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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 computationFri, 26 Nov 2010 23:41:32 +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/Nov/27/t12908163196galg86jqxwxxkc.htm/, Retrieved Mon, 29 Apr 2024 11:28:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102284, Retrieved Mon, 29 Apr 2024 11:28:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact151
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [minitut w6 - xt1] [2010-11-26 23:41:32] [54d0a09f418287eaabab8ba43e4b06f8] [Current]
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Dataseries X:
681
608
678
739
707
684
596
729
732
386
331
703
739
651
653
628
658
724
674
631
686
392
348
784
875
659
629
679
615
716
723
641
754
729
535
922
828
710
858
775
785
1006
789
734
906
536
394
991
841
892
782
813
793
978
775
797
946
594
438
1022
868




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102284&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102284&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102284&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean712.62295081967220.093281969156735.4657318756365
Geometric Mean693.060211834238
Harmonic Mean670.060718229844
Quadratic Mean729.421598838737
Winsorized Mean ( 1 / 20 )712.63934426229519.940883022838735.7376021636601
Winsorized Mean ( 2 / 20 )713.3934426229519.457355341334936.6644608225573
Winsorized Mean ( 3 / 20 )713.04918032786919.225458790343237.0887991856937
Winsorized Mean ( 4 / 20 )711.08196721311518.728098977248637.9687211220399
Winsorized Mean ( 5 / 20 )712.7213114754117.337963827915641.1075555670423
Winsorized Mean ( 6 / 20 )720.68852459016414.732357995996148.9187491090042
Winsorized Mean ( 7 / 20 )719.19672131147514.378733911296750.0180840502538
Winsorized Mean ( 8 / 20 )724.57377049180312.448241673987058.2069170464406
Winsorized Mean ( 9 / 20 )723.8360655737712.190858806110859.3753136744508
Winsorized Mean ( 10 / 20 )724.1639344262311.533490799199962.78792319117
Winsorized Mean ( 11 / 20 )722.36065573770510.743330191304367.2380577413869
Winsorized Mean ( 12 / 20 )722.3606557377059.862138031391173.2458472431067
Winsorized Mean ( 13 / 20 )719.3770491803289.2730340568718477.5773112412144
Winsorized Mean ( 14 / 20 )716.163934426238.6005203911644583.2698373882079
Winsorized Mean ( 15 / 20 )717.6393442622958.0484201615384589.1652435954734
Winsorized Mean ( 16 / 20 )719.2131147540987.477072962343496.189126196341
Winsorized Mean ( 17 / 20 )718.6557377049187.220375133901599.5316343510527
Winsorized Mean ( 18 / 20 )719.836065573776.95391466304498103.515228537270
Winsorized Mean ( 19 / 20 )719.5245901639346.81226018507571105.622006590451
Winsorized Mean ( 20 / 20 )722.1475409836075.75220727724782125.542684082331
Trimmed Mean ( 1 / 20 )713.84745762711919.006978532618137.5571244215422
Trimmed Mean ( 2 / 20 )715.14035087719317.849244042957940.0655820020197
Trimmed Mean ( 3 / 20 )716.10909090909116.741984819865342.7732493258139
Trimmed Mean ( 4 / 20 )717.28301886792515.460595949401846.3942671560261
Trimmed Mean ( 5 / 20 )719.1372549019614.027536493789051.2661118522396
Trimmed Mean ( 6 / 20 )720.73469387755112.735061126529156.594521747222
Trimmed Mean ( 7 / 20 )720.74468085106412.025084331417959.9367672597503
Trimmed Mean ( 8 / 20 )721.04444444444411.217948981389064.275960395317
Trimmed Mean ( 9 / 20 )720.41860465116310.765507887997466.9191469781346
Trimmed Mean ( 10 / 20 )719.85365853658510.242043966142870.2841796926679
Trimmed Mean ( 11 / 20 )719.1794871794879.734038930126373.8829474940425
Trimmed Mean ( 12 / 20 )718.7027027027039.280405337080877.4430293288002
Trimmed Mean ( 13 / 20 )718.1714285714298.9130709148560780.575082980031
Trimmed Mean ( 14 / 20 )7188.5718885157981883.7621719737383
Trimmed Mean ( 15 / 20 )718.2580645161298.281339009430186.7321170765063
Trimmed Mean ( 16 / 20 )718.3448275862078.0197225886675689.572278796935
Trimmed Mean ( 17 / 20 )718.2222222222227.7988116074264392.0938033095061
Trimmed Mean ( 18 / 20 )718.167.5258842226899495.4253319277495
Trimmed Mean ( 19 / 20 )717.9130434782617.17205629343487100.098634771651
Trimmed Mean ( 20 / 20 )717.6666666666676.6276237691496108.284159098963
Median723
Midrange676.5
Midmean - Weighted Average at Xnp715.766666666667
Midmean - Weighted Average at X(n+1)p718.258064516129
Midmean - Empirical Distribution Function718.258064516129
Midmean - Empirical Distribution Function - Averaging718.258064516129
Midmean - Empirical Distribution Function - Interpolation718.258064516129
Midmean - Closest Observation715.53125
Midmean - True Basic - Statistics Graphics Toolkit718.258064516129
Midmean - MS Excel (old versions)718.258064516129
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 712.622950819672 & 20.0932819691567 & 35.4657318756365 \tabularnewline
