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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 14 Oct 2011 13:24:48 -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/2011/Oct/14/t13186135876hhkdxzff79x55a.htm/, Retrieved Thu, 16 May 2024 08:29:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=129608, Retrieved Thu, 16 May 2024 08:29:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-10-14 17:24:48] [d22ab4133447fd2cf74cbadcaeb9b5f8] [Current]
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Dataseries X:
20,89
21,04
21,07
21,12
21,25
21,24
21,24
21,22
21,29
21,25
21,15
21,16
21,16
21,52
21,59
21,60
21,68
21,67
21,67
21,65
21,74
21,72
21,84
21,94
21,94
21,95
21,96
22,10
22,13
22,18
22,18
22,27
22,30
22,04
22,05
22,06
22,06
22,06
21,97
22,03
22,08
22,13
22,13
22,40
22,40
22,12
22,22
22,14
22,14
22,19
22,29
22,24
22,26
22,29
22,29
22,29
22,29
22,35
22,39
22,43




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=129608&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]1 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=129608&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=129608&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean21.86750.0563105919731056388.337242315693
Geometric Mean21.8631817954844
Harmonic Mean21.8588232964384
Quadratic Mean21.8717772102162
Winsorized Mean ( 1 / 20 )21.86950.0555432467532013393.738236030279
Winsorized Mean ( 2 / 20 )21.87050.0552939882920642395.53124445427
Winsorized Mean ( 3 / 20 )21.87250.0546145326368472400.488641831627
Winsorized Mean ( 4 / 20 )21.87183333333330.0537379557740349407.009031480527
Winsorized Mean ( 5 / 20 )21.86850.0529464205242213413.030754175268
Winsorized Mean ( 6 / 20 )21.86750.0528095528295449414.082279215324
Winsorized Mean ( 7 / 20 )21.87450.0512567619901757426.763204515195
Winsorized Mean ( 8 / 20 )21.87716666666670.0506840727981177431.637898434222
Winsorized Mean ( 9 / 20 )21.87716666666670.0506840727981177431.637898434222
Winsorized Mean ( 10 / 20 )21.87883333333330.0503300359978064434.707285611457
Winsorized Mean ( 11 / 20 )21.87516666666670.0498299320495248438.996518095297
Winsorized Mean ( 12 / 20 )21.88116666666670.0478734747609508457.062429162017
Winsorized Mean ( 13 / 20 )21.92666666666670.0373929104935535586.385664481688
Winsorized Mean ( 14 / 20 )21.93833333333330.0337958031248145649.143719186397
Winsorized Mean ( 15 / 20 )21.93333333333330.0323239837376279678.546725903746
Winsorized Mean ( 16 / 20 )21.9440.0296783129555406739.395127778087
Winsorized Mean ( 17 / 20 )21.94966666666670.0287350714537147763.863305578423
Winsorized Mean ( 18 / 20 )21.93766666666670.0271607130143907807.698481812438
Winsorized Mean ( 19 / 20 )21.94083333333330.0266334096998686823.808651636578
Winsorized Mean ( 20 / 20 )21.95083333333330.0240177566923899913.941864532606
Trimmed Mean ( 1 / 20 )21.87465517241380.0548606635831771398.731144388155
Trimmed Mean ( 2 / 20 )21.88017857142860.05398321713191405.314461306808
Trimmed Mean ( 3 / 20 )21.88555555555560.0530269413656742412.72521084391
Trimmed Mean ( 4 / 20 )21.89057692307690.0521255687900348419.95852383412
Trimmed Mean ( 5 / 20 )21.89620.0512878153170907426.927913864631
Trimmed Mean ( 6 / 20 )21.9031250.0504291479040974434.334624127574
Trimmed Mean ( 7 / 20 )21.91086956521740.0493071082733108444.375473081179
Trimmed Mean ( 8 / 20 )21.91795454545450.0482753067039771454.01999576833
Trimmed Mean ( 9 / 20 )21.92523809523810.0470318029343104466.178983737051
Trimmed Mean ( 10 / 20 )21.933250.0453185130846669483.979912558537
Trimmed Mean ( 11 / 20 )21.94184210526320.0430601406536164509.56271327043
Trimmed Mean ( 12 / 20 )21.95194444444440.0400095612470527548.667462482147
Trimmed Mean ( 13 / 20 )21.96235294117650.0363216439932997604.662964738817
Trimmed Mean ( 14 / 20 )21.96750.0348759321762342629.875637129765
Trimmed Mean ( 15 / 20 )21.97166666666670.0339000672475288648.130474380353
Trimmed Mean ( 16 / 20 )21.97714285714290.0327967007908789670.102245871478
Trimmed Mean ( 17 / 20 )21.98192307692310.0319712333717923687.553176985576
Trimmed Mean ( 18 / 20 )21.98666666666670.0309081544201823711.354886085009
Trimmed Mean ( 19 / 20 )21.99409090909090.0295101353995985745.30633666256
Trimmed Mean ( 20 / 20 )22.00250.0271920557284079809.151769169613
Median22.045
Midrange21.66
Midmean - Weighted Average at Xnp21.9593548387097
Midmean - Weighted Average at X(n+1)p21.9716666666667
Midmean - Empirical Distribution Function21.9593548387097
Midmean - Empirical Distribution Function - Averaging21.9716666666667
Midmean - Empirical Distribution Function - Interpolation21.9716666666667
Midmean - Closest Observation21.9593548387097
Midmean - True Basic - Statistics Graphics Toolkit21.9716666666667
Midmean - MS Excel (old versions)21.9675
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 21.8675 & 0.0563105919731056 & 388.337242315693 \tabularnewline
