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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 computationWed, 17 Dec 2008 08:20:10 -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/Dec/17/t12295273030mk6hlscgiorx16.htm/, Retrieved Sun, 19 May 2024 08:01:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34400, Retrieved Sun, 19 May 2024 08:01:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2008-12-17 15:20:10] [d592f629d96b926609f311957d74fcca] [Current]
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Dataseries X:
9682.35
9762.12
10124.63
10540.05
10601.61
10323.73
10418.40
10092.96
10364.91
10152.09
10032.80
10204.59
10001.60
10411.75
10673.38
10539.51
10723.78
10682.06
10283.19
10377.18
10486.64
10545.38
10554.27
10532.54
10324.31
10695.25
10827.81
10872.48
10971.19
11145.65
11234.68
11333.88
10997.97
11036.89
11257.35
11533.59
11963.12
12185.15
12377.62
12512.89
12631.48
12268.53
12754.80
13407.75
13480.21
13673.28
13239.71
13557.69
13901.28
13200.58
13406.97
12538.12
12419.57
12193.88
12656.63
12812.48
12056.67
11322.38
11530.75
11114.08




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34400&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34400&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34400&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean11392.4698333333151.41800186424075.2385429279918
Geometric Mean11335.0322074611
Harmonic Mean11279.6684402031
Quadratic Mean11451.6848616016
Winsorized Mean ( 1 / 20 )11389.9993333333150.14509654456575.8599487792974
Winsorized Mean ( 2 / 20 )11394.129147.79881292970377.0921550325261
Winsorized Mean ( 3 / 20 )11391.815146.60337192449877.7049998950015
Winsorized Mean ( 4 / 20 )11390.995144.83030501450078.6506318471092
Winsorized Mean ( 5 / 20 )11393.5691666667144.41797771798478.8930114290603
Winsorized Mean ( 6 / 20 )11379.5891666667140.15081718749181.1953108446258
Winsorized Mean ( 7 / 20 )11381.149138.23158033374682.3339281264191
Winsorized Mean ( 8 / 20 )11339.8823333333125.79336259118890.146905208238
Winsorized Mean ( 9 / 20 )11337.3113333333123.23464411678891.9977609753076
Winsorized Mean ( 10 / 20 )11321.0463333333120.08335315485494.2765673667876
Winsorized Mean ( 11 / 20 )11323.8788333333118.18087547806695.8182005973967
Winsorized Mean ( 12 / 20 )11307.6608333333114.38924540320698.8524820972064
Winsorized Mean ( 13 / 20 )11309.6845112.371229873077100.645730341959
Winsorized Mean ( 14 / 20 )11289.4615108.257248411392104.283654588176
Winsorized Mean ( 15 / 20 )11296.034104.1181337927108.492474735386
Winsorized Mean ( 16 / 20 )11279.183333333397.4508874505329115.742233122903
Winsorized Mean ( 17 / 20 )11260.007333333393.5848027059233120.318759112164
Winsorized Mean ( 18 / 20 )11257.550333333393.1210849150762120.891528955015
Winsorized Mean ( 19 / 20 )11218.552833333386.1054387568405130.288550819818
Winsorized Mean ( 20 / 20 )11190.332833333380.6038208225368138.83129508179
Trimmed Mean ( 1 / 20 )11378.6993103448147.50742009817977.1398435602176
Trimmed Mean ( 2 / 20 )11366.5921428571144.20264578347978.8237419715873
Trimmed Mean ( 3 / 20 )11351.2938888889141.58187134516980.1747694181484
Trimmed Mean ( 4 / 20 )11335.7088461538138.79283155860581.6735901909124
Trimmed Mean ( 5 / 20 )11319.123135.87980266434883.3024686381145
Trimmed Mean ( 6 / 20 )11300.5114583333132.20811315312685.4751738665605
Trimmed Mean ( 7 / 20 )11283.3206521739128.79904890668287.6040681041747
Trimmed Mean ( 8 / 20 )11264.2631818182124.83416099594590.2338197489392
Trimmed Mean ( 9 / 20 )11250.7597619048123.15295510149591.3559869727248
Trimmed Mean ( 10 / 20 )11236.3345121.3892001875592.56453195704
Trimmed Mean ( 11 / 20 )11222.9589473684119.65841840894293.791637033118
Trimmed Mean ( 12 / 20 )11207.6680555556117.52306087771395.365692246712
Trimmed Mean ( 13 / 20 )11192.9632352941115.37561431961897.0132493014243
Trimmed Mean ( 14 / 20 )11176.1284375112.58495633326199.268399628967
Trimmed Mean ( 15 / 20 )11159.938109.574968831138101.847512429579
Trimmed Mean ( 16 / 20 )11140.4957142857106.029486277008105.069788654644
Trimmed Mean ( 17 / 20 )11120.4926923077102.632037571957108.353034348665
Trimmed Mean ( 18 / 20 )11099.975833333398.4192455826439112.782573851499
Trimmed Mean ( 19 / 20 )11076.100909090991.2064859941799121.439838278581
Trimmed Mean ( 20 / 20 )11053.608582.5562849731369133.891786719772
Median11017.43
Midrange11791.815
Midmean - Weighted Average at Xnp11136.0174193548
Midmean - Weighted Average at X(n+1)p11159.938
Midmean - Empirical Distribution Function11136.0174193548
Midmean - Empirical Distribution Function - Averaging11159.938
Midmean - Empirical Distribution Function - Interpolation11159.938
Midmean - Closest Observation11136.0174193548
Midmean - True Basic - Statistics Graphics Toolkit11159.938
