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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 22 Oct 2009 09:44:00 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/22/t12562262804nydrrk8tou5hcm.htm/, Retrieved Fri, 03 May 2024 18:08:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49769, Retrieved Fri, 03 May 2024 18:08:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [workshop 3/part 2] [2009-10-22 15:44:00] [bebfa40a4e66abcf3fcee16e050bb8d6] [Current]
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Dataseries X:
1.436908929
1.411717837
1.377545552
1.348943246
1.320311666
1.285253017
1.254095745
1.220260273
1.202206488
1.188118812
1.299190218
1.359671133
1.419631059
1.396021307
1.365642626
1.340841502
1.299472705
1.285594244
1.247119212
1.230448329
1.211402173
1.206059338
1.29726206
1.355737705
1.410891576
1.413686003
1.354369179
1.304479295
1.304147696
1.289441991
1.262425237
1.259654419
1.204585727
1.198638691
1.314828123
1.354351739
1.435689999
1.407968081
1.347733625
1.356390977
1.334319012
1.321790492
1.292481913
1.290630619
1.214534007
1.183867141
1.296155497
1.332478319
1.416671793
1.360303256
1.33168649
1.314907675
1.30101151
1.279733914
1.285324542
1.265348075
1.221352518
1.208470561
1.291576557
1.324770741




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49769&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49769&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49769&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.307435869433330.00884337137834611147.843600986239
Geometric Mean1.30566839080629
Harmonic Mean1.30389873648609
Quadratic Mean1.30919924400516
Winsorized Mean ( 1 / 20 )1.307486415116670.00882183177585481148.210309189440
Winsorized Mean ( 2 / 20 )1.307301779750.0086189971825614151.676784672239
Winsorized Mean ( 3 / 20 )1.30733220630.00854896467456687152.922869150379
Winsorized Mean ( 4 / 20 )1.307291769566670.00847338325411776154.282148034714
Winsorized Mean ( 5 / 20 )1.307250556650.00841354056625121155.374606725462
Winsorized Mean ( 6 / 20 )1.307409052850.00834736780737484156.625307883871
Winsorized Mean ( 7 / 20 )1.307409999833330.0082078564744961159.287629345833
Winsorized Mean ( 8 / 20 )1.30623467450.00780393419940299167.381559239688
Winsorized Mean ( 9 / 20 )1.304322251150.0071193846886792183.207160195185
Winsorized Mean ( 10 / 20 )1.302520470983330.00675213599527249192.904952135931
Winsorized Mean ( 11 / 20 )1.303209151833330.00626467763145658208.024934162547
Winsorized Mean ( 12 / 20 )1.306416903833330.00561666378206303232.596600851454
Winsorized Mean ( 13 / 20 )1.307217785516670.00523764233093304249.581338877677
Winsorized Mean ( 14 / 20 )1.308362379316670.00499448523409686261.961407030419
Winsorized Mean ( 15 / 20 )1.308712952316670.00482598040608103271.180743019099
Winsorized Mean ( 16 / 20 )1.309487725116670.00469982498015231278.624785103004
Winsorized Mean ( 17 / 20 )1.312031306483330.00383194091369375342.393407423033
Winsorized Mean ( 18 / 20 )1.313324151083330.00354273403026071370.709214935529
Winsorized Mean ( 19 / 20 )1.311164295050.00318741247820061411.356956157175
Winsorized Mean ( 20 / 20 )1.309080032383330.00283914866019595461.081890756994
Trimmed Mean ( 1 / 20 )1.307334070620690.00860530240231495151.921920869277
Trimmed Mean ( 2 / 20 )1.3071708443750.00833791898181543156.774231942751
Trimmed Mean ( 3 / 20 )1.30709810250.00814134259462198160.550681574737
Trimmed Mean ( 4 / 20 )1.307008062576920.00792804343304749164.858842363142
Trimmed Mean ( 5 / 20 )1.306922950480.00768825211249966169.989606396386
Trimmed Mean ( 6 / 20 )1.30684104893750.00740369108980822176.512098233876
Trimmed Mean ( 7 / 20 )1.306717569826090.00705937090401804185.103968553675
Trimmed Mean ( 8 / 20 )1.306582680863640.00665601406206104196.301069781552
Trimmed Mean ( 9 / 20 )1.306644824857140.00625382510032321208.935300219639
Trimmed Mean ( 10 / 20 )1.3070319204750.00592975914297013220.419057327905
Trimmed Mean ( 11 / 20 )1.307744254605260.00559778781002995233.618046804505
Trimmed Mean ( 12 / 20 )1.308431391388890.00529324402358382247.188942274195
Trimmed Mean ( 13 / 20 )1.308727639558820.00507655706436957257.798272129016
Trimmed Mean ( 14 / 20 )1.308945406968750.00488348012669474268.035370885122
Trimmed Mean ( 15 / 20 )1.309028696633330.00467793332371932279.830558934208
Trimmed Mean ( 16 / 20 )1.309073802964290.00442613743464313295.759863378448
Trimmed Mean ( 17 / 20 )1.309014102653850.00408532837458807320.418331803214
Trimmed Mean ( 18 / 20 )1.308570396208330.00389910088287316335.608242904471
Trimmed Mean ( 19 / 20 )1.307850130318180.00369367580500718354.078213508951
Trimmed Mean ( 20 / 20 )1.307326841150.00351757540391782371.655669326639
Median1.302579603
Midrange1.310388035
Midmean - Weighted Average at Xnp1.307435978
Midmean - Weighted Average at X(n+1)p1.30902869663333
Midmean - Empirical Distribution Function1.307435978
Midmean - Empirical Distribution Function - Averaging1.30902869663333
Midmean - Empirical Distribution Function - Interpolation1.30902869663333
