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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 computationSun, 13 Dec 2009 03:46:37 -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/2009/Dec/13/t1260701264nfkhlujvbgx3fvm.htm/, Retrieved Sat, 27 Apr 2024 15:14:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67211, Retrieved Sat, 27 Apr 2024 15:14:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsshwpaper2
Estimated Impact131
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-12-13 10:46:37] [4407d6264e55b051ec65750e6dca2820] [Current]
-    D    [Central Tendency] [CT invoer] [2010-12-24 11:08:42] [6e5489189f7de5cfbcc25dd35ae15009]
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Dataseries X:
14497
14398,3
16629,6
16670,7
16614,8
16869,2
15663,9
16359,9
18447,7
16889
16505
18320,9
15052,1
15699,8
18135,3
16768,7
18883
19021
18101,9
17776,1
21489,9
17065,3
18690
18953,1
16398,9
16895,6
18553
19270
19422,1
17579,4
18637,3
18076,7
20438,6
18075,2
19563
19899,2
19227,5
17789,6
19220,8
21968,9
21131,5
19484,6
22168,7
20866,8
22176,2
23533,8
21479,6
24347,7
22751,6
20328,3
23650,4
23335,7
19614,9
18042,3
17282,5
16847,2
18159,5
16540,9
15952,7
18357,8
16394,3




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=67211&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=67211&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67211&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 Mean18638.7704918033300.28826603403662.0695931211999
Geometric Mean18498.1730508404
Harmonic Mean18361.9906665637
Quadratic Mean18783.3476252020
Winsorized Mean ( 1 / 20 )18628.9573770492296.48426695934662.8328699128024
Winsorized Mean ( 2 / 20 )18643.3344262295291.42524498518263.9729561767288
Winsorized Mean ( 3 / 20 )18663.6803278689282.96768976787265.9569307830845
Winsorized Mean ( 4 / 20 )18627.7327868852272.43933576230968.3738738929282
Winsorized Mean ( 5 / 20 )18601.2983606557257.3806688799172.2715440969454
Winsorized Mean ( 6 / 20 )18640.6131147541250.73284478932974.3445204812171
Winsorized Mean ( 7 / 20 )18621.6327868852244.83275428799976.058584730785
Winsorized Mean ( 8 / 20 )18559.4163934426230.92463814785580.3700139677583
Winsorized Mean ( 9 / 20 )18573.5508196721228.19945442077581.3917406893729
Winsorized Mean ( 10 / 20 )18522.3704918033215.48152481686385.9580444659717
Winsorized Mean ( 11 / 20 )18487.9639344262203.98039168370190.6359860466114
Winsorized Mean ( 12 / 20 )18406.6393442623187.71895538057298.0542391520643
Winsorized Mean ( 13 / 20 )18391.8918032787182.134593934330100.979673361284
Winsorized Mean ( 14 / 20 )18315.9016393443161.773552140288113.219382260093
Winsorized Mean ( 15 / 20 )18265.2950819672147.646096794003123.709975939636
Winsorized Mean ( 16 / 20 )18257.4524590164144.661863974444126.207778314275
Winsorized Mean ( 17 / 20 )18241.1213114754140.523289128572129.808527999837
Winsorized Mean ( 18 / 20 )18224.6262295082137.511725360001132.531434550739
Winsorized Mean ( 19 / 20 )18230.1081967213122.253481144243149.117293234474
Winsorized Mean ( 20 / 20 )18287.3868852459109.137057699269167.563495578536
Trimmed Mean ( 1 / 20 )18613.8813559322285.75334495399065.1396796734936
Trimmed Mean ( 2 / 20 )18597.7473684211272.53868455846868.2389268831716
Trimmed Mean ( 3 / 20 )18572.4672727273259.57870008096071.5485025039987
Trimmed Mean ( 4 / 20 )18537.4735849057247.56346797535974.8796813056068
Trimmed Mean ( 5 / 20 )18510.4843137255236.85887095065778.149846106383
Trimmed Mean ( 6 / 20 )18487.8734693878228.73472102007680.8267034708959
Trimmed Mean ( 7 / 20 )18454.8340425532220.30125529156683.7708982553388
Trimmed Mean ( 8 / 20 )18422.5333333333211.16100915623387.244010657777
Trimmed Mean ( 9 / 20 )18398.2604651163203.45438674971590.4294115208704
Trimmed Mean ( 10 / 20 )18369.2829268293193.87493372181894.7481068036699
Trimmed Mean ( 11 / 20 )18345.3384615385184.86654199282799.2355796986253
Trimmed Mean ( 12 / 20 )18323.9621621622176.040146439466104.089678023888
Trimmed Mean ( 13 / 20 )18311.9542857143168.859880321623108.444671705535
Trimmed Mean ( 14 / 20 )18300.5878787879160.396128108116114.096194806225
Trimmed Mean ( 15 / 20 )18298.4354838710154.729178983790118.261052013906
Trimmed Mean ( 16 / 20 )18303.0827586207150.636788488183121.504732956097
Trimmed Mean ( 17 / 20 )18309.5259259259145.104927316108126.181283189916
Trimmed Mean ( 18 / 20 )18319.344137.718408244262133.020300143959
Trimmed Mean ( 19 / 20 )18333.3126.773727811566144.614348070999
Trimmed Mean ( 20 / 20 )18349.0761904762115.899802355056158.318442461742
Median18320.9
Midrange19373
Midmean - Weighted Average at Xnp18254.5533333333
Midmean - Weighted Average at X(n+1)p18298.4354838710
Midmean - Empirical Distribution Function18298.4354838710
Midmean - Empirical Distribution Function - Averaging18298.4354838710
Midmean - Empirical Distribution Function - Interpolation18298.4354838710
Midmean - Closest Observation18250.63125
