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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Dec 2010 12:36:27 +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/Dec/20/t1292848511h9ecyklqem61r58.htm/, Retrieved Sat, 04 May 2024 01:35:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112878, Retrieved Sat, 04 May 2024 01:35:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Time needed to su...] [2010-09-25 09:42:08] [b98453cac15ba1066b407e146608df68]
-    D    [Central Tendency] [Central Tendency ...] [2010-12-20 12:36:27] [47bfda5353cd53c1cf7ea7aa9038654a] [Current]
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Dataseries X:
16,46
16,49
16,59
16,58
16,60
16,55
16,57
16,51
16,50
16,49
16,44
16,26
16,33
16,72
16,75
16,74
16,84
16,79
16,66
16,69
16,84
16,86
16,76
16,72
16,29
16,29
16,46
16,54
16,70
16,82
16,88
16,89
16,92
16,88
16,91
16,80
16,78
17,03
17,18
17,12
17,11
17,14
17,17
17,21
17,22
17,19
17,15
17,10
17,21
17,33
17,30
17,33
17,35
17,43
17,46
17,50
17,54
17,56
17,44
17,41
17,72
17,79
17,83
17,76
17,95
17,91
17,96
17,98
17,89
17,88
17,91
17,51
17,63




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112878&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112878&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112878&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17.05616438356160.0571266684281486298.567461622834
Geometric Mean17.0493158738721
Harmonic Mean17.0425082794281
Quadratic Mean17.0630510849838
Winsorized Mean ( 1 / 24 )17.0563013698630.0569875773698028299.298586763595
Winsorized Mean ( 2 / 24 )17.05602739726030.0569275286726668299.609482353123
Winsorized Mean ( 3 / 24 )17.05602739726030.0562740696772286303.088571611910
Winsorized Mean ( 4 / 24 )17.06205479452060.0552622634943469308.746940781134
Winsorized Mean ( 5 / 24 )17.06205479452050.0547607772814346311.574372051601
Winsorized Mean ( 6 / 24 )17.06123287671230.0545888692182028312.540507269259
Winsorized Mean ( 7 / 24 )17.05931506849310.0531726778236504320.828586535949
Winsorized Mean ( 8 / 24 )17.05493150684930.0523035293399808326.0761123019
Winsorized Mean ( 9 / 24 )17.05246575342470.051404468303491331.731196065432
Winsorized Mean ( 10 / 24 )17.04835616438360.0501667742602003339.833613298690
Winsorized Mean ( 11 / 24 )17.03931506849320.0470509005631375362.146417274801
Winsorized Mean ( 12 / 24 )17.02945205479450.0448580928436295379.629426381486
Winsorized Mean ( 13 / 24 )17.02945205479450.0437527517773252389.220137317626
Winsorized Mean ( 14 / 24 )17.02561643835620.0425522269758009400.111055246027
Winsorized Mean ( 15 / 24 )17.02561643835620.0419306642574973406.042135030378
Winsorized Mean ( 16 / 24 )17.01904109589040.0402579980536695422.74931488649
Winsorized Mean ( 17 / 24 )17.02835616438360.0375865382502078453.044014083671
Winsorized Mean ( 18 / 24 )17.03328767123290.0362208549684694470.261888794743
Winsorized Mean ( 19 / 24 )17.03068493150690.035092467962929485.308840332852
Winsorized Mean ( 20 / 24 )17.01972602739730.0319608854140696532.517350720983
Winsorized Mean ( 21 / 24 )17.01397260273970.0311424647357654546.327105034821
Winsorized Mean ( 22 / 24 )17.020.0303612195566653560.583542048907
Winsorized Mean ( 23 / 24 )17.0136986301370.0286309289615396594.241935111214
Winsorized Mean ( 24 / 24 )16.99068493150680.0246739227627551688.608985886672
Trimmed Mean ( 1 / 24 )17.05436619718310.0561421494193372303.771166112657
Trimmed Mean ( 2 / 24 )17.05231884057970.0551299112588688309.311559753989
Trimmed Mean ( 3 / 24 )17.05029850746270.0539552598506154316.008088083894
Trimmed Mean ( 4 / 24 )17.04815384615380.052839967166696322.637479928242
Trimmed Mean ( 5 / 24 )17.04412698412700.051850860867395328.714445604214
Trimmed Mean ( 6 / 24 )17.03983606557380.0507955786355696335.459040398481
Trimmed Mean ( 7 / 24 )17.03542372881360.0495457578174257343.832135772117
Trimmed Mean ( 8 / 24 )17.03105263157890.0483769685995837352.048777023319
Trimmed Mean ( 9 / 24 )17.02709090909090.0471430752489068361.179045261494
Trimmed Mean ( 10 / 24 )17.02320754716980.0458152831822535371.561766396846
Trimmed Mean ( 11 / 24 )17.01960784313730.0444371870276075383.003717867278
Trimmed Mean ( 12 / 24 )17.01693877551020.0434113022541842391.993280364448
Trimmed Mean ( 13 / 24 )17.01531914893620.0425775138630212399.631580267397
Trimmed Mean ( 14 / 24 )17.01355555555560.0417159170207776407.843259134914
Trimmed Mean ( 15 / 24 )17.01209302325580.0408323668919034416.632547123521
Trimmed Mean ( 16 / 24 )17.01048780487800.0397767416100319427.649101368019
Trimmed Mean ( 17 / 24 )17.00948717948720.0387401961268202439.06559284844
