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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 computationWed, 22 Dec 2010 17:07:51 +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/2010/Dec/22/t1293037607osq1u4oj7rxgstd.htm/, Retrieved Sun, 05 May 2024 20:59:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114415, Retrieved Sun, 05 May 2024 20:59:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central tendency] [2010-12-22 17:07:51] [039869833c16fe697975601e6b065e0f] [Current]
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Dataseries X:
1038,00
934,00
988,00
870,00
854,00
834,00
872,00
954,00
870,00
1238,00
1082,00
1053,00
934,00
787,00
1081,00
908,00
995,00
825,00
822,00
856,00
887,00
1094,00
990,00
936,00
1097,00
918,00
926,00
907,00
899,00
971,00
1087,00
1000,00
1071,00
1190,00
1116,00
1070,00
1314,00
1068,00
1185,00
1215,00
1145,00
1251,00
1363,00
1368,00
1535,00
1853,00
1866,00
2023,00
1373,00
1968,00
1424,00
1160,00
1243,00
1375,00
1539,00
1773,00
1906,00
2076,00
2004,00




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114415&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114415&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114415&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1186.118644067845.590483210942526.0168035197115
Geometric Mean1142.94983599613
Harmonic Mean1106.81290474958
Quadratic Mean1235.89238328054
Winsorized Mean ( 1 / 19 )1185.8135593220345.209955525896926.2290361830324
Winsorized Mean ( 2 / 19 )1185.2711864406844.992023648619526.3440292372145
Winsorized Mean ( 3 / 19 )1183.8983050847544.363191384348826.6864999595683
Winsorized Mean ( 4 / 19 )1181.0508474576342.929041963562427.511698221919
Winsorized Mean ( 5 / 19 )1177.8305084745841.933473742006228.0880738791431
Winsorized Mean ( 6 / 19 )1177.9322033898341.374922343757328.4697139393558
Winsorized Mean ( 7 / 19 )1168.440677966138.761799140148330.144129113859
Winsorized Mean ( 8 / 19 )1136.9830508474630.809035422451136.9042079785113
Winsorized Mean ( 9 / 19 )1138.6610169491530.338356960781137.5320594461038
Winsorized Mean ( 10 / 19 )1121.881355932226.023357362784543.1105541184546
Winsorized Mean ( 11 / 19 )1114.2372881355924.031118280497346.3664351833291
Winsorized Mean ( 12 / 19 )1114.0338983050823.924889359412746.5638056489818
Winsorized Mean ( 13 / 19 )1115.1355932203423.395769792860847.6639838352582
Winsorized Mean ( 14 / 19 )1115.8474576271222.901267177088248.724267045951
Winsorized Mean ( 15 / 19 )1105.4237288135620.344895887068554.3342042618257
Winsorized Mean ( 16 / 19 )1088.3389830508517.451688514588662.3629617352533
Winsorized Mean ( 17 / 19 )1086.6101694915316.995633518873763.9346670004883
Winsorized Mean ( 18 / 19 )1090.5762711864415.92701800790468.4733495400852
Winsorized Mean ( 19 / 19 )1088.6440677966113.953914351281178.0171097794261
Trimmed Mean ( 1 / 19 )1177.5087719298243.919748548184226.8104625106855
Trimmed Mean ( 2 / 19 )1168.642.289618724361327.6332593021657
Trimmed Mean ( 3 / 19 )1159.3207547169840.367800809855528.7189475636221
Trimmed Mean ( 4 / 19 )1149.843137254938.228870853127730.0778733871714
Trimmed Mean ( 5 / 19 )1140.4489795918436.087738665558131.6021181088932
Trimmed Mean ( 6 / 19 )1131.0638297872333.674125377508633.5885139437857
Trimmed Mean ( 7 / 19 )1120.8222222222230.62914847414836.5933196989865
Trimmed Mean ( 8 / 19 )1111.4883720930227.497435138480340.4215290079034
Trimmed Mean ( 9 / 19 )1106.9024390243926.185892796668142.2709451848528
Trimmed Mean ( 10 / 19 )1101.564102564124.53086944713544.9052205401043
Trimmed Mean ( 11 / 19 )1098.3243243243223.672377627598546.3968740953102
Trimmed Mean ( 12 / 19 )1095.8857142857123.064861827907347.5132139295865
Trimmed Mean ( 13 / 19 )1093.1818181818222.206224154154949.2286221463399
Trimmed Mean ( 14 / 19 )1089.9677419354821.103864186292551.6477803455277
Trimmed Mean ( 15 / 19 )1086.2068965517219.613091241694655.3817286202496
Trimmed Mean ( 16 / 19 )1083.4074074074118.377434079863158.9531380006168
Trimmed Mean ( 17 / 19 )1082.6817.638189627434461.3827168699901
Trimmed Mean ( 18 / 19 )1082.0869565217416.600265849040165.1849172996413
Trimmed Mean ( 19 / 19 )1080.761904761915.328607671668370.5062017315159
Median1081
Midrange1431.5
Midmean - Weighted Average at Xnp1080.86666666667
Midmean - Weighted Average at X(n+1)p1089.96774193548
Midmean - Empirical Distribution Function1089.96774193548
Midmean - Empirical Distribution Function - Averaging1089.96774193548
Midmean - Empirical Distribution Function - Interpolation1086.20689655172
Midmean - Closest Observation1080.86666666667
Midmean - True Basic - Statistics Graphics Toolkit1089.96774193548
Midmean - MS Excel (old versions)1089.96774193548
