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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 16 Dec 2007 05:05:49 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/16/t1197805799o6wvkrnpc4i2xb8.htm/, Retrieved Thu, 02 May 2024 09:10:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4145, Retrieved Thu, 02 May 2024 09:10:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordscentral tendency Tinne Van der Eycken
Estimated Impact256
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper: industriël...] [2007-12-16 12:05:49] [c8635c97647ba59406cb570a9fab7b02] [Current]
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Dataseries X:
86,5
104,1
110,9
114,5
112,2
96,4
92
102
99,7
102
98,9
87,4
94,4
109,3
116,4
101
105,5
97,8
95,5
113,7
103,7
100,8
113,8
84,6
95,3
110
107,5
107,6
116
96,9
97
108,1
101,9
107,2
110,2
78,7
96,5
115,2
104,7
109,1
108,4
95,5
97,8
115,1
96,2
112
111,8
82,5
100,8
116
116,3
116,6
112,9
100,9
104,1
117,4
103,3
111,6
115
92,6
105,2




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4145&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 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=4145&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4145&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean103.8852459016391.2006551855863086.5237972973154
Geometric Mean103.450647105992
Harmonic Mean102.996656768021
Quadratic Mean104.300712790108
Winsorized Mean ( 1 / 20 )103.9344262295081.1778995968927688.2370844711063
Winsorized Mean ( 2 / 20 )103.9967213114751.1566556444565089.9115668608025
Winsorized Mean ( 3 / 20 )104.0852459016391.1305925620407892.0625602858734
Winsorized Mean ( 4 / 20 )104.1245901639341.1120223681206193.6353378753627
Winsorized Mean ( 5 / 20 )104.5016393442621.02612457781609101.841084019909
Winsorized Mean ( 6 / 20 )104.4819672131150.999905755659334104.491814975322
Winsorized Mean ( 7 / 20 )104.6770491803280.95889677456785109.164043468081
Winsorized Mean ( 8 / 20 )104.7819672131150.936002744486896111.946217925413
Winsorized Mean ( 9 / 20 )104.7377049180330.91778470496571114.120124634182
Winsorized Mean ( 10 / 20 )104.6229508196720.897834046523243116.528161551472
Winsorized Mean ( 11 / 20 )104.7311475409840.873791252483042119.858315408137
Winsorized Mean ( 12 / 20 )104.6131147540980.840993672646113124.392273279468
Winsorized Mean ( 13 / 20 )104.4852459016390.813468711519147128.444086935457
Winsorized Mean ( 14 / 20 )104.5311475409840.79134160476342132.093582482921
Winsorized Mean ( 15 / 20 )104.5065573770490.779690525871423134.035946198329
Winsorized Mean ( 16 / 20 )104.6639344262300.738389300029652141.746277230759
Winsorized Mean ( 17 / 20 )104.4688524590160.708348116786674147.482360697061
Winsorized Mean ( 18 / 20 )104.5868852459020.627256474896553166.737035696842
Winsorized Mean ( 19 / 20 )104.7737704918030.580954093910517180.347761707901
Winsorized Mean ( 20 / 20 )104.9049180327870.495512243812203211.7100421691
Trimmed Mean ( 1 / 20 )104.0830508474581.1412389643337091.2018026901362
Trimmed Mean ( 2 / 20 )104.2421052631581.0958109669284895.1278171228243
Trimmed Mean ( 3 / 20 )104.3781818181821.0538232172073299.0471457772477
Trimmed Mean ( 4 / 20 )104.4905660377361.01438944777068103.008333009945
Trimmed Mean ( 5 / 20 )104.60.972306737689739107.579219546021
Trimmed Mean ( 6 / 20 )104.6244897959180.949841244398192110.149449092629
Trimmed Mean ( 7 / 20 )104.6553191489360.928900798242405112.665765113946
Trimmed Mean ( 8 / 20 )104.6511111111110.913211793628645114.596758212331
Trimmed Mean ( 9 / 20 )104.6279069767440.898092759376854116.500111914209
Trimmed Mean ( 10 / 20 )104.6097560975610.882027907846519118.601412911035
Trimmed Mean ( 11 / 20 )104.6076923076920.864827681036189120.957844668382
Trimmed Mean ( 12 / 20 )104.5891891891890.846763701112819123.516382494594
Trimmed Mean ( 13 / 20 )104.5857142857140.82956040659332126.073657149582
Trimmed Mean ( 14 / 20 )104.60.811587482914961128.883210007516
Trimmed Mean ( 15 / 20 )104.6096774193550.790744236870743132.292683957246
Trimmed Mean ( 16 / 20 )104.6241379310340.76233138606362137.242332984967
Trimmed Mean ( 17 / 20 )104.6185185185190.732498301526322142.824247237874
Trimmed Mean ( 18 / 20 )104.640.696060342211794150.331794033111
Trimmed Mean ( 19 / 20 )104.6478260869570.669548534261641156.296102122543
Trimmed Mean ( 20 / 20 )104.6285714285710.643100483044848162.693971139927
Median104.1
Midrange98.05
Midmean - Weighted Average at Xnp104.37
Midmean - Weighted Average at X(n+1)p104.609677419355
Midmean - Empirical Distribution Function104.609677419355
Midmean - Empirical Distribution Function - Averaging104.609677419355
Midmean - Empirical Distribution Function - Interpolation104.609677419355
Midmean - Closest Observation104.36875
Midmean - True Basic - Statistics Graphics Toolkit104.609677419355
Midmean - MS Excel (old versions)104.609677419355