Trimmed Mean ( 18 / 24 )17.00729729729730.0379319935335691448.362865037561
Trimmed Mean ( 19 / 24 )17.00428571428570.0370878713878491458.486429066316
Trimmed Mean ( 20 / 24 )17.00121212121210.0361414455482584470.407640405833
Trimmed Mean ( 21 / 24 )16.99903225806450.0355973746727688477.536122096903
Trimmed Mean ( 22 / 24 )16.99724137931030.0349344796709897486.546287203619
Trimmed Mean ( 23 / 24 )16.99444444444440.0340492911236180499.113017734938
Trimmed Mean ( 24 / 24 )16.9920.0331813200460741512.095358967204
Median16.92
Midrange17.12
Midmean - Weighted Average at Xnp16.9955555555556
Midmean - Weighted Average at X(n+1)p17.0072972972973
Midmean - Empirical Distribution Function17.0072972972973
Midmean - Empirical Distribution Function - Averaging17.0072972972973
Midmean - Empirical Distribution Function - Interpolation17.0072972972973
Midmean - Closest Observation16.9981578947368
Midmean - True Basic - Statistics Graphics Toolkit17.0072972972973
Midmean - MS Excel (old versions)17.0072972972973
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17.0561643835616 & 0.0571266684281486 & 298.567461622834 \tabularnewline
Geometric Mean & 17.0493158738721 &  &  \tabularnewline
Harmonic Mean & 17.0425082794281 &  &  \tabularnewline
Quadratic Mean & 17.0630510849838 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 17.056301369863 & 0.0569875773698028 & 299.298586763595 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 17.0560273972603 & 0.0569275286726668 & 299.609482353123 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 17.0560273972603 & 0.0562740696772286 & 303.088571611910 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 17.0620547945206 & 0.0552622634943469 & 308.746940781134 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 17.0620547945205 & 0.0547607772814346 & 311.574372051601 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 17.0612328767123 & 0.0545888692182028 & 312.540507269259 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 17.0593150684931 & 0.0531726778236504 & 320.828586535949 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 17.0549315068493 & 0.0523035293399808 & 326.0761123019 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 17.0524657534247 & 0.051404468303491 & 331.731196065432 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 17.0483561643836 & 0.0501667742602003 & 339.833613298690 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 17.0393150684932 & 0.0470509005631375 & 362.146417274801 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 17.0294520547945 & 0.0448580928436295 & 379.629426381486 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 17.0294520547945 & 0.0437527517773252 & 389.220137317626 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 17.0256164383562 & 0.0425522269758009 & 400.111055246027 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 17.0256164383562 & 0.0419306642574973 & 406.042135030378 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 17.0190410958904 & 0.0402579980536695 & 422.74931488649 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 17.0283561643836 & 0.0375865382502078 & 453.044014083671 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 17.0332876712329 & 0.0362208549684694 & 470.261888794743 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 17.0306849315069 & 0.035092467962929 & 485.308840332852 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 17.0197260273973 & 0.0319608854140696 & 532.517350720983 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 17.0139726027397 & 0.0311424647357654 & 546.327105034821 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 17.02 & 0.0303612195566653 & 560.583542048907 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 17.013698630137 & 0.0286309289615396 & 594.241935111214 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 16.9906849315068 & 0.0246739227627551 & 688.608985886672 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 17.0543661971831 & 0.0561421494193372 & 303.771166112657 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 17.0523188405797 & 0.0551299112588688 & 309.311559753989 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 17.0502985074627 & 0.0539552598506154 & 316.008088083894 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 17.0481538461538 & 0.052839967166696 & 322.637479928242 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 17.0441269841270 & 0.051850860867395 & 328.714445604214 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 17.0398360655738 & 0.0507955786355696 & 335.459040398481 