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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, 12 Oct 2012 03:01:31 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/12/t135002532997x2rw9bcwm7v58.htm/, Retrieved Mon, 13 May 2024 02:06:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=175241, Retrieved Mon, 13 May 2024 02:06:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-12 07:01:31] [50b2e07c322f56d9c76b19a7ea7f6b48] [Current]
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Dataseries X:
10
9,99
9,95
9,96
9,97
9,95
9,94
9,9
9,9
9,92
9,87
9,96
9,94
9,96
9,96
9,89
9,82
9,83
9,83
9,82
9,77
9,66
9,69
9,67
9,7
9,77
9,79
9,81
9,77
9,78
9,77
9,79
9,77
9,77
9,8
9,8
9,8
9,8
9,76
9,78
9,77
9,79
9,81
9,82
9,84
9,87
9,99
9,99
9,99
10,08
10,06
10,08
10,07
10,04
10,04
10,12
10,1
10,11
10,13
10,16
10,15
10,25
10,41
10,46
10,46
10,5
10,5
10,48
10,5
10,5
10,53
10,53




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175241&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=175241&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175241&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9.98250.0283979861636942351.521405160845
Geometric Mean9.97967893271351
Harmonic Mean9.97690422085853
Quadratic Mean9.98536748892543
Winsorized Mean ( 1 / 24 )9.982638888888890.0283761021140611351.797397992244
Winsorized Mean ( 2 / 24 )9.982361111111110.0280707892991308355.613837742005
Winsorized Mean ( 3 / 24 )9.982777777777780.0280106048427202356.392796008197
Winsorized Mean ( 4 / 24 )9.986111111111110.0275808354935829362.067027064301
Winsorized Mean ( 5 / 24 )9.986805555555560.0275021882675306363.127670366002
Winsorized Mean ( 6 / 24 )9.985138888888890.0270685626428647368.883232576112
Winsorized Mean ( 7 / 24 )9.983194444444440.0265724762505866375.696805608174
Winsorized Mean ( 8 / 24 )9.983194444444440.0265724762505866375.696805608174
Winsorized Mean ( 9 / 24 )9.976944444444440.0250200536853891398.757915146707
Winsorized Mean ( 10 / 24 )9.954722222222220.0199510082877742498.958352311566
Winsorized Mean ( 11 / 24 )9.940972222222220.0172754537910388575.4391370824
Winsorized Mean ( 12 / 24 )9.940972222222220.01675114706817593.450238468249
Winsorized Mean ( 13 / 24 )9.937361111111110.0161298441493736616.085376838375
Winsorized Mean ( 14 / 24 )9.937361111111110.0155418475118876639.393811032455
Winsorized Mean ( 15 / 24 )9.935277777777780.0152007590595597653.604056142811
Winsorized Mean ( 16 / 24 )9.933055555555550.0148448403023694669.125120461559
Winsorized Mean ( 17 / 24 )9.930694444444450.0137924567010418720.009107854901
Winsorized Mean ( 18 / 24 )9.930694444444440.0137924567010418720.009107854901
Winsorized Mean ( 19 / 24 )9.928055555555560.0133942839408569741.215849939672
Winsorized Mean ( 20 / 24 )9.925277777777780.012983937684775764.427403977467
Winsorized Mean ( 21 / 24 )9.922361111111110.0117510247539614844.382623546614
Winsorized Mean ( 22 / 24 )9.922361111111110.0117510247539614844.382623546614
Winsorized Mean ( 23 / 24 )9.912777777777780.009591055721462551033.54396696865
Winsorized Mean ( 24 / 24 )9.909444444444440.009171229954412721080.49241963195
Trimmed Mean ( 1 / 24 )9.979285714285710.0277450097567197359.678580104617
Trimmed Mean ( 2 / 24 )9.975735294117650.0269875562132451369.642038548926
Trimmed Mean ( 3 / 24 )9.972121212121210.0262714138666122379.580682743329
Trimmed Mean ( 4 / 24 )9.9681250.0254287393264031392.002327447272
Trimmed Mean ( 5 / 24 )9.962903225806450.0245492275668447405.833674345909
Trimmed Mean ( 6 / 24 )9.957166666666670.0234798767870696424.072355956743
Trimmed Mean ( 7 / 24 )9.951379310344830.0222813341371056446.624032883767
Trimmed Mean ( 8 / 24 )9.945535714285710.0209187041807353475.437466315187
Trimmed Mean ( 9 / 24 )9.939259259259260.0191555693912719518.870468229882
Trimmed Mean ( 10 / 24 )9.933461538461540.017348535686084572.58213132245
Trimmed Mean ( 11 / 24 )9.93040.0165466810285696600.144523415549
Trimmed Mean ( 12 / 24 )9.928958333333330.0162025072028131612.803821596787
Trimmed Mean ( 13 / 24 )9.927391304347830.0158660905467464625.698641710047
Trimmed Mean ( 14 / 24 )9.926136363636360.0155627893779727637.81216352421
Trimmed Mean ( 15 / 24 )9.92476190476190.0152799584649198649.528068256696
Trimmed Mean ( 16 / 24 )9.92350.0149681285334831662.975333075309
Trimmed Mean ( 17 / 24 )9.922368421052630.014619080901023678.727239299858
Trimmed Mean ( 18 / 24 )9.921388888888890.0143822685020936689.83477032463
Trimmed Mean ( 19 / 24 )9.920294117647060.0140249668777202707.331019327129
