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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 05 Mar 2016 12:07:51 +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/2016/Mar/05/t145717977477xlckqoufuebfo.htm/, Retrieved Sat, 27 Apr 2024 11:13:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293455, Retrieved Sat, 27 Apr 2024 11:13:17 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [robuustheid prijs...] [2016-03-05 12:07:51] [b54f462b245e496e54620f8b97639ccc] [Current]
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Dataseries X:
92,49
92,46
92,55
92,24
92,41
92,83
92,85
93,04
93,04
92,83
92,96
92,83
93,01
93,21
93,58
94,07
94,57
95,03
95,21
95,89
96,43
96,35
96,71
96,32
97,23
97,88
98,2
98,56
99,31
99,69
99,77
101,06
101,77
101,91
102,52
102,09
102,22
102,74
103,56
104,4
104,76
104,86
104,84
104,96
104,83
104,58
104,8
104,17
104,63
105,32
106,16
107,22
107,51
107,87
107,79
108,04
107,74
107,71
111,19
110,82




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293455&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293455&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293455&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean99.9270.743941454017485134.321053707072
Geometric Mean99.7640647831682
Harmonic Mean99.6018116652828
Quadratic Mean100.090253338341
Winsorized Mean ( 1 / 20 )99.92366666666660.741891382195209134.687730663482
Winsorized Mean ( 2 / 20 )99.83266666666670.721094776075144138.445971291107
Winsorized Mean ( 3 / 20 )99.82566666666670.719209561669606138.799137256917
Winsorized Mean ( 4 / 20 )99.82433333333330.717512824612907139.125503975748
Winsorized Mean ( 5 / 20 )99.84350.712778989882614140.076379098159
Winsorized Mean ( 6 / 20 )99.84050.712216418935375140.182811496037
Winsorized Mean ( 7 / 20 )99.81716666666670.707882498934358141.008100662088
Winsorized Mean ( 8 / 20 )99.78116666666670.700394000967553142.464336543181
Winsorized Mean ( 9 / 20 )99.63866666666670.670167255734816148.677312736529
Winsorized Mean ( 10 / 20 )99.5070.646525537922857153.9103935781
Winsorized Mean ( 11 / 20 )99.44650.635705970168972156.434742894686
Winsorized Mean ( 12 / 20 )99.42650.632780556789514157.126351202148
Winsorized Mean ( 13 / 20 )99.4590.625882324096007158.910063714698
Winsorized Mean ( 14 / 20 )99.5430.61109512237259162.892807282641
Winsorized Mean ( 15 / 20 )99.6580.590024168804983168.90494537172
Winsorized Mean ( 16 / 20 )99.78066666666670.567357830404482175.869021840292
Winsorized Mean ( 17 / 20 )99.87416666666670.541854020184594184.319323925367
Winsorized Mean ( 18 / 20 )99.91316666666670.531480901521149187.990135451163
Winsorized Mean ( 19 / 20 )100.07150.49127896185526203.69587906246
Winsorized Mean ( 20 / 20 )100.1381666666670.459409501343486217.971475064893
Trimmed Mean ( 1 / 20 )99.86534482758620.732332425431242136.366138326839
Trimmed Mean ( 2 / 20 )99.80285714285710.720127636336751138.590511052386
Trimmed Mean ( 3 / 20 )99.78629629629630.718006221944952138.976924219393
Trimmed Mean ( 4 / 20 )99.77115384615390.71528800293149139.483891016287
Trimmed Mean ( 5 / 20 )99.75520.71153798584905140.196591023831
Trimmed Mean ( 6 / 20 )99.7331250.707314441762438141.002528877386
Trimmed Mean ( 7 / 20 )99.70978260869560.701053002960163142.228593540967
Trimmed Mean ( 8 / 20 )99.68886363636360.69320160007125143.809338619699
Trimmed Mean ( 9 / 20 )99.67238095238090.684005234061435145.718740133835
Trimmed Mean ( 10 / 20 )99.6780.678664714621141146.873703395121
Trimmed Mean ( 11 / 20 )99.7050.675833477305573147.528945144159
Trimmed Mean ( 12 / 20 )99.74416666666670.672651278199553148.285106859005
Trimmed Mean ( 13 / 20 )99.79088235294120.66682761439278149.650194741578
Trimmed Mean ( 14 / 20 )99.838750.658407589898145151.636693640553
Trimmed Mean ( 15 / 20 )99.8810.648512418016679154.015555022774
Trimmed Mean ( 16 / 20 )99.91285714285710.638182948248085156.558330831518
Trimmed Mean ( 17 / 20 )99.93192307692310.627389467857644159.282117722126
Trimmed Mean ( 18 / 20 )99.94041666666670.616425083652538162.129055609619
Trimmed Mean ( 19 / 20 )99.94454545454540.599144313091822166.812140699111
Trimmed Mean ( 20 / 20 )99.92450.58387880636851171.139111250655
Median99.73
Midrange101.715
Midmean - Weighted Average at Xnp99.6777419354839
Midmean - Weighted Average at X(n+1)p99.881
Midmean - Empirical Distribution Function99.6777419354839
Midmean - Empirical Distribution Function - Averaging99.881
Midmean - Empirical Distribution Function - Interpolation99.881
Midmean - Closest Observation99.6777419354839
Midmean - True Basic - Statistics Graphics Toolkit99.881
Midmean - MS Excel (old versions)99.83875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 99.927 & 0.743941454017485 & 134.321053707072 \tabularnewline