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 17.0354237288136 & 0.0495457578174257 & 343.832135772117 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 17.0310526315789 & 0.0483769685995837 & 352.048777023319 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 17.0270909090909 & 0.0471430752489068 & 361.179045261494 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 17.0232075471698 & 0.0458152831822535 & 371.561766396846 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 17.0196078431373 & 0.0444371870276075 & 383.003717867278 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 17.0169387755102 & 0.0434113022541842 & 391.993280364448 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 17.0153191489362 & 0.0425775138630212 & 399.631580267397 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 17.0135555555556 & 0.0417159170207776 & 407.843259134914 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 17.0120930232558 & 0.0408323668919034 & 416.632547123521 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 17.0104878048780 & 0.0397767416100319 & 427.649101368019 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 17.0094871794872 & 0.0387401961268202 & 439.06559284844 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 17.0072972972973 & 0.0379319935335691 & 448.362865037561 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 17.0042857142857 & 0.0370878713878491 & 458.486429066316 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 17.0012121212121 & 0.0361414455482584 & 470.407640405833 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 16.9990322580645 & 0.0355973746727688 & 477.536122096903 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 16.9972413793103 & 0.0349344796709897 & 486.546287203619 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 16.9944444444444 & 0.0340492911236180 & 499.113017734938 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 16.992 & 0.0331813200460741 & 512.095358967204 \tabularnewline
Median & 16.92 &  &  \tabularnewline
Midrange & 17.12 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 16.9955555555556 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17.0072972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 17.0072972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17.0072972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17.0072972972973 &  &  \tabularnewline
Midmean - Closest Observation & 16.9981578947368 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17.0072972972973 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17.0072972972973 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112878&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]17.0561643835616[/C][C]0.0571266684281486[/C][C]298.567461622834[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17.0493158738721[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17.0425082794281[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17.0630510849838[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]17.056301369863[/C][C]0.0569875773698028[/C][C]299.298586763595[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]17.0560273972603[/C][C]0.0569275286726668[/C][C]299.609482353123[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]17.0560273972603[/C][C]0.0562740696772286[/C][C]303.088571611910[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]17.0620547945206[/C][C]0.0552622634943469[/C][C]308.746940781134[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]17.0620547945205[/C][C]0.0547607772814346[/C][C]311.574372051601[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]17.0612328767123[/C][C]0.0545888692182028[/C][C]312.540507269259[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]17.0593150684931[/C][C]0.0531726778236504[/C][C]320.828586535949[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]17.0549315068493[/C][C]0.0523035293399808[/C][C]326.0761123019[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]17.0524657534247[/C][C]0.051404468303491[/C][C]331.731196065432[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]17.0483561643836[/C][C]0.0501667742602003[/C][C]339.833613298690[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]17.0393150684932[/C][C]0.0470509005631375[/C][C]362.146417274801[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]17.0294520547945[/C][C]0.0448580928436295[/C][C]379.629426381486[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]17.0294520547945[/C][C]0.0437527517773252[/C][C]389.220137317626[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]17.0256164