Midmean - True Basic - Statistics Graphics Toolkit18298.4354838710
Midmean - MS Excel (old versions)18298.4354838710
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 18638.7704918033 & 300.288266034036 & 62.0695931211999 \tabularnewline
Geometric Mean & 18498.1730508404 &  &  \tabularnewline
Harmonic Mean & 18361.9906665637 &  &  \tabularnewline
Quadratic Mean & 18783.3476252020 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 18628.9573770492 & 296.484266959346 & 62.8328699128024 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 18643.3344262295 & 291.425244985182 & 63.9729561767288 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 18663.6803278689 & 282.967689767872 & 65.9569307830845 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 18627.7327868852 & 272.439335762309 & 68.3738738929282 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 18601.2983606557 & 257.38066887991 & 72.2715440969454 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 18640.6131147541 & 250.732844789329 & 74.3445204812171 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 18621.6327868852 & 244.832754287999 & 76.058584730785 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 18559.4163934426 & 230.924638147855 & 80.3700139677583 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 18573.5508196721 & 228.199454420775 & 81.3917406893729 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 18522.3704918033 & 215.481524816863 & 85.9580444659717 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 18487.9639344262 & 203.980391683701 & 90.6359860466114 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 18406.6393442623 & 187.718955380572 & 98.0542391520643 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 18391.8918032787 & 182.134593934330 & 100.979673361284 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 18315.9016393443 & 161.773552140288 & 113.219382260093 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 18265.2950819672 & 147.646096794003 & 123.709975939636 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 18257.4524590164 & 144.661863974444 & 126.207778314275 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 18241.1213114754 & 140.523289128572 & 129.808527999837 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 18224.6262295082 & 137.511725360001 & 132.531434550739 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 18230.1081967213 & 122.253481144243 & 149.117293234474 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 18287.3868852459 & 109.137057699269 & 167.563495578536 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 18613.8813559322 & 285.753344953990 & 65.1396796734936 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 18597.7473684211 & 272.538684558468 & 68.2389268831716 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 18572.4672727273 & 259.578700080960 & 71.5485025039987 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 18537.4735849057 & 247.563467975359 & 74.8796813056068 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 18510.4843137255 & 236.858870950657 & 78.149846106383 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 18487.8734693878 & 228.734721020076 & 80.8267034708959 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 18454.8340425532 & 220.301255291566 & 83.7708982553388 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 18422.5333333333 & 211.161009156233 & 87.244010657777 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 18398.2604651163 & 203.454386749715 & 90.4294115208704 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 18369.2829268293 & 193.874933721818 & 94.7481068036699 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 18345.3384615385 & 184.866541992827 & 99.2355796986253 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 18323.9621621622 & 176.040146439466 & 104.089678023888 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 18311.9542857143 & 168.859880321623 & 108.444671705535 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 18300.5878787879 & 160.396128108116 & 114.096194806225 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 18298.4354838710 & 154.729178983790 & 118.261052013906 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 18303.0827586207 & 150.636788488183 & 121.504732956097 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 18309.5259259259 & 145.104927316108 & 126.181283189916 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 18319.344 & 137.718408244262 & 133.020300143959 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 18333.3 & 126.773727811566 & 144.614348070999 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 18349.0761904762 & 115.899802355056 & 158.318442461742 \tabularnewline
Median & 18320.9 &  &  \tabularnewline
