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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 computationTue, 05 Mar 2013 14:52:54 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/05/t1362513231xot7d87vru9w887.htm/, Retrieved Sat, 04 May 2024 12:11:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207493, Retrieved Sat, 04 May 2024 12:11:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsyasmien.naciri@student.kdg.be
Estimated Impact64
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-03-05 19:52:54] [d06e8713ea83045a022ab0926c74dd0b] [Current]
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Dataseries X:
557
561
549
532
526
511
499
555
565
542
527
510
514
517
508
493
490
469
478
528
534
518
506
502
516
528
533
536
537
524
536
587
597
581
564
558
575
580
575
563
552
537
545
601
604
586
564
549
551
556
548
540
531
521
519
572
581
563
548
539
541
562
559
546
536
528
530
582
599
584
571
563
565




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207493&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207493&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207493&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean544.5753424657533.45078012754622157.812240228992
Geometric Mean543.781095692017
Harmonic Mean542.979435140058
Quadratic Mean545.361963500276
Winsorized Mean ( 1 / 24 )544.6575342465753.4056213701876159.928974786934
Winsorized Mean ( 2 / 24 )544.9315068493153.31044244946716164.60987169163
Winsorized Mean ( 3 / 24 )544.9726027397263.26417833442225166.955523536426
Winsorized Mean ( 4 / 24 )544.7534246575343.08077339256164176.823594352253
Winsorized Mean ( 5 / 24 )544.8904109589043.02636572713826180.04777349701
Winsorized Mean ( 6 / 24 )545.0547945205482.93290589526351185.841214817285
Winsorized Mean ( 7 / 24 )545.0547945205482.86305193219102190.375448098642
Winsorized Mean ( 8 / 24 )545.1643835616442.80471809077721194.374039000324
Winsorized Mean ( 9 / 24 )545.2876712328772.78343651218641195.904475940265
Winsorized Mean ( 10 / 24 )545.5616438356162.69039007298449202.781614946422
Winsorized Mean ( 11 / 24 )545.1095890410962.51218958598255216.985848553264
Winsorized Mean ( 12 / 24 )545.273972602742.48597743716676219.339871895291
Winsorized Mean ( 13 / 24 )544.9178082191782.37108673238404229.817745920784
Winsorized Mean ( 14 / 24 )544.9178082191782.31078088633782235.815438599536
Winsorized Mean ( 15 / 24 )544.0958904109592.06285961613383263.758079394027
Winsorized Mean ( 16 / 24 )544.7534246575341.96339996688232277.454127455521
Winsorized Mean ( 17 / 24 )544.9863013698631.86303188503971292.526556172304
Winsorized Mean ( 18 / 24 )545.2328767123291.82850344982912298.185314751954
Winsorized Mean ( 19 / 24 )545.2328767123291.75589034208696310.516473405904
Winsorized Mean ( 20 / 24 )545.2328767123291.75589034208696310.516473405904
Winsorized Mean ( 21 / 24 )545.2328767123291.75589034208696310.516473405904
Winsorized Mean ( 22 / 24 )545.5342465753421.63265317491699334.139702759026
Winsorized Mean ( 23 / 24 )545.5342465753421.54733558394856352.563627589578
Winsorized Mean ( 24 / 24 )545.2054794520551.41434256097954385.483329494417
Trimmed Mean ( 1 / 24 )544.8028169014093.27607138961026166.297602252868
Trimmed Mean ( 2 / 24 )544.956521739133.12153881862254174.579447318745
Trimmed Mean ( 3 / 24 )544.9701492537312.99924384781236181.702514669232
Trimmed Mean ( 4 / 24 )544.9692307692312.87437026805348189.596043636467
Trimmed Mean ( 5 / 24 )545.0317460317462.79390825281085195.078612722308
Trimmed Mean ( 6 / 24 )545.0655737704922.71404652746711200.831329991669
Trimmed Mean ( 7 / 24 )545.0677966101692.64374745170864206.172414939973
Trimmed Mean ( 8 / 24 )545.0701754385962.57589798065035211.603945316569
Trimmed Mean ( 9 / 24 )545.0545454545452.5064789019804217.458261876408
Trimmed Mean ( 10 / 24 )545.0188679245282.42499840139366224.750196788296
Trimmed Mean ( 11 / 24 )544.9411764705882.34485866704089232.398303629225
Trimmed Mean ( 12 / 24 )544.9183673469392.28493973757111238.482599075539
Trimmed Mean ( 13 / 24 )544.8723404255322.21374417998737246.131574439031
Trimmed Mean ( 14 / 24 )544.8666666666672.14819633058701253.639138522213
Trimmed Mean ( 15 / 24 )544.8604651162792.0762276773152262.428090651815
Trimmed Mean ( 16 / 24 )544.9512195121952.03773882919045267.429374022721
Trimmed Mean ( 17 / 24 )544.9743589743592.00690010102702271.550317175963
Trimmed Mean ( 18 / 24 )544.9729729729731.98473396167556274.582379047363
Trimmed Mean ( 19 / 24 )544.9428571428571.95793702834457278.32501722673
