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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, 14 Nov 2008 05:52:29 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/14/t1226667260bp00o3g9n6rz3pe.htm/, Retrieved Sat, 18 May 2024 22:03:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24931, Retrieved Sat, 18 May 2024 22:03:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact184
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper central ten...] [2008-11-14 12:52:29] [3817f5e632a8bfeb1be7b5e8c86bd450] [Current]
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Dataseries X:
12300.00
12092.80
12380.80
12196.90
9455.00
13168.00
13427.90
11980.50
11884.80
11691.70
12233.80
14341.40
13130.70
12421.10
14285.80
12864.60
11160.20
14316.20
14388.70
14013.90
13419.00
12769.60
13315.50
15332.90
14243.00
13824.40
14962.90
13202.90
12199.00
15508.90
14199.80
15169.60
14058.00
13786.20
14147.90
16541.70
13587.50
15582.40
15802.80
14130.50
12923.20
15612.20
16033.70
16036.60
14037.80
15330.60
15038.30
17401.80
14992.50
16043.70
16929.60
15921.30
14417.20
15961.00
17851.90
16483.90
14215.50
17429.70
17839.50
17629.20




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24931&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]3 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=24931&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24931&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean14294.1416666667233.33513902398661.2601330706444
Geometric Mean14179.6950373701
Harmonic Mean14062.6139136025
Quadratic Mean14406.0667055874
Winsorized Mean ( 1 / 20 )14322.355224.86956449528663.6918341179082
Winsorized Mean ( 2 / 20 )14333.0616666667219.12123626273465.4115589667486
Winsorized Mean ( 3 / 20 )14332.7416666667214.71007222448266.7539324921917
Winsorized Mean ( 4 / 20 )14337.2616666667213.04133842103167.2980266314894
Winsorized Mean ( 5 / 20 )14307.27202.16006085546470.7719909632849
Winsorized Mean ( 6 / 20 )14278.89192.09072683835774.3340932434267
Winsorized Mean ( 7 / 20 )14272.3916666667190.70974060031674.8382941623224
Winsorized Mean ( 8 / 20 )14218.3383333333178.98375803110279.4392658291521
Winsorized Mean ( 9 / 20 )14227.2033333333176.94973624734280.402512233454
Winsorized Mean ( 10 / 20 )14240.1866666667174.40587712112281.6496949628428
Winsorized Mean ( 11 / 20 )14234.2466666667170.76964365696583.3534951636943
Winsorized Mean ( 12 / 20 )14296.0066666667157.37205632589690.8420910321053
Winsorized Mean ( 13 / 20 )14290.915149.56819059355395.5478229915553
Winsorized Mean ( 14 / 20 )14260.115139.897972342983101.932249346967
Winsorized Mean ( 15 / 20 )14304.54130.505965276999109.608323034419
Winsorized Mean ( 16 / 20 )14294.8866666667125.762173506673113.666027455451
Winsorized Mean ( 17 / 20 )14254.9083333333116.248640847207122.624301062319
Winsorized Mean ( 18 / 20 )14287.9983333333111.039769851407128.674603274606
Winsorized Mean ( 19 / 20 )14269.7998.175828278615145.349321214826
Winsorized Mean ( 20 / 20 )14228.9991.0362229607558156.300311428055
Trimmed Mean ( 1 / 20 )14316.2344827586217.66585456637965.7716136105894
Trimmed Mean ( 2 / 20 )14309.6767857143208.78180121701868.538908574891
Trimmed Mean ( 3 / 20 )14296.6851851852201.64813381252270.8991693346254
Trimmed Mean ( 4 / 20 )14282.8173076923194.89292536770073.2854580572654
Trimmed Mean ( 5 / 20 )14266.484187.01689150732176.2844675954925
Trimmed Mean ( 6 / 20 )14256.2875180.94933968906878.7860708665593
Trimmed Mean ( 7 / 20 )14251.3739130435176.38636660196180.7963460418887
Trimmed Mean ( 8 / 20 )14247.2795454545170.81604002680583.4071527663256
Trimmed Mean ( 9 / 20 )14252.4476190476166.82220508558885.4349552071647
Trimmed Mean ( 10 / 20 )14256.655161.97240691526288.0190352882673
Trimmed Mean ( 11 / 20 )14259.2552631579156.07589405186191.3610352821033
Trimmed Mean ( 12 / 20 )14263.0444444444149.00316894704395.723094651186
Trimmed Mean ( 13 / 20 )14258.1970588235143.15475088264799.5998873311017
Trimmed Mean ( 14 / 20 )14253.478125137.169101821965103.911726005904
Trimmed Mean ( 15 / 20 )14252.53131.520933183723108.367007859430
Trimmed Mean ( 16 / 20 )14245.1126.095438680726112.970779506693
Trimmed Mean ( 17 / 20 )14237.9192307692119.368657143674119.276865229641
Trimmed Mean ( 18 / 20 )14235.4208333333112.541233181052126.490713056538
Trimmed Mean ( 19 / 20 )14227.4545454545103.450264045341137.529417413752
Trimmed Mean ( 20 / 20 )14220.7794.6207627432017150.292278224334
Median14207.65
Midrange13653.45
Midmean - Weighted Average at Xnp14209.6483870968
Midmean - Weighted Average at X(n+1)p14252.53
Midmean - Empirical Distribution Function14209.6483870968
Midmean - Empirical Distribution Function - Averaging14252.53
Midmean - Empirical Distribution Function - Interpolation14252.53
Midmean - Closest Observation14209.6483870968