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 103.885245901639 & 1.20065518558630 & 86.5237972973154 \tabularnewline
Geometric Mean & 103.450647105992 &  &  \tabularnewline
Harmonic Mean & 102.996656768021 &  &  \tabularnewline
Quadratic Mean & 104.300712790108 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 103.934426229508 & 1.17789959689276 & 88.2370844711063 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 103.996721311475 & 1.15665564445650 & 89.9115668608025 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 104.085245901639 & 1.13059256204078 & 92.0625602858734 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 104.124590163934 & 1.11202236812061 & 93.6353378753627 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 104.501639344262 & 1.02612457781609 & 101.841084019909 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 104.481967213115 & 0.999905755659334 & 104.491814975322 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 104.677049180328 & 0.95889677456785 & 109.164043468081 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 104.781967213115 & 0.936002744486896 & 111.946217925413 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 104.737704918033 & 0.91778470496571 & 114.120124634182 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 104.622950819672 & 0.897834046523243 & 116.528161551472 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 104.731147540984 & 0.873791252483042 & 119.858315408137 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 104.613114754098 & 0.840993672646113 & 124.392273279468 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 104.485245901639 & 0.813468711519147 & 128.444086935457 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 104.531147540984 & 0.79134160476342 & 132.093582482921 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 104.506557377049 & 0.779690525871423 & 134.035946198329 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 104.663934426230 & 0.738389300029652 & 141.746277230759 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 104.468852459016 & 0.708348116786674 & 147.482360697061 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 104.586885245902 & 0.627256474896553 & 166.737035696842 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 104.773770491803 & 0.580954093910517 & 180.347761707901 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 104.904918032787 & 0.495512243812203 & 211.7100421691 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 104.083050847458 & 1.14123896433370 & 91.2018026901362 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 104.242105263158 & 1.09581096692848 & 95.1278171228243 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 104.378181818182 & 1.05382321720732 & 99.0471457772477 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 104.490566037736 & 1.01438944777068 & 103.008333009945 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 104.6 & 0.972306737689739 & 107.579219546021 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 104.624489795918 & 0.949841244398192 & 110.149449092629 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 104.655319148936 & 0.928900798242405 & 112.665765113946 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 104.651111111111 & 0.913211793628645 & 114.596758212331 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 104.627906976744 & 0.898092759376854 & 116.500111914209 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 104.609756097561 & 0.882027907846519 & 118.601412911035 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 104.607692307692 & 0.864827681036189 & 120.957844668382 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 104.589189189189 & 0.846763701112819 & 123.516382494594 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 104.585714285714 & 0.82956040659332 & 126.073657149582 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 104.6 & 0.811587482914961 & 128.883210007516 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 104.609677419355 & 0.790744236870743 & 132.292683957246 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 104.624137931034 & 0.76233138606362 & 137.242332984967 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 104.618518518519 & 0.732498301526322 & 142.824247237874 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 104.64 & 0.696060342211794 & 150.331794033111 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 104.647826086957 & 0.669548534261641 & 156.296102122543 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 104.628571428571 & 0.643100483044848 & 162.693971139927 \tabularnewline
Median & 104.1 &  &  \tabularnewline
Midrange & 98.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 104.37 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 104.609677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 104.609677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 104.609677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 104.609677419355 &  &  \tabularnewline
