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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Nov 2007 14:59:26 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/07/t119447262300te33azgyjv9eu.htm/, Retrieved Tue, 30 Apr 2024 00:30:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=593, Retrieved Tue, 30 Apr 2024 00:30:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact307
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper stat] [2007-11-07 21:59:26] [0c12eff582f43eaf43ae2f09e879befe] [Current]
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Dataseries X:
1,05
1,00
1,05
1,07
1,12
1,06
1,05
1,12
1,04
1,11
1,07
1,20
1,13
1,17
1,03
1,01
1,06
1,05
1,02
1,06
1,06
1,05
0,99
1,06
1,07
1,05
1,10
1,03
1,01
1,01
0,97
1,04
1,06
0,97
0,96
1,09
1,01
1,08
1,03
0,99
1,01
0,97
0,97
1,05
1,03
1,02
1,02
1,11
1,05
1,08
1,07
1,04
1,05
1,08
1,06
1,11
1,12
1,10
1,01
1,14




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=593&T=0

[TABLE]
[ROW][C]Summary of compuational 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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=593&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=593&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.053166666666670.00641102363944023164.274338373618
Geometric Mean1.05202818995397
Harmonic Mean1.05090166863257
Quadratic Mean1.05431731466385
Winsorized Mean ( 1 / 20 )1.052833333333330.00619409079919121169.973829487744
Winsorized Mean ( 2 / 20 )1.051833333333330.0059064824421922178.081174984911
Winsorized Mean ( 3 / 20 )1.051333333333330.00578555900773772181.716811102827
Winsorized Mean ( 4 / 20 )1.050666666666670.00563918226765498186.315429577980
Winsorized Mean ( 5 / 20 )1.052333333333330.00526885458380049199.727154468984
Winsorized Mean ( 6 / 20 )1.052333333333330.00526885458380049199.727154468984
Winsorized Mean ( 7 / 20 )1.052333333333330.00479740199622369219.354837089259
Winsorized Mean ( 8 / 20 )1.053666666666670.00456569538930789230.779011042695
Winsorized Mean ( 9 / 20 )1.053666666666670.00456569538930789230.779011042695
Winsorized Mean ( 10 / 20 )1.0520.00423063885066379248.662208506628
Winsorized Mean ( 11 / 20 )1.0520.00423063885066379248.662208506628
Winsorized Mean ( 12 / 20 )1.050.00386202721861047271.877938855589
Winsorized Mean ( 13 / 20 )1.047833333333330.00350215161199098299.197022123676
Winsorized Mean ( 14 / 20 )1.050166666666670.00309447901538334339.367842356033
Winsorized Mean ( 15 / 20 )1.050166666666670.00309447901538334339.367842356033
Winsorized Mean ( 16 / 20 )1.04750.00268522847769071390.097158846181
Winsorized Mean ( 17 / 20 )1.050333333333330.00221661250517919473.846164306659
Winsorized Mean ( 18 / 20 )1.050333333333330.00221661250517919473.846164306659
Winsorized Mean ( 19 / 20 )1.050333333333330.00221661250517919473.846164306659
Winsorized Mean ( 20 / 20 )1.0470.00175151266343395597.769015239256
Trimmed Mean ( 1 / 20 )1.052241379310340.00590324847997699178.247855037680
Trimmed Mean ( 2 / 20 )1.051607142857140.00554073923589158189.795458346981
Trimmed Mean ( 3 / 20 )1.051481481481480.00528970234531067198.778950655630
Trimmed Mean ( 4 / 20 )1.051538461538460.00503670251265165208.775177588335
Trimmed Mean ( 5 / 20 )1.05180.00477826712676195220.121640774145
Trimmed Mean ( 6 / 20 )1.051666666666670.00458695859206245229.273198255274
Trimmed Mean ( 7 / 20 )1.051521739130430.00434021072201929242.274351748805
Trimmed Mean ( 8 / 20 )1.051363636363640.00417116484725447252.05516321314
Trimmed Mean ( 9 / 20 )1.050952380952380.00401520807839852261.742943437083
Trimmed Mean ( 10 / 20 )1.05050.00380536059142485276.057938469022
Trimmed Mean ( 11 / 20 )1.050263157894740.00362712324839813289.558166615533
Trimmed Mean ( 12 / 20 )1.050.00338061701891407310.594188612730
Trimmed Mean ( 13 / 20 )1.050.00315945797377605332.335485616568
Trimmed Mean ( 14 / 20 )1.05031250.0029609138941735354.725783166748
Trimmed Mean ( 15 / 20 )1.050333333333330.00281552891392259373.050096605121
Trimmed Mean ( 16 / 20 )1.050357142857140.00259640282586597404.543213554245
Trimmed Mean ( 17 / 20 )1.050769230769230.00241298263713202435.46489502226
Trimmed Mean ( 18 / 20 )1.050833333333330.00232477727362874452.014627488632
Trimmed Mean ( 19 / 20 )1.050909090909090.00217314292606254483.589495336695
Trimmed Mean ( 20 / 20 )1.0510.00190567020949807551.512005992275
Median1.05
Midrange1.08
Midmean - Weighted Average at Xnp1.05121212121212
Midmean - Weighted Average at X(n+1)p1.05121212121212
Midmean - Empirical Distribution Function1.05121212121212
Midmean - Empirical Distribution Function - Averaging1.05121212121212
Midmean - Empirical Distribution Function - Interpolation1.05121212121212
Midmean - Closest Observation1.05121212121212
Midmean - True Basic - Statistics Graphics Toolkit1.05121212121212
Midmean - MS Excel (old versions)1.05121212121212