Midmean - MS Excel (old versions)11176.1284375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 11392.4698333333 & 151.418001864240 & 75.2385429279918 \tabularnewline
Geometric Mean & 11335.0322074611 &  &  \tabularnewline
Harmonic Mean & 11279.6684402031 &  &  \tabularnewline
Quadratic Mean & 11451.6848616016 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 11389.9993333333 & 150.145096544565 & 75.8599487792974 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 11394.129 & 147.798812929703 & 77.0921550325261 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 11391.815 & 146.603371924498 & 77.7049998950015 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 11390.995 & 144.830305014500 & 78.6506318471092 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 11393.5691666667 & 144.417977717984 & 78.8930114290603 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 11379.5891666667 & 140.150817187491 & 81.1953108446258 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 11381.149 & 138.231580333746 & 82.3339281264191 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 11339.8823333333 & 125.793362591188 & 90.146905208238 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 11337.3113333333 & 123.234644116788 & 91.9977609753076 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 11321.0463333333 & 120.083353154854 & 94.2765673667876 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 11323.8788333333 & 118.180875478066 & 95.8182005973967 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 11307.6608333333 & 114.389245403206 & 98.8524820972064 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 11309.6845 & 112.371229873077 & 100.645730341959 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 11289.4615 & 108.257248411392 & 104.283654588176 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 11296.034 & 104.1181337927 & 108.492474735386 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 11279.1833333333 & 97.4508874505329 & 115.742233122903 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 11260.0073333333 & 93.5848027059233 & 120.318759112164 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 11257.5503333333 & 93.1210849150762 & 120.891528955015 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 11218.5528333333 & 86.1054387568405 & 130.288550819818 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 11190.3328333333 & 80.6038208225368 & 138.83129508179 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 11378.6993103448 & 147.507420098179 & 77.1398435602176 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 11366.5921428571 & 144.202645783479 & 78.8237419715873 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 11351.2938888889 & 141.581871345169 & 80.1747694181484 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 11335.7088461538 & 138.792831558605 & 81.6735901909124 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 11319.123 & 135.879802664348 & 83.3024686381145 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 11300.5114583333 & 132.208113153126 & 85.4751738665605 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 11283.3206521739 & 128.799048906682 & 87.6040681041747 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 11264.2631818182 & 124.834160995945 & 90.2338197489392 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 11250.7597619048 & 123.152955101495 & 91.3559869727248 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 11236.3345 & 121.38920018755 & 92.56453195704 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 11222.9589473684 & 119.658418408942 & 93.791637033118 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 11207.6680555556 & 117.523060877713 & 95.365692246712 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 11192.9632352941 & 115.375614319618 & 97.0132493014243 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 11176.1284375 & 112.584956333261 & 99.268399628967 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 11159.938 & 109.574968831138 & 101.847512429579 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 11140.4957142857 & 106.029486277008 & 105.069788654644 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 11120.4926923077 & 102.632037571957 & 108.353034348665 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 11099.9758333333 & 98.4192455826439 & 112.782573851499 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 11076.1009090909 & 91.2064859941799 & 121.439838278581 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 11053.6085 & 82.5562849731369 & 133.891786719772 \tabularnewline
Median & 11017.43 &  &  \tabularnewline
Midrange & 11791.815 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 11136.0174193548 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 11159.938 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 11136.0174193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 11159.938 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 11159.938 &  &  \tabularnewline
