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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 computationTue, 20 Oct 2009 09:12:53 -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/20/t1256051764a5k3hprgwqjrs4n.htm/, Retrieved Fri, 03 May 2024 01:55:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48718, Retrieved Fri, 03 May 2024 01:55:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsgetrimd gemiddelde, part 2 1e vraag
Estimated Impact92
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [shw ws 2 2/4] [2009-10-11 14:32:04] [55b7a497389226c9339ee8d75ebc3b97]
- RMP     [Central Tendency] [shw ws 3 8] [2009-10-20 15:12:53] [84778c3520b84fd5786bccf2e25a5aef] [Current]
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Dataseries X:
29.837
29.571
30.167
30.524
30.996
31.033
31.198
30.937
31.649
33.115
34.106
33.926
33.382
32.851
32.948
36.112
36.113
35.210
35.193
34.383
35.349
37.058
38.076
36.630
36.045
35.638
35.114
35.465
35.254
35.299
35.916
36.683
37.288
38.536
38.977
36.407
34.955
34.951
32.680
34.791
34.178
35.213
34.871
35.299
35.443
37.108
36.419
34.471
33.868
34.385
33.643
34.627
32.919
35.500
36.110
37.086
37.711
40.427
39.884
38.512
38.767




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=48718&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=48718&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48718&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 Mean34.93121311475410.3157197485517110.639937080255
Geometric Mean34.8443028129684
Harmonic Mean34.7560160754844
Quadratic Mean35.0167158261008
Winsorized Mean ( 1 / 20 )34.92667213114750.3120395105301111.930287519723
Winsorized Mean ( 2 / 20 )34.90775409836070.301864422989069115.640504279051
Winsorized Mean ( 3 / 20 )34.91498360655740.295104181373923118.314093158568
Winsorized Mean ( 4 / 20 )34.92691803278690.285341902380536122.403747018578
Winsorized Mean ( 5 / 20 )34.92978688524590.283805499966687123.076497422869
Winsorized Mean ( 6 / 20 )34.89054098360660.274291362750736127.202477809385
Winsorized Mean ( 7 / 20 )34.86759016393440.262014711322107133.074933037138
Winsorized Mean ( 8 / 20 )34.8712622950820.238734775100792146.066957695457
Winsorized Mean ( 9 / 20 )34.99681967213110.202354138938305172.94837583135
Winsorized Mean ( 10 / 20 )35.02124590163930.196468239699921178.253981178483
Winsorized Mean ( 11 / 20 )35.02845901639340.19334055937189181.174912962863
Winsorized Mean ( 12 / 20 )34.96039344262300.179931547820060194.298297692548
Winsorized Mean ( 13 / 20 )34.98468852459020.171576847223831203.900987170786
Winsorized Mean ( 14 / 20 )34.99754098360660.152983356667844228.766983192772
Winsorized Mean ( 15 / 20 )35.05877049180330.141510366480881247.747012205921
Winsorized Mean ( 16 / 20 )35.04067213114750.119867273413928292.328932936887
Winsorized Mean ( 17 / 20 )35.05655737704920.117208330063985299.0961253173
Winsorized Mean ( 18 / 20 )35.10908196721310.108760151953968322.811998111889
Winsorized Mean ( 19 / 20 )35.11126229508200.102236041311136343.433312213522
Winsorized Mean ( 20 / 20 )35.13618032786880.0857619163069018409.694440620157
Trimmed Mean ( 1 / 20 )34.92891525423730.298979915125144116.826962237972
Trimmed Mean ( 2 / 20 )34.93131578947370.282869475995217123.489166395827
Trimmed Mean ( 3 / 20 )34.94438181818180.269887539231181129.477566536516
Trimmed Mean ( 4 / 20 )34.95566037735850.257100716886699135.960960360772
Trimmed Mean ( 5 / 20 )34.96425490196080.245110231853595142.647063884485
Trimmed Mean ( 6 / 20 )34.97283673469390.230409614450158151.785492190297
Trimmed Mean ( 7 / 20 )34.99063829787230.214740700348690162.943672257078
Trimmed Mean ( 8 / 20 )35.01446666666670.198335894050187176.541250056365
Trimmed Mean ( 9 / 20 )35.03986046511630.184331516739707190.091532283087
Trimmed Mean ( 10 / 20 )35.04697560975610.177235280058241197.742659352243
Trimmed Mean ( 11 / 20 )35.0510.169415291991584206.893956194587
Trimmed Mean ( 12 / 20 )35.05437837837840.159677294457892219.532642367149
Trimmed Mean ( 13 / 20 )35.06802857142860.150254766759573233.390456274456
Trimmed Mean ( 14 / 20 )35.07987878787880.139694334590279251.118836642642
Trimmed Mean ( 15 / 20 )35.09145161290320.130866137291884268.147683878185
Trimmed Mean ( 16 / 20 )35.09603448275860.122060718181775287.529313324971
Trimmed Mean ( 17 / 20 )35.10385185185190.116659971770101300.907426250968
Trimmed Mean ( 18 / 20 )35.110640.109156262303177321.65483921098
Trimmed Mean ( 19 / 20 )35.11086956521740.100797517543225348.3306972333
Trimmed Mean ( 20 / 20 )35.11080952380950.089949526032993390.33901647165
Median35.21
Midrange34.999
Midmean - Weighted Average at Xnp35.0476
Midmean - Weighted Average at X(n+1)p35.0914516129032
Midmean - Empirical Distribution Function35.0914516129032
Midmean - Empirical Distribution Function - Averaging35.0914516129032
Midmean - Empirical Distribution Function - Interpolation35.0914516129032
Midmean - Closest Observation35.03803125