Midmean - True Basic - Statistics Graphics Toolkit14252.53
Midmean - MS Excel (old versions)14253.478125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 14294.1416666667 & 233.335139023986 & 61.2601330706444 \tabularnewline
Geometric Mean & 14179.6950373701 &  &  \tabularnewline
Harmonic Mean & 14062.6139136025 &  &  \tabularnewline
Quadratic Mean & 14406.0667055874 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 14322.355 & 224.869564495286 & 63.6918341179082 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 14333.0616666667 & 219.121236262734 & 65.4115589667486 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 14332.7416666667 & 214.710072224482 & 66.7539324921917 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 14337.2616666667 & 213.041338421031 & 67.2980266314894 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 14307.27 & 202.160060855464 & 70.7719909632849 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 14278.89 & 192.090726838357 & 74.3340932434267 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 14272.3916666667 & 190.709740600316 & 74.8382941623224 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 14218.3383333333 & 178.983758031102 & 79.4392658291521 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 14227.2033333333 & 176.949736247342 & 80.402512233454 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 14240.1866666667 & 174.405877121122 & 81.6496949628428 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 14234.2466666667 & 170.769643656965 & 83.3534951636943 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 14296.0066666667 & 157.372056325896 & 90.8420910321053 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 14290.915 & 149.568190593553 & 95.5478229915553 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 14260.115 & 139.897972342983 & 101.932249346967 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 14304.54 & 130.505965276999 & 109.608323034419 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 14294.8866666667 & 125.762173506673 & 113.666027455451 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 14254.9083333333 & 116.248640847207 & 122.624301062319 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 14287.9983333333 & 111.039769851407 & 128.674603274606 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 14269.79 & 98.175828278615 & 145.349321214826 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 14228.99 & 91.0362229607558 & 156.300311428055 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 14316.2344827586 & 217.665854566379 & 65.7716136105894 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 14309.6767857143 & 208.781801217018 & 68.538908574891 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 14296.6851851852 & 201.648133812522 & 70.8991693346254 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 14282.8173076923 & 194.892925367700 & 73.2854580572654 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 14266.484 & 187.016891507321 & 76.2844675954925 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 14256.2875 & 180.949339689068 & 78.7860708665593 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 14251.3739130435 & 176.386366601961 & 80.7963460418887 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 14247.2795454545 & 170.816040026805 & 83.4071527663256 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 14252.4476190476 & 166.822205085588 & 85.4349552071647 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 14256.655 & 161.972406915262 & 88.0190352882673 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 14259.2552631579 & 156.075894051861 & 91.3610352821033 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 14263.0444444444 & 149.003168947043 & 95.723094651186 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 14258.1970588235 & 143.154750882647 & 99.5998873311017 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 14253.478125 & 137.169101821965 & 103.911726005904 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 14252.53 & 131.520933183723 & 108.367007859430 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 14245.1 & 126.095438680726 & 112.970779506693 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 14237.9192307692 & 119.368657143674 & 119.276865229641 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 14235.4208333333 & 112.541233181052 & 126.490713056538 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 14227.4545454545 & 103.450264045341 & 137.529417413752 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 14220.77 & 94.6207627432017 & 150.292278224334 \tabularnewline
Median & 14207.65 &  &  \tabularnewline
