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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 14:48:29 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224535868uepvgxsi1lmr7fp.htm/, Retrieved Sun, 18 Oct 2026 23:37:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18123, Retrieved Sun, 18 Oct 2026 23:37:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact489

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
F RM D  [Pearson Correlation] [Pearson Correlation] [2008-10-20 11:08:13] [8af599f2ccf50a86f2698320831f9f94]
F RM D      [Central Tendency] [Verbruik Tabak] [2008-10-20 20:48:29] [6d5cd2fe15d123a10639b4bf141c23b5] [Current]
Feedback Forum
2008-10-27 23:01:51 [Jeroen Michel] [reply] 
Ook bij deze laatste analyse is geen conclusie getrokken in het word document. Alleen is er een grafische weergave gemaakt. Bij de vorige berekeningen zijn ook dezelfde opmerkingen gemaakt.

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
149,77
149,68
149,59
147,61
145,53
144,8
144,63
144,28
144,02
143,96
143,82
143,46
143,26
142,99
142,65
142,56
142,54
142,45
142,44
142,41
142,38
142,11
140,58
136,52
135,73
135,71
135,68
135,63
135,56
135,29
134,44
131,6
130,03
129,74
128,25
123,96
123,72
123,7
123,7
123,7
123,58
123,58
123,09
120,59
120,26
120,26
120,25
120,24
120,22
120,1
120,03
119,73
118,5
118,02
117,96
117,95
117,71
116,72
115,16
114,92
114,86

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18123&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]2 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=18123&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18123&T=0