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1186.1186440678 & 45.5904832109425 & 26.0168035197115 \tabularnewline
Geometric Mean & 1142.94983599613 &  &  \tabularnewline
Harmonic Mean & 1106.81290474958 &  &  \tabularnewline
Quadratic Mean & 1235.89238328054 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 1185.81355932203 & 45.2099555258969 & 26.2290361830324 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 1185.27118644068 & 44.9920236486195 & 26.3440292372145 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 1183.89830508475 & 44.3631913843488 & 26.6864999595683 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 1181.05084745763 & 42.9290419635624 & 27.511698221919 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 1177.83050847458 & 41.9334737420062 & 28.0880738791431 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 1177.93220338983 & 41.3749223437573 & 28.4697139393558 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 1168.4406779661 & 38.7617991401483 & 30.144129113859 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 1136.98305084746 & 30.8090354224511 & 36.9042079785113 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 1138.66101694915 & 30.3383569607811 & 37.5320594461038 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 1121.8813559322 & 26.0233573627845 & 43.1105541184546 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 1114.23728813559 & 24.0311182804973 & 46.3664351833291 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 1114.03389830508 & 23.9248893594127 & 46.5638056489818 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 1115.13559322034 & 23.3957697928608 & 47.6639838352582 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 1115.84745762712 & 22.9012671770882 & 48.724267045951 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 1105.42372881356 & 20.3448958870685 & 54.3342042618257 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 1088.33898305085 & 17.4516885145886 & 62.3629617352533 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 1086.61016949153 & 16.9956335188737 & 63.9346670004883 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 1090.57627118644 & 15.927018007904 & 68.4733495400852 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 1088.64406779661 & 13.9539143512811 & 78.0171097794261 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 1177.50877192982 & 43.9197485481842 & 26.8104625106855 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 1168.6 & 42.2896187243613 & 27.6332593021657 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 1159.32075471698 & 40.3678008098555 & 28.7189475636221 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 1149.8431372549 & 38.2288708531277 & 30.0778733871714 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 1140.44897959184 & 36.0877386655581 & 31.6021181088932 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 1131.06382978723 & 33.6741253775086 & 33.5885139437857 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 1120.82222222222 & 30.629148474148 & 36.5933196989865 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 1111.48837209302 & 27.4974351384803 & 40.4215290079034 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 1106.90243902439 & 26.1858927966681 & 42.2709451848528 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 1101.5641025641 & 24.530869447135 & 44.9052205401043 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 1098.32432432432 & 23.6723776275985 & 46.3968740953102 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 1095.88571428571 & 23.0648618279073 & 47.5132139295865 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 1093.18181818182 & 22.2062241541549 & 49.2286221463399 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 1089.96774193548 & 21.1038641862925 & 51.6477803455277 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 1086.20689655172 & 19.6130912416946 & 55.3817286202496 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 1083.40740740741 & 18.3774340798631 & 58.9531380006168 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 1082.68 & 17.6381896274344 & 61.3827168699901 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 1082.08695652174 & 16.6002658490401 & 65.1849172996413 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 1080.7619047619 & 15.3286076716683 & 70.5062017315159 \tabularnewline
Median & 1081 &  &  \tabularnewline
Midrange & 1431.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1080.86666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1089.96774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1089.96774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1089.96774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1086.20689655172 &  &  \tabularnewline