Midrange & 13653.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 14209.6483870968 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 14252.53 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 14209.6483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 14252.53 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 14252.53 &  &  \tabularnewline
Midmean - Closest Observation & 14209.6483870968 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 14252.53 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 14253.478125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24931&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]14294.1416666667[/C][C]233.335139023986[/C][C]61.2601330706444[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]14179.6950373701[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]14062.6139136025[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]14406.0667055874[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]14322.355[/C][C]224.869564495286[/C][C]63.6918341179082[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]14333.0616666667[/C][C]219.121236262734[/C][C]65.4115589667486[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]14332.7416666667[/C][C]214.710072224482[/C][C]66.7539324921917[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]14337.2616666667[/C][C]213.041338421031[/C][C]67.2980266314894[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]14307.27[/C][C]202.160060855464[/C][C]70.7719909632849[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]14278.89[/C][C]192.090726838357[/C][C]74.3340932434267[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]14272.3916666667[/C][C]190.709740600316[/C][C]74.8382941623224[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]14218.3383333333[/C][C]178.983758031102[/C][C]79.4392658291521[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]14227.2033333333[/C][C]176.949736247342[/C][C]80.402512233454[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]14240.1866666667[/C][C]174.405877121122[/C][C]81.6496949628428[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]14234.2466666667[/C][C]170.769643656965[/C][C]83.3534951636943[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]14296.0066666667[/C][C]157.372056325896[/C][C]90.8420910321053[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]14290.915[/C][C]149.568190593553[/C][C]95.5478229915553[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]14260.115[/C][C]139.897972342983[/C][C]101.932249346967[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]14304.54[/C][C]130.505965276999[/C][C]109.608323034419[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]14294.8866666667[/C][C]125.762173506673[/C][C]113.666027455451[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]14254.9083333333[/C][C]116.248640847207[/C][C]122.624301062319[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]14287.9983333333[/C][C]111.039769851407[/C][C]128.674603274606[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]14269.79[/C][C]98.175828278615[/C][C]145.349321214826[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]14228.99[/C][C]91.0362229607558[/C][C]156.300311428055[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]14316.2344827586[/C][C]217.665854566379[/C][C]65.7716136105894[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]14309.6767857143[/C][C]208.781801217018[/C][C]68.538908574891[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]14296.6851851852[/C][C]201.648133812522[/C][C]70.8991693346254[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]14282.8173076923[/C][C]194.892925367700[/C][C]73.2854580572654[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]14266.484[/C][C]187.016891507321[/C][C]76.2844675954925[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]14256.2875[/C][C]180.949339689068[/C][C]78.7860708665593[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]14251.3739130435[/C][C]176.386366601961[/C][C]80.7963460418887[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]14247.2795454545[/C][C]170.816040026805[/C][C]83.4071527663256[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]14252.4476190476[/C][C]166.822205085588[/C][C]85.4349552071647[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]14256.655[/C][C]161.972406915262[/C][C]88.0190352882673[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]14259.2552631579[/C][C]156.075894051861[/C][C]91.3610352821033[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]14263.0444444444[/C][C]149.003168947043[/C][C]95.723094651186[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]14258.1970588235[/C][C]143.154750882647[/C][C]99.5998873311017[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]14253.478125[/C][C]137.169101821965[/C][C]103.911726005904[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]14252.53[/C][C]131.520933183723[/C][C]108.367007859430[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]14245.1[/C][C]126.095438680726[/C][C]112.970779506693[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]14237.9192307692[/C][C]119.368657143674[/C][C]119.276865229641[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]14235.4208333333[/C][C]112.541233181052[/C][C]126.490713056538[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]14227.4545454545[/C][C]103.450264045341[/C][C]137.529417413752[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]14220.77[/C][C]94.6207627432017[/C][C]150.292278224334[/C][/ROW]