Trimmed Mean ( 20 / 24 )544.9090909090911.93373345341868281.791210647847
Trimmed Mean ( 21 / 24 )544.8709677419351.89381672733649287.710505392068
Trimmed Mean ( 22 / 24 )544.8275862068971.83095237911162297.565131907608
Trimmed Mean ( 23 / 24 )544.7407407407411.77317185868565307.212602135771
Trimmed Mean ( 24 / 24 )544.641.70965883536258318.566481648073
Median545
Midrange536.5
Midmean - Weighted Average at Xnp544.444444444444
Midmean - Weighted Average at X(n+1)p545.473684210526
Midmean - Empirical Distribution Function545.473684210526
Midmean - Empirical Distribution Function - Averaging545.473684210526
Midmean - Empirical Distribution Function - Interpolation545.473684210526
Midmean - Closest Observation544.974358974359
Midmean - True Basic - Statistics Graphics Toolkit545.473684210526
Midmean - MS Excel (old versions)545.473684210526
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 544.575342465753 & 3.45078012754622 & 157.812240228992 \tabularnewline
Geometric Mean & 543.781095692017 &  &  \tabularnewline
Harmonic Mean & 542.979435140058 &  &  \tabularnewline
Quadratic Mean & 545.361963500276 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 544.657534246575 & 3.4056213701876 & 159.928974786934 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 544.931506849315 & 3.31044244946716 & 164.60987169163 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 544.972602739726 & 3.26417833442225 & 166.955523536426 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 544.753424657534 & 3.08077339256164 & 176.823594352253 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 544.890410958904 & 3.02636572713826 & 180.04777349701 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 545.054794520548 & 2.93290589526351 & 185.841214817285 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 545.054794520548 & 2.86305193219102 & 190.375448098642 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 545.164383561644 & 2.80471809077721 & 194.374039000324 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 545.287671232877 & 2.78343651218641 & 195.904475940265 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 545.561643835616 & 2.69039007298449 & 202.781614946422 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 545.109589041096 & 2.51218958598255 & 216.985848553264 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 545.27397260274 & 2.48597743716676 & 219.339871895291 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 544.917808219178 & 2.37108673238404 & 229.817745920784 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 544.917808219178 & 2.31078088633782 & 235.815438599536 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 544.095890410959 & 2.06285961613383 & 263.758079394027 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 544.753424657534 & 1.96339996688232 & 277.454127455521 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 544.986301369863 & 1.86303188503971 & 292.526556172304 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 545.232876712329 & 1.82850344982912 & 298.185314751954 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 545.232876712329 & 1.75589034208696 & 310.516473405904 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 545.232876712329 & 1.75589034208696 & 310.516473405904 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 545.232876712329 & 1.75589034208696 & 310.516473405904 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 545.534246575342 & 1.63265317491699 & 334.139702759026 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 545.534246575342 & 1.54733558394856 & 352.563627589578 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 545.205479452055 & 1.41434256097954 & 385.483329494417 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 544.802816901409 & 3.27607138961026 & 166.297602252868 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 544.95652173913 & 3.12153881862254 & 174.579447318745 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 544.970149253731 & 2.99924384781236 & 181.702514669232 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 544.969230769231 & 2.87437026805348 & 189.596043636467 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 545.031746031746 & 2.79390825281085 & 195.078612722308 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 545.065573770492 & 2.71404652746711 & 200.831329991669 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 545.067796610169 & 2.64374745170864 & 