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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 15:23:22 -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/t1255987667r5pwmaonzkzhg4s.htm/, Retrieved Mon, 29 Apr 2024 22:47:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48259, Retrieved Mon, 29 Apr 2024 22:47:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [workshop 3] [2009-10-19 21:23:22] [6c94b261890ba36343a04d1029691995] [Current]
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Dataseries X:
117596
114412
115305
115101
114261
113272
111126
109597
108918
119936
122989
121006
118999
116080
116600
115415
115129
113173
113001
111988
111342
120174
120840
120852
114494
110969
109112
110684
108237
103698
103254
99647
94171
105276
106457
103134
101036
97593
99329
100212
98916
94925
95056
89641
90407
100692
100869
100036
98528
99010
103515
107370
109092
110954
111016
108409
110390
120540
121751
120046




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48259&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48259&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48259&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108926.31109.2050131452098.2021346001086
Geometric Mean108585.604610720
Harmonic Mean108237.628708735
Quadratic Mean109258.997989182
Winsorized Mean ( 1 / 20 )108918.4333333331101.2499263142698.9043728682638
Winsorized Mean ( 2 / 20 )109019.0666666671063.65596283258102.494669776816
Winsorized Mean ( 3 / 20 )109049.0666666671053.44507493906103.516613500684
Winsorized Mean ( 4 / 20 )1090571051.31516263509103.733879122082
Winsorized Mean ( 5 / 20 )109243.4166666671001.78166799671109.049127326440
Winsorized Mean ( 6 / 20 )109300.316666667976.872099109137111.888052454711
Winsorized Mean ( 7 / 20 )109330.65965.691174221307113.214921000142
Winsorized Mean ( 8 / 20 )109328.516666667960.653173066037113.806438922938
Winsorized Mean ( 9 / 20 )109235.816666667926.24206317777117.934415860902
Winsorized Mean ( 10 / 20 )109054.983333333876.372731595728124.439042203838
Winsorized Mean ( 11 / 20 )108943.7834.122671240847130.608726697159
Winsorized Mean ( 12 / 20 )108874.9811.838324995934134.109091241221
Winsorized Mean ( 13 / 20 )108834.816666667771.87623473372141.000346647818
Winsorized Mean ( 14 / 20 )108850.45760.812367057234143.071346777689
Winsorized Mean ( 15 / 20 )108848.2747.102331459564145.693829903262
Winsorized Mean ( 16 / 20 )109400.2650.497770203364168.179208309659
Winsorized Mean ( 17 / 20 )109262.216666667619.843355048315176.273917880672
Winsorized Mean ( 18 / 20 )109315.916666667603.512608423689181.132780228384
Winsorized Mean ( 19 / 20 )109326.05587.258229336745186.163504466296
Winsorized Mean ( 20 / 20 )109522.383333333456.413753891198239.962933631141
Trimmed Mean ( 1 / 20 )109016.3448275861070.02778812675101.881788526667
Trimmed Mean ( 2 / 20 )109121.251031.3496006998105.804326608512
Trimmed Mean ( 3 / 20 )109178.0185185191008.56036825547108.251347122995
Trimmed Mean ( 4 / 20 )109227.615384615984.734726724144110.920852510174
Trimmed Mean ( 5 / 20 )109278.8955.294127160716114.392831373091
Trimmed Mean ( 6 / 20 )109287.645833333935.049759498922116.878962561200
Trimmed Mean ( 7 / 20 )109284.891304348916.351327172015119.260907976874
Trimmed Mean ( 8 / 20 )109275.977272727894.799288021747122.123451298579
Trimmed Mean ( 9 / 20 )109266.595238095867.475798736296125.959243355573
Trimmed Mean ( 10 / 20 )109271.725840.616762270189129.989942985313
Trimmed Mean ( 11 / 20 )109305.947368421817.822288642193133.654889193468
Trimmed Mean ( 12 / 20 )109360.833333333797.38463214894137.149411869912
Trimmed Mean ( 13 / 20 )109432.294117647773.971664984316141.390569020204
Trimmed Mean ( 14 / 20 )109518.46875751.135507329885145.803876506002
Trimmed Mean ( 15 / 20 )109613.9720.089750711993152.222552663218
Trimmed Mean ( 16 / 20 )109723.285714286677.285200641734162.004552307243
Trimmed Mean ( 17 / 20 )109769.884615385649.726295810363168.947886707395
Trimmed Mean ( 18 / 20 )109844.541666667616.038627444925178.307880014370
Trimmed Mean ( 19 / 20 )109924.636363636566.794119403021193.941031850180
Trimmed Mean ( 20 / 20 )110019.15488.462594996307225.235567937053
Median110537
Midrange106315
Midmean - Weighted Average at Xnp109331.806451613
Midmean - Weighted Average at X(n+1)p109613.9
Midmean - Empirical Distribution Function109331.806451613
Midmean - Empirical Distribution Function - Averaging109613.9
Midmean - Empirical Distribution Function - Interpolation109613.9
Midmean - Closest Observation109331.806451613
Midmean - True Basic - Statistics Graphics Toolkit109613.9
Midmean - MS Excel (old versions)109518.46875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108926.3 & 1109.20501314520 & 98.2021346001086 \tabularnewline