Geometric Mean & 693.060211834238 &  &  \tabularnewline
Harmonic Mean & 670.060718229844 &  &  \tabularnewline
Quadratic Mean & 729.421598838737 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 712.639344262295 & 19.9408830228387 & 35.7376021636601 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 713.39344262295 & 19.4573553413349 & 36.6644608225573 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 713.049180327869 & 19.2254587903432 & 37.0887991856937 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 711.081967213115 & 18.7280989772486 & 37.9687211220399 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 712.72131147541 & 17.3379638279156 & 41.1075555670423 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 720.688524590164 & 14.7323579959961 & 48.9187491090042 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 719.196721311475 & 14.3787339112967 & 50.0180840502538 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 724.573770491803 & 12.4482416739870 & 58.2069170464406 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 723.83606557377 & 12.1908588061108 & 59.3753136744508 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 724.16393442623 & 11.5334907991999 & 62.78792319117 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 722.360655737705 & 10.7433301913043 & 67.2380577413869 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 722.360655737705 & 9.8621380313911 & 73.2458472431067 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 719.377049180328 & 9.27303405687184 & 77.5773112412144 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 716.16393442623 & 8.60052039116445 & 83.2698373882079 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 717.639344262295 & 8.04842016153845 & 89.1652435954734 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 719.213114754098 & 7.4770729623434 & 96.189126196341 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 718.655737704918 & 7.2203751339015 & 99.5316343510527 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 719.83606557377 & 6.95391466304498 & 103.515228537270 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 719.524590163934 & 6.81226018507571 & 105.622006590451 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 722.147540983607 & 5.75220727724782 & 125.542684082331 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 713.847457627119 & 19.0069785326181 & 37.5571244215422 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 715.140350877193 & 17.8492440429579 & 40.0655820020197 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 716.109090909091 & 16.7419848198653 & 42.7732493258139 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 717.283018867925 & 15.4605959494018 & 46.3942671560261 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 719.13725490196 & 14.0275364937890 & 51.2661118522396 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 720.734693877551 & 12.7350611265291 & 56.594521747222 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 720.744680851064 & 12.0250843314179 & 59.9367672597503 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 721.044444444444 & 11.2179489813890 & 64.275960395317 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 720.418604651163 & 10.7655078879974 & 66.9191469781346 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 719.853658536585 & 10.2420439661428 & 70.2841796926679 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 719.179487179487 & 9.7340389301263 & 73.8829474940425 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 718.702702702703 & 9.2804053370808 & 77.4430293288002 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 718.171428571429 & 8.91307091485607 & 80.575082980031 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 718 & 8.57188851579818 & 83.7621719737383 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 718.258064516129 & 8.2813390094301 & 86.7321170765063 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 718.344827586207 & 8.01972258866756 & 89.572278796935 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 718.222222222222 & 7.79881160742643 & 92.0938033095061 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 718.16 & 7.52588422268994 & 95.4253319277495 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 717.913043478261 & 7.17205629343487 & 100.098634771651 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 717.666666666667 & 6.6276237691496 & 108.284159098963 \tabularnewline
Median & 723 &  &  \tabularnewline
Midrange & 676.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 715.766666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 718.258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 718.258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 718.258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 718.258064516129 &  &  \tabularnewline