Midmean - True Basic - Statistics Graphics Toolkit35.0914516129032
Midmean - MS Excel (old versions)35.0914516129032
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 34.9312131147541 & 0.3157197485517 & 110.639937080255 \tabularnewline
Geometric Mean & 34.8443028129684 &  &  \tabularnewline
Harmonic Mean & 34.7560160754844 &  &  \tabularnewline
Quadratic Mean & 35.0167158261008 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 34.9266721311475 & 0.3120395105301 & 111.930287519723 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 34.9077540983607 & 0.301864422989069 & 115.640504279051 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 34.9149836065574 & 0.295104181373923 & 118.314093158568 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 34.9269180327869 & 0.285341902380536 & 122.403747018578 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 34.9297868852459 & 0.283805499966687 & 123.076497422869 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 34.8905409836066 & 0.274291362750736 & 127.202477809385 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 34.8675901639344 & 0.262014711322107 & 133.074933037138 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 34.871262295082 & 0.238734775100792 & 146.066957695457 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 34.9968196721311 & 0.202354138938305 & 172.94837583135 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 35.0212459016393 & 0.196468239699921 & 178.253981178483 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 35.0284590163934 & 0.19334055937189 & 181.174912962863 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 34.9603934426230 & 0.179931547820060 & 194.298297692548 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 34.9846885245902 & 0.171576847223831 & 203.900987170786 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 34.9975409836066 & 0.152983356667844 & 228.766983192772 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 35.0587704918033 & 0.141510366480881 & 247.747012205921 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 35.0406721311475 & 0.119867273413928 & 292.328932936887 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 35.0565573770492 & 0.117208330063985 & 299.0961253173 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 35.1090819672131 & 0.108760151953968 & 322.811998111889 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 35.1112622950820 & 0.102236041311136 & 343.433312213522 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 35.1361803278688 & 0.0857619163069018 & 409.694440620157 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 34.9289152542373 & 0.298979915125144 & 116.826962237972 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 34.9313157894737 & 0.282869475995217 & 123.489166395827 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 34.9443818181818 & 0.269887539231181 & 129.477566536516 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 34.9556603773585 & 0.257100716886699 & 135.960960360772 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 34.9642549019608 & 0.245110231853595 & 142.647063884485 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 34.9728367346939 & 0.230409614450158 & 151.785492190297 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 34.9906382978723 & 0.214740700348690 & 162.943672257078 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 35.0144666666667 & 0.198335894050187 & 176.541250056365 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 35.0398604651163 & 0.184331516739707 & 190.091532283087 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 35.0469756097561 & 0.177235280058241 & 197.742659352243 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 35.051 & 0.169415291991584 & 206.893956194587 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 35.0543783783784 & 0.159677294457892 & 219.532642367149 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 35.0680285714286 & 0.150254766759573 & 233.390456274456 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 35.0798787878788 & 0.139694334590279 & 251.118836642642 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 35.0914516129032 & 0.130866137291884 & 268.147683878185 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 35.0960344827586 & 0.122060718181775 & 287.529313324971 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 35.1038518518519 & 0.116659971770101 & 300.907426250968 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 35.11064 & 0.109156262303177 & 321.65483921098 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 35.1108695652174 & 0.100797517543225 & 348.3306972333 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 35.1108095238095 & 0.089949526032993 & 390.33901647165 \tabularnewline
Median & 35.21 &  &  \tabularnewline
