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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 15:39:44 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/07/t1331152836of3z8p2bbw40qbk.htm/, Retrieved Fri, 03 May 2024 08:57:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163704, Retrieved Fri, 03 May 2024 08:57:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W51a
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [opgave oef 2 stap 1] [2012-03-07 20:39:44] [d94b10b2615af2e11b32dea0ad6a3c7b] [Current]
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Dataseries X:
227,81
227,81
227,01
227,26
227,1
227,59
227,59
227,7
227,75
226,33
225,95
226,33
226,33
226,22
224,84
221,88
222,37
221,8
221,8
221,8
221,9
220,2
219,95
220,05
220,05
220,05
220,62
221,53
221,61
221,5
221,5
221,87
222,27
220,86
221,49
221,67
221,67
221,72
221,67
220,29
220,75
219,59
219,59
219,59
219,82
221,59
220,9
221,01
221,01
219,69
221
219,82
218,04
217,97
217,97
217,53
217
217,18
217,68
217,71




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163704&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163704&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163704&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean222.0196666666670.408433411003685543.588405564263
Geometric Mean221.997619474859
Harmonic Mean221.975690815128
Quadratic Mean222.041830833742
Winsorized Mean ( 1 / 20 )222.0226666666670.407819048902616544.414654646708
Winsorized Mean ( 2 / 20 )222.0323333333330.405066038186247548.138605565456
Winsorized Mean ( 3 / 20 )222.0373333333330.403075736015229550.857601919617
Winsorized Mean ( 4 / 20 )222.0320.400975279962796553.729895819515
Winsorized Mean ( 5 / 20 )222.0536666666670.397107477138428559.17775275045
Winsorized Mean ( 6 / 20 )222.0206666666670.389444836405153570.095289274014
Winsorized Mean ( 7 / 20 )222.0101666666670.383782578194738578.479012025436
Winsorized Mean ( 8 / 20 )222.2048333333330.349586074176309635.622668485552
Winsorized Mean ( 9 / 20 )222.1028333333330.326489207967156680.276186512346
Winsorized Mean ( 10 / 20 )222.1028333333330.326489207967156680.276186512346
Winsorized Mean ( 11 / 20 )222.1211666666670.324127955802304685.288518594013
Winsorized Mean ( 12 / 20 )222.1251666666670.316030776201609702.85928901103
Winsorized Mean ( 13 / 20 )222.0666666666670.303257145706157732.271835341481
Winsorized Mean ( 14 / 20 )221.8380.244159205261904908.579300796951
Winsorized Mean ( 15 / 20 )221.24550.1229584526311481799.35169372775
Winsorized Mean ( 16 / 20 )221.2188333333330.1188925098890641860.66248866095
Winsorized Mean ( 17 / 20 )221.1140.1042644941759312120.70275454369
Winsorized Mean ( 18 / 20 )221.1530.09580621330829582308.33671808267
Winsorized Mean ( 19 / 20 )221.1783333333330.09062687104374192440.53811839735
Winsorized Mean ( 20 / 20 )221.2650.06978073002259233170.861066205
Trimmed Mean ( 1 / 20 )222.0063793103450.401072344981558553.532005106344
Trimmed Mean ( 2 / 20 )221.9889285714290.392629718705973565.390030339676
Trimmed Mean ( 3 / 20 )221.9648148148150.383856423770572578.24957736667
Trimmed Mean ( 4 / 20 )221.9369230769230.373727659376749593.846662157783
Trimmed Mean ( 5 / 20 )221.90840.361711505292857613.495553093711
Trimmed Mean ( 6 / 20 )221.8720833333330.347669158574466638.170162240064
Trimmed Mean ( 7 / 20 )221.8397826086960.332162798268658667.864624711128
Trimmed Mean ( 8 / 20 )221.8065909090910.313736592358893706.983489689208
Trimmed Mean ( 9 / 20 )221.7354761904760.299078764089045741.394919381366
Trimmed Mean ( 10 / 20 )221.674250.286632724772062773.3738364183
Trimmed Mean ( 11 / 20 )221.6065789473680.26930823248603822.873392698324
Trimmed Mean ( 12 / 20 )221.5286111111110.245224274665787903.371460321492
Trimmed Mean ( 13 / 20 )221.4408823529410.2123207507165961042.95449976304
Trimmed Mean ( 14 / 20 )221.3506250.1660735708882681332.84678480793
Trimmed Mean ( 15 / 20 )221.2810.1226005100212531804.89461227887
Trimmed Mean ( 16 / 20 )221.2860714285710.1171467890358331888.96403605979
Trimmed Mean ( 17 / 20 )221.2957692307690.1100799333029252010.31888910937
Trimmed Mean ( 18 / 20 )221.32250.1037542560677582133.14140921083
Trimmed Mean ( 19 / 20 )221.3481818181820.0971111657452262279.32782105505
Trimmed Mean ( 20 / 20 )221.3750.08811625096547482512.30615890295
Median221.515
Midrange222.405
Midmean - Weighted Average at Xnp221.238064516129
Midmean - Weighted Average at X(n+1)p221.281
Midmean - Empirical Distribution Function221.238064516129
Midmean - Empirical Distribution Function - Averaging221.281
Midmean - Empirical Distribution Function - Interpolation221.281
Midmean - Closest Observation221.238064516129
Midmean - True Basic - Statistics Graphics Toolkit221.281
Midmean - MS Excel (old versions)221.350625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 222.019666666667 & 0.408433411003685 & 543.588405564263 \tabularnewline