206.172414939973 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 545.070175438596 & 2.57589798065035 & 211.603945316569 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 545.054545454545 & 2.5064789019804 & 217.458261876408 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 545.018867924528 & 2.42499840139366 & 224.750196788296 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 544.941176470588 & 2.34485866704089 & 232.398303629225 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 544.918367346939 & 2.28493973757111 & 238.482599075539 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 544.872340425532 & 2.21374417998737 & 246.131574439031 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 544.866666666667 & 2.14819633058701 & 253.639138522213 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 544.860465116279 & 2.0762276773152 & 262.428090651815 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 544.951219512195 & 2.03773882919045 & 267.429374022721 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 544.974358974359 & 2.00690010102702 & 271.550317175963 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 544.972972972973 & 1.98473396167556 & 274.582379047363 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 544.942857142857 & 1.95793702834457 & 278.32501722673 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 544.909090909091 & 1.93373345341868 & 281.791210647847 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 544.870967741935 & 1.89381672733649 & 287.710505392068 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 544.827586206897 & 1.83095237911162 & 297.565131907608 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 544.740740740741 & 1.77317185868565 & 307.212602135771 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 544.64 & 1.70965883536258 & 318.566481648073 \tabularnewline
Median & 545 &  &  \tabularnewline
Midrange & 536.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 544.444444444444 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 545.473684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 545.473684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 545.473684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 545.473684210526 &  &  \tabularnewline
Midmean - Closest Observation & 544.974358974359 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 545.473684210526 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 545.473684210526 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207493&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]544.575342465753[/C][C]3.45078012754622[/C][C]157.812240228992[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]543.781095692017[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]542.979435140058[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]545.361963500276[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]544.657534246575[/C][C]3.4056213701876[/C][C]159.928974786934[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]544.931506849315[/C][C]3.31044244946716[/C][C]164.60987169163[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]544.972602739726[/C][C]3.26417833442225[/C][C]166.955523536426[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]544.753424657534[/C][C]3.08077339256164[/C][C]176.823594352253[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]544.890410958904[/C][C]3.02636572713826[/C][C]180.04777349701[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]545.054794520548[/C][C]2.93290589526351[/C][C]185.841214817285[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]545.054794520548[/C][C]2.86305193219102[/C][C]190.375448098642[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]545.164383561644[/C][C]2.80471809077721[/C][C]194.374039000324[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]545.287671232877[/C][C]2.78343651218641[/C][C]195.904475940265[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]545.561643835616[/C][C]2.69039007298449[/C][C]202.781614946422[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]545.109589041096[/C][C]2.51218958598255[/C][C]216.985848553264[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]545.27397260274[/C][C]2.48597743716676[/C][C]219.339871895291[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]544.917808219178[/C][C]2.37108673238404[/C][C]229.817745920784[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]544.917808219178[/C][C]2.31078088633782[/C][C]235.815438599536[