Midmean - Closest Observation & 1080.86666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1089.96774193548 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1089.96774193548 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114415&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]1186.1186440678[/C][C]45.5904832109425[/C][C]26.0168035197115[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1142.94983599613[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1106.81290474958[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1235.89238328054[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]1185.81355932203[/C][C]45.2099555258969[/C][C]26.2290361830324[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]1185.27118644068[/C][C]44.9920236486195[/C][C]26.3440292372145[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]1183.89830508475[/C][C]44.3631913843488[/C][C]26.6864999595683[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]1181.05084745763[/C][C]42.9290419635624[/C][C]27.511698221919[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]1177.83050847458[/C][C]41.9334737420062[/C][C]28.0880738791431[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]1177.93220338983[/C][C]41.3749223437573[/C][C]28.4697139393558[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]1168.4406779661[/C][C]38.7617991401483[/C][C]30.144129113859[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]1136.98305084746[/C][C]30.8090354224511[/C][C]36.9042079785113[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]1138.66101694915[/C][C]30.3383569607811[/C][C]37.5320594461038[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]1121.8813559322[/C][C]26.0233573627845[/C][C]43.1105541184546[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]1114.23728813559[/C][C]24.0311182804973[/C][C]46.3664351833291[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]1114.03389830508[/C][C]23.9248893594127[/C][C]46.5638056489818[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]1115.13559322034[/C][C]23.3957697928608[/C][C]47.6639838352582[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]1115.84745762712[/C][C]22.9012671770882[/C][C]48.724267045951[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]1105.42372881356[/C][C]20.3448958870685[/C][C]54.3342042618257[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]1088.33898305085[/C][C]17.4516885145886[/C][C]62.3629617352533[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]1086.61016949153[/C][C]16.9956335188737[/C][C]63.9346670004883[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]1090.57627118644[/C][C]15.927018007904[/C][C]68.4733495400852[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]1088.64406779661[/C][C]13.9539143512811[/C][C]78.0171097794261[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]1177.50877192982[/C][C]43.9197485481842[/C][C]26.8104625106855[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]1168.6[/C][C]42.2896187243613[/C][C]27.6332593021657[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]1159.32075471698[/C][C]40.3678008098555[/C][C]28.7189475636221[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]1149.8431372549[/C][C]38.2288708531277[/C][C]30.0778733871714[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]1140.44897959184[/C][C]36.0877386655581[/C][C]31.6021181088932[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]1131.06382978723[/C][C]33.6741253775086[/C][C]33.5885139437857[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]1120.82222222222[/C][C]30.629148474148[/C][C]36.5933196989865[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]1111.48837209302[/C][C]27.4974351384803[/C][C]40.4215290079034[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]1106.90243902439[/C][C]26.1858927966681[/C][C]42.2709451848528[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]1101.5641025641[/C][C]24.530869447135[/C][C]44.9052205401043[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]1098.32432432432[/C][C]23.6723776275985[/C][C]46.3968740953102[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]1095.88571428571[/C][C]23.0648618279073[/C][C]47.5132139295865[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]1093.18181818182[/C][C]22.2062241541549[/C][C]49.2286221463399[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]1089.96774193548[/C][C]21.1038641862925[/C][C]51.6477803455277[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]1086.20689655172[/C][C]19.6130912416946[/C][C]55.3817286202496[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]1083.40740740741[/C][C]18.3774340798631[/C][C]58.9531380006168[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]1082.68[/C][C]17.6381896274344[/C][C]61.3827168699901[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]1082.08695652174[/C][C]16.6002658490401[/C][C]65.1849172996413[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]1080.7619047619[/C][C]15.3286076716683[/C][C]70.5062017315159[/C][/ROW]