Geometric Mean & 21.8631817954844 &  &  \tabularnewline
Harmonic Mean & 21.8588232964384 &  &  \tabularnewline
Quadratic Mean & 21.8717772102162 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 21.8695 & 0.0555432467532013 & 393.738236030279 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 21.8705 & 0.0552939882920642 & 395.53124445427 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 21.8725 & 0.0546145326368472 & 400.488641831627 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 21.8718333333333 & 0.0537379557740349 & 407.009031480527 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 21.8685 & 0.0529464205242213 & 413.030754175268 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 21.8675 & 0.0528095528295449 & 414.082279215324 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 21.8745 & 0.0512567619901757 & 426.763204515195 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 21.8771666666667 & 0.0506840727981177 & 431.637898434222 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 21.8771666666667 & 0.0506840727981177 & 431.637898434222 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 21.8788333333333 & 0.0503300359978064 & 434.707285611457 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 21.8751666666667 & 0.0498299320495248 & 438.996518095297 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 21.8811666666667 & 0.0478734747609508 & 457.062429162017 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 21.9266666666667 & 0.0373929104935535 & 586.385664481688 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 21.9383333333333 & 0.0337958031248145 & 649.143719186397 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 21.9333333333333 & 0.0323239837376279 & 678.546725903746 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 21.944 & 0.0296783129555406 & 739.395127778087 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 21.9496666666667 & 0.0287350714537147 & 763.863305578423 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 21.9376666666667 & 0.0271607130143907 & 807.698481812438 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 21.9408333333333 & 0.0266334096998686 & 823.808651636578 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 21.9508333333333 & 0.0240177566923899 & 913.941864532606 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 21.8746551724138 & 0.0548606635831771 & 398.731144388155 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 21.8801785714286 & 0.05398321713191 & 405.314461306808 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 21.8855555555556 & 0.0530269413656742 & 412.72521084391 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 21.8905769230769 & 0.0521255687900348 & 419.95852383412 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 21.8962 & 0.0512878153170907 & 426.927913864631 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 21.903125 & 0.0504291479040974 & 434.334624127574 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 21.9108695652174 & 0.0493071082733108 & 444.375473081179 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 21.9179545454545 & 0.0482753067039771 & 454.01999576833 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 21.9252380952381 & 0.0470318029343104 & 466.178983737051 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 21.93325 & 0.0453185130846669 & 483.979912558537 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 21.9418421052632 & 0.0430601406536164 & 509.56271327043 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 21.9519444444444 & 0.0400095612470527 & 548.667462482147 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 21.9623529411765 & 0.0363216439932997 & 604.662964738817 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 21.9675 & 0.0348759321762342 & 629.875637129765 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 21.9716666666667 & 0.0339000672475288 & 648.130474380353 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 21.9771428571429 & 0.0327967007908789 & 670.102245871478 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 21.9819230769231 & 0.0319712333717923 & 687.553176985576 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 21.9866666666667 & 0.0309081544201823 & 711.354886085009 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 21.9940909090909 & 0.0295101353995985 & 745.30633666256 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 22.0025 & 0.0271920557284079 & 809.151769169613 \tabularnewline
Median & 22.045 &  &  \tabularnewline
Midrange & 21.66 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 21.9593548387097 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 21.9716666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 21.9593548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 21.9716666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 21.9716666666667 &  &  \tabularnewline