383562[/C][C]0.0425522269758009[/C][C]400.111055246027[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]17.0256164383562[/C][C]0.0419306642574973[/C][C]406.042135030378[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]17.0190410958904[/C][C]0.0402579980536695[/C][C]422.74931488649[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]17.0283561643836[/C][C]0.0375865382502078[/C][C]453.044014083671[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]17.0332876712329[/C][C]0.0362208549684694[/C][C]470.261888794743[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]17.0306849315069[/C][C]0.035092467962929[/C][C]485.308840332852[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]17.0197260273973[/C][C]0.0319608854140696[/C][C]532.517350720983[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]17.0139726027397[/C][C]0.0311424647357654[/C][C]546.327105034821[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]17.02[/C][C]0.0303612195566653[/C][C]560.583542048907[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]17.013698630137[/C][C]0.0286309289615396[/C][C]594.241935111214[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]16.9906849315068[/C][C]0.0246739227627551[/C][C]688.608985886672[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]17.0543661971831[/C][C]0.0561421494193372[/C][C]303.771166112657[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]17.0523188405797[/C][C]0.0551299112588688[/C][C]309.311559753989[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]17.0502985074627[/C][C]0.0539552598506154[/C][C]316.008088083894[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]17.0481538461538[/C][C]0.052839967166696[/C][C]322.637479928242[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]17.0441269841270[/C][C]0.051850860867395[/C][C]328.714445604214[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]17.0398360655738[/C][C]0.0507955786355696[/C][C]335.459040398481[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]17.0354237288136[/C][C]0.0495457578174257[/C][C]343.832135772117[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]17.0310526315789[/C][C]0.0483769685995837[/C][C]352.048777023319[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]17.0270909090909[/C][C]0.0471430752489068[/C][C]361.179045261494[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]17.0232075471698[/C][C]0.0458152831822535[/C][C]371.561766396846[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]17.0196078431373[/C][C]0.0444371870276075[/C][C]383.003717867278[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]17.0169387755102[/C][C]0.0434113022541842[/C][C]391.993280364448[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]17.0153191489362[/C][C]0.0425775138630212[/C][C]399.631580267397[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]17.0135555555556[/C][C]0.0417159170207776[/C][C]407.843259134914[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]17.0120930232558[/C][C]0.0408323668919034[/C][C]416.632547123521[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]17.0104878048780[/C][C]0.0397767416100319[/C][C]427.649101368019[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]17.0094871794872[/C][C]0.0387401961268202[/C][C]439.06559284844[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]17.0072972972973[/C][C]0.0379319935335691[/C][C]448.362865037561[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]17.0042857142857[/C][C]0.0370878713878491[/C][C]458.486429066316[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]17.0012121212121[/C][C]0.0361414455482584[/C][C]470.407640405833[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]16.9990322580645[/C][C]0.0355973746727688[/C][C]477.536122096903[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]16.9972413793103[/C][C]0.0349344796709897[/C][C]486.546287203619[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]16.9944444444444[/C][C]0.0340492911236180[/C][C]499.113017734938[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]16.992[/C][C]0.0331813200460741[/C][C]512.095358967204[/C][/ROW]
[ROW][C]Median[/C][C]16.92[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]17.12[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]16.9955555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17.0072972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]17.0072972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17.0072972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17.0072972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]16.9981578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17.0072972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17.0072972972973[/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=112878&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112878&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 Mean17.05616438356160.0571266684281486298.567461622834