Midmean - Closest Observation & 715.53125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 718.258064516129 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 718.258064516129 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102284&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]712.622950819672[/C][C]20.0932819691567[/C][C]35.4657318756365[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]693.060211834238[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]670.060718229844[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]729.421598838737[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]712.639344262295[/C][C]19.9408830228387[/C][C]35.7376021636601[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]713.39344262295[/C][C]19.4573553413349[/C][C]36.6644608225573[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]713.049180327869[/C][C]19.2254587903432[/C][C]37.0887991856937[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]711.081967213115[/C][C]18.7280989772486[/C][C]37.9687211220399[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]712.72131147541[/C][C]17.3379638279156[/C][C]41.1075555670423[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]720.688524590164[/C][C]14.7323579959961[/C][C]48.9187491090042[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]719.196721311475[/C][C]14.3787339112967[/C][C]50.0180840502538[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]724.573770491803[/C][C]12.4482416739870[/C][C]58.2069170464406[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]723.83606557377[/C][C]12.1908588061108[/C][C]59.3753136744508[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]724.16393442623[/C][C]11.5334907991999[/C][C]62.78792319117[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]722.360655737705[/C][C]10.7433301913043[/C][C]67.2380577413869[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]722.360655737705[/C][C]9.8621380313911[/C][C]73.2458472431067[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]719.377049180328[/C][C]9.27303405687184[/C][C]77.5773112412144[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]716.16393442623[/C][C]8.60052039116445[/C][C]83.2698373882079[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]717.639344262295[/C][C]8.04842016153845[/C][C]89.1652435954734[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]719.213114754098[/C][C]7.4770729623434[/C][C]96.189126196341[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]718.655737704918[/C][C]7.2203751339015[/C][C]99.5316343510527[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]719.83606557377[/C][C]6.95391466304498[/C][C]103.515228537270[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]719.524590163934[/C][C]6.81226018507571[/C][C]105.622006590451[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]722.147540983607[/C][C]5.75220727724782[/C][C]125.542684082331[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]713.847457627119[/C][C]19.0069785326181[/C][C]37.5571244215422[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]715.140350877193[/C][C]17.8492440429579[/C][C]40.0655820020197[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]716.109090909091[/C][C]16.7419848198653[/C][C]42.7732493258139[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]717.283018867925[/C][C]15.4605959494018[/C][C]46.3942671560261[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]719.13725490196[/C][C]14.0275364937890[/C][C]51.2661118522396[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]720.734693877551[/C][C]12.7350611265291[/C][C]56.594521747222[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]720.744680851064[/C][C]12.0250843314179[/C][C]59.9367672597503[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]721.044444444444[/C][C]11.2179489813890[/C][C]64.275960395317[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]720.418604651163[/C][C]10.7655078879974[/C][C]66.9191469781346[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]719.853658536585[/C][C]10.2420439661428[/C][C]70.2841796926679[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]719.179487179487[/C][C]9.7340389301263[/C][C]73.8829474940425[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]718.702702702703[/C][C]9.2804053370808[/C][C]77.4430293288002[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]718.171428571429[/C][C]8.91307091485607[/C][C]80.575082980031[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]718[/C][C]8.57188851579818[/C][C]83.7621719737383[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]718.258064516129[/C][C]8.2813390094301[/C][C]86.7321170765063[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]718.344827586207[/C][C]8.01972258866756[/C][C]89.572278796935[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]718.222222222222[/C][C]7.79881160742643[/C][C]92.0938033095061[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]718.16[/C][C]7.52588422268994[/C][C]95.4253319277495[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]717.913043478261[/C][C]7.17205629343487[/C][C]100.098634771651[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]717.666666666667[/C][C]6.6276237691496[/C][C]108.284159098963[/C][/ROW]
