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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 14 Mar 2017 19:40:39 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Mar/14/t1489520453pufwcwzvhgmae55.htm/, Retrieved Tue, 14 May 2024 00:35:34 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 00:35:34 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
93,43
93,59
95,28
94,95
94,49
94,45
94,35
95,52
96,89
97,54
97,65
97,35
98,2
99,46
100,35
99,72
99,69
99,62
99,77
100,19
100,82
100,36
101,08
100,73
101,51
102,12
102,88
103,47
103,53
103,67
103,68
103,76
103,67
103,01
103,39
103,43
103,4
104,8
105,53
107,45
108,73
109,04
108,75
108,75
108,76
108,41
110,15
109,93
110,6
112,17
113,47
113,35
114,12
115
114,01
113,86
113,83
112,7
111,79
113,77




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean103.9328333333330.818810391455988126.931502601625
Geometric Mean103.743300053552
Harmonic Mean103.554732154378
Quadratic Mean104.122958187264
Winsorized Mean ( 1 / 20 )103.9208333333330.814998329056783127.510486375602
Winsorized Mean ( 2 / 20 )103.94250.808954952025624128.489849452961
Winsorized Mean ( 3 / 20 )103.940.806380908436903128.896900847365
Winsorized Mean ( 4 / 20 )103.9406666666670.805433170000528129.049399178083
Winsorized Mean ( 5 / 20 )103.9740.796900889853053130.472937505657
Winsorized Mean ( 6 / 20 )103.9770.784430568236718132.550928291493
Winsorized Mean ( 7 / 20 )103.9910.77634427609679133.949593243391
Winsorized Mean ( 8 / 20 )104.0870.726499862936985143.271878372024
Winsorized Mean ( 9 / 20 )104.07650.699290593920555148.831545719066
Winsorized Mean ( 10 / 20 )104.0448333333330.681838553536328152.594529590193
Winsorized Mean ( 11 / 20 )103.8468333333330.637927279725875162.787886070584
Winsorized Mean ( 12 / 20 )103.8668333333330.604108087555608171.934187727246
Winsorized Mean ( 13 / 20 )104.0921666666670.554526116804661187.71373162093
Winsorized Mean ( 14 / 20 )103.9218333333330.513111506018221202.532650533943
Winsorized Mean ( 15 / 20 )103.8693333333330.498891701995685208.200162315451
Winsorized Mean ( 16 / 20 )103.8746666666670.497314282211865208.871271914154
Winsorized Mean ( 17 / 20 )103.8888333333330.495312952014325209.74382541551
Winsorized Mean ( 18 / 20 )104.0088333333330.476874007195014218.105478101262
Winsorized Mean ( 19 / 20 )103.9581666666670.453074025933421229.450731483652
Winsorized Mean ( 20 / 20 )103.64150.400106258838302259.034938120989
Trimmed Mean ( 1 / 20 )103.9231034482760.804666787717556129.150481956705
Trimmed Mean ( 2 / 20 )103.9255357142860.791564164140113131.291360097361
Trimmed Mean ( 3 / 20 )103.9161111111110.778927411070344133.409236386119
Trimmed Mean ( 4 / 20 )103.9069230769230.764000225970959136.003785790598
Trimmed Mean ( 5 / 20 )103.89680.745274004672655139.407519044803
Trimmed Mean ( 6 / 20 )103.87750.724222651248606143.43310005688
Trimmed Mean ( 7 / 20 )103.8558695652170.701039226926398148.145589542197
Trimmed Mean ( 8 / 20 )103.8295454545450.673281302203605154.214211971606
Trimmed Mean ( 9 / 20 )103.7835714285710.651419946531937159.318995344094
Trimmed Mean ( 10 / 20 )103.734750.629870152216984164.692277662118
Trimmed Mean ( 11 / 20 )103.6857894736840.605543221741207171.227727024243
Trimmed Mean ( 12 / 20 )103.6613888888890.585063577169017177.179699666969
Trimmed Mean ( 13 / 20 )103.6311764705880.565919623662832183.119955798406
Trimmed Mean ( 14 / 20 )103.56468750.551868158704354187.662009243555
Trimmed Mean ( 15 / 20 )103.5136666666670.542984829349969190.638229783671
Trimmed Mean ( 16 / 20 )103.4628571428570.532399444549214194.333142534474
Trimmed Mean ( 17 / 20 )103.4034615384620.514756086318916200.878560325362
Trimmed Mean ( 18 / 20 )103.3320833333330.485893760069914212.663943900957
Trimmed Mean ( 19 / 20 )103.2295454545450.444011854524055232.492768836542
Trimmed Mean ( 20 / 20 )103.11450.382815384253367269.358297083885
Median103.415
Midrange104.215
Midmean - Weighted Average at Xnp103.388064516129
Midmean - Weighted Average at X(n+1)p103.513666666667
Midmean - Empirical Distribution Function103.388064516129
Midmean - Empirical Distribution Function - Averaging103.513666666667
Midmean - Empirical Distribution Function - Interpolation103.513666666667
Midmean - Closest Observation103.388064516129
Midmean - True Basic - Statistics Graphics Toolkit103.513666666667
Midmean - MS Excel (old versions)103.5646875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 103.932833333333 & 0.818810391455988 & 126.931502601625 \tabularnewline
Geometric Mean & 103.743300053552 &  &  \tabularnewline
Harmonic Mean & 103.554732154378 &  &  \tabularnewline