Midrange & 34.999 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 35.0476 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 35.0914516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 35.0914516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 35.0914516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 35.0914516129032 &  &  \tabularnewline
Midmean - Closest Observation & 35.03803125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 35.0914516129032 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 35.0914516129032 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48718&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]34.9312131147541[/C][C]0.3157197485517[/C][C]110.639937080255[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]34.8443028129684[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]34.7560160754844[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]35.0167158261008[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]34.9266721311475[/C][C]0.3120395105301[/C][C]111.930287519723[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]34.9077540983607[/C][C]0.301864422989069[/C][C]115.640504279051[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]34.9149836065574[/C][C]0.295104181373923[/C][C]118.314093158568[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]34.9269180327869[/C][C]0.285341902380536[/C][C]122.403747018578[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]34.9297868852459[/C][C]0.283805499966687[/C][C]123.076497422869[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]34.8905409836066[/C][C]0.274291362750736[/C][C]127.202477809385[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]34.8675901639344[/C][C]0.262014711322107[/C][C]133.074933037138[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]34.871262295082[/C][C]0.238734775100792[/C][C]146.066957695457[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]34.9968196721311[/C][C]0.202354138938305[/C][C]172.94837583135[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]35.0212459016393[/C][C]0.196468239699921[/C][C]178.253981178483[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]35.0284590163934[/C][C]0.19334055937189[/C][C]181.174912962863[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]34.9603934426230[/C][C]0.179931547820060[/C][C]194.298297692548[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]34.9846885245902[/C][C]0.171576847223831[/C][C]203.900987170786[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]34.9975409836066[/C][C]0.152983356667844[/C][C]228.766983192772[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]35.0587704918033[/C][C]0.141510366480881[/C][C]247.747012205921[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]35.0406721311475[/C][C]0.119867273413928[/C][C]292.328932936887[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]35.0565573770492[/C][C]0.117208330063985[/C][C]299.0961253173[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]35.1090819672131[/C][C]0.108760151953968[/C][C]322.811998111889[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]35.1112622950820[/C][C]0.102236041311136[/C][C]343.433312213522[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]35.1361803278688[/C][C]0.0857619163069018[/C][C]409.694440620157[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]34.9289152542373[/C][C]0.298979915125144[/C][C]116.826962237972[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]34.9313157894737[/C][C]0.282869475995217[/C][C]123.489166395827[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]34.9443818181818[/C][C]0.269887539231181[/C][C]129.477566536516[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]34.9556603773585[/C][C]0.257100716886699[/C][C]135.960960360772[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]34.9642549019608[/C][C]0.245110231853595[/C][C]142.647063884485[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]34.9728367346939[/C][C]0.230409614450158[/C][C]151.785492190297[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]34.9906382978723[/C][C]0.214740700348690[/C][C]162.943672257078[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]35.0144666666667[/C][C]0.198335894050187[/C][C]176.541250056365[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]35.0398604651163[/C][C]0.184331516739707[/C][C]190.091532283087[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]35.0469756097561[/C][C]0.177235280058241[/C][C]197.742659352243[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]35.051[/C][C]0.169415291991584[/C][C]206.893956194587[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]35.0543783783784[/C][C]0.159677294457892[/C][C]219.532642367149[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]35.0680285714286[/C][C]0.150254766759573[/C][C]233.390456274456[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]35.0798787878788[/C][C]0.139694334590279[/C][C]251.118836642642[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]35.0914516129032[/C][C]0.130866137291884[/C][C]268.147683878185[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]35.0960344827586[/C][C]0.122060718181775[/C][C]287.529313324971[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]35.1038518518519[/C][C]0.116659971770101[/C][C]300.907426250968[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]35.11064[/C][C]0.109156262303177[/C][C]321.65483921098[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]35.1108695652174[/C][C]0.100797517543225[/C][C]348.3306972333[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]35.1108095238095[/C][C]0.089949526032993[/C][C]390.33901647165[/C][/ROW]