Trimmed Mean ( 20 / 24 )9.9193750.0136113796970794728.756027732327
Trimmed Mean ( 21 / 24 )9.918666666666670.0131195505015981756.021836682471
Trimmed Mean ( 22 / 24 )9.918214285714280.0127662498525825776.908990521432
Trimmed Mean ( 23 / 24 )9.917692307692310.0121946733933959813.280683110651
Trimmed Mean ( 24 / 24 )9.918333333333330.0120636396235209822.167574866476
Median9.94
Midrange10.095
Midmean - Weighted Average at Xnp9.92236842105263
Midmean - Weighted Average at X(n+1)p9.92236842105263
Midmean - Empirical Distribution Function9.92236842105263
Midmean - Empirical Distribution Function - Averaging9.92236842105263
Midmean - Empirical Distribution Function - Interpolation9.92236842105263
Midmean - Closest Observation9.92236842105263
Midmean - True Basic - Statistics Graphics Toolkit9.92236842105263
Midmean - MS Excel (old versions)9.92236842105263
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9.9825 & 0.0283979861636942 & 351.521405160845 \tabularnewline
Geometric Mean & 9.97967893271351 &  &  \tabularnewline
Harmonic Mean & 9.97690422085853 &  &  \tabularnewline
Quadratic Mean & 9.98536748892543 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 9.98263888888889 & 0.0283761021140611 & 351.797397992244 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 9.98236111111111 & 0.0280707892991308 & 355.613837742005 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 9.98277777777778 & 0.0280106048427202 & 356.392796008197 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 9.98611111111111 & 0.0275808354935829 & 362.067027064301 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 9.98680555555556 & 0.0275021882675306 & 363.127670366002 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 9.98513888888889 & 0.0270685626428647 & 368.883232576112 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 9.98319444444444 & 0.0265724762505866 & 375.696805608174 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 9.98319444444444 & 0.0265724762505866 & 375.696805608174 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 9.97694444444444 & 0.0250200536853891 & 398.757915146707 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 9.95472222222222 & 0.0199510082877742 & 498.958352311566 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 9.94097222222222 & 0.0172754537910388 & 575.4391370824 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 9.94097222222222 & 0.01675114706817 & 593.450238468249 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 9.93736111111111 & 0.0161298441493736 & 616.085376838375 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 9.93736111111111 & 0.0155418475118876 & 639.393811032455 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 9.93527777777778 & 0.0152007590595597 & 653.604056142811 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 9.93305555555555 & 0.0148448403023694 & 669.125120461559 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 9.93069444444445 & 0.0137924567010418 & 720.009107854901 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 9.93069444444444 & 0.0137924567010418 & 720.009107854901 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 9.92805555555556 & 0.0133942839408569 & 741.215849939672 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 9.92527777777778 & 0.012983937684775 & 764.427403977467 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 9.92236111111111 & 0.0117510247539614 & 844.382623546614 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 9.92236111111111 & 0.0117510247539614 & 844.382623546614 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 9.91277777777778 & 0.00959105572146255 & 1033.54396696865 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 9.90944444444444 & 0.00917122995441272 & 1080.49241963195 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 9.97928571428571 & 0.0277450097567197 & 359.678580104617 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 9.97573529411765 & 0.0269875562132451 & 369.642038548926 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 9.97212121212121 & 0.0262714138666122 & 379.580682743329 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 9.968125 & 0.0254287393264031 & 392.002327447272 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 9.96290322580645 & 0.0245492275668447 & 405.833674345909 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 9.95716666666667 & 0.0234798767870696 & 424.072355956743 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 9.95137931034483 & 0.0222813341371056 & 446.624032883767 