Geometric Mean & 99.7640647831682 &  &  \tabularnewline
Harmonic Mean & 99.6018116652828 &  &  \tabularnewline
Quadratic Mean & 100.090253338341 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 99.9236666666666 & 0.741891382195209 & 134.687730663482 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 99.8326666666667 & 0.721094776075144 & 138.445971291107 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 99.8256666666667 & 0.719209561669606 & 138.799137256917 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 99.8243333333333 & 0.717512824612907 & 139.125503975748 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 99.8435 & 0.712778989882614 & 140.076379098159 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 99.8405 & 0.712216418935375 & 140.182811496037 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 99.8171666666667 & 0.707882498934358 & 141.008100662088 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 99.7811666666667 & 0.700394000967553 & 142.464336543181 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 99.6386666666667 & 0.670167255734816 & 148.677312736529 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 99.507 & 0.646525537922857 & 153.9103935781 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 99.4465 & 0.635705970168972 & 156.434742894686 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 99.4265 & 0.632780556789514 & 157.126351202148 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 99.459 & 0.625882324096007 & 158.910063714698 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 99.543 & 0.61109512237259 & 162.892807282641 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 99.658 & 0.590024168804983 & 168.90494537172 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 99.7806666666667 & 0.567357830404482 & 175.869021840292 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 99.8741666666667 & 0.541854020184594 & 184.319323925367 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 99.9131666666667 & 0.531480901521149 & 187.990135451163 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 100.0715 & 0.49127896185526 & 203.69587906246 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 100.138166666667 & 0.459409501343486 & 217.971475064893 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 99.8653448275862 & 0.732332425431242 & 136.366138326839 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 99.8028571428571 & 0.720127636336751 & 138.590511052386 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 99.7862962962963 & 0.718006221944952 & 138.976924219393 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 99.7711538461539 & 0.71528800293149 & 139.483891016287 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 99.7552 & 0.71153798584905 & 140.196591023831 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 99.733125 & 0.707314441762438 & 141.002528877386 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 99.7097826086956 & 0.701053002960163 & 142.228593540967 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 99.6888636363636 & 0.69320160007125 & 143.809338619699 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 99.6723809523809 & 0.684005234061435 & 145.718740133835 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 99.678 & 0.678664714621141 & 146.873703395121 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 99.705 & 0.675833477305573 & 147.528945144159 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 99.7441666666667 & 0.672651278199553 & 148.285106859005 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 99.7908823529412 & 0.66682761439278 & 149.650194741578 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 99.83875 & 0.658407589898145 & 151.636693640553 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 99.881 & 0.648512418016679 & 154.015555022774 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 99.9128571428571 & 0.638182948248085 & 156.558330831518 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 99.9319230769231 & 0.627389467857644 & 159.282117722126 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 99.9404166666667 & 0.616425083652538 & 162.129055609619 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 99.9445454545454 & 0.599144313091822 & 166.812140699111 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 99.9245 & 0.58387880636851 & 171.139111250655 \tabularnewline
Median & 99.73 &  &  \tabularnewline
Midrange & 101.715 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.6777419354839 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.881 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.6777419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.881 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.881 &  &  \tabularnewline