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.05316666666667 & 0.00641102363944023 & 164.274338373618 \tabularnewline
Geometric Mean & 1.05202818995397 &  &  \tabularnewline
Harmonic Mean & 1.05090166863257 &  &  \tabularnewline
Quadratic Mean & 1.05431731466385 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.05283333333333 & 0.00619409079919121 & 169.973829487744 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.05183333333333 & 0.0059064824421922 & 178.081174984911 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.05133333333333 & 0.00578555900773772 & 181.716811102827 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.05066666666667 & 0.00563918226765498 & 186.315429577980 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.05233333333333 & 0.00526885458380049 & 199.727154468984 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.05233333333333 & 0.00526885458380049 & 199.727154468984 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.05233333333333 & 0.00479740199622369 & 219.354837089259 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.05366666666667 & 0.00456569538930789 & 230.779011042695 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.05366666666667 & 0.00456569538930789 & 230.779011042695 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.052 & 0.00423063885066379 & 248.662208506628 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.052 & 0.00423063885066379 & 248.662208506628 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.05 & 0.00386202721861047 & 271.877938855589 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.04783333333333 & 0.00350215161199098 & 299.197022123676 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.05016666666667 & 0.00309447901538334 & 339.367842356033 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.05016666666667 & 0.00309447901538334 & 339.367842356033 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.0475 & 0.00268522847769071 & 390.097158846181 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.05033333333333 & 0.00221661250517919 & 473.846164306659 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.05033333333333 & 0.00221661250517919 & 473.846164306659 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.05033333333333 & 0.00221661250517919 & 473.846164306659 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.047 & 0.00175151266343395 & 597.769015239256 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.05224137931034 & 0.00590324847997699 & 178.247855037680 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.05160714285714 & 0.00554073923589158 & 189.795458346981 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.05148148148148 & 0.00528970234531067 & 198.778950655630 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.05153846153846 & 0.00503670251265165 & 208.775177588335 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.0518 & 0.00477826712676195 & 220.121640774145 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.05166666666667 & 0.00458695859206245 & 229.273198255274 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.05152173913043 & 0.00434021072201929 & 242.274351748805 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.05136363636364 & 0.00417116484725447 & 252.05516321314 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.05095238095238 & 0.00401520807839852 & 261.742943437083 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.0505 & 0.00380536059142485 & 276.057938469022 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.05026315789474 & 0.00362712324839813 & 289.558166615533 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.05 & 0.00338061701891407 & 310.594188612730 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.05 & 0.00315945797377605 & 332.335485616568 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.0503125 & 0.0029609138941735 & 354.725783166748 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.05033333333333 & 0.00281552891392259 & 373.050096605121 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.05035714285714 & 0.00259640282586597 & 404.543213554245 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.05076923076923 & 0.00241298263713202 & 435.46489502226 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.05083333333333 & 0.00232477727362874 & 452.014627488632 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.05090909090909 & 0.00217314292606254 & 483.589495336695 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.051 & 0.00190567020949807 & 551.512005992275 \tabularnewline
Median & 1.05 &  &  \tabularnewline
Midrange & 1.08 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.05121212121212 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.05121212121212 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.05121212121212 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.05121212121212 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.05121212121212 &  &  \tabularnewline
