333330.556531675683107221.543244923113
Median124.35
Midrange130.8
Midmean - Weighted Average at Xnp122.889189189189
Midmean - Weighted Average at X(n+1)p123.105555555556
Midmean - Empirical Distribution Function122.889189189189
Midmean - Empirical Distribution Function - Averaging123.105555555556
Midmean - Empirical Distribution Function - Interpolation123.105555555556
Midmean - Closest Observation122.889189189189
Midmean - True Basic - Statistics Graphics Toolkit123.105555555556
Midmean - MS Excel (old versions)123.107894736842
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')