Midmean - Closest Observation & 11136.0174193548 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 11159.938 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 11176.1284375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34400&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]11392.4698333333[/C][C]151.418001864240[/C][C]75.2385429279918[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]11335.0322074611[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]11279.6684402031[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]11451.6848616016[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]11389.9993333333[/C][C]150.145096544565[/C][C]75.8599487792974[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]11394.129[/C][C]147.798812929703[/C][C]77.0921550325261[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]11391.815[/C][C]146.603371924498[/C][C]77.7049998950015[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]11390.995[/C][C]144.830305014500[/C][C]78.6506318471092[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]11393.5691666667[/C][C]144.417977717984[/C][C]78.8930114290603[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]11379.5891666667[/C][C]140.150817187491[/C][C]81.1953108446258[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]11381.149[/C][C]138.231580333746[/C][C]82.3339281264191[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]11339.8823333333[/C][C]125.793362591188[/C][C]90.146905208238[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]11337.3113333333[/C][C]123.234644116788[/C][C]91.9977609753076[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]11321.0463333333[/C][C]120.083353154854[/C][C]94.2765673667876[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]11323.8788333333[/C][C]118.180875478066[/C][C]95.8182005973967[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]11307.6608333333[/C][C]114.389245403206[/C][C]98.8524820972064[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]11309.6845[/C][C]112.371229873077[/C][C]100.645730341959[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]11289.4615[/C][C]108.257248411392[/C][C]104.283654588176[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]11296.034[/C][C]104.1181337927[/C][C]108.492474735386[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]11279.1833333333[/C][C]97.4508874505329[/C][C]115.742233122903[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]11260.0073333333[/C][C]93.5848027059233[/C][C]120.318759112164[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]11257.5503333333[/C][C]93.1210849150762[/C][C]120.891528955015[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]11218.5528333333[/C][C]86.1054387568405[/C][C]130.288550819818[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]11190.3328333333[/C][C]80.6038208225368[/C][C]138.83129508179[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]11378.6993103448[/C][C]147.507420098179[/C][C]77.1398435602176[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]11366.5921428571[/C][C]144.202645783479[/C][C]78.8237419715873[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]11351.2938888889[/C][C]141.581871345169[/C][C]80.1747694181484[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]11335.7088461538[/C][C]138.792831558605[/C][C]81.6735901909124[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]11319.123[/C][C]135.879802664348[/C][C]83.3024686381145[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]11300.5114583333[/C][C]132.208113153126[/C][C]85.4751738665605[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]11283.3206521739[/C][C]128.799048906682[/C][C]87.6040681041747[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]11264.2631818182[/C][C]124.834160995945[/C][C]90.2338197489392[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]11250.7597619048[/C][C]123.152955101495[/C][C]91.3559869727248[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]11236.3345[/C][C]121.38920018755[/C][C]92.56453195704[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]11222.9589473684[/C][C]119.658418408942[/C][C]93.791637033118[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]11207.6680555556[/C][C]117.523060877713[/C][C]95.365692246712[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]11192.9632352941[/C][C]115.375614319618[/C][C]97.0132493014243[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]11176.1284375[/C][C]112.584956333261[/C][C]99.268399628967[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]11159.938[/C][C]109.574968831138[/C][C]101.847512429579[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]11140.4957142857[/C][C]106.029486277008[/C][C]105.069788654644[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]11120.4926923077[/C][C]102.632037571957[/C][C]108.353034348665[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]11099.9758333333[/C][C]98.4192455826439[/C][C]112.782573851499[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]11076.1009090909[/C][C]91.2064859941799[/C][C]121.439838278581[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]11053.6085[/C][C]82.5562849731369[/C][C]133.891786719772[/C][/ROW]