[ROW][C]Median[/C][C]723[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]676.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]715.766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]718.258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]718.258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]718.258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]718.258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]715.53125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]718.258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]718.258064516129[/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=102284&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102284&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 Mean712.62295081967220.093281969156735.4657318756365
Geometric Mean693.060211834238
Harmonic Mean670.060718229844
Quadratic Mean729.421598838737
Winsorized Mean ( 1 / 20 )712.63934426229519.940883022838735.7376021636601
Winsorized Mean ( 2 / 20 )713.3934426229519.457355341334936.6644608225573
Winsorized Mean ( 3 / 20 )713.04918032786919.225458790343237.0887991856937
Winsorized Mean ( 4 / 20 )711.08196721311518.728098977248637.9687211220399
Winsorized Mean ( 5 / 20 )712.7213114754117.337963827915641.1075555670423
Winsorized Mean ( 6 / 20 )720.68852459016414.732357995996148.9187491090042
Winsorized Mean ( 7 / 20 )719.19672131147514.378733911296750.0180840502538
Winsorized Mean ( 8 / 20 )724.57377049180312.448241673987058.2069170464406
Winsorized Mean ( 9 / 20 )723.8360655737712.190858806110859.3753136744508
Winsorized Mean ( 10 / 20 )724.1639344262311.533490799199962.78792319117
Winsorized Mean ( 11 / 20 )722.36065573770510.743330191304367.2380577413869
Winsorized Mean ( 12 / 20 )722.3606557377059.862138031391173.2458472431067
Winsorized Mean ( 13 / 20 )719.3770491803289.2730340568718477.5773112412144
Winsorized Mean ( 14 / 20 )716.163934426238.6005203911644583.2698373882079
Winsorized Mean ( 15 / 20 )717.6393442622958.0484201615384589.1652435954734
Winsorized Mean ( 16 / 20 )719.2131147540987.477072962343496.189126196341
Winsorized Mean ( 17 / 20 )718.6557377049187.220375133901599.5316343510527
Winsorized Mean ( 18 / 20 )719.836065573776.95391466304498103.515228537270
Winsorized Mean ( 19 / 20 )719.5245901639346.81226018507571105.622006590451
Winsorized Mean ( 20 / 20 )722.1475409836075.75220727724782125.542684082331
Trimmed Mean ( 1 / 20 )713.84745762711919.006978532618137.5571244215422
Trimmed Mean ( 2 / 20 )715.14035087719317.849244042957940.0655820020197
Trimmed Mean ( 3 / 20 )716.10909090909116.741984819865342.7732493258139
Trimmed Mean ( 4 / 20 )717.28301886792515.460595949401846.3942671560261
Trimmed Mean ( 5 / 20 )719.1372549019614.027536493789051.2661118522396
Trimmed Mean ( 6 / 20 )720.73469387755112.735061126529156.594521747222
Trimmed Mean ( 7 / 20 )720.74468085106412.025084331417959.9367672597503
Trimmed Mean ( 8 / 20 )721.04444444444411.217948981389064.275960395317
Trimmed Mean ( 9 / 20 )720.41860465116310.765507887997466.9191469781346
Trimmed Mean ( 10 / 20 )719.85365853658510.242043966142870.2841796926679
Trimmed Mean ( 11 / 20 )719.1794871794879.734038930126373.8829474940425
Trimmed Mean ( 12 / 20 )718.7027027027039.280405337080877.4430293288002
Trimmed Mean ( 13 / 20 )718.1714285714298.9130709148560780.575082980031
Trimmed Mean ( 14 / 20 )7188.5718885157981883.7621719737383
Trimmed Mean ( 15 / 20 )718.2580645161298.281339009430186.7321170765063
Trimmed Mean ( 16 / 20 )718.3448275862078.0197225886675689.572278796935
Trimmed Mean ( 17 / 20 )718.2222222222227.7988116074264392.0938033095061
Trimmed Mean ( 18 / 20 )718.167.5258842226899495.4253319277495
Trimmed Mean ( 19 / 20 )717.9130434782617.17205629343487100.098634771651
Trimmed Mean ( 20 / 20 )717.6666666666676.6276237691496108.284159098963
Median723
Midrange676.5
Midmean - Weighted Average at Xnp715.766666666667
Midmean - Weighted Average at X(n+1)p718.258064516129
Midmean - Empirical Distribution Function718.258064516129
Midmean - Empirical Distribution Function - Averaging718.258064516129
Midmean - Empirical Distribution Function - Interpolation718.258064516129
Midmean - Closest Observation715.53125
Midmean - True Basic - Statistics Graphics Toolkit718.258064516129
Midmean - MS Excel (old versions)718.258064516129
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')