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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 19 Oct 2009 14:06:30 -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/2009/Oct/19/t1255982855imb316e3yyt5roa.htm/, Retrieved Mon, 29 Apr 2024 20:18:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48218, Retrieved Mon, 29 Apr 2024 20:18:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [Part 3.1 Mediaan] [2009-10-19 20:06:30] [026d431dc78a3ce53a040b5408fc0322] [Current]
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Post a new message
Dataseries X:
115.6
111.3
114.6
137.5
83.7
106.0
123.4
126.5
120.0
141.6
90.5
96.5
113.5
120.1
123.9
144.4
90.8
114.2
138.1
135.0
131.3
144.6
101.7
108.7
135.3
124.3
138.3
158.2
93.5
124.8
154.4
152.8
148.9
170.3
124.8
134.4
154.0
147.9
168.1
175.7
116.7
140.8
164.2
173.8
167.8
166.6
135.1
158.1
151.8
166.7
165.3
187.0
125.2
144.4
181.7
175.9
166.3
181.5
121.8
134.8
162.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48218&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48218&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48218&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean138.1573770491803.2953042091270841.9255304765255
Geometric Mean135.696440882773
Harmonic Mean133.135393222266
Quadratic Mean140.495560865640
Winsorized Mean ( 1 / 20 )138.1819672131153.2458460281155442.5719414957399
Winsorized Mean ( 2 / 20 )138.1852459016393.2419811423162742.6237044065319
Winsorized Mean ( 3 / 20 )138.0426229508203.151888547425243.7967970230381
Winsorized Mean ( 4 / 20 )138.2262295081973.1040436360019344.5310200877958
Winsorized Mean ( 5 / 20 )138.4967213114752.9813371841400546.4545647665223
Winsorized Mean ( 6 / 20 )138.5754098360662.8310366671218848.9486453656376
Winsorized Mean ( 7 / 20 )138.6327868852462.7266291779105650.8440194245561
Winsorized Mean ( 8 / 20 )138.9344262295082.6587774885432152.255003221662
Winsorized Mean ( 9 / 20 )139.0967213114752.5745644941422454.0272817511289
Winsorized Mean ( 10 / 20 )139.1950819672132.5527617384036154.5272517498088
Winsorized Mean ( 11 / 20 )139.2131147540982.5313676678821554.9952172181175
Winsorized Mean ( 12 / 20 )139.2131147540982.4648251973731756.4799138301823
Winsorized Mean ( 13 / 20 )139.2131147540982.3865441043069858.3325129013378
Winsorized Mean ( 14 / 20 )139.6721311475412.2188587269104362.9477350015981
Winsorized Mean ( 15 / 20 )138.5409836065572.0203004930544368.574444288286
Winsorized Mean ( 16 / 20 )138.9606557377051.9493774804125271.284631701141
Winsorized Mean ( 17 / 20 )138.3754098360661.7195717724287980.470854461991
Winsorized Mean ( 18 / 20 )138.4049180327871.6799499508377482.386334166544
Winsorized Mean ( 19 / 20 )138.1557377049181.6046696280689186.096063194751
Winsorized Mean ( 20 / 20 )137.9918032786891.5315307087758190.1005787791152
Trimmed Mean ( 1 / 20 )138.2525423728813.1702291324729143.6096372204614
Trimmed Mean ( 2 / 20 )138.3280701754393.0771204299251844.9537394864984
Trimmed Mean ( 3 / 20 )138.4072727272732.9644877420385246.6884280763115
Trimmed Mean ( 4 / 20 )138.5471698113212.8685214173375348.299158226232
Trimmed Mean ( 5 / 20 )138.6431372549022.7673690413451950.0992586039443
Trimmed Mean ( 6 / 20 )138.6795918367352.6827649389422251.6927852394754
Trimmed Mean ( 7 / 20 )138.7021276595742.6216957342977452.9055015214142
Trimmed Mean ( 8 / 20 )138.7155555555562.5717658036932653.9378645428558
Trimmed Mean ( 9 / 20 )138.6767441860472.5232141195120154.9603551730546
Trimmed Mean ( 10 / 20 )138.6073170731712.4790251581381255.9120251838316
Trimmed Mean ( 11 / 20 )138.5153846153852.4227735816809157.1722366723527
Trimmed Mean ( 12 / 20 )138.4108108108112.3498060228669658.9030794303343
Trimmed Mean ( 13 / 20 )138.2942857142862.2661036892366961.0273423811725
Trimmed Mean ( 14 / 20 )138.1636363636362.1700737409872363.667714950913
Trimmed Mean ( 15 / 20 )137.9516129032262.0815981813389466.27197032546
Trimmed Mean ( 16 / 20 )137.8689655172412.0162095799183668.3802749924558
Trimmed Mean ( 17 / 20 )137.7148148148151.9365704089507071.112733200046
Trimmed Mean ( 18 / 20 )137.621.8926084293024472.71446003795
Trimmed Mean ( 19 / 20 )137.5043478260871.8288042083409175.1881186618826
Trimmed Mean ( 20 / 20 )137.4047619047621.7483390238748478.5916003866527
Median137.5
Midrange135.35
Midmean - Weighted Average at Xnp137.276666666667
Midmean - Weighted Average at X(n+1)p137.951612903226
Midmean - Empirical Distribution Function137.951612903226
Midmean - Empirical Distribution Function - Averaging137.951612903226
Midmean - Empirical Distribution Function - Interpolation137.951612903226
Midmean - Closest Observation137.390625
Midmean - True Basic - Statistics Graphics Toolkit137.951612903226
Midmean - MS Excel (old versions)137.951612903226
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 138.157377049180 & 3.29530420912708 & 41.9255304765255 \tabularnewline
