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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, 20 Oct 2008 13:33:08 -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/2008/Oct/20/t1224531872hyirnjw6hjl7i8z.htm/, Retrieved Sun, 19 May 2024 01:53:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17994, Retrieved Sun, 19 May 2024 01:53:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Investigating Ass...] [2007-10-22 10:34:53] [b9964c45117f7aac638ab9056d451faa]
-    D    [Central Tendency] [Central tendency ] [2008-10-20 19:33:08] [7ed4ec9f8cdf7df79ef87b9dc09dff20] [Current]
F R  D      [Central Tendency] [Central tendency ...] [2008-10-20 21:55:56] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
12300
12092,8
12380,8
12196,9
9455
13168
13427,9
11980,5
11884,8
11691,7
12233,8
14341,4
13130,7
12421,1
14285,8
12864,6
11160,2
14316,2
14388,7
14013,9
13419
12769,6
13315,5
15332,9
14243
13824,4
14962,9
13202,9
12199
15508,9
14199,8
15169,6
14058
13786,2
14147,9
16541,7
13587,5
15582,4
15802,8
14130,5
12923,2
15612,2
16033,7
16036,6
14037,8
15330,6
15038,3
17401,8
14992,5
16043,7
16929,6
15921,3
14417,2
15961
17851,9
16483,9
14215,5
17429,7
17839,5
17629,2




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=17994&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=17994&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17994&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 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=17994&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=17994&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17994&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')