Midmean - Closest Observation & 99.6777419354839 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.881 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.83875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293455&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]99.927[/C][C]0.743941454017485[/C][C]134.321053707072[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]99.7640647831682[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.6018116652828[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]100.090253338341[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]99.9236666666666[/C][C]0.741891382195209[/C][C]134.687730663482[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]99.8326666666667[/C][C]0.721094776075144[/C][C]138.445971291107[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]99.8256666666667[/C][C]0.719209561669606[/C][C]138.799137256917[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]99.8243333333333[/C][C]0.717512824612907[/C][C]139.125503975748[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]99.8435[/C][C]0.712778989882614[/C][C]140.076379098159[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]99.8405[/C][C]0.712216418935375[/C][C]140.182811496037[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]99.8171666666667[/C][C]0.707882498934358[/C][C]141.008100662088[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]99.7811666666667[/C][C]0.700394000967553[/C][C]142.464336543181[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]99.6386666666667[/C][C]0.670167255734816[/C][C]148.677312736529[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]99.507[/C][C]0.646525537922857[/C][C]153.9103935781[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]99.4465[/C][C]0.635705970168972[/C][C]156.434742894686[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]99.4265[/C][C]0.632780556789514[/C][C]157.126351202148[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]99.459[/C][C]0.625882324096007[/C][C]158.910063714698[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]99.543[/C][C]0.61109512237259[/C][C]162.892807282641[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]99.658[/C][C]0.590024168804983[/C][C]168.90494537172[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]99.7806666666667[/C][C]0.567357830404482[/C][C]175.869021840292[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]99.8741666666667[/C][C]0.541854020184594[/C][C]184.319323925367[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]99.9131666666667[/C][C]0.531480901521149[/C][C]187.990135451163[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]100.0715[/C][C]0.49127896185526[/C][C]203.69587906246[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]100.138166666667[/C][C]0.459409501343486[/C][C]217.971475064893[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]99.8653448275862[/C][C]0.732332425431242[/C][C]136.366138326839[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]99.8028571428571[/C][C]0.720127636336751[/C][C]138.590511052386[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]99.7862962962963[/C][C]0.718006221944952[/C][C]138.976924219393[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]99.7711538461539[/C][C]0.71528800293149[/C][C]139.483891016287[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]99.7552[/C][C]0.71153798584905[/C][C]140.196591023831[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]99.733125[/C][C]0.707314441762438[/C][C]141.002528877386[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]99.7097826086956[/C][C]0.701053002960163[/C][C]142.228593540967[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]99.6888636363636[/C][C]0.69320160007125[/C][C]143.809338619699[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]99.6723809523809[/C][C]0.684005234061435[/C][C]145.718740133835[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]99.678[/C][C]0.678664714621141[/C][C]146.873703395121[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]99.705[/C][C]0.675833477305573[/C][C]147.528945144159[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]99.7441666666667[/C][C]0.672651278199553[/C][C]148.285106859005[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]99.7908823529412[/C][C]0.66682761439278[/C][C]149.650194741578[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]99.83875[/C][C]0.658407589898145[/C][C]151.636693640553[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]99.881[/C][C]0.648512418016679[/C][C]154.015555022774[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]99.9128571428571[/C][C]0.638182948248085[/C][C]156.558330831518[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]99.9319230769231[/C][C]0.627389467857644[/C][C]159.282117722126[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]99.9404166666667[/C][C]0.616425083652538[/C][C]162.129055609619[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]99.9445454545454[/C][C]0.599144313091822[/C][C]166.812140699111[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]99.9245[/C][C]0.58387880636851[/C][C]171.139111250655[/C][/ROW]