Geometric Mean & 135.696440882773 &  &  \tabularnewline
Harmonic Mean & 133.135393222266 &  &  \tabularnewline
Quadratic Mean & 140.495560865640 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 138.181967213115 & 3.24584602811554 & 42.5719414957399 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 138.185245901639 & 3.24198114231627 & 42.6237044065319 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 138.042622950820 & 3.1518885474252 & 43.7967970230381 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 138.226229508197 & 3.10404363600193 & 44.5310200877958 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 138.496721311475 & 2.98133718414005 & 46.4545647665223 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 138.575409836066 & 2.83103666712188 & 48.9486453656376 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 138.632786885246 & 2.72662917791056 & 50.8440194245561 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 138.934426229508 & 2.65877748854321 & 52.255003221662 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 139.096721311475 & 2.57456449414224 & 54.0272817511289 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 139.195081967213 & 2.55276173840361 & 54.5272517498088 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 139.213114754098 & 2.53136766788215 & 54.9952172181175 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 139.213114754098 & 2.46482519737317 & 56.4799138301823 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 139.213114754098 & 2.38654410430698 & 58.3325129013378 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 139.672131147541 & 2.21885872691043 & 62.9477350015981 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 138.540983606557 & 2.02030049305443 & 68.574444288286 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 138.960655737705 & 1.94937748041252 & 71.284631701141 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 138.375409836066 & 1.71957177242879 & 80.470854461991 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 138.404918032787 & 1.67994995083774 & 82.386334166544 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 138.155737704918 & 1.60466962806891 & 86.096063194751 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 137.991803278689 & 1.53153070877581 & 90.1005787791152 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 138.252542372881 & 3.17022913247291 & 43.6096372204614 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 138.328070175439 & 3.07712042992518 & 44.9537394864984 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 138.407272727273 & 2.96448774203852 & 46.6884280763115 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 138.547169811321 & 2.86852141733753 & 48.299158226232 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 138.643137254902 & 2.76736904134519 & 50.0992586039443 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 138.679591836735 & 2.68276493894222 & 51.6927852394754 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 138.702127659574 & 2.62169573429774 & 52.9055015214142 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 138.715555555556 & 2.57176580369326 & 53.9378645428558 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 138.676744186047 & 2.52321411951201 & 54.9603551730546 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 138.607317073171 & 2.47902515813812 & 55.9120251838316 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 138.515384615385 & 2.42277358168091 & 57.1722366723527 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 138.410810810811 & 2.34980602286696 & 58.9030794303343 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 138.294285714286 & 2.26610368923669 & 61.0273423811725 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 138.163636363636 & 2.17007374098723 & 63.667714950913 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 137.951612903226 & 2.08159818133894 & 66.27197032546 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 137.868965517241 & 2.01620957991836 & 68.3802749924558 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 137.714814814815 & 1.93657040895070 & 71.112733200046 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 137.62 & 1.89260842930244 & 72.71446003795 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 137.504347826087 & 1.82880420834091 & 75.1881186618826 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 137.404761904762 & 1.74833902387484 & 78.5916003866527 \tabularnewline
Median & 137.5 &  &  \tabularnewline
Midrange & 135.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 137.276666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 137.951612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 137.951612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 137.951612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 137.951612903226 &  &  \tabularnewline