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 9.94553571428571 & 0.0209187041807353 & 475.437466315187 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 9.93925925925926 & 0.0191555693912719 & 518.870468229882 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 9.93346153846154 & 0.017348535686084 & 572.58213132245 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 9.9304 & 0.0165466810285696 & 600.144523415549 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 9.92895833333333 & 0.0162025072028131 & 612.803821596787 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 9.92739130434783 & 0.0158660905467464 & 625.698641710047 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 9.92613636363636 & 0.0155627893779727 & 637.81216352421 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 9.9247619047619 & 0.0152799584649198 & 649.528068256696 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 9.9235 & 0.0149681285334831 & 662.975333075309 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 9.92236842105263 & 0.014619080901023 & 678.727239299858 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 9.92138888888889 & 0.0143822685020936 & 689.83477032463 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 9.92029411764706 & 0.0140249668777202 & 707.331019327129 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 9.919375 & 0.0136113796970794 & 728.756027732327 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 9.91866666666667 & 0.0131195505015981 & 756.021836682471 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 9.91821428571428 & 0.0127662498525825 & 776.908990521432 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 9.91769230769231 & 0.0121946733933959 & 813.280683110651 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 9.91833333333333 & 0.0120636396235209 & 822.167574866476 \tabularnewline
Median & 9.94 &  &  \tabularnewline
Midrange & 10.095 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 9.92236842105263 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 9.92236842105263 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 9.92236842105263 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 9.92236842105263 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 9.92236842105263 &  &  \tabularnewline
Midmean - Closest Observation & 9.92236842105263 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 9.92236842105263 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 9.92236842105263 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175241&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]9.9825[/C][C]0.0283979861636942[/C][C]351.521405160845[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]9.97967893271351[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9.97690422085853[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9.98536748892543[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]9.98263888888889[/C][C]0.0283761021140611[/C][C]351.797397992244[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]9.98236111111111[/C][C]0.0280707892991308[/C][C]355.613837742005[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]9.98277777777778[/C][C]0.0280106048427202[/C][C]356.392796008197[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]9.98611111111111[/C][C]0.0275808354935829[/C][C]362.067027064301[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]9.98680555555556[/C][C]0.0275021882675306[/C][C]363.127670366002[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]9.98513888888889[/C][C]0.0270685626428647[/C][C]368.883232576112[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]9.98319444444444[/C][C]0.0265724762505866[/C][C]375.696805608174[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]9.98319444444444[/C][C]0.0265724762505866[/C][C]375.696805608174[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]9.97694444444444[/C][C]0.0250200536853891[/C][C]398.757915146707[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]9.95472222222222[/C][C]0.0199510082877742[/C][C]498.958352311566[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]9.94097222222222[/C][C]0.0172754537910388[/C][C]575.4391370824[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]9.94097222222222[/C][C]0.01675114706817[/C][C]593.450238468249[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]9.93736111111111[/C][C]0.0161298441493736[/C][C]616.085376838375[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]9.93736111111111[/C][C]0.0155418475118876[/C][C]639.393811032455[