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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 05 Mar 2016 17:37:22 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/05/t145719945734k3ky37c4coiyr.htm/, Retrieved Sat, 27 Apr 2024 06:57:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293527, Retrieved Sat, 27 Apr 2024 06:57:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-05 17:37:22] [4661a511bc27dc3517a7b8e15be46886] [Current]
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Dataseries X:
17887
17118
15945
15085
14027
15158
23783
25166
21839
18522
16850
16679
17806
17542
16380
15434
14478
15506
22357
27204
24182
20760
18731
18377
18775
18943
17974
17192
1604
17101
25972
28139
26131
22600
20320
19662
20440
19694
18260
16832
15539
16676
25216
26994
24865
21793
19505
18696
19221
18742
17633
16379
15007
15762
24146
25720
23731
20542
18807
18459




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293527&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293527&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293527&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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean19331.4666666667561.8065787280134.4094700892168
Geometric Mean18521.8522344739
Harmonic Mean16091.4329638614
Quadratic Mean19807.260657816
Winsorized Mean ( 1 / 20 )19522.9333333333479.34664153358740.7282155370341
Winsorized Mean ( 2 / 20 )19530.9666666667474.6457221582141.1485151027161
Winsorized Mean ( 3 / 20 )19514.2666666667459.02651282109342.5122865926318
Winsorized Mean ( 4 / 20 )19508.8666666667455.59658316468642.8204850246094
Winsorized Mean ( 5 / 20 )19493.95449.60933728328743.3575292670521
Winsorized Mean ( 6 / 20 )19471.15433.59619373694244.9061829445231
Winsorized Mean ( 7 / 20 )19473.7166666667430.97006076075445.185776089159
Winsorized Mean ( 8 / 20 )19437.9833333333421.40821928793446.126255833781
Winsorized Mean ( 9 / 20 )19368.9833333333394.39596273164449.1105010284104
Winsorized Mean ( 10 / 20 )19393.4833333333388.49464835850949.919563667803
Winsorized Mean ( 11 / 20 )19406.5363.17687127694253.435396179735
Winsorized Mean ( 12 / 20 )19396.3361.02827979752453.7251541925692
Winsorized Mean ( 13 / 20 )19215.3833333333303.71208125521963.2684193987859
Winsorized Mean ( 14 / 20 )19159.3833333333293.011661798865.3877842803724
Winsorized Mean ( 15 / 20 )19068.1333333333264.00336569788672.2268569680058
Winsorized Mean ( 16 / 20 )19060.6666666667261.13566475090472.9914341070514
Winsorized Mean ( 17 / 20 )18839.1200.86977497168493.7876293367464
Winsorized Mean ( 18 / 20 )18778.8189.6605707320299.0126726262647
Winsorized Mean ( 19 / 20 )18769.9333333333181.12211267176103.631373643202
Winsorized Mean ( 20 / 20 )18846.6158.032057464429119.258081571469
Trimmed Mean ( 1 / 20 )19485.2586206897468.0056233603241.6346677221181
Trimmed Mean ( 2 / 20 )19444.8928571429453.93229347999442.8365488343469
Trimmed Mean ( 3 / 20 )19397.0740740741439.51621237980544.1327840196079
Trimmed Mean ( 4 / 20 )19352429.02836046988945.1065751895863
Trimmed Mean ( 5 / 20 )19304.94416.9857066115946.2964070324405
Trimmed Mean ( 6 / 20 )19257.6875403.63022690031247.7112124329485
Trimmed Mean ( 7 / 20 )19211.2826086957391.5289201663349.0673399056558
Trimmed Mean ( 8 / 20 )19160.1590909091376.37531865097350.9070551161115
Trimmed Mean ( 9 / 20 )19110.5476190476359.26130691490253.1940046178542
Trimmed Mean ( 10 / 20 )19067.475344.6009099864155.3320506343178
Trimmed Mean ( 11 / 20 )19016326.20028275060158.2954736876756
Trimmed Mean ( 12 / 20 )18956.8333333333308.35409325221761.4774823755223
Trimmed Mean ( 13 / 20 )18892.2058823529283.58050279872766.6202566675107
Trimmed Mean ( 14 / 20 )18845.59375268.47097991252570.1960180431434
Trimmed Mean ( 15 / 20 )18800.7666666667250.09347072568175.174960034397
Trimmed Mean ( 16 / 20 )18762.5714285714233.63901421739280.3058148974794
Trimmed Mean ( 17 / 20 )18719.5769230769208.94764285729989.5897970759186
Trimmed Mean ( 18 / 20 )18702197.75870049934294.569796184832
Trimmed Mean ( 19 / 20 )18690.3636363636184.286732468381101.42001752389
Trimmed Mean ( 20 / 20 )18677.8165.281109819477113.006259580422
Median18713.5
Midrange14871.5
Midmean - Weighted Average at Xnp18732.3225806452
Midmean - Weighted Average at X(n+1)p18800.7666666667
Midmean - Empirical Distribution Function18732.3225806452
Midmean - Empirical Distribution Function - Averaging18800.7666666667
Midmean - Empirical Distribution Function - Interpolation18800.7666666667
Midmean - Closest Observation18732.3225806452
Midmean - True Basic - Statistics Graphics Toolkit18800.7666666667
Midmean - MS Excel (old versions)18845.59375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 19331.4666666667 & 561.80657872801 & 34.4094700892168 \tabularnewline
Geometric Mean & 18521.8522344739 &  &  \tabularnewline
Harmonic Mean & 16091.4329638614 &  &  \tabularnewline
Quadratic Mean & 19807.260657816 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 19522.9333333333 & 479.346641533587 & 40.7282155370341 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 19530.9666666667 & 474.64572215821 & 41.1485151027161 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 19514.2666666667 & 459.026512821093 & 42.5122865926318 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 19508.8666666667 & 455.596583164686 & 42.8204850246094 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 19493.95 & 449.609337283287 & 43.3575292670521 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 19471.15 & 433.596193736942 & 44.9061829445231 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 19473.7166666667 & 430.970060760754 & 45.185776089159 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 19437.9833333333 & 421.408219287934 & 46.126255833781 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 