Midmean - Closest Observation & 21.9593548387097 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 21.9716666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 21.9675 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=129608&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]21.8675[/C][C]0.0563105919731056[/C][C]388.337242315693[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]21.8631817954844[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21.8588232964384[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]21.8717772102162[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]21.8695[/C][C]0.0555432467532013[/C][C]393.738236030279[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]21.8705[/C][C]0.0552939882920642[/C][C]395.53124445427[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]21.8725[/C][C]0.0546145326368472[/C][C]400.488641831627[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]21.8718333333333[/C][C]0.0537379557740349[/C][C]407.009031480527[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]21.8685[/C][C]0.0529464205242213[/C][C]413.030754175268[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]21.8675[/C][C]0.0528095528295449[/C][C]414.082279215324[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]21.8745[/C][C]0.0512567619901757[/C][C]426.763204515195[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]21.8771666666667[/C][C]0.0506840727981177[/C][C]431.637898434222[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]21.8771666666667[/C][C]0.0506840727981177[/C][C]431.637898434222[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]21.8788333333333[/C][C]0.0503300359978064[/C][C]434.707285611457[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]21.8751666666667[/C][C]0.0498299320495248[/C][C]438.996518095297[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]21.8811666666667[/C][C]0.0478734747609508[/C][C]457.062429162017[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]21.9266666666667[/C][C]0.0373929104935535[/C][C]586.385664481688[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]21.9383333333333[/C][C]0.0337958031248145[/C][C]649.143719186397[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]21.9333333333333[/C][C]0.0323239837376279[/C][C]678.546725903746[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]21.944[/C][C]0.0296783129555406[/C][C]739.395127778087[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]21.9496666666667[/C][C]0.0287350714537147[/C][C]763.863305578423[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]21.9376666666667[/C][C]0.0271607130143907[/C][C]807.698481812438[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]21.9408333333333[/C][C]0.0266334096998686[/C][C]823.808651636578[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]21.9508333333333[/C][C]0.0240177566923899[/C][C]913.941864532606[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]21.8746551724138[/C][C]0.0548606635831771[/C][C]398.731144388155[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]21.8801785714286[/C][C]0.05398321713191[/C][C]405.314461306808[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]21.8855555555556[/C][C]0.0530269413656742[/C][C]412.72521084391[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]21.8905769230769[/C][C]0.0521255687900348[/C][C]419.95852383412[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]21.8962[/C][C]0.0512878153170907[/C][C]426.927913864631[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]21.903125[/C][C]0.0504291479040974[/C][C]434.334624127574[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]21.9108695652174[/C][C]0.0493071082733108[/C][C]444.375473081179[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]21.9179545454545[/C][C]0.0482753067039771[/C][C]454.01999576833[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]21.9252380952381[/C][C]0.0470318029343104[/C][C]466.178983737051[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]21.93325[/C][C]0.0453185130846669[/C][C]483.979912558537[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]21.9418421052632[/C][C]0.0430601406536164[/C][C]509.56271327043[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]21.9519444444444[/C][C]0.0400095612470527[/C][C]548.667462482147[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]21.9623529411765[/C][C]0.0363216439932997[/C][C]604.662964738817[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]21.9675[/C][C]0.0348759321762342[/C][C]629.875637129765[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]21.9716666666667[/C][C]0.0339000672475288[/C][C]648.130474380353[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]21.9771428571429[/C][C]0.0327967007908789[/C][C]670.102245871478[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]21.9819230769231[/C][C]0.0319712333717923[/C][C]687.553176985576[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]21.9866666666667[/C][C]0.0309081544201823[/C][C]711.354886085009[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]21.9940909090909[/C][C]0.0295101353995985[/C][C]745.30633666256[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]22.0025[/C][C]0.0271920557284079[/C][C]809.151769169613[/C][/ROW]