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]9.93527777777778[/C][C]0.0152007590595597[/C][C]653.604056142811[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]9.93305555555555[/C][C]0.0148448403023694[/C][C]669.125120461559[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]9.93069444444445[/C][C]0.0137924567010418[/C][C]720.009107854901[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]9.93069444444444[/C][C]0.0137924567010418[/C][C]720.009107854901[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]9.92805555555556[/C][C]0.0133942839408569[/C][C]741.215849939672[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]9.92527777777778[/C][C]0.012983937684775[/C][C]764.427403977467[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]9.92236111111111[/C][C]0.0117510247539614[/C][C]844.382623546614[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]9.92236111111111[/C][C]0.0117510247539614[/C][C]844.382623546614[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]9.91277777777778[/C][C]0.00959105572146255[/C][C]1033.54396696865[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]9.90944444444444[/C][C]0.00917122995441272[/C][C]1080.49241963195[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]9.97928571428571[/C][C]0.0277450097567197[/C][C]359.678580104617[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]9.97573529411765[/C][C]0.0269875562132451[/C][C]369.642038548926[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]9.97212121212121[/C][C]0.0262714138666122[/C][C]379.580682743329[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]9.968125[/C][C]0.0254287393264031[/C][C]392.002327447272[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]9.96290322580645[/C][C]0.0245492275668447[/C][C]405.833674345909[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]9.95716666666667[/C][C]0.0234798767870696[/C][C]424.072355956743[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]9.95137931034483[/C][C]0.0222813341371056[/C][C]446.624032883767[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]9.94553571428571[/C][C]0.0209187041807353[/C][C]475.437466315187[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]9.93925925925926[/C][C]0.0191555693912719[/C][C]518.870468229882[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]9.93346153846154[/C][C]0.017348535686084[/C][C]572.58213132245[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]9.9304[/C][C]0.0165466810285696[/C][C]600.144523415549[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]9.92895833333333[/C][C]0.0162025072028131[/C][C]612.803821596787[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]9.92739130434783[/C][C]0.0158660905467464[/C][C]625.698641710047[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]9.92613636363636[/C][C]0.0155627893779727[/C][C]637.81216352421[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]9.9247619047619[/C][C]0.0152799584649198[/C][C]649.528068256696[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]9.9235[/C][C]0.0149681285334831[/C][C]662.975333075309[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]9.92236842105263[/C][C]0.014619080901023[/C][C]678.727239299858[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]9.92138888888889[/C][C]0.0143822685020936[/C][C]689.83477032463[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]9.92029411764706[/C][C]0.0140249668777202[/C][C]707.331019327129[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]9.919375[/C][C]0.0136113796970794[/C][C]728.756027732327[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]9.91866666666667[/C][C]0.0131195505015981[/C][C]756.021836682471[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]9.91821428571428[/C][C]0.0127662498525825[/C][C]776.908990521432[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]9.91769230769231[/C][C]0.0121946733933959[/C][C]813.280683110651[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]9.91833333333333[/C][C]0.0120636396235209[/C][C]822.167574866476[/C][/ROW]
[ROW][C]Median[/C][C]9.94[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]10.095[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]9.92236842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]9.92236842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]9.92236842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]9.92236842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]9.92236842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]9.92236842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]9.92236842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]9.92236842105263[/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=175241&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175241&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 Mean9.98250.0283979861636942351.521405160845