Midmean - Closest Observation1.307435978
Midmean - True Basic - Statistics Graphics Toolkit1.30902869663333
Midmean - MS Excel (old versions)1.30894540696875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.30743586943333 & 0.00884337137834611 & 147.843600986239 \tabularnewline
Geometric Mean & 1.30566839080629 &  &  \tabularnewline
Harmonic Mean & 1.30389873648609 &  &  \tabularnewline
Quadratic Mean & 1.30919924400516 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.30748641511667 & 0.00882183177585481 & 148.210309189440 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.30730177975 & 0.0086189971825614 & 151.676784672239 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.3073322063 & 0.00854896467456687 & 152.922869150379 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.30729176956667 & 0.00847338325411776 & 154.282148034714 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.30725055665 & 0.00841354056625121 & 155.374606725462 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.30740905285 & 0.00834736780737484 & 156.625307883871 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.30740999983333 & 0.0082078564744961 & 159.287629345833 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.3062346745 & 0.00780393419940299 & 167.381559239688 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.30432225115 & 0.0071193846886792 & 183.207160195185 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.30252047098333 & 0.00675213599527249 & 192.904952135931 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.30320915183333 & 0.00626467763145658 & 208.024934162547 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.30641690383333 & 0.00561666378206303 & 232.596600851454 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.30721778551667 & 0.00523764233093304 & 249.581338877677 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.30836237931667 & 0.00499448523409686 & 261.961407030419 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.30871295231667 & 0.00482598040608103 & 271.180743019099 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.30948772511667 & 0.00469982498015231 & 278.624785103004 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.31203130648333 & 0.00383194091369375 & 342.393407423033 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.31332415108333 & 0.00354273403026071 & 370.709214935529 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.31116429505 & 0.00318741247820061 & 411.356956157175 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.30908003238333 & 0.00283914866019595 & 461.081890756994 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.30733407062069 & 0.00860530240231495 & 151.921920869277 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.307170844375 & 0.00833791898181543 & 156.774231942751 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.3070981025 & 0.00814134259462198 & 160.550681574737 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.30700806257692 & 0.00792804343304749 & 164.858842363142 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.30692295048 & 0.00768825211249966 & 169.989606396386 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.3068410489375 & 0.00740369108980822 & 176.512098233876 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.30671756982609 & 0.00705937090401804 & 185.103968553675 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.30658268086364 & 0.00665601406206104 & 196.301069781552 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.30664482485714 & 0.00625382510032321 & 208.935300219639 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.307031920475 & 0.00592975914297013 & 220.419057327905 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.30774425460526 & 0.00559778781002995 & 233.618046804505 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.30843139138889 & 0.00529324402358382 & 247.188942274195 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.30872763955882 & 0.00507655706436957 & 257.798272129016 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.30894540696875 & 0.00488348012669474 & 268.035370885122 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.30902869663333 & 0.00467793332371932 & 279.830558934208 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.30907380296429 & 0.00442613743464313 & 295.759863378448 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.30901410265385 & 0.00408532837458807 & 320.418331803214 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.30857039620833 & 0.00389910088287316 & 335.608242904471 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.30785013031818 & 0.00369367580500718 & 354.078213508951 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.30732684115 & 0.00351757540391782 & 371.655669326639 \tabularnewline
Median & 1.302579603 &  &  \tabularnewline