Geometric Mean17.0493158738721
Harmonic Mean17.0425082794281
Quadratic Mean17.0630510849838
Winsorized Mean ( 1 / 24 )17.0563013698630.0569875773698028299.298586763595
Winsorized Mean ( 2 / 24 )17.05602739726030.0569275286726668299.609482353123
Winsorized Mean ( 3 / 24 )17.05602739726030.0562740696772286303.088571611910
Winsorized Mean ( 4 / 24 )17.06205479452060.0552622634943469308.746940781134
Winsorized Mean ( 5 / 24 )17.06205479452050.0547607772814346311.574372051601
Winsorized Mean ( 6 / 24 )17.06123287671230.0545888692182028312.540507269259
Winsorized Mean ( 7 / 24 )17.05931506849310.0531726778236504320.828586535949
Winsorized Mean ( 8 / 24 )17.05493150684930.0523035293399808326.0761123019
Winsorized Mean ( 9 / 24 )17.05246575342470.051404468303491331.731196065432
Winsorized Mean ( 10 / 24 )17.04835616438360.0501667742602003339.833613298690
Winsorized Mean ( 11 / 24 )17.03931506849320.0470509005631375362.146417274801
Winsorized Mean ( 12 / 24 )17.02945205479450.0448580928436295379.629426381486
Winsorized Mean ( 13 / 24 )17.02945205479450.0437527517773252389.220137317626
Winsorized Mean ( 14 / 24 )17.02561643835620.0425522269758009400.111055246027
Winsorized Mean ( 15 / 24 )17.02561643835620.0419306642574973406.042135030378
Winsorized Mean ( 16 / 24 )17.01904109589040.0402579980536695422.74931488649
Winsorized Mean ( 17 / 24 )17.02835616438360.0375865382502078453.044014083671
Winsorized Mean ( 18 / 24 )17.03328767123290.0362208549684694470.261888794743
Winsorized Mean ( 19 / 24 )17.03068493150690.035092467962929485.308840332852
Winsorized Mean ( 20 / 24 )17.01972602739730.0319608854140696532.517350720983
Winsorized Mean ( 21 / 24 )17.01397260273970.0311424647357654546.327105034821
Winsorized Mean ( 22 / 24 )17.020.0303612195566653560.583542048907
Winsorized Mean ( 23 / 24 )17.0136986301370.0286309289615396594.241935111214
Winsorized Mean ( 24 / 24 )16.99068493150680.0246739227627551688.608985886672
Trimmed Mean ( 1 / 24 )17.05436619718310.0561421494193372303.771166112657
Trimmed Mean ( 2 / 24 )17.05231884057970.0551299112588688309.311559753989
Trimmed Mean ( 3 / 24 )17.05029850746270.0539552598506154316.008088083894
Trimmed Mean ( 4 / 24 )17.04815384615380.052839967166696322.637479928242
Trimmed Mean ( 5 / 24 )17.04412698412700.051850860867395328.714445604214
Trimmed Mean ( 6 / 24 )17.03983606557380.0507955786355696335.459040398481
Trimmed Mean ( 7 / 24 )17.03542372881360.0495457578174257343.832135772117
Trimmed Mean ( 8 / 24 )17.03105263157890.0483769685995837352.048777023319
Trimmed Mean ( 9 / 24 )17.02709090909090.0471430752489068361.179045261494
Trimmed Mean ( 10 / 24 )17.02320754716980.0458152831822535371.561766396846
Trimmed Mean ( 11 / 24 )17.01960784313730.0444371870276075383.003717867278
Trimmed Mean ( 12 / 24 )17.01693877551020.0434113022541842391.993280364448
Trimmed Mean ( 13 / 24 )17.01531914893620.0425775138630212399.631580267397
Trimmed Mean ( 14 / 24 )17.01355555555560.0417159170207776407.843259134914
Trimmed Mean ( 15 / 24 )17.01209302325580.0408323668919034416.632547123521
Trimmed Mean ( 16 / 24 )17.01048780487800.0397767416100319427.649101368019
Trimmed Mean ( 17 / 24 )17.00948717948720.0387401961268202439.06559284844
Trimmed Mean ( 18 / 24 )17.00729729729730.0379319935335691448.362865037561
Trimmed Mean ( 19 / 24 )17.00428571428570.0370878713878491458.486429066316
Trimmed Mean ( 20 / 24 )17.00121212121210.0361414455482584470.407640405833
Trimmed Mean ( 21 / 24 )16.99903225806450.0355973746727688477.536122096903
Trimmed Mean ( 22 / 24 )16.99724137931030.0349344796709897486.546287203619
Trimmed Mean ( 23 / 24 )16.99444444444440.0340492911236180499.113017734938
Trimmed Mean ( 24 / 24 )16.9920.0331813200460741512.095358967204
Median16.92
Midrange17.12
Midmean - Weighted Average at Xnp16.9955555555556
Midmean - Weighted Average at X(n+1)p17.0072972972973
Midmean - Empirical Distribution Function17.0072972972973
Midmean - Empirical Distribution Function - Averaging17.0072972972973
Midmean - Empirical Distribution Function - Interpolation17.0072972972973
Midmean - Closest Observation16.9981578947368
Midmean - True Basic - Statistics Graphics Toolkit17.0072972972973
Midmean - MS Excel (old versions)17.0072972972973
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')