Geometric Mean9.97967893271351
Harmonic Mean9.97690422085853
Quadratic Mean9.98536748892543
Winsorized Mean ( 1 / 24 )9.982638888888890.0283761021140611351.797397992244
Winsorized Mean ( 2 / 24 )9.982361111111110.0280707892991308355.613837742005
Winsorized Mean ( 3 / 24 )9.982777777777780.0280106048427202356.392796008197
Winsorized Mean ( 4 / 24 )9.986111111111110.0275808354935829362.067027064301
Winsorized Mean ( 5 / 24 )9.986805555555560.0275021882675306363.127670366002
Winsorized Mean ( 6 / 24 )9.985138888888890.0270685626428647368.883232576112
Winsorized Mean ( 7 / 24 )9.983194444444440.0265724762505866375.696805608174
Winsorized Mean ( 8 / 24 )9.983194444444440.0265724762505866375.696805608174
Winsorized Mean ( 9 / 24 )9.976944444444440.0250200536853891398.757915146707
Winsorized Mean ( 10 / 24 )9.954722222222220.0199510082877742498.958352311566
Winsorized Mean ( 11 / 24 )9.940972222222220.0172754537910388575.4391370824
Winsorized Mean ( 12 / 24 )9.940972222222220.01675114706817593.450238468249
Winsorized Mean ( 13 / 24 )9.937361111111110.0161298441493736616.085376838375
Winsorized Mean ( 14 / 24 )9.937361111111110.0155418475118876639.393811032455
Winsorized Mean ( 15 / 24 )9.935277777777780.0152007590595597653.604056142811
Winsorized Mean ( 16 / 24 )9.933055555555550.0148448403023694669.125120461559
Winsorized Mean ( 17 / 24 )9.930694444444450.0137924567010418720.009107854901
Winsorized Mean ( 18 / 24 )9.930694444444440.0137924567010418720.009107854901
Winsorized Mean ( 19 / 24 )9.928055555555560.0133942839408569741.215849939672
Winsorized Mean ( 20 / 24 )9.925277777777780.012983937684775764.427403977467
Winsorized Mean ( 21 / 24 )9.922361111111110.0117510247539614844.382623546614
Winsorized Mean ( 22 / 24 )9.922361111111110.0117510247539614844.382623546614
Winsorized Mean ( 23 / 24 )9.912777777777780.009591055721462551033.54396696865
Winsorized Mean ( 24 / 24 )9.909444444444440.009171229954412721080.49241963195
Trimmed Mean ( 1 / 24 )9.979285714285710.0277450097567197359.678580104617
Trimmed Mean ( 2 / 24 )9.975735294117650.0269875562132451369.642038548926
Trimmed Mean ( 3 / 24 )9.972121212121210.0262714138666122379.580682743329
Trimmed Mean ( 4 / 24 )9.9681250.0254287393264031392.002327447272
Trimmed Mean ( 5 / 24 )9.962903225806450.0245492275668447405.833674345909
Trimmed Mean ( 6 / 24 )9.957166666666670.0234798767870696424.072355956743
Trimmed Mean ( 7 / 24 )9.951379310344830.0222813341371056446.624032883767
Trimmed Mean ( 8 / 24 )9.945535714285710.0209187041807353475.437466315187
Trimmed Mean ( 9 / 24 )9.939259259259260.0191555693912719518.870468229882
Trimmed Mean ( 10 / 24 )9.933461538461540.017348535686084572.58213132245
Trimmed Mean ( 11 / 24 )9.93040.0165466810285696600.144523415549
Trimmed Mean ( 12 / 24 )9.928958333333330.0162025072028131612.803821596787
Trimmed Mean ( 13 / 24 )9.927391304347830.0158660905467464625.698641710047
Trimmed Mean ( 14 / 24 )9.926136363636360.0155627893779727637.81216352421
Trimmed Mean ( 15 / 24 )9.92476190476190.0152799584649198649.528068256696
Trimmed Mean ( 16 / 24 )9.92350.0149681285334831662.975333075309
Trimmed Mean ( 17 / 24 )9.922368421052630.014619080901023678.727239299858
Trimmed Mean ( 18 / 24 )9.921388888888890.0143822685020936689.83477032463
Trimmed Mean ( 19 / 24 )9.920294117647060.0140249668777202707.331019327129
Trimmed Mean ( 20 / 24 )9.9193750.0136113796970794728.756027732327
Trimmed Mean ( 21 / 24 )9.918666666666670.0131195505015981756.021836682471
Trimmed Mean ( 22 / 24 )9.918214285714280.0127662498525825776.908990521432
Trimmed Mean ( 23 / 24 )9.917692307692310.0121946733933959813.280683110651
Trimmed Mean ( 24 / 24 )9.918333333333330.0120636396235209822.167574866476
Median9.94
Midrange10.095
Midmean - Weighted Average at Xnp9.92236842105263
Midmean - Weighted Average at X(n+1)p9.92236842105263
Midmean - Empirical Distribution Function9.92236842105263
Midmean - Empirical Distribution Function - Averaging9.92236842105263
Midmean - Empirical Distribution Function - Interpolation9.92236842105263
Midmean - Closest Observation9.92236842105263
Midmean - True Basic - Statistics Graphics Toolkit9.92236842105263
Midmean - MS Excel (old versions)9.92236842105263
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')