19368.9833333333 & 394.395962731644 & 49.1105010284104 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 19393.4833333333 & 388.494648358509 & 49.919563667803 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 19406.5 & 363.176871276942 & 53.435396179735 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 19396.3 & 361.028279797524 & 53.7251541925692 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 19215.3833333333 & 303.712081255219 & 63.2684193987859 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 19159.3833333333 & 293.0116617988 & 65.3877842803724 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 19068.1333333333 & 264.003365697886 & 72.2268569680058 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 19060.6666666667 & 261.135664750904 & 72.9914341070514 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 18839.1 & 200.869774971684 & 93.7876293367464 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 18778.8 & 189.66057073202 & 99.0126726262647 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 18769.9333333333 & 181.12211267176 & 103.631373643202 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 18846.6 & 158.032057464429 & 119.258081571469 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 19485.2586206897 & 468.00562336032 & 41.6346677221181 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 19444.8928571429 & 453.932293479994 & 42.8365488343469 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 19397.0740740741 & 439.516212379805 & 44.1327840196079 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 19352 & 429.028360469889 & 45.1065751895863 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 19304.94 & 416.98570661159 & 46.2964070324405 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 19257.6875 & 403.630226900312 & 47.7112124329485 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 19211.2826086957 & 391.52892016633 & 49.0673399056558 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 19160.1590909091 & 376.375318650973 & 50.9070551161115 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 19110.5476190476 & 359.261306914902 & 53.1940046178542 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 19067.475 & 344.60090998641 & 55.3320506343178 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 19016 & 326.200282750601 & 58.2954736876756 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 18956.8333333333 & 308.354093252217 & 61.4774823755223 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 18892.2058823529 & 283.580502798727 & 66.6202566675107 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 18845.59375 & 268.470979912525 & 70.1960180431434 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 18800.7666666667 & 250.093470725681 & 75.174960034397 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 18762.5714285714 & 233.639014217392 & 80.3058148974794 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 18719.5769230769 & 208.947642857299 & 89.5897970759186 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 18702 & 197.758700499342 & 94.569796184832 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 18690.3636363636 & 184.286732468381 & 101.42001752389 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 18677.8 & 165.281109819477 & 113.006259580422 \tabularnewline
Median & 18713.5 &  &  \tabularnewline
Midrange & 14871.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18732.3225806452 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 18800.7666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18732.3225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 18800.7666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 18800.7666666667 &  &  \tabularnewline
Midmean - Closest Observation & 18732.3225806452 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 18800.7666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 18845.59375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293527&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]19331.4666666667[/C][C]561.80657872801[/C][C]34.4094700892168[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]18521.8522344739[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]16091.4329638614[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]19807.260657816[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]19522.9333333333[/C][C]479.346641533587[/C][C]40.7282155370341[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]19530.9666666667[/C][C]474.64572215821[/C][C]41.1485151027161[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]19514.2666666667[/C][C]459.026512821093[/C][C]42.5122865926318[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]19508.8666666667[/C][C]455.596583164686[/C][C]42.8204850246094[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]19493.95[/C][C]449.609337283287[/C][C]43.3575292670521[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]19471.15[/C][C]433.596193736942[/C][C]44.9061829445231[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]19473.7166666667[/C][C]430.970060760754[/C][C]45.185776089159[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]19437.9833333333[/C][C]421.408219287934[/C][C]46.126255833781[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]19368.9833333333[/C][C]394.395962731644[/C][C]49.1105010284104[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]19393.4833333333[/C][C]388.494648358509[/C][C]49.919563667803[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]19406.5[/C][C]363.176871276942[/C][C]53.435396179735[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]19396.3[/C][C]361.028279797524[/C][C]53.7251541925692[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]19215.3833333333[/C][C]303.712081255219[/C][C]63.2684193987859[