Quadratic Mean & 104.122958187264 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 103.920833333333 & 0.814998329056783 & 127.510486375602 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 103.9425 & 0.808954952025624 & 128.489849452961 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 103.94 & 0.806380908436903 & 128.896900847365 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 103.940666666667 & 0.805433170000528 & 129.049399178083 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 103.974 & 0.796900889853053 & 130.472937505657 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 103.977 & 0.784430568236718 & 132.550928291493 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 103.991 & 0.77634427609679 & 133.949593243391 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 104.087 & 0.726499862936985 & 143.271878372024 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 104.0765 & 0.699290593920555 & 148.831545719066 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 104.044833333333 & 0.681838553536328 & 152.594529590193 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 103.846833333333 & 0.637927279725875 & 162.787886070584 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 103.866833333333 & 0.604108087555608 & 171.934187727246 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 104.092166666667 & 0.554526116804661 & 187.71373162093 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 103.921833333333 & 0.513111506018221 & 202.532650533943 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 103.869333333333 & 0.498891701995685 & 208.200162315451 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 103.874666666667 & 0.497314282211865 & 208.871271914154 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 103.888833333333 & 0.495312952014325 & 209.74382541551 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 104.008833333333 & 0.476874007195014 & 218.105478101262 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 103.958166666667 & 0.453074025933421 & 229.450731483652 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 103.6415 & 0.400106258838302 & 259.034938120989 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 103.923103448276 & 0.804666787717556 & 129.150481956705 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 103.925535714286 & 0.791564164140113 & 131.291360097361 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 103.916111111111 & 0.778927411070344 & 133.409236386119 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 103.906923076923 & 0.764000225970959 & 136.003785790598 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 103.8968 & 0.745274004672655 & 139.407519044803 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 103.8775 & 0.724222651248606 & 143.43310005688 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 103.855869565217 & 0.701039226926398 & 148.145589542197 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 103.829545454545 & 0.673281302203605 & 154.214211971606 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 103.783571428571 & 0.651419946531937 & 159.318995344094 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 103.73475 & 0.629870152216984 & 164.692277662118 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 103.685789473684 & 0.605543221741207 & 171.227727024243 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 103.661388888889 & 0.585063577169017 & 177.179699666969 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 103.631176470588 & 0.565919623662832 & 183.119955798406 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 103.5646875 & 0.551868158704354 & 187.662009243555 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 103.513666666667 & 0.542984829349969 & 190.638229783671 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 103.462857142857 & 0.532399444549214 & 194.333142534474 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 103.403461538462 & 0.514756086318916 & 200.878560325362 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 103.332083333333 & 0.485893760069914 & 212.663943900957 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 103.229545454545 & 0.444011854524055 & 232.492768836542 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 103.1145 & 0.382815384253367 & 269.358297083885 \tabularnewline
Median & 103.415 &  &  \tabularnewline
Midrange & 104.215 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 103.388064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 103.513666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 103.388064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 103.513666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 103.513666666667 &  &  \tabularnewline
