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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, 05 Jun 2009 08:17:56 -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/Jun/05/t124421168529xs4cbc0xkcnq4.htm/, Retrieved Thu, 09 May 2024 20:57:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41845, Retrieved Thu, 09 May 2024 20:57:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Jurgen Leemans - ...] [2009-06-05 14:17:56] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
163,40
162,89
162,29
161,26
161,43
161,44
161,44
161,44
161,92
162,23
161,89
161,40
161,40
159,55
158,93
158,59
158,29
158,03
158,03
163,94
164,36
164,39
163,22
163,22
163,56
162,82
162,80
162,44
161,98
161,53
161,53
161,52
162,07
161,84
161,54
161,47
161,47
161,54
161,57
160,75
160,31
160,57
160,57
159,65
158,76
158,95
159,25
158,72
158,72
158,72
158,53
157,92
157,89
157,81
157,81
157,88
157,52
156,11
155,61
155,31
155,31
155,31
153,09
151,94
151,73
151,65
151,65
151,09
149,94
149,47
149,15
149,22




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41845&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41845&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41845&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean159.0495833333330.469385667059117338.846271829817
Geometric Mean158.999500394690
Harmonic Mean158.948497995282
Quadratic Mean159.098751989832
Winsorized Mean ( 1 / 24 )159.0501388888890.469031169947643339.103558739269
Winsorized Mean ( 2 / 24 )159.0454166666670.465204699315536341.882652734749
Winsorized Mean ( 3 / 24 )159.0491666666670.457344890199452347.766357676597
Winsorized Mean ( 4 / 24 )159.1041666666670.438923082352959362.487581682304
Winsorized Mean ( 5 / 24 )159.1305555555560.427422804572817372.302445852408
Winsorized Mean ( 6 / 24 )159.1305555555560.427422804572817372.302445852408
Winsorized Mean ( 7 / 24 )159.106250.421313452124798377.643412992355
Winsorized Mean ( 8 / 24 )159.1218055555560.414609538129004383.787132041437
Winsorized Mean ( 9 / 24 )159.2630555555560.380272822276126418.812616169321
Winsorized Mean ( 10 / 24 )159.5213888888890.308163086202406517.652489967967
Winsorized Mean ( 11 / 24 )159.4984722222220.30515803518293522.674987491675
Winsorized Mean ( 12 / 24 )159.4884722222220.303878467215649524.842953446386
Winsorized Mean ( 13 / 24 )159.513750.289862929501274550.307520435444
Winsorized Mean ( 14 / 24 )159.5934722222220.269604718457382591.953557546695
Winsorized Mean ( 15 / 24 )159.8747222222220.218522207326317731.617734317881
Winsorized Mean ( 16 / 24 )159.93250.208116013413489768.477626381604
Winsorized Mean ( 17 / 24 )159.9206944444440.206561510274668774.203743145542
Winsorized Mean ( 18 / 24 )159.8706944444440.195490467649096817.79278737729
Winsorized Mean ( 19 / 24 )159.8654166666670.194146635761791823.426149206183
Winsorized Mean ( 20 / 24 )159.873750.192955296328098828.553312826164
Winsorized Mean ( 21 / 24 )159.9029166666670.188061879810118850.267565272225
Winsorized Mean ( 22 / 24 )159.9029166666670.188061879810118850.267565272225
Winsorized Mean ( 23 / 24 )159.9827777777780.176220783571873907.854195941237
Winsorized Mean ( 24 / 24 )160.0461111111110.163532928199369978.678195720884
Trimmed Mean ( 1 / 24 )159.1147142857140.454895602494556349.782924726380
Trimmed Mean ( 2 / 24 )159.1830882352940.437923418952581363.49526274714
Trimmed Mean ( 3 / 24 )159.2581818181820.419898750649224379.277579587807
Trimmed Mean ( 4 / 24 )159.33656250.401715024921299396.640784175837
Trimmed Mean ( 5 / 24 )159.4040322580650.386807941886915412.101239391478
Trimmed Mean ( 6 / 24 )159.4696666666670.372394600161918428.227655818126
Trimmed Mean ( 7 / 24 )159.5398275862070.354481079232924450.065848172889
Trimmed Mean ( 8 / 24 )159.6194642857140.333638580763993478.420283170503
Trimmed Mean ( 9 / 24 )159.7024074074070.308996361767041516.842355340775
Trimmed Mean ( 10 / 24 )159.770.287827195937016555.090006279191
Trimmed Mean ( 11 / 24 )159.80580.280392595028718569.935878597766
Trimmed Mean ( 12 / 24 )159.8477083333330.271382760690396589.012020979821
Trimmed Mean ( 13 / 24 )159.8945652173910.259862599614544615.304262539373
Trimmed Mean ( 14 / 24 )159.94250.248242261514214644.30004393447
Trimmed Mean ( 15 / 24 )159.9852380952380.238165715469290671.739161868860
Trimmed Mean ( 16 / 24 )159.99850.237304724039118674.232258324639
Trimmed Mean ( 17 / 24 )160.0063157894740.237757847169854672.980167401857
Trimmed Mean ( 18 / 24 )160.0163888888890.237863557253919672.723433283524