As an alternative you can also use a QR Code:  
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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean131.8722950819671.4423246527787291.4303827698623
Geometric Mean131.397283855814
Harmonic Mean130.922311300983
Quadratic Mean132.344702328526
Winsorized Mean ( 1 / 20 )131.8718032786891.4418271746436291.4615881832603
Winsorized Mean ( 2 / 20 )131.8767213114751.4396885425414891.6008688092172
Winsorized Mean ( 3 / 20 )131.8560655737711.4062921693240493.761501663733
Winsorized Mean ( 4 / 20 )131.7845901639341.3707640479197896.139514575047
Winsorized Mean ( 5 / 20 )131.7444262295081.3576188477514497.0408052655648
Winsorized Mean ( 6 / 20 )131.7286885245901.3547852949370297.2321511141837
Winsorized Mean ( 7 / 20 )131.6954098360661.3473060669020197.7472105791713
Winsorized Mean ( 8 / 20 )131.7242622950821.3314921671579998.9298063812433
Winsorized Mean ( 9 / 20 )131.8968852459021.30095336082747101.384791505523
Winsorized Mean ( 10 / 20 )131.9231147540981.28980359289718102.281553160951
Winsorized Mean ( 11 / 20 )131.8708196721311.27796857446765103.187842257438
Winsorized Mean ( 12 / 20 )131.8550819672131.26843080249089103.951340276727
Winsorized Mean ( 13 / 20 )131.8018032786891.2592067610661104.670501583949
Winsorized Mean ( 14 / 20 )131.7260655737701.24738229245684105.602000581813
Winsorized Mean ( 15 / 20 )131.7063934426231.24378070372156105.891973599960
Winsorized Mean ( 16 / 20 )131.7011475409841.24301803305966105.952724770054
Winsorized Mean ( 17 / 20 )131.7680327868851.22532731926059107.537007227097
Winsorized Mean ( 18 / 20 )132.5027868852461.11680220524338118.644811286319
Winsorized Mean ( 19 / 20 )132.6460655737701.09415447003607121.231571232714
Winsorized Mean ( 20 / 20 )132.6362295081971.09269209747629121.384816284969
Trimmed Mean ( 1 / 20 )131.8572881355931.4306632179385992.1651486403514
Trimmed Mean ( 2 / 20 )131.8417543859651.4159410228274993.1124617907394
Trimmed Mean ( 3 / 20 )131.8223636363641.3982075818689194.279537134367
Trimmed Mean ( 4 / 20 )131.8094339622641.3905345688483194.7904762061642
Trimmed Mean ( 5 / 20 )131.8168627450981.3921225574342794.6876853917523
Trimmed Mean ( 6 / 20 )131.8348979591841.3956086413461694.4640883220812
Trimmed Mean ( 7 / 20 )131.8578723404261.3978960977512894.3259463650684
Trimmed Mean ( 8 / 20 )131.8893333333331.3996667857426394.229094150688
Trimmed Mean ( 9 / 20 )131.9186046511631.4025148896387594.0586125863814
Trimmed Mean ( 10 / 20 )131.9221951219511.4096641405994993.5841320797512
Trimmed Mean ( 11 / 20 )131.9220512820511.4170612697784093.0955168245347
Trimmed Mean ( 12 / 20 )131.9297297297301.4245439440120592.611905925602
Trimmed Mean ( 13 / 20 )131.9405714285711.4312140314577592.187868850185
Trimmed Mean ( 14 / 20 )131.9603030303031.4363247821109891.8735822662336
Trimmed Mean ( 15 / 20 )131.9932258064521.4395056190694991.6934425666036
Trimmed Mean ( 16 / 20 )132.0334482758621.4374271689292291.8540091142269
Trimmed Mean ( 17 / 20 )132.0803703703701.4265945226468592.5843806867511
Trimmed Mean ( 18 / 20 )132.12521.4077657380876093.8545358970642
Trimmed Mean ( 19 / 20 )132.0695652173911.4064936187938693.8998680496307
Trimmed Mean ( 20 / 20 )131.9814285714291.3988269380881694.3515062355132
Median134.44
Midrange132.315
Midmean - Weighted Average at Xnp131.641
Midmean - Weighted Average at X(n+1)p131.993225806452
Midmean - Empirical Distribution Function131.993225806452
Midmean - Empirical Distribution Function - Averaging131.993225806452
Midmean - Empirical Distribution Function - Interpolation131.993225806452
Midmean - Closest Observation131.62625
Midmean - True Basic - Statistics Graphics Toolkit131.993225806452
Midmean - MS Excel (old versions)131.993225806452
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 131.872295081967 & 1.44232465277872 & 91.4303827698623 \tabularnewline
Geometric Mean & 131.397283855814 &  &  \tabularnewline
Harmonic Mean & 130.922311300983 &  &  \tabularnewline
Quadratic Mean & 132.344702328526 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 131.871803278689 & 1.44182717464362 & 91.4615881832603 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 131.876721311475 & 1.43968854254148 & 91.6008688092172 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 131.856065573771 & 1.40629216932404 & 93.761501663733 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 131.784590163934 & 1.37076404791978 & 96.139514575047 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 131.744426229508 & 1.35761884775144 & 97.0408052655648 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 131.728688524590 & 1.35478529493702 & 97.2321511141837 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 131.695409836066 & 1.34730606690201 & 97.7472105791713 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 131.724262295082 & 1.33149216715799 & 98.9298063812433 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 131.896885245902 & 1.30095336082747 & 101.384791505523 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 131.923114754098 & 1.28980359289718 & 102.281553160951 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 131.870819672131 & 1.27796857446765 & 103.187842257438 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 131.855081967213 & 1.26843080249089 & 103.951340276727 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 131.801803278689 & 1.2592067610661 & 104.670501583949 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 131.726065573770 & 1.24738229245684 & 105.602000581813 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 131.706393442623 & 1.24378070372156 & 105.891973599960 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 131.701147540984 & 1.24301803305966 & 105.952724770054 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 131.768032786885 & 1.22532731926059 & 107.537007227097 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 132.502786885246 & 1.11680220524338 & 118.644811286319 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 132.646065573770 & 1.09415447003607 & 121.231571232714 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 132.636229508197 & 1.09269209747629 & 121.384816284969 