Midmean - Closest Observation & 103.388064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 103.513666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 103.5646875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]103.932833333333[/C][C]0.818810391455988[/C][C]126.931502601625[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]103.743300053552[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]103.554732154378[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]104.122958187264[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]103.920833333333[/C][C]0.814998329056783[/C][C]127.510486375602[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]103.9425[/C][C]0.808954952025624[/C][C]128.489849452961[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]103.94[/C][C]0.806380908436903[/C][C]128.896900847365[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]103.940666666667[/C][C]0.805433170000528[/C][C]129.049399178083[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]103.974[/C][C]0.796900889853053[/C][C]130.472937505657[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]103.977[/C][C]0.784430568236718[/C][C]132.550928291493[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]103.991[/C][C]0.77634427609679[/C][C]133.949593243391[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]104.087[/C][C]0.726499862936985[/C][C]143.271878372024[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]104.0765[/C][C]0.699290593920555[/C][C]148.831545719066[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]104.044833333333[/C][C]0.681838553536328[/C][C]152.594529590193[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]103.846833333333[/C][C]0.637927279725875[/C][C]162.787886070584[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]103.866833333333[/C][C]0.604108087555608[/C][C]171.934187727246[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]104.092166666667[/C][C]0.554526116804661[/C][C]187.71373162093[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]103.921833333333[/C][C]0.513111506018221[/C][C]202.532650533943[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]103.869333333333[/C][C]0.498891701995685[/C][C]208.200162315451[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]103.874666666667[/C][C]0.497314282211865[/C][C]208.871271914154[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]103.888833333333[/C][C]0.495312952014325[/C][C]209.74382541551[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]104.008833333333[/C][C]0.476874007195014[/C][C]218.105478101262[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]103.958166666667[/C][C]0.453074025933421[/C][C]229.450731483652[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]103.6415[/C][C]0.400106258838302[/C][C]259.034938120989[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]103.923103448276[/C][C]0.804666787717556[/C][C]129.150481956705[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]103.925535714286[/C][C]0.791564164140113[/C][C]131.291360097361[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]103.916111111111[/C][C]0.778927411070344[/C][C]133.409236386119[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]103.906923076923[/C][C]0.764000225970959[/C][C]136.003785790598[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]103.8968[/C][C]0.745274004672655[/C][C]139.407519044803[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]103.8775[/C][C]0.724222651248606[/C][C]143.43310005688[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]103.855869565217[/C][C]0.701039226926398[/C][C]148.145589542197[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]103.829545454545[/C][C]0.673281302203605[/C][C]154.214211971606[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]103.783571428571[/C][C]0.651419946531937[/C][C]159.318995344094[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]103.73475[/C][C]0.629870152216984[/C][C]164.692277662118[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]103.685789473684[/C][C]0.605543221741207[/C][C]171.227727024243[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]103.661388888889[/C][C]0.585063577169017[/C][C]177.179699666969[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]103.631176470588[/C][C]0.565919623662832[/C][C]183.119955798406[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]103.5646875[/C][C]0.551868158704354[/C][C]187.662009243555[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]103.513666666667[/C][C]0.542984829349969[/C][C]190.638229783671[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]103.462857142857[/C][C]0.532399444549214[/C][C]194.333142534474[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]103.403461538462[/C][C]0.514756086318916[/C][C]200.878560325362[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]103.332083333333[/C][C]0.485893760069914[/C][C]212.663943900957[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]103.229545454545[/C][C]0.444011854524055[/C][C]232.492768836542[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]103.1145[/C][C]0.382815384253367[/C][C]269.358297083885[/C][/ROW]