Trimmed Mean ( 19 / 24 )160.0335294117650.239394989930309668.491556395363
Trimmed Mean ( 20 / 24 )160.05343750.240599306074788665.228175887793
Trimmed Mean ( 21 / 24 )160.0750.241283802944206663.430358966181
Trimmed Mean ( 22 / 24 )160.0960714285710.242173982719601661.078740295307
Trimmed Mean ( 23 / 24 )160.1203846153850.241781516611895662.252379169282
Trimmed Mean ( 24 / 24 )160.1383333333330.243319932130479658.138985701592
Median160.44
Midrange156.77
Midmean - Weighted Average at Xnp159.900263157895
Midmean - Weighted Average at X(n+1)p160.016388888889
Midmean - Empirical Distribution Function159.900263157895
Midmean - Empirical Distribution Function - Averaging160.016388888889
Midmean - Empirical Distribution Function - Interpolation160.016388888889
Midmean - Closest Observation159.900263157895
Midmean - True Basic - Statistics Graphics Toolkit160.016388888889
Midmean - MS Excel (old versions)159.95
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 159.049583333333 & 0.469385667059117 & 338.846271829817 \tabularnewline
Geometric Mean & 158.999500394690 &  &  \tabularnewline
Harmonic Mean & 158.948497995282 &  &  \tabularnewline
Quadratic Mean & 159.098751989832 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 159.050138888889 & 0.469031169947643 & 339.103558739269 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 159.045416666667 & 0.465204699315536 & 341.882652734749 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 159.049166666667 & 0.457344890199452 & 347.766357676597 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 159.104166666667 & 0.438923082352959 & 362.487581682304 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 159.130555555556 & 0.427422804572817 & 372.302445852408 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 159.130555555556 & 0.427422804572817 & 372.302445852408 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 159.10625 & 0.421313452124798 & 377.643412992355 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 159.121805555556 & 0.414609538129004 & 383.787132041437 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 159.263055555556 & 0.380272822276126 & 418.812616169321 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 159.521388888889 & 0.308163086202406 & 517.652489967967 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 159.498472222222 & 0.30515803518293 & 522.674987491675 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 159.488472222222 & 0.303878467215649 & 524.842953446386 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 159.51375 & 0.289862929501274 & 550.307520435444 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 159.593472222222 & 0.269604718457382 & 591.953557546695 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 159.874722222222 & 0.218522207326317 & 731.617734317881 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 159.9325 & 0.208116013413489 & 768.477626381604 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 159.920694444444 & 0.206561510274668 & 774.203743145542 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 159.870694444444 & 0.195490467649096 & 817.79278737729 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 159.865416666667 & 0.194146635761791 & 823.426149206183 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 159.87375 & 0.192955296328098 & 828.553312826164 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 159.902916666667 & 0.188061879810118 & 850.267565272225 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 159.902916666667 & 0.188061879810118 & 850.267565272225 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 159.982777777778 & 0.176220783571873 & 907.854195941237 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 160.046111111111 & 0.163532928199369 & 978.678195720884 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 159.114714285714 & 0.454895602494556 & 349.782924726380 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 159.183088235294 & 0.437923418952581 & 363.49526274714 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 159.258181818182 & 0.419898750649224 & 379.277579587807 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 159.3365625 & 0.401715024921299 & 396.640784175837 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 159.404032258065 & 0.386807941886915 & 412.101239391478 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 159.469666666667 & 0.372394600161918 & 428.227655818126 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 