Geometric Mean & 108585.604610720 &  &  \tabularnewline
Harmonic Mean & 108237.628708735 &  &  \tabularnewline
Quadratic Mean & 109258.997989182 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 108918.433333333 & 1101.24992631426 & 98.9043728682638 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 109019.066666667 & 1063.65596283258 & 102.494669776816 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 109049.066666667 & 1053.44507493906 & 103.516613500684 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 109057 & 1051.31516263509 & 103.733879122082 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 109243.416666667 & 1001.78166799671 & 109.049127326440 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 109300.316666667 & 976.872099109137 & 111.888052454711 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 109330.65 & 965.691174221307 & 113.214921000142 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 109328.516666667 & 960.653173066037 & 113.806438922938 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 109235.816666667 & 926.24206317777 & 117.934415860902 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 109054.983333333 & 876.372731595728 & 124.439042203838 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 108943.7 & 834.122671240847 & 130.608726697159 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 108874.9 & 811.838324995934 & 134.109091241221 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 108834.816666667 & 771.87623473372 & 141.000346647818 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 108850.45 & 760.812367057234 & 143.071346777689 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 108848.2 & 747.102331459564 & 145.693829903262 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 109400.2 & 650.497770203364 & 168.179208309659 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 109262.216666667 & 619.843355048315 & 176.273917880672 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 109315.916666667 & 603.512608423689 & 181.132780228384 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 109326.05 & 587.258229336745 & 186.163504466296 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 109522.383333333 & 456.413753891198 & 239.962933631141 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 109016.344827586 & 1070.02778812675 & 101.881788526667 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 109121.25 & 1031.3496006998 & 105.804326608512 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 109178.018518519 & 1008.56036825547 & 108.251347122995 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 109227.615384615 & 984.734726724144 & 110.920852510174 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 109278.8 & 955.294127160716 & 114.392831373091 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 109287.645833333 & 935.049759498922 & 116.878962561200 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 109284.891304348 & 916.351327172015 & 119.260907976874 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 109275.977272727 & 894.799288021747 & 122.123451298579 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 109266.595238095 & 867.475798736296 & 125.959243355573 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 109271.725 & 840.616762270189 & 129.989942985313 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 109305.947368421 & 817.822288642193 & 133.654889193468 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 109360.833333333 & 797.38463214894 & 137.149411869912 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 109432.294117647 & 773.971664984316 & 141.390569020204 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 109518.46875 & 751.135507329885 & 145.803876506002 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 109613.9 & 720.089750711993 & 152.222552663218 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 109723.285714286 & 677.285200641734 & 162.004552307243 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 109769.884615385 & 649.726295810363 & 168.947886707395 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 109844.541666667 & 616.038627444925 & 178.307880014370 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 109924.636363636 & 566.794119403021 & 193.941031850180 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 110019.15 & 488.462594996307 & 225.235567937053 \tabularnewline
Median & 110537 &  &  \tabularnewline
Midrange & 106315 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 109331.806451613 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 109613.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 109331.806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 109613.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 109613.9 &  &  \tabularnewline