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 131.857288135593 & 1.43066321793859 & 92.1651486403514 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 131.841754385965 & 1.41594102282749 & 93.1124617907394 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 131.822363636364 & 1.39820758186891 & 94.279537134367 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 131.809433962264 & 1.39053456884831 & 94.7904762061642 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 131.816862745098 & 1.39212255743427 & 94.6876853917523 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 131.834897959184 & 1.39560864134616 & 94.4640883220812 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 131.857872340426 & 1.39789609775128 & 94.3259463650684 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 131.889333333333 & 1.39966678574263 & 94.229094150688 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 131.918604651163 & 1.40251488963875 & 94.0586125863814 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 131.922195121951 & 1.40966414059949 & 93.5841320797512 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 131.922051282051 & 1.41706126977840 & 93.0955168245347 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 131.929729729730 & 1.42454394401205 & 92.611905925602 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 131.940571428571 & 1.43121403145775 & 92.187868850185 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 131.960303030303 & 1.43632478211098 & 91.8735822662336 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 131.993225806452 & 1.43950561906949 & 91.6934425666036 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 132.033448275862 & 1.43742716892922 & 91.8540091142269 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 132.080370370370 & 1.42659452264685 & 92.5843806867511 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 132.1252 & 1.40776573808760 & 93.8545358970642 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 132.069565217391 & 1.40649361879386 & 93.8998680496307 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 131.981428571429 & 1.39882693808816 & 94.3515062355132 \tabularnewline
Median & 134.44 &  &  \tabularnewline
Midrange & 132.315 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 131.641 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 131.993225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 131.993225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 131.993225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 131.993225806452 &  &  \tabularnewline
Midmean - Closest Observation & 131.62625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 131.993225806452 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 131.993225806452 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18123&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]131.872295081967[/C][C]1.44232465277872[/C][C]91.4303827698623[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]131.397283855814[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]130.922311300983[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]132.344702328526[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]131.871803278689[/C][C]1.44182717464362[/C][C]91.4615881832603[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]131.876721311475[/C][C]1.43968854254148[/C][C]91.6008688092172[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]131.856065573771[/C][C]1.40629216932404[/C][C]93.761501663733[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]131.784590163934[/C][C]1.37076404791978[/C][C]96.139514575047[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]131.744426229508[/C][C]1.35761884775144[/C][C]97.0408052655648[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]131.728688524590[/C][C]1.35478529493702[/C][C]97.2321511141837[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]131.695409836066[/C][C]1.34730606690201[/C][C]97.7472105791713[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]131.724262295082[/C][C]1.33149216715799[/C][C]98.9298063812433[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]131.896885245902[/C][C]1.30095336082747[/C][C]101.384791505523[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]131.923114754098[/C][C]1.28980359289718[/C][C]102.281553160951[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]131.870819672131[/C][C]1.27796857446765[/C][C]103.187842257438[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]131.855081967213[/C][C]1.26843080249089[/C][C]103.951340276727[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]131.801803278689[/C][C]1.2592067610661[/C][C]104.670501583949[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]131.726065573770[/C][C]1.24738229245684[/C][C]105.602000581813[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]131.706393442623[/C][C]1.24378070372156[/C][C]105.891973599960[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]131.701147540984[/C][C]1.24301803305966[/C][C]105.952724770054[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]131.768032786885[/C][C]1.22532731926059[/C][C]107.537007227097[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]132.502786885246[/C][C]1.11680220524338[/C][C]118.644811286319[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]132.646065573770[/C][C]1.09415447003607[/C][C]121.231571232714[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]132.636229508197[/C][C]1.09269209747629[/C][C]121.384816284969[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]131.857288135593[/C][C]1.43066321793859[/C][C]92.1651486403514[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]131.841754385965[/C][C]1.41594102282749[/C][C]93.1124617907394[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]131.822363636364[/C][C]1.39820758186891[/C][C]94.279537134367[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]131.809433962264[/C][C]1.39053456884831[/C][C]94.7904762061642[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]131.816862745098[/C][C]1.39212255743427[/C][C]94.6876853917523[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]131.834897959184[/C][C]1.39