159.539827586207 & 0.354481079232924 & 450.065848172889 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 159.619464285714 & 0.333638580763993 & 478.420283170503 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 159.702407407407 & 0.308996361767041 & 516.842355340775 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 159.77 & 0.287827195937016 & 555.090006279191 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 159.8058 & 0.280392595028718 & 569.935878597766 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 159.847708333333 & 0.271382760690396 & 589.012020979821 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 159.894565217391 & 0.259862599614544 & 615.304262539373 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 159.9425 & 0.248242261514214 & 644.30004393447 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 159.985238095238 & 0.238165715469290 & 671.739161868860 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 159.9985 & 0.237304724039118 & 674.232258324639 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 160.006315789474 & 0.237757847169854 & 672.980167401857 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 160.016388888889 & 0.237863557253919 & 672.723433283524 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 160.033529411765 & 0.239394989930309 & 668.491556395363 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 160.0534375 & 0.240599306074788 & 665.228175887793 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 160.075 & 0.241283802944206 & 663.430358966181 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 160.096071428571 & 0.242173982719601 & 661.078740295307 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 160.120384615385 & 0.241781516611895 & 662.252379169282 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 160.138333333333 & 0.243319932130479 & 658.138985701592 \tabularnewline
Median & 160.44 &  &  \tabularnewline
Midrange & 156.77 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 159.900263157895 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 160.016388888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 159.900263157895 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 160.016388888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 160.016388888889 &  &  \tabularnewline
Midmean - Closest Observation & 159.900263157895 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 160.016388888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 159.95 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41845&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]159.049583333333[/C][C]0.469385667059117[/C][C]338.846271829817[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]158.999500394690[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]158.948497995282[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]159.098751989832[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]159.050138888889[/C][C]0.469031169947643[/C][C]339.103558739269[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]159.045416666667[/C][C]0.465204699315536[/C][C]341.882652734749[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]159.049166666667[/C][C]0.457344890199452[/C][C]347.766357676597[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]159.104166666667[/C][C]0.438923082352959[/C][C]362.487581682304[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]159.130555555556[/C][C]0.427422804572817[/C][C]372.302445852408[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]159.130555555556[/C][C]0.427422804572817[/C][C]372.302445852408[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]159.10625[/C][C]0.421313452124798[/C][C]377.643412992355[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]159.121805555556[/C][C]0.414609538129004[/C][C]383.787132041437[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]159.263055555556[/C][C]0.380272822276126[/C][C]418.812616169321[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]159.521388888889[/C][C]0.308163086202406[/C][C]517.652489967967[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]159.498472222222[/C][C]0.30515803518293[/C][C]522.674987491675[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]159.488472222222[/C][C]0.303878467215649[/C][C]524.842953446386[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]159.51375[/C][C]0.289862929501274[/C][C]550.307520435444[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]159.593472222222[/C][C]0.269604