Midrange & 1.310388035 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.307435978 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.30902869663333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.307435978 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.30902869663333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.30902869663333 &  &  \tabularnewline
Midmean - Closest Observation & 1.307435978 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.30902869663333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.30894540696875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49769&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]1.30743586943333[/C][C]0.00884337137834611[/C][C]147.843600986239[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.30566839080629[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.30389873648609[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.30919924400516[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.30748641511667[/C][C]0.00882183177585481[/C][C]148.210309189440[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.30730177975[/C][C]0.0086189971825614[/C][C]151.676784672239[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.3073322063[/C][C]0.00854896467456687[/C][C]152.922869150379[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.30729176956667[/C][C]0.00847338325411776[/C][C]154.282148034714[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.30725055665[/C][C]0.00841354056625121[/C][C]155.374606725462[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.30740905285[/C][C]0.00834736780737484[/C][C]156.625307883871[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.30740999983333[/C][C]0.0082078564744961[/C][C]159.287629345833[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.3062346745[/C][C]0.00780393419940299[/C][C]167.381559239688[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.30432225115[/C][C]0.0071193846886792[/C][C]183.207160195185[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.30252047098333[/C][C]0.00675213599527249[/C][C]192.904952135931[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.30320915183333[/C][C]0.00626467763145658[/C][C]208.024934162547[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.30641690383333[/C][C]0.00561666378206303[/C][C]232.596600851454[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.30721778551667[/C][C]0.00523764233093304[/C][C]249.581338877677[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.30836237931667[/C][C]0.00499448523409686[/C][C]261.961407030419[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.30871295231667[/C][C]0.00482598040608103[/C][C]271.180743019099[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.30948772511667[/C][C]0.00469982498015231[/C][C]278.624785103004[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.31203130648333[/C][C]0.00383194091369375[/C][C]342.393407423033[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.31332415108333[/C][C]0.00354273403026071[/C][C]370.709214935529[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.31116429505[/C][C]0.00318741247820061[/C][C]411.356956157175[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.30908003238333[/C][C]0.00283914866019595[/C][C]461.081890756994[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.30733407062069[/C][C]0.00860530240231495[/C][C]151.921920869277[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.307170844375[/C][C]0.00833791898181543[/C][C]156.774231942751[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.3070981025[/C][C]0.00814134259462198[/C][C]160.550681574737[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.30700806257692[/C][C]0.00792804343304749[/C][C]164.858842363142[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.30692295048[/C][C]0.00768825211249966[/C][C]169.989606396386[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.3068410489375[/C][C]0.00740369108980822[/C][C]176.512098233876[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.30671756982609[/C][C]0.00705937090401804[/C][C]185.103968553675[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.30658268086364[/C][C]0.00665601406206104[/C][C]196.301069781552[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.30664482485714[/C][C]0.00625382510032321[/C][C]208.935300219639[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.307031920475[/C][C]0.00592975914297013[/C][C]220.419057327905[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.30774425460526[/C][C]0.00559778781002995[/C][C]233.618046804505[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.30843139138889[/C][C]0.00529324402358382[/C][C]247.188942274195[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.30872763955882[/C][C]0.00507655706436957[/C][C]257.798272129016[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.30894540696875[/C][C]0.00488348012669474[/C][C]268.035370885122[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.30902869663333[/C][C]0.00467793332371932[/C][C]279.830558934208[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.30907380296429[/C][C]0.00442613743464313[/C][C]295.759863378448[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.30901410265385[/C][C]0.00408532837458807[/C][C]320.418331803214[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.30857039620833[/C][C]0.00389910088287316[/C][C]335.608242904471[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.30785013031818[/C][C]0.00369367580500718[/C][C]354.078213508951[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.30732684115[/C][C]0.00351757540391782[/C][C]371.655669326639[/C][/ROW]