Geometric Mean & 221.997619474859 &  &  \tabularnewline
Harmonic Mean & 221.975690815128 &  &  \tabularnewline
Quadratic Mean & 222.041830833742 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 222.022666666667 & 0.407819048902616 & 544.414654646708 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 222.032333333333 & 0.405066038186247 & 548.138605565456 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 222.037333333333 & 0.403075736015229 & 550.857601919617 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 222.032 & 0.400975279962796 & 553.729895819515 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 222.053666666667 & 0.397107477138428 & 559.17775275045 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 222.020666666667 & 0.389444836405153 & 570.095289274014 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 222.010166666667 & 0.383782578194738 & 578.479012025436 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 222.204833333333 & 0.349586074176309 & 635.622668485552 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 222.102833333333 & 0.326489207967156 & 680.276186512346 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 222.102833333333 & 0.326489207967156 & 680.276186512346 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 222.121166666667 & 0.324127955802304 & 685.288518594013 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 222.125166666667 & 0.316030776201609 & 702.85928901103 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 222.066666666667 & 0.303257145706157 & 732.271835341481 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 221.838 & 0.244159205261904 & 908.579300796951 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 221.2455 & 0.122958452631148 & 1799.35169372775 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 221.218833333333 & 0.118892509889064 & 1860.66248866095 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 221.114 & 0.104264494175931 & 2120.70275454369 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 221.153 & 0.0958062133082958 & 2308.33671808267 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 221.178333333333 & 0.0906268710437419 & 2440.53811839735 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 221.265 & 0.0697807300225923 & 3170.861066205 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 222.006379310345 & 0.401072344981558 & 553.532005106344 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 221.988928571429 & 0.392629718705973 & 565.390030339676 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 221.964814814815 & 0.383856423770572 & 578.24957736667 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 221.936923076923 & 0.373727659376749 & 593.846662157783 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 221.9084 & 0.361711505292857 & 613.495553093711 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 221.872083333333 & 0.347669158574466 & 638.170162240064 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 221.839782608696 & 0.332162798268658 & 667.864624711128 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 221.806590909091 & 0.313736592358893 & 706.983489689208 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 221.735476190476 & 0.299078764089045 & 741.394919381366 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 221.67425 & 0.286632724772062 & 773.3738364183 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 221.606578947368 & 0.26930823248603 & 822.873392698324 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 221.528611111111 & 0.245224274665787 & 903.371460321492 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 221.440882352941 & 0.212320750716596 & 1042.95449976304 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 221.350625 & 0.166073570888268 & 1332.84678480793 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 221.281 & 0.122600510021253 & 1804.89461227887 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 221.286071428571 & 0.117146789035833 & 1888.96403605979 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 221.295769230769 & 0.110079933302925 & 2010.31888910937 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 221.3225 & 0.103754256067758 & 2133.14140921083 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 221.348181818182 & 0.097111165745226 & 2279.32782105505 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 221.375 & 0.0881162509654748 & 2512.30615890295 \tabularnewline
Median & 221.515 &  &  \tabularnewline
Midrange & 222.405 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 221.238064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 221.281 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 221.238064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 221.281 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 221.281 &  &  \tabularnewline