718457382[/C][C]591.953557546695[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]159.874722222222[/C][C]0.218522207326317[/C][C]731.617734317881[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]159.9325[/C][C]0.208116013413489[/C][C]768.477626381604[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]159.920694444444[/C][C]0.206561510274668[/C][C]774.203743145542[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]159.870694444444[/C][C]0.195490467649096[/C][C]817.79278737729[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]159.865416666667[/C][C]0.194146635761791[/C][C]823.426149206183[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]159.87375[/C][C]0.192955296328098[/C][C]828.553312826164[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]159.902916666667[/C][C]0.188061879810118[/C][C]850.267565272225[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]159.902916666667[/C][C]0.188061879810118[/C][C]850.267565272225[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]159.982777777778[/C][C]0.176220783571873[/C][C]907.854195941237[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]160.046111111111[/C][C]0.163532928199369[/C][C]978.678195720884[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]159.114714285714[/C][C]0.454895602494556[/C][C]349.782924726380[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]159.183088235294[/C][C]0.437923418952581[/C][C]363.49526274714[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]159.258181818182[/C][C]0.419898750649224[/C][C]379.277579587807[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]159.3365625[/C][C]0.401715024921299[/C][C]396.640784175837[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]159.404032258065[/C][C]0.386807941886915[/C][C]412.101239391478[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]159.469666666667[/C][C]0.372394600161918[/C][C]428.227655818126[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]159.539827586207[/C][C]0.354481079232924[/C][C]450.065848172889[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]159.619464285714[/C][C]0.333638580763993[/C][C]478.420283170503[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]159.702407407407[/C][C]0.308996361767041[/C][C]516.842355340775[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]159.77[/C][C]0.287827195937016[/C][C]555.090006279191[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]159.8058[/C][C]0.280392595028718[/C][C]569.935878597766[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]159.847708333333[/C][C]0.271382760690396[/C][C]589.012020979821[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]159.894565217391[/C][C]0.259862599614544[/C][C]615.304262539373[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]159.9425[/C][C]0.248242261514214[/C][C]644.30004393447[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]159.985238095238[/C][C]0.238165715469290[/C][C]671.739161868860[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]159.9985[/C][C]0.237304724039118[/C][C]674.232258324639[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]160.006315789474[/C][C]0.237757847169854[/C][C]672.980167401857[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]160.016388888889[/C][C]0.237863557253919[/C][C]672.723433283524[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]160.033529411765[/C][C]0.239394989930309[/C][C]668.491556395363[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]160.0534375[/C][C]0.240599306074788[/C][C]665.228175887793[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]160.075[/C][C]0.241283802944206[/C][C]663.430358966181[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]160.096071428571[/C][C]0.242173982719601[/C][C]661.078740295307[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]160.120384615385[/C][C]0.241781516611895[/C][C]662.252379169282[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]160.138333333333[/C][C]0.243319932130479[/C][C]658.138985701592[/C][/ROW]
[ROW][C]Median[/C][C]160.44[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]156.77[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]159.900263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]160.016388888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]159.900263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]160.016388888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]160.016388888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]159.900263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]160.016388888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]159.95[/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=41845&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41845&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 Mean159.0495833333330.469385667059117338.846271829817