Midmean - Closest Observation & 104.36875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 104.609677419355 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 104.609677419355 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4145&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]103.885245901639[/C][C]1.20065518558630[/C][C]86.5237972973154[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]103.450647105992[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]102.996656768021[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]104.300712790108[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]103.934426229508[/C][C]1.17789959689276[/C][C]88.2370844711063[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]103.996721311475[/C][C]1.15665564445650[/C][C]89.9115668608025[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]104.085245901639[/C][C]1.13059256204078[/C][C]92.0625602858734[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]104.124590163934[/C][C]1.11202236812061[/C][C]93.6353378753627[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]104.501639344262[/C][C]1.02612457781609[/C][C]101.841084019909[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]104.481967213115[/C][C]0.999905755659334[/C][C]104.491814975322[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]104.677049180328[/C][C]0.95889677456785[/C][C]109.164043468081[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]104.781967213115[/C][C]0.936002744486896[/C][C]111.946217925413[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]104.737704918033[/C][C]0.91778470496571[/C][C]114.120124634182[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]104.622950819672[/C][C]0.897834046523243[/C][C]116.528161551472[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]104.731147540984[/C][C]0.873791252483042[/C][C]119.858315408137[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]104.613114754098[/C][C]0.840993672646113[/C][C]124.392273279468[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]104.485245901639[/C][C]0.813468711519147[/C][C]128.444086935457[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]104.531147540984[/C][C]0.79134160476342[/C][C]132.093582482921[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]104.506557377049[/C][C]0.779690525871423[/C][C]134.035946198329[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]104.663934426230[/C][C]0.738389300029652[/C][C]141.746277230759[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]104.468852459016[/C][C]0.708348116786674[/C][C]147.482360697061[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]104.586885245902[/C][C]0.627256474896553[/C][C]166.737035696842[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]104.773770491803[/C][C]0.580954093910517[/C][C]180.347761707901[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]104.904918032787[/C][C]0.495512243812203[/C][C]211.7100421691[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]104.083050847458[/C][C]1.14123896433370[/C][C]91.2018026901362[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]104.242105263158[/C][C]1.09581096692848[/C][C]95.1278171228243[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]104.378181818182[/C][C]1.05382321720732[/C][C]99.0471457772477[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]104.490566037736[/C][C]1.01438944777068[/C][C]103.008333009945[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]104.6[/C][C]0.972306737689739[/C][C]107.579219546021[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]104.624489795918[/C][C]0.949841244398192[/C][C]110.149449092629[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]104.655319148936[/C][C]0.928900798242405[/C][C]112.665765113946[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]104.651111111111[/C][C]0.913211793628645[/C][C]114.596758212331[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]104.627906976744[/C][C]0.898092759376854[/C][C]116.500111914209[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]104.609756097561[/C][C]0.882027907846519[/C][C]118.601412911035[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]104.607692307692[/C][C]0.864827681036189[/C][C]120.957844668382[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]104.589189189189[/C][C]0.846763701112819[/C][C]123.516382494594[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]104.585714285714[/C][C]0.82956040659332[/C][C]126.073657149582[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]104.6[/C][C]0.811587482914961[/C][C]128.883210007516[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]104.609677419355[/C][C]0.790744236870743[/C][C]132.292683957246[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]104.624137931034[/C][C]0.76233138606362[/C][C]137.242332984967[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]104.618518518519[/C][C]0.732498301526322[/C][C]142.824247237874[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]104.64[/C][C]0.696060342211794[/C][C]150.331794033111[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]104.647826086957[/C][C]0.669548534261641[/C][C]156.296102122543[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]104.628571428571[/C][C]0.643100483044848[/C][C]162.693971139927[/C][/ROW]