Midmean - Closest Observation & 1.05121212121212 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.05121212121212 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.05121212121212 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=593&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]1.05316666666667[/C][C]0.00641102363944023[/C][C]164.274338373618[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.05202818995397[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.05090166863257[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.05431731466385[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.05283333333333[/C][C]0.00619409079919121[/C][C]169.973829487744[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.05183333333333[/C][C]0.0059064824421922[/C][C]178.081174984911[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.05133333333333[/C][C]0.00578555900773772[/C][C]181.716811102827[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.05066666666667[/C][C]0.00563918226765498[/C][C]186.315429577980[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.05233333333333[/C][C]0.00526885458380049[/C][C]199.727154468984[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.05233333333333[/C][C]0.00526885458380049[/C][C]199.727154468984[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.05233333333333[/C][C]0.00479740199622369[/C][C]219.354837089259[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.05366666666667[/C][C]0.00456569538930789[/C][C]230.779011042695[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.05366666666667[/C][C]0.00456569538930789[/C][C]230.779011042695[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.052[/C][C]0.00423063885066379[/C][C]248.662208506628[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.052[/C][C]0.00423063885066379[/C][C]248.662208506628[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.05[/C][C]0.00386202721861047[/C][C]271.877938855589[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.04783333333333[/C][C]0.00350215161199098[/C][C]299.197022123676[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.05016666666667[/C][C]0.00309447901538334[/C][C]339.367842356033[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.05016666666667[/C][C]0.00309447901538334[/C][C]339.367842356033[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.0475[/C][C]0.00268522847769071[/C][C]390.097158846181[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.05033333333333[/C][C]0.00221661250517919[/C][C]473.846164306659[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.05033333333333[/C][C]0.00221661250517919[/C][C]473.846164306659[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.05033333333333[/C][C]0.00221661250517919[/C][C]473.846164306659[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.047[/C][C]0.00175151266343395[/C][C]597.769015239256[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.05224137931034[/C][C]0.00590324847997699[/C][C]178.247855037680[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.05160714285714[/C][C]0.00554073923589158[/C][C]189.795458346981[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.05148148148148[/C][C]0.00528970234531067[/C][C]198.778950655630[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.05153846153846[/C][C]0.00503670251265165[/C][C]208.775177588335[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.0518[/C][C]0.00477826712676195[/C][C]220.121640774145[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.05166666666667[/C][C]0.00458695859206245[/C][C]229.273198255274[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.05152173913043[/C][C]0.00434021072201929[/C][C]242.274351748805[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.05136363636364[/C][C]0.00417116484725447[/C][C]252.05516321314[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.05095238095238[/C][C]0.00401520807839852[/C][C]261.742943437083[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.0505[/C][C]0.00380536059142485[/C][C]276.057938469022[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.05026315789474[/C][C]0.00362712324839813[/C][C]289.558166615533[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.05[/C][C]0.00338061701891407[/C][C]310.594188612730[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.05[/C][C]0.00315945797377605[/C][C]332.335485616568[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.0503125[/C][C]0.0029609138941735[/C][C]354.725783166748[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.05033333333333[/C][C]0.00281552891392259[/C][C]373.050096605121[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.05035714285714[/C][C]0.00259640282586597[/C][C]404.543213554245[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.05076923076923[/C][C]0.00241298263713202[/C][C]435.46489502226[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.05083333333333[/C][C]0.00232477727362874[/C][C]452.014627488632[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.05090909090909[/C][C]0.00217314292606254[/C][C]483.589495336695[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.051[/C][C]0.00190567020949807[/C][C]551.512005992275[/C][/ROW]