Midrange & 19373 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18254.5533333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 18298.4354838710 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18298.4354838710 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 18298.4354838710 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 18298.4354838710 &  &  \tabularnewline
Midmean - Closest Observation & 18250.63125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 18298.4354838710 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 18298.4354838710 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67211&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]18638.7704918033[/C][C]300.288266034036[/C][C]62.0695931211999[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]18498.1730508404[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]18361.9906665637[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]18783.3476252020[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]18628.9573770492[/C][C]296.484266959346[/C][C]62.8328699128024[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]18643.3344262295[/C][C]291.425244985182[/C][C]63.9729561767288[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]18663.6803278689[/C][C]282.967689767872[/C][C]65.9569307830845[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]18627.7327868852[/C][C]272.439335762309[/C][C]68.3738738929282[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]18601.2983606557[/C][C]257.38066887991[/C][C]72.2715440969454[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]18640.6131147541[/C][C]250.732844789329[/C][C]74.3445204812171[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]18621.6327868852[/C][C]244.832754287999[/C][C]76.058584730785[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]18559.4163934426[/C][C]230.924638147855[/C][C]80.3700139677583[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]18573.5508196721[/C][C]228.199454420775[/C][C]81.3917406893729[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]18522.3704918033[/C][C]215.481524816863[/C][C]85.9580444659717[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]18487.9639344262[/C][C]203.980391683701[/C][C]90.6359860466114[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]18406.6393442623[/C][C]187.718955380572[/C][C]98.0542391520643[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]18391.8918032787[/C][C]182.134593934330[/C][C]100.979673361284[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]18315.9016393443[/C][C]161.773552140288[/C][C]113.219382260093[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]18265.2950819672[/C][C]147.646096794003[/C][C]123.709975939636[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]18257.4524590164[/C][C]144.661863974444[/C][C]126.207778314275[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]18241.1213114754[/C][C]140.523289128572[/C][C]129.808527999837[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]18224.6262295082[/C][C]137.511725360001[/C][C]132.531434550739[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]18230.1081967213[/C][C]122.253481144243[/C][C]149.117293234474[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]18287.3868852459[/C][C]109.137057699269[/C][C]167.563495578536[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]18613.8813559322[/C][C]285.753344953990[/C][C]65.1396796734936[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]18597.7473684211[/C][C]272.538684558468[/C][C]68.2389268831716[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]18572.4672727273[/C][C]259.578700080960[/C][C]71.5485025039987[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]18537.4735849057[/C][C]247.563467975359[/C][C]74.8796813056068[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]18510.4843137255[/C][C]236.858870950657[/C][C]78.149846106383[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]18487.8734693878[/C][C]228.734721020076[/C][C]80.8267034708959[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]18454.8340425532[/C][C]220.301255291566[/C][C]83.7708982553388[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]18422.5333333333[/C][C]211.161009156233[/C][C]87.244010657777[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]18398.2604651163[/C][C]203.454386749715[/C][C]90.4294115208704[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]18369.2829268293[/C][C]193.874933721818[/C][C]94.7481068036699[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]18345.3384615385[/C][C]184.866541992827[/C][C]99.2355796986253[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]18323.9621621622[/C][C]176.040146439466[/C][C]104.089678023888[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]18311.9542857143[/C][C]168.859880321623[/C][C]108.444671705535[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]18300.5878787879[/C][C]160.396128108116[/C][C]114.096194806225[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]18298.4354838710[/C][C]154.729178983790[/C][C]118.261052013906[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]18303.0827586207[/C][C]150.636788488183[/C][C]121.504732956097[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]18309.5259259259[/C][C]145.104927316108[/C][C]126.181283189916[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]18319.344[/C][C]137.718408244262[/C][C]133.020300143959[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]18333.3[/C][C]126.773727811566[/C][C]144.614348070999[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]18349.0761904762[/C][C]115.899802355056[/C][C]158.318442461742[/C][/ROW]