Midmean - Closest Observation & 221.238064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 221.281 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 221.350625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163704&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]222.019666666667[/C][C]0.408433411003685[/C][C]543.588405564263[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]221.997619474859[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]221.975690815128[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]222.041830833742[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]222.022666666667[/C][C]0.407819048902616[/C][C]544.414654646708[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]222.032333333333[/C][C]0.405066038186247[/C][C]548.138605565456[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]222.037333333333[/C][C]0.403075736015229[/C][C]550.857601919617[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]222.032[/C][C]0.400975279962796[/C][C]553.729895819515[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]222.053666666667[/C][C]0.397107477138428[/C][C]559.17775275045[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]222.020666666667[/C][C]0.389444836405153[/C][C]570.095289274014[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]222.010166666667[/C][C]0.383782578194738[/C][C]578.479012025436[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]222.204833333333[/C][C]0.349586074176309[/C][C]635.622668485552[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]222.102833333333[/C][C]0.326489207967156[/C][C]680.276186512346[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]222.102833333333[/C][C]0.326489207967156[/C][C]680.276186512346[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]222.121166666667[/C][C]0.324127955802304[/C][C]685.288518594013[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]222.125166666667[/C][C]0.316030776201609[/C][C]702.85928901103[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]222.066666666667[/C][C]0.303257145706157[/C][C]732.271835341481[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]221.838[/C][C]0.244159205261904[/C][C]908.579300796951[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]221.2455[/C][C]0.122958452631148[/C][C]1799.35169372775[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]221.218833333333[/C][C]0.118892509889064[/C][C]1860.66248866095[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]221.114[/C][C]0.104264494175931[/C][C]2120.70275454369[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]221.153[/C][C]0.0958062133082958[/C][C]2308.33671808267[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]221.178333333333[/C][C]0.0906268710437419[/C][C]2440.53811839735[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]221.265[/C][C]0.0697807300225923[/C][C]3170.861066205[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]222.006379310345[/C][C]0.401072344981558[/C][C]553.532005106344[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]221.988928571429[/C][C]0.392629718705973[/C][C]565.390030339676[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]221.964814814815[/C][C]0.383856423770572[/C][C]578.24957736667[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]221.936923076923[/C][C]0.373727659376749[/C][C]593.846662157783[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]221.9084[/C][C]0.361711505292857[/C][C]613.495553093711[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]221.872083333333[/C][C]0.347669158574466[/C][C]638.170162240064[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]221.839782608696[/C][C]0.332162798268658[/C][C]667.864624711128[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]221.806590909091[/C][C]0.313736592358893[/C][C]706.983489689208[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]221.735476190476[/C][C]0.299078764089045[/C][C]741.394919381366[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]221.67425[/C][C]0.286632724772062[/C][C]773.3738364183[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]221.606578947368[/C][C]0.26930823248603[/C][C]822.873392698324[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]221.528611111111[/C][C]0.245224274665787[/C][C]903.371460321492[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]221.440882352941[/C][C]0.212320750716596[/C][C]1042.95449976304[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]221.350625[/C][C]0.166073570888268[/C][C]1332.84678480793[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]221.281[/C][C]0.122600510021253[/C][C]1804.89461227887[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]221.286071428571[/C][C]0.117146789035833[/C][C]1888.96403605979[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]221.295769230769[/C][C]0.110079933302925[/C][C]2010.31888910937[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]221.3225[/C][C]0.103754256067758[/C][C]2133.14140921083[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]221.348181818182[/C][C]0.097111165745226[/C][C]2279.32782105505[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]221.375[/C][C]0.0881162509654748[/C][C]2512.30615890295[/C][/ROW]