[ROW][C]Median[/C][C]1081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1431.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1080.86666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1089.96774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1089.96774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1089.96774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1086.20689655172[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1080.86666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1089.96774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1089.96774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114415&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114415&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 Mean1186.118644067845.590483210942526.0168035197115
Geometric Mean1142.94983599613
Harmonic Mean1106.81290474958
Quadratic Mean1235.89238328054
Winsorized Mean ( 1 / 19 )1185.8135593220345.209955525896926.2290361830324
Winsorized Mean ( 2 / 19 )1185.2711864406844.992023648619526.3440292372145
Winsorized Mean ( 3 / 19 )1183.8983050847544.363191384348826.6864999595683
Winsorized Mean ( 4 / 19 )1181.0508474576342.929041963562427.511698221919
Winsorized Mean ( 5 / 19 )1177.8305084745841.933473742006228.0880738791431
Winsorized Mean ( 6 / 19 )1177.9322033898341.374922343757328.4697139393558
Winsorized Mean ( 7 / 19 )1168.440677966138.761799140148330.144129113859
Winsorized Mean ( 8 / 19 )1136.9830508474630.809035422451136.9042079785113
Winsorized Mean ( 9 / 19 )1138.6610169491530.338356960781137.5320594461038
Winsorized Mean ( 10 / 19 )1121.881355932226.023357362784543.1105541184546
Winsorized Mean ( 11 / 19 )1114.2372881355924.031118280497346.3664351833291
Winsorized Mean ( 12 / 19 )1114.0338983050823.924889359412746.5638056489818
Winsorized Mean ( 13 / 19 )1115.1355932203423.395769792860847.6639838352582
Winsorized Mean ( 14 / 19 )1115.8474576271222.901267177088248.724267045951
Winsorized Mean ( 15 / 19 )1105.4237288135620.344895887068554.3342042618257
Winsorized Mean ( 16 / 19 )1088.3389830508517.451688514588662.3629617352533
Winsorized Mean ( 17 / 19 )1086.6101694915316.995633518873763.9346670004883
Winsorized Mean ( 18 / 19 )1090.5762711864415.92701800790468.4733495400852
Winsorized Mean ( 19 / 19 )1088.6440677966113.953914351281178.0171097794261
Trimmed Mean ( 1 / 19 )1177.5087719298243.919748548184226.8104625106855
Trimmed Mean ( 2 / 19 )1168.642.289618724361327.6332593021657
Trimmed Mean ( 3 / 19 )1159.3207547169840.367800809855528.7189475636221
Trimmed Mean ( 4 / 19 )1149.843137254938.228870853127730.0778733871714
Trimmed Mean ( 5 / 19 )1140.4489795918436.087738665558131.6021181088932
Trimmed Mean ( 6 / 19 )1131.0638297872333.674125377508633.5885139437857
Trimmed Mean ( 7 / 19 )1120.8222222222230.62914847414836.5933196989865
Trimmed Mean ( 8 / 19 )1111.4883720930227.497435138480340.4215290079034
Trimmed Mean ( 9 / 19 )1106.9024390243926.185892796668142.2709451848528
Trimmed Mean ( 10 / 19 )1101.564102564124.53086944713544.9052205401043
Trimmed Mean ( 11 / 19 )1098.3243243243223.672377627598546.3968740953102
Trimmed Mean ( 12 / 19 )1095.8857142857123.064861827907347.5132139295865
Trimmed Mean ( 13 / 19 )1093.1818181818222.206224154154949.2286221463399
Trimmed Mean ( 14 / 19 )1089.9677419354821.103864186292551.6477803455277
Trimmed Mean ( 15 / 19 )1086.2068965517219.613091241694655.3817286202496
Trimmed Mean ( 16 / 19 )1083.4074074074118.377434079863158.9531380006168
Trimmed Mean ( 17 / 19 )1082.6817.638189627434461.3827168699901
Trimmed Mean ( 18 / 19 )1082.0869565217416.600265849040165.1849172996413
Trimmed Mean ( 19 / 19 )1080.761904761915.328607671668370.5062017315159
Median1081
Midrange1431.5
Midmean - Weighted Average at Xnp1080.86666666667
Midmean - Weighted Average at X(n+1)p1089.96774193548
Midmean - Empirical Distribution Function1089.96774193548
Midmean - Empirical Distribution Function - Averaging1089.96774193548
Midmean - Empirical Distribution Function - Interpolation1086.20689655172
Midmean - Closest Observation1080.86666666667
Midmean - True Basic - Statistics Graphics Toolkit1089.96774193548
Midmean - MS Excel (old versions)1089.96774193548
Number of observations59



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')