[ROW][C]Median[/C][C]1.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.05121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.05121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.05121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.05121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.05121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.05121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.05121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.05121212121212[/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=593&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=593&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 Mean1.053166666666670.00641102363944023164.274338373618
Geometric Mean1.05202818995397
Harmonic Mean1.05090166863257
Quadratic Mean1.05431731466385
Winsorized Mean ( 1 / 20 )1.052833333333330.00619409079919121169.973829487744
Winsorized Mean ( 2 / 20 )1.051833333333330.0059064824421922178.081174984911
Winsorized Mean ( 3 / 20 )1.051333333333330.00578555900773772181.716811102827
Winsorized Mean ( 4 / 20 )1.050666666666670.00563918226765498186.315429577980
Winsorized Mean ( 5 / 20 )1.052333333333330.00526885458380049199.727154468984
Winsorized Mean ( 6 / 20 )1.052333333333330.00526885458380049199.727154468984
Winsorized Mean ( 7 / 20 )1.052333333333330.00479740199622369219.354837089259
Winsorized Mean ( 8 / 20 )1.053666666666670.00456569538930789230.779011042695
Winsorized Mean ( 9 / 20 )1.053666666666670.00456569538930789230.779011042695
Winsorized Mean ( 10 / 20 )1.0520.00423063885066379248.662208506628
Winsorized Mean ( 11 / 20 )1.0520.00423063885066379248.662208506628
Winsorized Mean ( 12 / 20 )1.050.00386202721861047271.877938855589
Winsorized Mean ( 13 / 20 )1.047833333333330.00350215161199098299.197022123676
Winsorized Mean ( 14 / 20 )1.050166666666670.00309447901538334339.367842356033
Winsorized Mean ( 15 / 20 )1.050166666666670.00309447901538334339.367842356033
Winsorized Mean ( 16 / 20 )1.04750.00268522847769071390.097158846181
Winsorized Mean ( 17 / 20 )1.050333333333330.00221661250517919473.846164306659
Winsorized Mean ( 18 / 20 )1.050333333333330.00221661250517919473.846164306659
Winsorized Mean ( 19 / 20 )1.050333333333330.00221661250517919473.846164306659
Winsorized Mean ( 20 / 20 )1.0470.00175151266343395597.769015239256
Trimmed Mean ( 1 / 20 )1.052241379310340.00590324847997699178.247855037680
Trimmed Mean ( 2 / 20 )1.051607142857140.00554073923589158189.795458346981
Trimmed Mean ( 3 / 20 )1.051481481481480.00528970234531067198.778950655630
Trimmed Mean ( 4 / 20 )1.051538461538460.00503670251265165208.775177588335
Trimmed Mean ( 5 / 20 )1.05180.00477826712676195220.121640774145
Trimmed Mean ( 6 / 20 )1.051666666666670.00458695859206245229.273198255274
Trimmed Mean ( 7 / 20 )1.051521739130430.00434021072201929242.274351748805
Trimmed Mean ( 8 / 20 )1.051363636363640.00417116484725447252.05516321314
Trimmed Mean ( 9 / 20 )1.050952380952380.00401520807839852261.742943437083
Trimmed Mean ( 10 / 20 )1.05050.00380536059142485276.057938469022
Trimmed Mean ( 11 / 20 )1.050263157894740.00362712324839813289.558166615533
Trimmed Mean ( 12 / 20 )1.050.00338061701891407310.594188612730
Trimmed Mean ( 13 / 20 )1.050.00315945797377605332.335485616568
Trimmed Mean ( 14 / 20 )1.05031250.0029609138941735354.725783166748
Trimmed Mean ( 15 / 20 )1.050333333333330.00281552891392259373.050096605121
Trimmed Mean ( 16 / 20 )1.050357142857140.00259640282586597404.543213554245
Trimmed Mean ( 17 / 20 )1.050769230769230.00241298263713202435.46489502226
Trimmed Mean ( 18 / 20 )1.050833333333330.00232477727362874452.014627488632
Trimmed Mean ( 19 / 20 )1.050909090909090.00217314292606254483.589495336695
Trimmed Mean ( 20 / 20 )1.0510.00190567020949807551.512005992275
Median1.05
Midrange1.08
Midmean - Weighted Average at Xnp1.05121212121212
Midmean - Weighted Average at X(n+1)p1.05121212121212
Midmean - Empirical Distribution Function1.05121212121212
Midmean - Empirical Distribution Function - Averaging1.05121212121212
Midmean - Empirical Distribution Function - Interpolation1.05121212121212
Midmean - Closest Observation1.05121212121212
Midmean - True Basic - Statistics Graphics Toolkit1.05121212121212
Midmean - MS Excel (old versions)1.05121212121212
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')