[ROW][C]Median[/C][C]18320.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19373[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18254.5533333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]18298.4354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18298.4354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]18298.4354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]18298.4354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18250.63125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]18298.4354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]18298.4354838710[/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=67211&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67211&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 Mean18638.7704918033300.28826603403662.0695931211999
Geometric Mean18498.1730508404
Harmonic Mean18361.9906665637
Quadratic Mean18783.3476252020
Winsorized Mean ( 1 / 20 )18628.9573770492296.48426695934662.8328699128024
Winsorized Mean ( 2 / 20 )18643.3344262295291.42524498518263.9729561767288
Winsorized Mean ( 3 / 20 )18663.6803278689282.96768976787265.9569307830845
Winsorized Mean ( 4 / 20 )18627.7327868852272.43933576230968.3738738929282
Winsorized Mean ( 5 / 20 )18601.2983606557257.3806688799172.2715440969454
Winsorized Mean ( 6 / 20 )18640.6131147541250.73284478932974.3445204812171
Winsorized Mean ( 7 / 20 )18621.6327868852244.83275428799976.058584730785
Winsorized Mean ( 8 / 20 )18559.4163934426230.92463814785580.3700139677583
Winsorized Mean ( 9 / 20 )18573.5508196721228.19945442077581.3917406893729
Winsorized Mean ( 10 / 20 )18522.3704918033215.48152481686385.9580444659717
Winsorized Mean ( 11 / 20 )18487.9639344262203.98039168370190.6359860466114
Winsorized Mean ( 12 / 20 )18406.6393442623187.71895538057298.0542391520643
Winsorized Mean ( 13 / 20 )18391.8918032787182.134593934330100.979673361284
Winsorized Mean ( 14 / 20 )18315.9016393443161.773552140288113.219382260093
Winsorized Mean ( 15 / 20 )18265.2950819672147.646096794003123.709975939636
Winsorized Mean ( 16 / 20 )18257.4524590164144.661863974444126.207778314275
Winsorized Mean ( 17 / 20 )18241.1213114754140.523289128572129.808527999837
Winsorized Mean ( 18 / 20 )18224.6262295082137.511725360001132.531434550739
Winsorized Mean ( 19 / 20 )18230.1081967213122.253481144243149.117293234474
Winsorized Mean ( 20 / 20 )18287.3868852459109.137057699269167.563495578536
Trimmed Mean ( 1 / 20 )18613.8813559322285.75334495399065.1396796734936
Trimmed Mean ( 2 / 20 )18597.7473684211272.53868455846868.2389268831716
Trimmed Mean ( 3 / 20 )18572.4672727273259.57870008096071.5485025039987
Trimmed Mean ( 4 / 20 )18537.4735849057247.56346797535974.8796813056068
Trimmed Mean ( 5 / 20 )18510.4843137255236.85887095065778.149846106383
Trimmed Mean ( 6 / 20 )18487.8734693878228.73472102007680.8267034708959
Trimmed Mean ( 7 / 20 )18454.8340425532220.30125529156683.7708982553388
Trimmed Mean ( 8 / 20 )18422.5333333333211.16100915623387.244010657777
Trimmed Mean ( 9 / 20 )18398.2604651163203.45438674971590.4294115208704
Trimmed Mean ( 10 / 20 )18369.2829268293193.87493372181894.7481068036699
Trimmed Mean ( 11 / 20 )18345.3384615385184.86654199282799.2355796986253
Trimmed Mean ( 12 / 20 )18323.9621621622176.040146439466104.089678023888
Trimmed Mean ( 13 / 20 )18311.9542857143168.859880321623108.444671705535
Trimmed Mean ( 14 / 20 )18300.5878787879160.396128108116114.096194806225
Trimmed Mean ( 15 / 20 )18298.4354838710154.729178983790118.261052013906
Trimmed Mean ( 16 / 20 )18303.0827586207150.636788488183121.504732956097
Trimmed Mean ( 17 / 20 )18309.5259259259145.104927316108126.181283189916
Trimmed Mean ( 18 / 20 )18319.344137.718408244262133.020300143959
Trimmed Mean ( 19 / 20 )18333.3126.773727811566144.614348070999
Trimmed Mean ( 20 / 20 )18349.0761904762115.899802355056158.318442461742
Median18320.9
Midrange19373
Midmean - Weighted Average at Xnp18254.5533333333
Midmean - Weighted Average at X(n+1)p18298.4354838710
Midmean - Empirical Distribution Function18298.4354838710
Midmean - Empirical Distribution Function - Averaging18298.4354838710
Midmean - Empirical Distribution Function - Interpolation18298.4354838710
Midmean - Closest Observation18250.63125
Midmean - True Basic - Statistics Graphics Toolkit18298.4354838710
Midmean - MS Excel (old versions)18298.4354838710
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')