[ROW][C]Median[/C][C]221.515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]222.405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]221.238064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]221.281[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]221.238064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]221.281[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]221.281[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]221.238064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]221.281[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]221.350625[/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=163704&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163704&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 Mean222.0196666666670.408433411003685543.588405564263
Geometric Mean221.997619474859
Harmonic Mean221.975690815128
Quadratic Mean222.041830833742
Winsorized Mean ( 1 / 20 )222.0226666666670.407819048902616544.414654646708
Winsorized Mean ( 2 / 20 )222.0323333333330.405066038186247548.138605565456
Winsorized Mean ( 3 / 20 )222.0373333333330.403075736015229550.857601919617
Winsorized Mean ( 4 / 20 )222.0320.400975279962796553.729895819515
Winsorized Mean ( 5 / 20 )222.0536666666670.397107477138428559.17775275045
Winsorized Mean ( 6 / 20 )222.0206666666670.389444836405153570.095289274014
Winsorized Mean ( 7 / 20 )222.0101666666670.383782578194738578.479012025436
Winsorized Mean ( 8 / 20 )222.2048333333330.349586074176309635.622668485552
Winsorized Mean ( 9 / 20 )222.1028333333330.326489207967156680.276186512346
Winsorized Mean ( 10 / 20 )222.1028333333330.326489207967156680.276186512346
Winsorized Mean ( 11 / 20 )222.1211666666670.324127955802304685.288518594013
Winsorized Mean ( 12 / 20 )222.1251666666670.316030776201609702.85928901103
Winsorized Mean ( 13 / 20 )222.0666666666670.303257145706157732.271835341481
Winsorized Mean ( 14 / 20 )221.8380.244159205261904908.579300796951
Winsorized Mean ( 15 / 20 )221.24550.1229584526311481799.35169372775
Winsorized Mean ( 16 / 20 )221.2188333333330.1188925098890641860.66248866095
Winsorized Mean ( 17 / 20 )221.1140.1042644941759312120.70275454369
Winsorized Mean ( 18 / 20 )221.1530.09580621330829582308.33671808267
Winsorized Mean ( 19 / 20 )221.1783333333330.09062687104374192440.53811839735
Winsorized Mean ( 20 / 20 )221.2650.06978073002259233170.861066205
Trimmed Mean ( 1 / 20 )222.0063793103450.401072344981558553.532005106344
Trimmed Mean ( 2 / 20 )221.9889285714290.392629718705973565.390030339676
Trimmed Mean ( 3 / 20 )221.9648148148150.383856423770572578.24957736667
Trimmed Mean ( 4 / 20 )221.9369230769230.373727659376749593.846662157783
Trimmed Mean ( 5 / 20 )221.90840.361711505292857613.495553093711
Trimmed Mean ( 6 / 20 )221.8720833333330.347669158574466638.170162240064
Trimmed Mean ( 7 / 20 )221.8397826086960.332162798268658667.864624711128
Trimmed Mean ( 8 / 20 )221.8065909090910.313736592358893706.983489689208
Trimmed Mean ( 9 / 20 )221.7354761904760.299078764089045741.394919381366
Trimmed Mean ( 10 / 20 )221.674250.286632724772062773.3738364183
Trimmed Mean ( 11 / 20 )221.6065789473680.26930823248603822.873392698324
Trimmed Mean ( 12 / 20 )221.5286111111110.245224274665787903.371460321492
Trimmed Mean ( 13 / 20 )221.4408823529410.2123207507165961042.95449976304
Trimmed Mean ( 14 / 20 )221.3506250.1660735708882681332.84678480793
Trimmed Mean ( 15 / 20 )221.2810.1226005100212531804.89461227887
Trimmed Mean ( 16 / 20 )221.2860714285710.1171467890358331888.96403605979
Trimmed Mean ( 17 / 20 )221.2957692307690.1100799333029252010.31888910937
Trimmed Mean ( 18 / 20 )221.32250.1037542560677582133.14140921083
Trimmed Mean ( 19 / 20 )221.3481818181820.0971111657452262279.32782105505
Trimmed Mean ( 20 / 20 )221.3750.08811625096547482512.30615890295
Median221.515
Midrange222.405
Midmean - Weighted Average at Xnp221.238064516129
Midmean - Weighted Average at X(n+1)p221.281
Midmean - Empirical Distribution Function221.238064516129
Midmean - Empirical Distribution Function - Averaging221.281
Midmean - Empirical Distribution Function - Interpolation221.281
Midmean - Closest Observation221.238064516129
Midmean - True Basic - Statistics Graphics Toolkit221.281
Midmean - MS Excel (old versions)221.350625
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')