Midmean - Closest Observation & 137.390625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 137.951612903226 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 137.951612903226 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48218&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]138.157377049180[/C][C]3.29530420912708[/C][C]41.9255304765255[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]135.696440882773[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]133.135393222266[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]140.495560865640[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]138.181967213115[/C][C]3.24584602811554[/C][C]42.5719414957399[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]138.185245901639[/C][C]3.24198114231627[/C][C]42.6237044065319[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]138.042622950820[/C][C]3.1518885474252[/C][C]43.7967970230381[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]138.226229508197[/C][C]3.10404363600193[/C][C]44.5310200877958[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]138.496721311475[/C][C]2.98133718414005[/C][C]46.4545647665223[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]138.575409836066[/C][C]2.83103666712188[/C][C]48.9486453656376[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]138.632786885246[/C][C]2.72662917791056[/C][C]50.8440194245561[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]138.934426229508[/C][C]2.65877748854321[/C][C]52.255003221662[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]139.096721311475[/C][C]2.57456449414224[/C][C]54.0272817511289[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]139.195081967213[/C][C]2.55276173840361[/C][C]54.5272517498088[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]139.213114754098[/C][C]2.53136766788215[/C][C]54.9952172181175[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]139.213114754098[/C][C]2.46482519737317[/C][C]56.4799138301823[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]139.213114754098[/C][C]2.38654410430698[/C][C]58.3325129013378[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]139.672131147541[/C][C]2.21885872691043[/C][C]62.9477350015981[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]138.540983606557[/C][C]2.02030049305443[/C][C]68.574444288286[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]138.960655737705[/C][C]1.94937748041252[/C][C]71.284631701141[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]138.375409836066[/C][C]1.71957177242879[/C][C]80.470854461991[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]138.404918032787[/C][C]1.67994995083774[/C][C]82.386334166544[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]138.155737704918[/C][C]1.60466962806891[/C][C]86.096063194751[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]137.991803278689[/C][C]1.53153070877581[/C][C]90.1005787791152[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]138.252542372881[/C][C]3.17022913247291[/C][C]43.6096372204614[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]138.328070175439[/C][C]3.07712042992518[/C][C]44.9537394864984[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]138.407272727273[/C][C]2.96448774203852[/C][C]46.6884280763115[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]138.547169811321[/C][C]2.86852141733753[/C][C]48.299158226232[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]138.643137254902[/C][C]2.76736904134519[/C][C]50.0992586039443[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]138.679591836735[/C][C]2.68276493894222[/C][C]51.6927852394754[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]138.702127659574[/C][C]2.62169573429774[/C][C]52.9055015214142[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]138.715555555556[/C][C]2.57176580369326[/C][C]53.9378645428558[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]138.676744186047[/C][C]2.52321411951201[/C][C]54.9603551730546[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]138.607317073171[/C][C]2.47902515813812[/C][C]55.9120251838316[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]138.515384615385[/C][C]2.42277358168091[/C][C]57.1722366723527[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]138.410810810811[/C][C]2.34980602286696[/C][C]58.9030794303343[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]138.294285714286[/C][C]2.26610368923669[/C][C]61.0273423811725[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]138.163636363636[/C][C]2.17007374098723[/C][C]63.667714950913[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]137.951612903226[/C][C]2.08159818133894[/C][C]66.27197032546[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]137.868965517241[/C][C]2.01620957991836[/C][C]68.3802749924558[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]137.714814814815[/C][C]1.93657040895070[/C][C]71.112733200046[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]137.62[/C][C]1.89260842930244[/C][C]72.71446003795[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]137.504347826087[/C][C]1.82880420834091[/C][C]75.1881186618826[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]137.404761904762[/C][C]1.74833902387484[/C][C]78.5916003866527[/C][/ROW]