[ROW][C]Median[/C][C]1.302579603[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.310388035[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.307435978[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.30902869663333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.307435978[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.30902869663333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.30902869663333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.307435978[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.30902869663333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.30894540696875[/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=49769&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49769&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 Mean1.307435869433330.00884337137834611147.843600986239
Geometric Mean1.30566839080629
Harmonic Mean1.30389873648609
Quadratic Mean1.30919924400516
Winsorized Mean ( 1 / 20 )1.307486415116670.00882183177585481148.210309189440
Winsorized Mean ( 2 / 20 )1.307301779750.0086189971825614151.676784672239
Winsorized Mean ( 3 / 20 )1.30733220630.00854896467456687152.922869150379
Winsorized Mean ( 4 / 20 )1.307291769566670.00847338325411776154.282148034714
Winsorized Mean ( 5 / 20 )1.307250556650.00841354056625121155.374606725462
Winsorized Mean ( 6 / 20 )1.307409052850.00834736780737484156.625307883871
Winsorized Mean ( 7 / 20 )1.307409999833330.0082078564744961159.287629345833
Winsorized Mean ( 8 / 20 )1.30623467450.00780393419940299167.381559239688
Winsorized Mean ( 9 / 20 )1.304322251150.0071193846886792183.207160195185
Winsorized Mean ( 10 / 20 )1.302520470983330.00675213599527249192.904952135931
Winsorized Mean ( 11 / 20 )1.303209151833330.00626467763145658208.024934162547
Winsorized Mean ( 12 / 20 )1.306416903833330.00561666378206303232.596600851454
Winsorized Mean ( 13 / 20 )1.307217785516670.00523764233093304249.581338877677
Winsorized Mean ( 14 / 20 )1.308362379316670.00499448523409686261.961407030419
Winsorized Mean ( 15 / 20 )1.308712952316670.00482598040608103271.180743019099
Winsorized Mean ( 16 / 20 )1.309487725116670.00469982498015231278.624785103004
Winsorized Mean ( 17 / 20 )1.312031306483330.00383194091369375342.393407423033
Winsorized Mean ( 18 / 20 )1.313324151083330.00354273403026071370.709214935529
Winsorized Mean ( 19 / 20 )1.311164295050.00318741247820061411.356956157175
Winsorized Mean ( 20 / 20 )1.309080032383330.00283914866019595461.081890756994
Trimmed Mean ( 1 / 20 )1.307334070620690.00860530240231495151.921920869277
Trimmed Mean ( 2 / 20 )1.3071708443750.00833791898181543156.774231942751
Trimmed Mean ( 3 / 20 )1.30709810250.00814134259462198160.550681574737
Trimmed Mean ( 4 / 20 )1.307008062576920.00792804343304749164.858842363142
Trimmed Mean ( 5 / 20 )1.306922950480.00768825211249966169.989606396386
Trimmed Mean ( 6 / 20 )1.30684104893750.00740369108980822176.512098233876
Trimmed Mean ( 7 / 20 )1.306717569826090.00705937090401804185.103968553675
Trimmed Mean ( 8 / 20 )1.306582680863640.00665601406206104196.301069781552
Trimmed Mean ( 9 / 20 )1.306644824857140.00625382510032321208.935300219639
Trimmed Mean ( 10 / 20 )1.3070319204750.00592975914297013220.419057327905
Trimmed Mean ( 11 / 20 )1.307744254605260.00559778781002995233.618046804505
Trimmed Mean ( 12 / 20 )1.308431391388890.00529324402358382247.188942274195
Trimmed Mean ( 13 / 20 )1.308727639558820.00507655706436957257.798272129016
Trimmed Mean ( 14 / 20 )1.308945406968750.00488348012669474268.035370885122
Trimmed Mean ( 15 / 20 )1.309028696633330.00467793332371932279.830558934208
Trimmed Mean ( 16 / 20 )1.309073802964290.00442613743464313295.759863378448
Trimmed Mean ( 17 / 20 )1.309014102653850.00408532837458807320.418331803214
Trimmed Mean ( 18 / 20 )1.308570396208330.00389910088287316335.608242904471
Trimmed Mean ( 19 / 20 )1.307850130318180.00369367580500718354.078213508951
Trimmed Mean ( 20 / 20 )1.307326841150.00351757540391782371.655669326639
Median1.302579603
Midrange1.310388035
Midmean - Weighted Average at Xnp1.307435978
Midmean - Weighted Average at X(n+1)p1.30902869663333
Midmean - Empirical Distribution Function1.307435978
Midmean - Empirical Distribution Function - Averaging1.30902869663333
Midmean - Empirical Distribution Function - Interpolation1.30902869663333
Midmean - Closest Observation1.307435978
Midmean - True Basic - Statistics Graphics Toolkit1.30902869663333
Midmean - MS Excel (old versions)1.30894540696875
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')