[ROW][C]Median[/C][C]104.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]98.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]104.37[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]104.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]104.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]104.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]104.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]104.36875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]104.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]104.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4145&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4145&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 Mean103.8852459016391.2006551855863086.5237972973154
Geometric Mean103.450647105992
Harmonic Mean102.996656768021
Quadratic Mean104.300712790108
Winsorized Mean ( 1 / 20 )103.9344262295081.1778995968927688.2370844711063
Winsorized Mean ( 2 / 20 )103.9967213114751.1566556444565089.9115668608025
Winsorized Mean ( 3 / 20 )104.0852459016391.1305925620407892.0625602858734
Winsorized Mean ( 4 / 20 )104.1245901639341.1120223681206193.6353378753627
Winsorized Mean ( 5 / 20 )104.5016393442621.02612457781609101.841084019909
Winsorized Mean ( 6 / 20 )104.4819672131150.999905755659334104.491814975322
Winsorized Mean ( 7 / 20 )104.6770491803280.95889677456785109.164043468081
Winsorized Mean ( 8 / 20 )104.7819672131150.936002744486896111.946217925413
Winsorized Mean ( 9 / 20 )104.7377049180330.91778470496571114.120124634182
Winsorized Mean ( 10 / 20 )104.6229508196720.897834046523243116.528161551472
Winsorized Mean ( 11 / 20 )104.7311475409840.873791252483042119.858315408137
Winsorized Mean ( 12 / 20 )104.6131147540980.840993672646113124.392273279468
Winsorized Mean ( 13 / 20 )104.4852459016390.813468711519147128.444086935457
Winsorized Mean ( 14 / 20 )104.5311475409840.79134160476342132.093582482921
Winsorized Mean ( 15 / 20 )104.5065573770490.779690525871423134.035946198329
Winsorized Mean ( 16 / 20 )104.6639344262300.738389300029652141.746277230759
Winsorized Mean ( 17 / 20 )104.4688524590160.708348116786674147.482360697061
Winsorized Mean ( 18 / 20 )104.5868852459020.627256474896553166.737035696842
Winsorized Mean ( 19 / 20 )104.7737704918030.580954093910517180.347761707901
Winsorized Mean ( 20 / 20 )104.9049180327870.495512243812203211.7100421691
Trimmed Mean ( 1 / 20 )104.0830508474581.1412389643337091.2018026901362
Trimmed Mean ( 2 / 20 )104.2421052631581.0958109669284895.1278171228243
Trimmed Mean ( 3 / 20 )104.3781818181821.0538232172073299.0471457772477
Trimmed Mean ( 4 / 20 )104.4905660377361.01438944777068103.008333009945
Trimmed Mean ( 5 / 20 )104.60.972306737689739107.579219546021
Trimmed Mean ( 6 / 20 )104.6244897959180.949841244398192110.149449092629
Trimmed Mean ( 7 / 20 )104.6553191489360.928900798242405112.665765113946
Trimmed Mean ( 8 / 20 )104.6511111111110.913211793628645114.596758212331
Trimmed Mean ( 9 / 20 )104.6279069767440.898092759376854116.500111914209
Trimmed Mean ( 10 / 20 )104.6097560975610.882027907846519118.601412911035
Trimmed Mean ( 11 / 20 )104.6076923076920.864827681036189120.957844668382
Trimmed Mean ( 12 / 20 )104.5891891891890.846763701112819123.516382494594
Trimmed Mean ( 13 / 20 )104.5857142857140.82956040659332126.073657149582
Trimmed Mean ( 14 / 20 )104.60.811587482914961128.883210007516
Trimmed Mean ( 15 / 20 )104.6096774193550.790744236870743132.292683957246
Trimmed Mean ( 16 / 20 )104.6241379310340.76233138606362137.242332984967
Trimmed Mean ( 17 / 20 )104.6185185185190.732498301526322142.824247237874
Trimmed Mean ( 18 / 20 )104.640.696060342211794150.331794033111
Trimmed Mean ( 19 / 20 )104.6478260869570.669548534261641156.296102122543
Trimmed Mean ( 20 / 20 )104.6285714285710.643100483044848162.693971139927
Median104.1
Midrange98.05
Midmean - Weighted Average at Xnp104.37
Midmean - Weighted Average at X(n+1)p104.609677419355
Midmean - Empirical Distribution Function104.609677419355
Midmean - Empirical Distribution Function - Averaging104.609677419355
Midmean - Empirical Distribution Function - Interpolation104.609677419355
Midmean - Closest Observation104.36875
Midmean - True Basic - Statistics Graphics Toolkit104.609677419355
Midmean - MS Excel (old versions)104.609677419355
Number of observations61



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')