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]544.095890410959[/C][C]2.06285961613383[/C][C]263.758079394027[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]544.753424657534[/C][C]1.96339996688232[/C][C]277.454127455521[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]544.986301369863[/C][C]1.86303188503971[/C][C]292.526556172304[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]545.232876712329[/C][C]1.82850344982912[/C][C]298.185314751954[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]545.232876712329[/C][C]1.75589034208696[/C][C]310.516473405904[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]545.232876712329[/C][C]1.75589034208696[/C][C]310.516473405904[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]545.232876712329[/C][C]1.75589034208696[/C][C]310.516473405904[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]545.534246575342[/C][C]1.63265317491699[/C][C]334.139702759026[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]545.534246575342[/C][C]1.54733558394856[/C][C]352.563627589578[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]545.205479452055[/C][C]1.41434256097954[/C][C]385.483329494417[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]544.802816901409[/C][C]3.27607138961026[/C][C]166.297602252868[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]544.95652173913[/C][C]3.12153881862254[/C][C]174.579447318745[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]544.970149253731[/C][C]2.99924384781236[/C][C]181.702514669232[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]544.969230769231[/C][C]2.87437026805348[/C][C]189.596043636467[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]545.031746031746[/C][C]2.79390825281085[/C][C]195.078612722308[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]545.065573770492[/C][C]2.71404652746711[/C][C]200.831329991669[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]545.067796610169[/C][C]2.64374745170864[/C][C]206.172414939973[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]545.070175438596[/C][C]2.57589798065035[/C][C]211.603945316569[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]545.054545454545[/C][C]2.5064789019804[/C][C]217.458261876408[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]545.018867924528[/C][C]2.42499840139366[/C][C]224.750196788296[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]544.941176470588[/C][C]2.34485866704089[/C][C]232.398303629225[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]544.918367346939[/C][C]2.28493973757111[/C][C]238.482599075539[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]544.872340425532[/C][C]2.21374417998737[/C][C]246.131574439031[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]544.866666666667[/C][C]2.14819633058701[/C][C]253.639138522213[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]544.860465116279[/C][C]2.0762276773152[/C][C]262.428090651815[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]544.951219512195[/C][C]2.03773882919045[/C][C]267.429374022721[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]544.974358974359[/C][C]2.00690010102702[/C][C]271.550317175963[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]544.972972972973[/C][C]1.98473396167556[/C][C]274.582379047363[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]544.942857142857[/C][C]1.95793702834457[/C][C]278.32501722673[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]544.909090909091[/C][C]1.93373345341868[/C][C]281.791210647847[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]544.870967741935[/C][C]1.89381672733649[/C][C]287.710505392068[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]544.827586206897[/C][C]1.83095237911162[/C][C]297.565131907608[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]544.740740740741[/C][C]1.77317185868565[/C][C]307.212602135771[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]544.64[/C][C]1.70965883536258[/C][C]318.566481648073[/C][/ROW]
[ROW][C]Median[/C][C]545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]536.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]544.444444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]545.473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]545.473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]545.473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]545.473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]544.974358974359[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]545.473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]545.473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207493&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207493&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 Mean544.5753424657533.45078012754622157.812240228992