[ROW][C]Median[/C][C]35.21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]34.999[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]35.0476[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]35.0914516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]35.0914516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]35.0914516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]35.0914516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]35.03803125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]35.0914516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]35.0914516129032[/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=48718&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48718&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 Mean34.93121311475410.3157197485517110.639937080255
Geometric Mean34.8443028129684
Harmonic Mean34.7560160754844
Quadratic Mean35.0167158261008
Winsorized Mean ( 1 / 20 )34.92667213114750.3120395105301111.930287519723
Winsorized Mean ( 2 / 20 )34.90775409836070.301864422989069115.640504279051
Winsorized Mean ( 3 / 20 )34.91498360655740.295104181373923118.314093158568
Winsorized Mean ( 4 / 20 )34.92691803278690.285341902380536122.403747018578
Winsorized Mean ( 5 / 20 )34.92978688524590.283805499966687123.076497422869
Winsorized Mean ( 6 / 20 )34.89054098360660.274291362750736127.202477809385
Winsorized Mean ( 7 / 20 )34.86759016393440.262014711322107133.074933037138
Winsorized Mean ( 8 / 20 )34.8712622950820.238734775100792146.066957695457
Winsorized Mean ( 9 / 20 )34.99681967213110.202354138938305172.94837583135
Winsorized Mean ( 10 / 20 )35.02124590163930.196468239699921178.253981178483
Winsorized Mean ( 11 / 20 )35.02845901639340.19334055937189181.174912962863
Winsorized Mean ( 12 / 20 )34.96039344262300.179931547820060194.298297692548
Winsorized Mean ( 13 / 20 )34.98468852459020.171576847223831203.900987170786
Winsorized Mean ( 14 / 20 )34.99754098360660.152983356667844228.766983192772
Winsorized Mean ( 15 / 20 )35.05877049180330.141510366480881247.747012205921
Winsorized Mean ( 16 / 20 )35.04067213114750.119867273413928292.328932936887
Winsorized Mean ( 17 / 20 )35.05655737704920.117208330063985299.0961253173
Winsorized Mean ( 18 / 20 )35.10908196721310.108760151953968322.811998111889
Winsorized Mean ( 19 / 20 )35.11126229508200.102236041311136343.433312213522
Winsorized Mean ( 20 / 20 )35.13618032786880.0857619163069018409.694440620157
Trimmed Mean ( 1 / 20 )34.92891525423730.298979915125144116.826962237972
Trimmed Mean ( 2 / 20 )34.93131578947370.282869475995217123.489166395827
Trimmed Mean ( 3 / 20 )34.94438181818180.269887539231181129.477566536516
Trimmed Mean ( 4 / 20 )34.95566037735850.257100716886699135.960960360772
Trimmed Mean ( 5 / 20 )34.96425490196080.245110231853595142.647063884485
Trimmed Mean ( 6 / 20 )34.97283673469390.230409614450158151.785492190297
Trimmed Mean ( 7 / 20 )34.99063829787230.214740700348690162.943672257078
Trimmed Mean ( 8 / 20 )35.01446666666670.198335894050187176.541250056365
Trimmed Mean ( 9 / 20 )35.03986046511630.184331516739707190.091532283087
Trimmed Mean ( 10 / 20 )35.04697560975610.177235280058241197.742659352243
Trimmed Mean ( 11 / 20 )35.0510.169415291991584206.893956194587
Trimmed Mean ( 12 / 20 )35.05437837837840.159677294457892219.532642367149
Trimmed Mean ( 13 / 20 )35.06802857142860.150254766759573233.390456274456
Trimmed Mean ( 14 / 20 )35.07987878787880.139694334590279251.118836642642
Trimmed Mean ( 15 / 20 )35.09145161290320.130866137291884268.147683878185
Trimmed Mean ( 16 / 20 )35.09603448275860.122060718181775287.529313324971
Trimmed Mean ( 17 / 20 )35.10385185185190.116659971770101300.907426250968
Trimmed Mean ( 18 / 20 )35.110640.109156262303177321.65483921098
Trimmed Mean ( 19 / 20 )35.11086956521740.100797517543225348.3306972333
Trimmed Mean ( 20 / 20 )35.11080952380950.089949526032993390.33901647165
Median35.21
Midrange34.999
Midmean - Weighted Average at Xnp35.0476
Midmean - Weighted Average at X(n+1)p35.0914516129032
Midmean - Empirical Distribution Function35.0914516129032
Midmean - Empirical Distribution Function - Averaging35.0914516129032
Midmean - Empirical Distribution Function - Interpolation35.0914516129032
Midmean - Closest Observation35.03803125
Midmean - True Basic - Statistics Graphics Toolkit35.0914516129032
Midmean - MS Excel (old versions)35.0914516129032
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')