[ROW][C]Median[/C][C]14207.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]13653.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]14209.6483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]14252.53[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]14209.6483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]14252.53[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]14252.53[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]14209.6483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]14252.53[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]14253.478125[/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=24931&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24931&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 Mean14294.1416666667233.33513902398661.2601330706444
Geometric Mean14179.6950373701
Harmonic Mean14062.6139136025
Quadratic Mean14406.0667055874
Winsorized Mean ( 1 / 20 )14322.355224.86956449528663.6918341179082
Winsorized Mean ( 2 / 20 )14333.0616666667219.12123626273465.4115589667486
Winsorized Mean ( 3 / 20 )14332.7416666667214.71007222448266.7539324921917
Winsorized Mean ( 4 / 20 )14337.2616666667213.04133842103167.2980266314894
Winsorized Mean ( 5 / 20 )14307.27202.16006085546470.7719909632849
Winsorized Mean ( 6 / 20 )14278.89192.09072683835774.3340932434267
Winsorized Mean ( 7 / 20 )14272.3916666667190.70974060031674.8382941623224
Winsorized Mean ( 8 / 20 )14218.3383333333178.98375803110279.4392658291521
Winsorized Mean ( 9 / 20 )14227.2033333333176.94973624734280.402512233454
Winsorized Mean ( 10 / 20 )14240.1866666667174.40587712112281.6496949628428
Winsorized Mean ( 11 / 20 )14234.2466666667170.76964365696583.3534951636943
Winsorized Mean ( 12 / 20 )14296.0066666667157.37205632589690.8420910321053
Winsorized Mean ( 13 / 20 )14290.915149.56819059355395.5478229915553
Winsorized Mean ( 14 / 20 )14260.115139.897972342983101.932249346967
Winsorized Mean ( 15 / 20 )14304.54130.505965276999109.608323034419
Winsorized Mean ( 16 / 20 )14294.8866666667125.762173506673113.666027455451
Winsorized Mean ( 17 / 20 )14254.9083333333116.248640847207122.624301062319
Winsorized Mean ( 18 / 20 )14287.9983333333111.039769851407128.674603274606
Winsorized Mean ( 19 / 20 )14269.7998.175828278615145.349321214826
Winsorized Mean ( 20 / 20 )14228.9991.0362229607558156.300311428055
Trimmed Mean ( 1 / 20 )14316.2344827586217.66585456637965.7716136105894
Trimmed Mean ( 2 / 20 )14309.6767857143208.78180121701868.538908574891
Trimmed Mean ( 3 / 20 )14296.6851851852201.64813381252270.8991693346254
Trimmed Mean ( 4 / 20 )14282.8173076923194.89292536770073.2854580572654
Trimmed Mean ( 5 / 20 )14266.484187.01689150732176.2844675954925
Trimmed Mean ( 6 / 20 )14256.2875180.94933968906878.7860708665593
Trimmed Mean ( 7 / 20 )14251.3739130435176.38636660196180.7963460418887
Trimmed Mean ( 8 / 20 )14247.2795454545170.81604002680583.4071527663256
Trimmed Mean ( 9 / 20 )14252.4476190476166.82220508558885.4349552071647
Trimmed Mean ( 10 / 20 )14256.655161.97240691526288.0190352882673
Trimmed Mean ( 11 / 20 )14259.2552631579156.07589405186191.3610352821033
Trimmed Mean ( 12 / 20 )14263.0444444444149.00316894704395.723094651186
Trimmed Mean ( 13 / 20 )14258.1970588235143.15475088264799.5998873311017
Trimmed Mean ( 14 / 20 )14253.478125137.169101821965103.911726005904
Trimmed Mean ( 15 / 20 )14252.53131.520933183723108.367007859430
Trimmed Mean ( 16 / 20 )14245.1126.095438680726112.970779506693
Trimmed Mean ( 17 / 20 )14237.9192307692119.368657143674119.276865229641
Trimmed Mean ( 18 / 20 )14235.4208333333112.541233181052126.490713056538
Trimmed Mean ( 19 / 20 )14227.4545454545103.450264045341137.529417413752
Trimmed Mean ( 20 / 20 )14220.7794.6207627432017150.292278224334
Median14207.65
Midrange13653.45
Midmean - Weighted Average at Xnp14209.6483870968
Midmean - Weighted Average at X(n+1)p14252.53
Midmean - Empirical Distribution Function14209.6483870968
Midmean - Empirical Distribution Function - Averaging14252.53
Midmean - Empirical Distribution Function - Interpolation14252.53
Midmean - Closest Observation14209.6483870968
Midmean - True Basic - Statistics Graphics Toolkit14252.53
Midmean - MS Excel (old versions)14253.478125
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')