Geometric Mean158.999500394690
Harmonic Mean158.948497995282
Quadratic Mean159.098751989832
Winsorized Mean ( 1 / 24 )159.0501388888890.469031169947643339.103558739269
Winsorized Mean ( 2 / 24 )159.0454166666670.465204699315536341.882652734749
Winsorized Mean ( 3 / 24 )159.0491666666670.457344890199452347.766357676597
Winsorized Mean ( 4 / 24 )159.1041666666670.438923082352959362.487581682304
Winsorized Mean ( 5 / 24 )159.1305555555560.427422804572817372.302445852408
Winsorized Mean ( 6 / 24 )159.1305555555560.427422804572817372.302445852408
Winsorized Mean ( 7 / 24 )159.106250.421313452124798377.643412992355
Winsorized Mean ( 8 / 24 )159.1218055555560.414609538129004383.787132041437
Winsorized Mean ( 9 / 24 )159.2630555555560.380272822276126418.812616169321
Winsorized Mean ( 10 / 24 )159.5213888888890.308163086202406517.652489967967
Winsorized Mean ( 11 / 24 )159.4984722222220.30515803518293522.674987491675
Winsorized Mean ( 12 / 24 )159.4884722222220.303878467215649524.842953446386
Winsorized Mean ( 13 / 24 )159.513750.289862929501274550.307520435444
Winsorized Mean ( 14 / 24 )159.5934722222220.269604718457382591.953557546695
Winsorized Mean ( 15 / 24 )159.8747222222220.218522207326317731.617734317881
Winsorized Mean ( 16 / 24 )159.93250.208116013413489768.477626381604
Winsorized Mean ( 17 / 24 )159.9206944444440.206561510274668774.203743145542
Winsorized Mean ( 18 / 24 )159.8706944444440.195490467649096817.79278737729
Winsorized Mean ( 19 / 24 )159.8654166666670.194146635761791823.426149206183
Winsorized Mean ( 20 / 24 )159.873750.192955296328098828.553312826164
Winsorized Mean ( 21 / 24 )159.9029166666670.188061879810118850.267565272225
Winsorized Mean ( 22 / 24 )159.9029166666670.188061879810118850.267565272225
Winsorized Mean ( 23 / 24 )159.9827777777780.176220783571873907.854195941237
Winsorized Mean ( 24 / 24 )160.0461111111110.163532928199369978.678195720884
Trimmed Mean ( 1 / 24 )159.1147142857140.454895602494556349.782924726380
Trimmed Mean ( 2 / 24 )159.1830882352940.437923418952581363.49526274714
Trimmed Mean ( 3 / 24 )159.2581818181820.419898750649224379.277579587807
Trimmed Mean ( 4 / 24 )159.33656250.401715024921299396.640784175837
Trimmed Mean ( 5 / 24 )159.4040322580650.386807941886915412.101239391478
Trimmed Mean ( 6 / 24 )159.4696666666670.372394600161918428.227655818126
Trimmed Mean ( 7 / 24 )159.5398275862070.354481079232924450.065848172889
Trimmed Mean ( 8 / 24 )159.6194642857140.333638580763993478.420283170503
Trimmed Mean ( 9 / 24 )159.7024074074070.308996361767041516.842355340775
Trimmed Mean ( 10 / 24 )159.770.287827195937016555.090006279191
Trimmed Mean ( 11 / 24 )159.80580.280392595028718569.935878597766
Trimmed Mean ( 12 / 24 )159.8477083333330.271382760690396589.012020979821
Trimmed Mean ( 13 / 24 )159.8945652173910.259862599614544615.304262539373
Trimmed Mean ( 14 / 24 )159.94250.248242261514214644.30004393447
Trimmed Mean ( 15 / 24 )159.9852380952380.238165715469290671.739161868860
Trimmed Mean ( 16 / 24 )159.99850.237304724039118674.232258324639
Trimmed Mean ( 17 / 24 )160.0063157894740.237757847169854672.980167401857
Trimmed Mean ( 18 / 24 )160.0163888888890.237863557253919672.723433283524
Trimmed Mean ( 19 / 24 )160.0335294117650.239394989930309668.491556395363
Trimmed Mean ( 20 / 24 )160.05343750.240599306074788665.228175887793
Trimmed Mean ( 21 / 24 )160.0750.241283802944206663.430358966181
Trimmed Mean ( 22 / 24 )160.0960714285710.242173982719601661.078740295307
Trimmed Mean ( 23 / 24 )160.1203846153850.241781516611895662.252379169282
Trimmed Mean ( 24 / 24 )160.1383333333330.243319932130479658.138985701592
Median160.44
Midrange156.77
Midmean - Weighted Average at Xnp159.900263157895
Midmean - Weighted Average at X(n+1)p160.016388888889
Midmean - Empirical Distribution Function159.900263157895
Midmean - Empirical Distribution Function - Averaging160.016388888889
Midmean - Empirical Distribution Function - Interpolation160.016388888889
Midmean - Closest Observation159.900263157895
Midmean - True Basic - Statistics Graphics Toolkit160.016388888889
Midmean - MS Excel (old versions)159.95
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')