[ROW][C]Median[/C][C]137.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]135.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]137.276666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]137.951612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]137.951612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]137.951612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]137.951612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]137.390625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]137.951612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]137.951612903226[/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=48218&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48218&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 Mean138.1573770491803.2953042091270841.9255304765255
Geometric Mean135.696440882773
Harmonic Mean133.135393222266
Quadratic Mean140.495560865640
Winsorized Mean ( 1 / 20 )138.1819672131153.2458460281155442.5719414957399
Winsorized Mean ( 2 / 20 )138.1852459016393.2419811423162742.6237044065319
Winsorized Mean ( 3 / 20 )138.0426229508203.151888547425243.7967970230381
Winsorized Mean ( 4 / 20 )138.2262295081973.1040436360019344.5310200877958
Winsorized Mean ( 5 / 20 )138.4967213114752.9813371841400546.4545647665223
Winsorized Mean ( 6 / 20 )138.5754098360662.8310366671218848.9486453656376
Winsorized Mean ( 7 / 20 )138.6327868852462.7266291779105650.8440194245561
Winsorized Mean ( 8 / 20 )138.9344262295082.6587774885432152.255003221662
Winsorized Mean ( 9 / 20 )139.0967213114752.5745644941422454.0272817511289
Winsorized Mean ( 10 / 20 )139.1950819672132.5527617384036154.5272517498088
Winsorized Mean ( 11 / 20 )139.2131147540982.5313676678821554.9952172181175
Winsorized Mean ( 12 / 20 )139.2131147540982.4648251973731756.4799138301823
Winsorized Mean ( 13 / 20 )139.2131147540982.3865441043069858.3325129013378
Winsorized Mean ( 14 / 20 )139.6721311475412.2188587269104362.9477350015981
Winsorized Mean ( 15 / 20 )138.5409836065572.0203004930544368.574444288286
Winsorized Mean ( 16 / 20 )138.9606557377051.9493774804125271.284631701141
Winsorized Mean ( 17 / 20 )138.3754098360661.7195717724287980.470854461991
Winsorized Mean ( 18 / 20 )138.4049180327871.6799499508377482.386334166544
Winsorized Mean ( 19 / 20 )138.1557377049181.6046696280689186.096063194751
Winsorized Mean ( 20 / 20 )137.9918032786891.5315307087758190.1005787791152
Trimmed Mean ( 1 / 20 )138.2525423728813.1702291324729143.6096372204614
Trimmed Mean ( 2 / 20 )138.3280701754393.0771204299251844.9537394864984
Trimmed Mean ( 3 / 20 )138.4072727272732.9644877420385246.6884280763115
Trimmed Mean ( 4 / 20 )138.5471698113212.8685214173375348.299158226232
Trimmed Mean ( 5 / 20 )138.6431372549022.7673690413451950.0992586039443
Trimmed Mean ( 6 / 20 )138.6795918367352.6827649389422251.6927852394754
Trimmed Mean ( 7 / 20 )138.7021276595742.6216957342977452.9055015214142
Trimmed Mean ( 8 / 20 )138.7155555555562.5717658036932653.9378645428558
Trimmed Mean ( 9 / 20 )138.6767441860472.5232141195120154.9603551730546
Trimmed Mean ( 10 / 20 )138.6073170731712.4790251581381255.9120251838316
Trimmed Mean ( 11 / 20 )138.5153846153852.4227735816809157.1722366723527
Trimmed Mean ( 12 / 20 )138.4108108108112.3498060228669658.9030794303343
Trimmed Mean ( 13 / 20 )138.2942857142862.2661036892366961.0273423811725
Trimmed Mean ( 14 / 20 )138.1636363636362.1700737409872363.667714950913
Trimmed Mean ( 15 / 20 )137.9516129032262.0815981813389466.27197032546
Trimmed Mean ( 16 / 20 )137.8689655172412.0162095799183668.3802749924558
Trimmed Mean ( 17 / 20 )137.7148148148151.9365704089507071.112733200046
Trimmed Mean ( 18 / 20 )137.621.8926084293024472.71446003795
Trimmed Mean ( 19 / 20 )137.5043478260871.8288042083409175.1881186618826
Trimmed Mean ( 20 / 20 )137.4047619047621.7483390238748478.5916003866527
Median137.5
Midrange135.35
Midmean - Weighted Average at Xnp137.276666666667
Midmean - Weighted Average at X(n+1)p137.951612903226
Midmean - Empirical Distribution Function137.951612903226
Midmean - Empirical Distribution Function - Averaging137.951612903226
Midmean - Empirical Distribution Function - Interpolation137.951612903226
Midmean - Closest Observation137.390625
Midmean - True Basic - Statistics Graphics Toolkit137.951612903226
Midmean - MS Excel (old versions)137.951612903226
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')