[ROW][C]Median[/C][C]99.73[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.715[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.6777419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.881[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.6777419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.881[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.881[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.6777419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.881[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.83875[/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=293455&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293455&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 Mean99.9270.743941454017485134.321053707072
Geometric Mean99.7640647831682
Harmonic Mean99.6018116652828
Quadratic Mean100.090253338341
Winsorized Mean ( 1 / 20 )99.92366666666660.741891382195209134.687730663482
Winsorized Mean ( 2 / 20 )99.83266666666670.721094776075144138.445971291107
Winsorized Mean ( 3 / 20 )99.82566666666670.719209561669606138.799137256917
Winsorized Mean ( 4 / 20 )99.82433333333330.717512824612907139.125503975748
Winsorized Mean ( 5 / 20 )99.84350.712778989882614140.076379098159
Winsorized Mean ( 6 / 20 )99.84050.712216418935375140.182811496037
Winsorized Mean ( 7 / 20 )99.81716666666670.707882498934358141.008100662088
Winsorized Mean ( 8 / 20 )99.78116666666670.700394000967553142.464336543181
Winsorized Mean ( 9 / 20 )99.63866666666670.670167255734816148.677312736529
Winsorized Mean ( 10 / 20 )99.5070.646525537922857153.9103935781
Winsorized Mean ( 11 / 20 )99.44650.635705970168972156.434742894686
Winsorized Mean ( 12 / 20 )99.42650.632780556789514157.126351202148
Winsorized Mean ( 13 / 20 )99.4590.625882324096007158.910063714698
Winsorized Mean ( 14 / 20 )99.5430.61109512237259162.892807282641
Winsorized Mean ( 15 / 20 )99.6580.590024168804983168.90494537172
Winsorized Mean ( 16 / 20 )99.78066666666670.567357830404482175.869021840292
Winsorized Mean ( 17 / 20 )99.87416666666670.541854020184594184.319323925367
Winsorized Mean ( 18 / 20 )99.91316666666670.531480901521149187.990135451163
Winsorized Mean ( 19 / 20 )100.07150.49127896185526203.69587906246
Winsorized Mean ( 20 / 20 )100.1381666666670.459409501343486217.971475064893
Trimmed Mean ( 1 / 20 )99.86534482758620.732332425431242136.366138326839
Trimmed Mean ( 2 / 20 )99.80285714285710.720127636336751138.590511052386
Trimmed Mean ( 3 / 20 )99.78629629629630.718006221944952138.976924219393
Trimmed Mean ( 4 / 20 )99.77115384615390.71528800293149139.483891016287
Trimmed Mean ( 5 / 20 )99.75520.71153798584905140.196591023831
Trimmed Mean ( 6 / 20 )99.7331250.707314441762438141.002528877386
Trimmed Mean ( 7 / 20 )99.70978260869560.701053002960163142.228593540967
Trimmed Mean ( 8 / 20 )99.68886363636360.69320160007125143.809338619699
Trimmed Mean ( 9 / 20 )99.67238095238090.684005234061435145.718740133835
Trimmed Mean ( 10 / 20 )99.6780.678664714621141146.873703395121
Trimmed Mean ( 11 / 20 )99.7050.675833477305573147.528945144159
Trimmed Mean ( 12 / 20 )99.74416666666670.672651278199553148.285106859005
Trimmed Mean ( 13 / 20 )99.79088235294120.66682761439278149.650194741578
Trimmed Mean ( 14 / 20 )99.838750.658407589898145151.636693640553
Trimmed Mean ( 15 / 20 )99.8810.648512418016679154.015555022774
Trimmed Mean ( 16 / 20 )99.91285714285710.638182948248085156.558330831518
Trimmed Mean ( 17 / 20 )99.93192307692310.627389467857644159.282117722126
Trimmed Mean ( 18 / 20 )99.94041666666670.616425083652538162.129055609619
Trimmed Mean ( 19 / 20 )99.94454545454540.599144313091822166.812140699111
Trimmed Mean ( 20 / 20 )99.92450.58387880636851171.139111250655
Median99.73
Midrange101.715
Midmean - Weighted Average at Xnp99.6777419354839
Midmean - Weighted Average at X(n+1)p99.881
Midmean - Empirical Distribution Function99.6777419354839
Midmean - Empirical Distribution Function - Averaging99.881
Midmean - Empirical Distribution Function - Interpolation99.881
Midmean - Closest Observation99.6777419354839
Midmean - True Basic - Statistics Graphics Toolkit99.881
Midmean - MS Excel (old versions)99.83875
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')