[ROW][C]Median[/C][C]103.415[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]104.215[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]103.388064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]103.513666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]103.388064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]103.513666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]103.513666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]103.388064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]103.513666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]103.5646875[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean103.9328333333330.818810391455988126.931502601625
Geometric Mean103.743300053552
Harmonic Mean103.554732154378
Quadratic Mean104.122958187264
Winsorized Mean ( 1 / 20 )103.9208333333330.814998329056783127.510486375602
Winsorized Mean ( 2 / 20 )103.94250.808954952025624128.489849452961
Winsorized Mean ( 3 / 20 )103.940.806380908436903128.896900847365
Winsorized Mean ( 4 / 20 )103.9406666666670.805433170000528129.049399178083
Winsorized Mean ( 5 / 20 )103.9740.796900889853053130.472937505657
Winsorized Mean ( 6 / 20 )103.9770.784430568236718132.550928291493
Winsorized Mean ( 7 / 20 )103.9910.77634427609679133.949593243391
Winsorized Mean ( 8 / 20 )104.0870.726499862936985143.271878372024
Winsorized Mean ( 9 / 20 )104.07650.699290593920555148.831545719066
Winsorized Mean ( 10 / 20 )104.0448333333330.681838553536328152.594529590193
Winsorized Mean ( 11 / 20 )103.8468333333330.637927279725875162.787886070584
Winsorized Mean ( 12 / 20 )103.8668333333330.604108087555608171.934187727246
Winsorized Mean ( 13 / 20 )104.0921666666670.554526116804661187.71373162093
Winsorized Mean ( 14 / 20 )103.9218333333330.513111506018221202.532650533943
Winsorized Mean ( 15 / 20 )103.8693333333330.498891701995685208.200162315451
Winsorized Mean ( 16 / 20 )103.8746666666670.497314282211865208.871271914154
Winsorized Mean ( 17 / 20 )103.8888333333330.495312952014325209.74382541551
Winsorized Mean ( 18 / 20 )104.0088333333330.476874007195014218.105478101262
Winsorized Mean ( 19 / 20 )103.9581666666670.453074025933421229.450731483652
Winsorized Mean ( 20 / 20 )103.64150.400106258838302259.034938120989
Trimmed Mean ( 1 / 20 )103.9231034482760.804666787717556129.150481956705
Trimmed Mean ( 2 / 20 )103.9255357142860.791564164140113131.291360097361
Trimmed Mean ( 3 / 20 )103.9161111111110.778927411070344133.409236386119
Trimmed Mean ( 4 / 20 )103.9069230769230.764000225970959136.003785790598
Trimmed Mean ( 5 / 20 )103.89680.745274004672655139.407519044803
Trimmed Mean ( 6 / 20 )103.87750.724222651248606143.43310005688
Trimmed Mean ( 7 / 20 )103.8558695652170.701039226926398148.145589542197
Trimmed Mean ( 8 / 20 )103.8295454545450.673281302203605154.214211971606
Trimmed Mean ( 9 / 20 )103.7835714285710.651419946531937159.318995344094
Trimmed Mean ( 10 / 20 )103.734750.629870152216984164.692277662118
Trimmed Mean ( 11 / 20 )103.6857894736840.605543221741207171.227727024243
Trimmed Mean ( 12 / 20 )103.6613888888890.585063577169017177.179699666969
Trimmed Mean ( 13 / 20 )103.6311764705880.565919623662832183.119955798406
Trimmed Mean ( 14 / 20 )103.56468750.551868158704354187.662009243555
Trimmed Mean ( 15 / 20 )103.5136666666670.542984829349969190.638229783671
Trimmed Mean ( 16 / 20 )103.4628571428570.532399444549214194.333142534474
Trimmed Mean ( 17 / 20 )103.4034615384620.514756086318916200.878560325362
Trimmed Mean ( 18 / 20 )103.3320833333330.485893760069914212.663943900957
Trimmed Mean ( 19 / 20 )103.2295454545450.444011854524055232.492768836542
Trimmed Mean ( 20 / 20 )103.11450.382815384253367269.358297083885
Median103.415
Midrange104.215
Midmean - Weighted Average at Xnp103.388064516129
Midmean - Weighted Average at X(n+1)p103.513666666667
Midmean - Empirical Distribution Function103.388064516129
Midmean - Empirical Distribution Function - Averaging103.513666666667
Midmean - Empirical Distribution Function - Interpolation103.513666666667
Midmean - Closest Observation103.388064516129
Midmean - True Basic - Statistics Graphics Toolkit103.513666666667
Midmean - MS Excel (old versions)103.5646875
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')