Midmean - Closest Observation & 109331.806451613 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 109613.9 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 109518.46875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48259&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]108926.3[/C][C]1109.20501314520[/C][C]98.2021346001086[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]108585.604610720[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]108237.628708735[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]109258.997989182[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]108918.433333333[/C][C]1101.24992631426[/C][C]98.9043728682638[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]109019.066666667[/C][C]1063.65596283258[/C][C]102.494669776816[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]109049.066666667[/C][C]1053.44507493906[/C][C]103.516613500684[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]109057[/C][C]1051.31516263509[/C][C]103.733879122082[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]109243.416666667[/C][C]1001.78166799671[/C][C]109.049127326440[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]109300.316666667[/C][C]976.872099109137[/C][C]111.888052454711[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]109330.65[/C][C]965.691174221307[/C][C]113.214921000142[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]109328.516666667[/C][C]960.653173066037[/C][C]113.806438922938[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]109235.816666667[/C][C]926.24206317777[/C][C]117.934415860902[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]109054.983333333[/C][C]876.372731595728[/C][C]124.439042203838[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]108943.7[/C][C]834.122671240847[/C][C]130.608726697159[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]108874.9[/C][C]811.838324995934[/C][C]134.109091241221[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]108834.816666667[/C][C]771.87623473372[/C][C]141.000346647818[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]108850.45[/C][C]760.812367057234[/C][C]143.071346777689[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]108848.2[/C][C]747.102331459564[/C][C]145.693829903262[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]109400.2[/C][C]650.497770203364[/C][C]168.179208309659[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]109262.216666667[/C][C]619.843355048315[/C][C]176.273917880672[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]109315.916666667[/C][C]603.512608423689[/C][C]181.132780228384[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]109326.05[/C][C]587.258229336745[/C][C]186.163504466296[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]109522.383333333[/C][C]456.413753891198[/C][C]239.962933631141[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]109016.344827586[/C][C]1070.02778812675[/C][C]101.881788526667[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]109121.25[/C][C]1031.3496006998[/C][C]105.804326608512[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]109178.018518519[/C][C]1008.56036825547[/C][C]108.251347122995[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]109227.615384615[/C][C]984.734726724144[/C][C]110.920852510174[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]109278.8[/C][C]955.294127160716[/C][C]114.392831373091[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]109287.645833333[/C][C]935.049759498922[/C][C]116.878962561200[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]109284.891304348[/C][C]916.351327172015[/C][C]119.260907976874[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]109275.977272727[/C][C]894.799288021747[/C][C]122.123451298579[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]109266.595238095[/C][C]867.475798736296[/C][C]125.959243355573[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]109271.725[/C][C]840.616762270189[/C][C]129.989942985313[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]109305.947368421[/C][C]817.822288642193[/C][C]133.654889193468[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]109360.833333333[/C][C]797.38463214894[/C][C]137.149411869912[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]109432.294117647[/C][C]773.971664984316[/C][C]141.390569020204[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]109518.46875[/C][C]751.135507329885[/C][C]145.803876506002[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]109613.9[/C][C]720.089750711993[/C][C]152.222552663218[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]109723.285714286[/C][C]677.285200641734[/C][C]162.004552307243[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]109769.884615385[/C][C]649.726295810363[/C][C]168.947886707395[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]109844.541666667[/C][C]616.038627444925[/C][C]178.307880014370[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]109924.636363636[/C][C]566.794119403021[/C][C]193.941031850180[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]110019.15[/C][C]488.462594996307[/C][C]225.235567937053[/C][/ROW]