560864134616[/C][C]94.4640883220812[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]131.857872340426[/C][C]1.39789609775128[/C][C]94.3259463650684[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]131.889333333333[/C][C]1.39966678574263[/C][C]94.229094150688[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]131.918604651163[/C][C]1.40251488963875[/C][C]94.0586125863814[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]131.922195121951[/C][C]1.40966414059949[/C][C]93.5841320797512[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]131.922051282051[/C][C]1.41706126977840[/C][C]93.0955168245347[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]131.929729729730[/C][C]1.42454394401205[/C][C]92.611905925602[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]131.940571428571[/C][C]1.43121403145775[/C][C]92.187868850185[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]131.960303030303[/C][C]1.43632478211098[/C][C]91.8735822662336[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]131.993225806452[/C][C]1.43950561906949[/C][C]91.6934425666036[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]132.033448275862[/C][C]1.43742716892922[/C][C]91.8540091142269[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]132.080370370370[/C][C]1.42659452264685[/C][C]92.5843806867511[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]132.1252[/C][C]1.40776573808760[/C][C]93.8545358970642[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]132.069565217391[/C][C]1.40649361879386[/C][C]93.8998680496307[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]131.981428571429[/C][C]1.39882693808816[/C][C]94.3515062355132[/C][/ROW]
[ROW][C]Median[/C][C]134.44[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]132.315[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]131.641[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]131.993225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]131.993225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]131.993225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]131.993225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]131.62625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]131.993225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]131.993225806452[/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=18123&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18123&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean131.8722950819671.4423246527787291.4303827698623
Geometric Mean131.397283855814
Harmonic Mean130.922311300983
Quadratic Mean132.344702328526
Winsorized Mean ( 1 / 20 )131.8718032786891.4418271746436291.4615881832603
Winsorized Mean ( 2 / 20 )131.8767213114751.4396885425414891.6008688092172
Winsorized Mean ( 3 / 20 )131.8560655737711.4062921693240493.761501663733
Winsorized Mean ( 4 / 20 )131.7845901639341.3707640479197896.139514575047
Winsorized Mean ( 5 / 20 )131.7444262295081.3576188477514497.0408052655648
Winsorized Mean ( 6 / 20 )131.7286885245901.3547852949370297.2321511141837
Winsorized Mean ( 7 / 20 )131.6954098360661.3473060669020197.7472105791713
Winsorized Mean ( 8 / 20 )131.7242622950821.3314921671579998.9298063812433
Winsorized Mean ( 9 / 20 )131.8968852459021.30095336082747101.384791505523
Winsorized Mean ( 10 / 20 )131.9231147540981.28980359289718102.281553160951
Winsorized Mean ( 11 / 20 )131.8708196721311.27796857446765103.187842257438
Winsorized Mean ( 12 / 20 )131.8550819672131.26843080249089103.951340276727
Winsorized Mean ( 13 / 20 )131.8018032786891.2592067610661104.670501583949
Winsorized Mean ( 14 / 20 )131.7260655737701.24738229245684105.602000581813
Winsorized Mean ( 15 / 20 )131.7063934426231.24378070372156105.891973599960
Winsorized Mean ( 16 / 20 )131.7011475409841.24301803305966105.952724770054
Winsorized Mean ( 17 / 20 )131.7680327868851.22532731926059107.537007227097
Winsorized Mean ( 18 / 20 )132.5027868852461.11680220524338118.644811286319
Winsorized Mean ( 19 / 20 )132.6460655737701.09415447003607121.231571232714
Winsorized Mean ( 20 / 20 )132.6362295081971.09269209747629121.384816284969
Trimmed Mean ( 1 / 20 )131.8572881355931.4306632179385992.1651486403514
Trimmed Mean ( 2 / 20 )131.8417543859651.4159410228274993.1124617907394
Trimmed Mean ( 3 / 20 )131.8223636363641.3982075818689194.279537134367
Trimmed Mean ( 4 / 20 )131.8094339622641.3905345688483194.7904762061642
Trimmed Mean ( 5 / 20 )131.8168627450981.3921225574342794.6876853917523
Trimmed Mean ( 6 / 20 )131.8348979591841.3956086413461694.4640883220812
Trimmed Mean ( 7 / 20 )131.8578723404261.3978960977512894.3259463650684
Trimmed Mean ( 8 / 20 )131.8893333333331.3996667857426394.229094150688
Trimmed Mean ( 9 / 20 )131.9186046511631.4025148896387594.0586125863814
Trimmed Mean ( 10 / 20 )131.9221951219511.4096641405994993.5841320797512
Trimmed Mean ( 11 / 20 )131.9220512820511.4170612697784093.0955168245347
Trimmed Mean ( 12 / 20 )131.9297297297301.4245439440120592.611905925602
Trimmed Mean ( 13 / 20 )131.9405714285711.4312140314577592.187868850185
Trimmed Mean ( 14 / 20 )131.9603030303031.4363247821109891.8735822662336
Trimmed Mean ( 15 / 20 )131.9932258064521.4395056190694991.6934425666036
Trimmed Mean ( 16 / 20 )132.0334482758621.4374271689292291.8540091142269
Trimmed Mean ( 17 / 20 )132.0803703703701.4265945226468592.5843806867511
Trimmed Mean ( 18 / 20 )132.12521.4077657380876093.8545358970642
Trimmed Mean ( 19 / 20 )132.0695652173911.4064936187938693.8998680496307
Trimmed Mean ( 20 / 20 )131.9814285714291.3988269380881694.3515062355132
Median134.44
Midrange132.315
Midmean - Weighted Average at Xnp131.641
Midmean - Weighted Average at X(n+1)p131.993225806452
Midmean - Empirical Distribution Function131.993225806452
Midmean - Empirical Distribution Function - Averaging131.993225806452
Midmean - Empirical Distribution Function - Interpolation131.993225806452
Midmean - Closest Observation131.62625
Midmean - True Basic - Statistics Graphics Toolkit131.993225806452
Midmean - MS Excel (old versions)131.993225806452
Number of observations61


Figures (Output of Computation)

Input Parameters & R Code

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')