[ROW][C]Median[/C][C]22.045[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]21.66[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]21.9593548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]21.9716666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]21.9593548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]21.9716666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]21.9716666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]21.9593548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]21.9716666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]21.9675[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=129608&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=129608&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 Mean21.86750.0563105919731056388.337242315693
Geometric Mean21.8631817954844
Harmonic Mean21.8588232964384
Quadratic Mean21.8717772102162
Winsorized Mean ( 1 / 20 )21.86950.0555432467532013393.738236030279
Winsorized Mean ( 2 / 20 )21.87050.0552939882920642395.53124445427
Winsorized Mean ( 3 / 20 )21.87250.0546145326368472400.488641831627
Winsorized Mean ( 4 / 20 )21.87183333333330.0537379557740349407.009031480527
Winsorized Mean ( 5 / 20 )21.86850.0529464205242213413.030754175268
Winsorized Mean ( 6 / 20 )21.86750.0528095528295449414.082279215324
Winsorized Mean ( 7 / 20 )21.87450.0512567619901757426.763204515195
Winsorized Mean ( 8 / 20 )21.87716666666670.0506840727981177431.637898434222
Winsorized Mean ( 9 / 20 )21.87716666666670.0506840727981177431.637898434222
Winsorized Mean ( 10 / 20 )21.87883333333330.0503300359978064434.707285611457
Winsorized Mean ( 11 / 20 )21.87516666666670.0498299320495248438.996518095297
Winsorized Mean ( 12 / 20 )21.88116666666670.0478734747609508457.062429162017
Winsorized Mean ( 13 / 20 )21.92666666666670.0373929104935535586.385664481688
Winsorized Mean ( 14 / 20 )21.93833333333330.0337958031248145649.143719186397
Winsorized Mean ( 15 / 20 )21.93333333333330.0323239837376279678.546725903746
Winsorized Mean ( 16 / 20 )21.9440.0296783129555406739.395127778087
Winsorized Mean ( 17 / 20 )21.94966666666670.0287350714537147763.863305578423
Winsorized Mean ( 18 / 20 )21.93766666666670.0271607130143907807.698481812438
Winsorized Mean ( 19 / 20 )21.94083333333330.0266334096998686823.808651636578
Winsorized Mean ( 20 / 20 )21.95083333333330.0240177566923899913.941864532606
Trimmed Mean ( 1 / 20 )21.87465517241380.0548606635831771398.731144388155
Trimmed Mean ( 2 / 20 )21.88017857142860.05398321713191405.314461306808
Trimmed Mean ( 3 / 20 )21.88555555555560.0530269413656742412.72521084391
Trimmed Mean ( 4 / 20 )21.89057692307690.0521255687900348419.95852383412
Trimmed Mean ( 5 / 20 )21.89620.0512878153170907426.927913864631
Trimmed Mean ( 6 / 20 )21.9031250.0504291479040974434.334624127574
Trimmed Mean ( 7 / 20 )21.91086956521740.0493071082733108444.375473081179
Trimmed Mean ( 8 / 20 )21.91795454545450.0482753067039771454.01999576833
Trimmed Mean ( 9 / 20 )21.92523809523810.0470318029343104466.178983737051
Trimmed Mean ( 10 / 20 )21.933250.0453185130846669483.979912558537
Trimmed Mean ( 11 / 20 )21.94184210526320.0430601406536164509.56271327043
Trimmed Mean ( 12 / 20 )21.95194444444440.0400095612470527548.667462482147
Trimmed Mean ( 13 / 20 )21.96235294117650.0363216439932997604.662964738817
Trimmed Mean ( 14 / 20 )21.96750.0348759321762342629.875637129765
Trimmed Mean ( 15 / 20 )21.97166666666670.0339000672475288648.130474380353
Trimmed Mean ( 16 / 20 )21.97714285714290.0327967007908789670.102245871478
Trimmed Mean ( 17 / 20 )21.98192307692310.0319712333717923687.553176985576
Trimmed Mean ( 18 / 20 )21.98666666666670.0309081544201823711.354886085009
Trimmed Mean ( 19 / 20 )21.99409090909090.0295101353995985745.30633666256
Trimmed Mean ( 20 / 20 )22.00250.0271920557284079809.151769169613
Median22.045
Midrange21.66
Midmean - Weighted Average at Xnp21.9593548387097
Midmean - Weighted Average at X(n+1)p21.9716666666667
Midmean - Empirical Distribution Function21.9593548387097
Midmean - Empirical Distribution Function - Averaging21.9716666666667
Midmean - Empirical Distribution Function - Interpolation21.9716666666667
Midmean - Closest Observation21.9593548387097
Midmean - True Basic - Statistics Graphics Toolkit21.9716666666667
Midmean - MS Excel (old versions)21.9675
Number of observations60



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')