[ROW][C]Median[/C][C]110537[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]106315[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]109331.806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]109613.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]109331.806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]109613.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]109613.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]109331.806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]109613.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]109518.46875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48259&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48259&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 Mean108926.31109.2050131452098.2021346001086
Geometric Mean108585.604610720
Harmonic Mean108237.628708735
Quadratic Mean109258.997989182
Winsorized Mean ( 1 / 20 )108918.4333333331101.2499263142698.9043728682638
Winsorized Mean ( 2 / 20 )109019.0666666671063.65596283258102.494669776816
Winsorized Mean ( 3 / 20 )109049.0666666671053.44507493906103.516613500684
Winsorized Mean ( 4 / 20 )1090571051.31516263509103.733879122082
Winsorized Mean ( 5 / 20 )109243.4166666671001.78166799671109.049127326440
Winsorized Mean ( 6 / 20 )109300.316666667976.872099109137111.888052454711
Winsorized Mean ( 7 / 20 )109330.65965.691174221307113.214921000142
Winsorized Mean ( 8 / 20 )109328.516666667960.653173066037113.806438922938
Winsorized Mean ( 9 / 20 )109235.816666667926.24206317777117.934415860902
Winsorized Mean ( 10 / 20 )109054.983333333876.372731595728124.439042203838
Winsorized Mean ( 11 / 20 )108943.7834.122671240847130.608726697159
Winsorized Mean ( 12 / 20 )108874.9811.838324995934134.109091241221
Winsorized Mean ( 13 / 20 )108834.816666667771.87623473372141.000346647818
Winsorized Mean ( 14 / 20 )108850.45760.812367057234143.071346777689
Winsorized Mean ( 15 / 20 )108848.2747.102331459564145.693829903262
Winsorized Mean ( 16 / 20 )109400.2650.497770203364168.179208309659
Winsorized Mean ( 17 / 20 )109262.216666667619.843355048315176.273917880672
Winsorized Mean ( 18 / 20 )109315.916666667603.512608423689181.132780228384
Winsorized Mean ( 19 / 20 )109326.05587.258229336745186.163504466296
Winsorized Mean ( 20 / 20 )109522.383333333456.413753891198239.962933631141
Trimmed Mean ( 1 / 20 )109016.3448275861070.02778812675101.881788526667
Trimmed Mean ( 2 / 20 )109121.251031.3496006998105.804326608512
Trimmed Mean ( 3 / 20 )109178.0185185191008.56036825547108.251347122995
Trimmed Mean ( 4 / 20 )109227.615384615984.734726724144110.920852510174
Trimmed Mean ( 5 / 20 )109278.8955.294127160716114.392831373091
Trimmed Mean ( 6 / 20 )109287.645833333935.049759498922116.878962561200
Trimmed Mean ( 7 / 20 )109284.891304348916.351327172015119.260907976874
Trimmed Mean ( 8 / 20 )109275.977272727894.799288021747122.123451298579
Trimmed Mean ( 9 / 20 )109266.595238095867.475798736296125.959243355573
Trimmed Mean ( 10 / 20 )109271.725840.616762270189129.989942985313
Trimmed Mean ( 11 / 20 )109305.947368421817.822288642193133.654889193468
Trimmed Mean ( 12 / 20 )109360.833333333797.38463214894137.149411869912
Trimmed Mean ( 13 / 20 )109432.294117647773.971664984316141.390569020204
Trimmed Mean ( 14 / 20 )109518.46875751.135507329885145.803876506002
Trimmed Mean ( 15 / 20 )109613.9720.089750711993152.222552663218
Trimmed Mean ( 16 / 20 )109723.285714286677.285200641734162.004552307243
Trimmed Mean ( 17 / 20 )109769.884615385649.726295810363168.947886707395
Trimmed Mean ( 18 / 20 )109844.541666667616.038627444925178.307880014370
Trimmed Mean ( 19 / 20 )109924.636363636566.794119403021193.941031850180
Trimmed Mean ( 20 / 20 )110019.15488.462594996307225.235567937053
Median110537
Midrange106315
Midmean - Weighted Average at Xnp109331.806451613
Midmean - Weighted Average at X(n+1)p109613.9
Midmean - Empirical Distribution Function109331.806451613
Midmean - Empirical Distribution Function - Averaging109613.9
Midmean - Empirical Distribution Function - Interpolation109613.9
Midmean - Closest Observation109331.806451613
Midmean - True Basic - Statistics Graphics Toolkit109613.9
Midmean - MS Excel (old versions)109518.46875
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')