Geometric Mean543.781095692017
Harmonic Mean542.979435140058
Quadratic Mean545.361963500276
Winsorized Mean ( 1 / 24 )544.6575342465753.4056213701876159.928974786934
Winsorized Mean ( 2 / 24 )544.9315068493153.31044244946716164.60987169163
Winsorized Mean ( 3 / 24 )544.9726027397263.26417833442225166.955523536426
Winsorized Mean ( 4 / 24 )544.7534246575343.08077339256164176.823594352253
Winsorized Mean ( 5 / 24 )544.8904109589043.02636572713826180.04777349701
Winsorized Mean ( 6 / 24 )545.0547945205482.93290589526351185.841214817285
Winsorized Mean ( 7 / 24 )545.0547945205482.86305193219102190.375448098642
Winsorized Mean ( 8 / 24 )545.1643835616442.80471809077721194.374039000324
Winsorized Mean ( 9 / 24 )545.2876712328772.78343651218641195.904475940265
Winsorized Mean ( 10 / 24 )545.5616438356162.69039007298449202.781614946422
Winsorized Mean ( 11 / 24 )545.1095890410962.51218958598255216.985848553264
Winsorized Mean ( 12 / 24 )545.273972602742.48597743716676219.339871895291
Winsorized Mean ( 13 / 24 )544.9178082191782.37108673238404229.817745920784
Winsorized Mean ( 14 / 24 )544.9178082191782.31078088633782235.815438599536
Winsorized Mean ( 15 / 24 )544.0958904109592.06285961613383263.758079394027
Winsorized Mean ( 16 / 24 )544.7534246575341.96339996688232277.454127455521
Winsorized Mean ( 17 / 24 )544.9863013698631.86303188503971292.526556172304
Winsorized Mean ( 18 / 24 )545.2328767123291.82850344982912298.185314751954
Winsorized Mean ( 19 / 24 )545.2328767123291.75589034208696310.516473405904
Winsorized Mean ( 20 / 24 )545.2328767123291.75589034208696310.516473405904
Winsorized Mean ( 21 / 24 )545.2328767123291.75589034208696310.516473405904
Winsorized Mean ( 22 / 24 )545.5342465753421.63265317491699334.139702759026
Winsorized Mean ( 23 / 24 )545.5342465753421.54733558394856352.563627589578
Winsorized Mean ( 24 / 24 )545.2054794520551.41434256097954385.483329494417
Trimmed Mean ( 1 / 24 )544.8028169014093.27607138961026166.297602252868
Trimmed Mean ( 2 / 24 )544.956521739133.12153881862254174.579447318745
Trimmed Mean ( 3 / 24 )544.9701492537312.99924384781236181.702514669232
Trimmed Mean ( 4 / 24 )544.9692307692312.87437026805348189.596043636467
Trimmed Mean ( 5 / 24 )545.0317460317462.79390825281085195.078612722308
Trimmed Mean ( 6 / 24 )545.0655737704922.71404652746711200.831329991669
Trimmed Mean ( 7 / 24 )545.0677966101692.64374745170864206.172414939973
Trimmed Mean ( 8 / 24 )545.0701754385962.57589798065035211.603945316569
Trimmed Mean ( 9 / 24 )545.0545454545452.5064789019804217.458261876408
Trimmed Mean ( 10 / 24 )545.0188679245282.42499840139366224.750196788296
Trimmed Mean ( 11 / 24 )544.9411764705882.34485866704089232.398303629225
Trimmed Mean ( 12 / 24 )544.9183673469392.28493973757111238.482599075539
Trimmed Mean ( 13 / 24 )544.8723404255322.21374417998737246.131574439031
Trimmed Mean ( 14 / 24 )544.8666666666672.14819633058701253.639138522213
Trimmed Mean ( 15 / 24 )544.8604651162792.0762276773152262.428090651815
Trimmed Mean ( 16 / 24 )544.9512195121952.03773882919045267.429374022721
Trimmed Mean ( 17 / 24 )544.9743589743592.00690010102702271.550317175963
Trimmed Mean ( 18 / 24 )544.9729729729731.98473396167556274.582379047363
Trimmed Mean ( 19 / 24 )544.9428571428571.95793702834457278.32501722673
Trimmed Mean ( 20 / 24 )544.9090909090911.93373345341868281.791210647847
Trimmed Mean ( 21 / 24 )544.8709677419351.89381672733649287.710505392068
Trimmed Mean ( 22 / 24 )544.8275862068971.83095237911162297.565131907608
Trimmed Mean ( 23 / 24 )544.7407407407411.77317185868565307.212602135771
Trimmed Mean ( 24 / 24 )544.641.70965883536258318.566481648073
Median545
Midrange536.5
Midmean - Weighted Average at Xnp544.444444444444
Midmean - Weighted Average at X(n+1)p545.473684210526
Midmean - Empirical Distribution Function545.473684210526
Midmean - Empirical Distribution Function - Averaging545.473684210526
Midmean - Empirical Distribution Function - Interpolation545.473684210526
Midmean - Closest Observation544.974358974359
Midmean - True Basic - Statistics Graphics Toolkit545.473684210526
Midmean - MS Excel (old versions)545.473684210526
Number of observations73



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')