[ROW][C]Median[/C][C]11017.43[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]11791.815[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]11136.0174193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]11159.938[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]11136.0174193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]11159.938[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]11159.938[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]11136.0174193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]11159.938[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]11176.1284375[/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=34400&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34400&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 Mean11392.4698333333151.41800186424075.2385429279918
Geometric Mean11335.0322074611
Harmonic Mean11279.6684402031
Quadratic Mean11451.6848616016
Winsorized Mean ( 1 / 20 )11389.9993333333150.14509654456575.8599487792974
Winsorized Mean ( 2 / 20 )11394.129147.79881292970377.0921550325261
Winsorized Mean ( 3 / 20 )11391.815146.60337192449877.7049998950015
Winsorized Mean ( 4 / 20 )11390.995144.83030501450078.6506318471092
Winsorized Mean ( 5 / 20 )11393.5691666667144.41797771798478.8930114290603
Winsorized Mean ( 6 / 20 )11379.5891666667140.15081718749181.1953108446258
Winsorized Mean ( 7 / 20 )11381.149138.23158033374682.3339281264191
Winsorized Mean ( 8 / 20 )11339.8823333333125.79336259118890.146905208238
Winsorized Mean ( 9 / 20 )11337.3113333333123.23464411678891.9977609753076
Winsorized Mean ( 10 / 20 )11321.0463333333120.08335315485494.2765673667876
Winsorized Mean ( 11 / 20 )11323.8788333333118.18087547806695.8182005973967
Winsorized Mean ( 12 / 20 )11307.6608333333114.38924540320698.8524820972064
Winsorized Mean ( 13 / 20 )11309.6845112.371229873077100.645730341959
Winsorized Mean ( 14 / 20 )11289.4615108.257248411392104.283654588176
Winsorized Mean ( 15 / 20 )11296.034104.1181337927108.492474735386
Winsorized Mean ( 16 / 20 )11279.183333333397.4508874505329115.742233122903
Winsorized Mean ( 17 / 20 )11260.007333333393.5848027059233120.318759112164
Winsorized Mean ( 18 / 20 )11257.550333333393.1210849150762120.891528955015
Winsorized Mean ( 19 / 20 )11218.552833333386.1054387568405130.288550819818
Winsorized Mean ( 20 / 20 )11190.332833333380.6038208225368138.83129508179
Trimmed Mean ( 1 / 20 )11378.6993103448147.50742009817977.1398435602176
Trimmed Mean ( 2 / 20 )11366.5921428571144.20264578347978.8237419715873
Trimmed Mean ( 3 / 20 )11351.2938888889141.58187134516980.1747694181484
Trimmed Mean ( 4 / 20 )11335.7088461538138.79283155860581.6735901909124
Trimmed Mean ( 5 / 20 )11319.123135.87980266434883.3024686381145
Trimmed Mean ( 6 / 20 )11300.5114583333132.20811315312685.4751738665605
Trimmed Mean ( 7 / 20 )11283.3206521739128.79904890668287.6040681041747
Trimmed Mean ( 8 / 20 )11264.2631818182124.83416099594590.2338197489392
Trimmed Mean ( 9 / 20 )11250.7597619048123.15295510149591.3559869727248
Trimmed Mean ( 10 / 20 )11236.3345121.3892001875592.56453195704
Trimmed Mean ( 11 / 20 )11222.9589473684119.65841840894293.791637033118
Trimmed Mean ( 12 / 20 )11207.6680555556117.52306087771395.365692246712
Trimmed Mean ( 13 / 20 )11192.9632352941115.37561431961897.0132493014243
Trimmed Mean ( 14 / 20 )11176.1284375112.58495633326199.268399628967
Trimmed Mean ( 15 / 20 )11159.938109.574968831138101.847512429579
Trimmed Mean ( 16 / 20 )11140.4957142857106.029486277008105.069788654644
Trimmed Mean ( 17 / 20 )11120.4926923077102.632037571957108.353034348665
Trimmed Mean ( 18 / 20 )11099.975833333398.4192455826439112.782573851499
Trimmed Mean ( 19 / 20 )11076.100909090991.2064859941799121.439838278581
Trimmed Mean ( 20 / 20 )11053.608582.5562849731369133.891786719772
Median11017.43
Midrange11791.815
Midmean - Weighted Average at Xnp11136.0174193548
Midmean - Weighted Average at X(n+1)p11159.938
Midmean - Empirical Distribution Function11136.0174193548
Midmean - Empirical Distribution Function - Averaging11159.938
Midmean - Empirical Distribution Function - Interpolation11159.938
Midmean - Closest Observation11136.0174193548
Midmean - True Basic - Statistics Graphics Toolkit11159.938
Midmean - MS Excel (old versions)11176.1284375
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')