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]19159.3833333333[/C][C]293.0116617988[/C][C]65.3877842803724[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]19068.1333333333[/C][C]264.003365697886[/C][C]72.2268569680058[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]19060.6666666667[/C][C]261.135664750904[/C][C]72.9914341070514[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]18839.1[/C][C]200.869774971684[/C][C]93.7876293367464[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]18778.8[/C][C]189.66057073202[/C][C]99.0126726262647[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]18769.9333333333[/C][C]181.12211267176[/C][C]103.631373643202[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]18846.6[/C][C]158.032057464429[/C][C]119.258081571469[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]19485.2586206897[/C][C]468.00562336032[/C][C]41.6346677221181[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]19444.8928571429[/C][C]453.932293479994[/C][C]42.8365488343469[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]19397.0740740741[/C][C]439.516212379805[/C][C]44.1327840196079[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]19352[/C][C]429.028360469889[/C][C]45.1065751895863[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]19304.94[/C][C]416.98570661159[/C][C]46.2964070324405[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]19257.6875[/C][C]403.630226900312[/C][C]47.7112124329485[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]19211.2826086957[/C][C]391.52892016633[/C][C]49.0673399056558[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]19160.1590909091[/C][C]376.375318650973[/C][C]50.9070551161115[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]19110.5476190476[/C][C]359.261306914902[/C][C]53.1940046178542[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]19067.475[/C][C]344.60090998641[/C][C]55.3320506343178[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]19016[/C][C]326.200282750601[/C][C]58.2954736876756[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]18956.8333333333[/C][C]308.354093252217[/C][C]61.4774823755223[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]18892.2058823529[/C][C]283.580502798727[/C][C]66.6202566675107[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]18845.59375[/C][C]268.470979912525[/C][C]70.1960180431434[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]18800.7666666667[/C][C]250.093470725681[/C][C]75.174960034397[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]18762.5714285714[/C][C]233.639014217392[/C][C]80.3058148974794[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]18719.5769230769[/C][C]208.947642857299[/C][C]89.5897970759186[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]18702[/C][C]197.758700499342[/C][C]94.569796184832[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]18690.3636363636[/C][C]184.286732468381[/C][C]101.42001752389[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]18677.8[/C][C]165.281109819477[/C][C]113.006259580422[/C][/ROW]
[ROW][C]Median[/C][C]18713.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]14871.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18732.3225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]18800.7666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18732.3225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]18800.7666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]18800.7666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18732.3225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]18800.7666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]18845.59375[/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=293527&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293527&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 Mean19331.4666666667561.8065787280134.4094700892168
Geometric Mean18521.8522344739
Harmonic Mean16091.4329638614
Quadratic Mean19807.260657816
Winsorized Mean ( 1 / 20 )19522.9333333333479.34664153358740.7282155370341
Winsorized Mean ( 2 / 20 )19530.9666666667474.6457221582141.1485151027161
Winsorized Mean ( 3 / 20 )19514.2666666667459.02651282109342.5122865926318
Winsorized Mean ( 4 / 20 )19508.8666666667455.59658316468642.8204850246094
Winsorized Mean ( 5 / 20 )19493.95449.60933728328743.3575292670521
Winsorized Mean ( 6 / 20 )19471.15433.59619373694244.9061829445231
Winsorized Mean ( 7 / 20 )19473.7166666667430.97006076075445.185776089159
Winsorized Mean ( 8 / 20 )19437.9833333333421.40821928793446.126255833781
Winsorized Mean ( 9 / 20 )19368.9833333333394.39596273164449.1105010284104
Winsorized Mean ( 10 / 20 )19393.4833333333388.49464835850949.919563667803
Winsorized Mean ( 11 / 20 )19406.5363.17687127694253.435396179735
Winsorized Mean ( 12 / 20 )19396.3361.02827979752453.7251541925692
Winsorized Mean ( 13 / 20 )19215.3833333333303.71208125521963.2684193987859
Winsorized Mean ( 14 / 20 )19159.3833333333293.011661798865.3877842803724
Winsorized Mean ( 15 / 20 )19068.1333333333264.00336569788672.2268569680058
Winsorized Mean ( 16 / 20 )19060.6666666667261.13566475090472.9914341070514
Winsorized Mean ( 17 / 20 )18839.1200.86977497168493.7876293367464
Winsorized Mean ( 18 / 20 )18778.8189.6605707320299.0126726262647
Winsorized Mean ( 19 / 20 )18769.9333333333181.12211267176103.631373643202
Winsorized Mean ( 20 / 20 )18846.6158.032057464429119.258081571469
Trimmed Mean ( 1 / 20 )19485.2586206897468.0056233603241.6346677221181
Trimmed Mean ( 2 / 20 )19444.8928571429453.93229347999442.8365488343469
Trimmed Mean ( 3 / 20 )19397.0740740741439.51621237980544.1327840196079
Trimmed Mean ( 4 / 20 )19352429.02836046988945.1065751895863
Trimmed Mean ( 5 / 20 )19304.94416.9857066115946.2964070324405
Trimmed Mean ( 6 / 20 )19257.6875403.63022690031247.7112124329485
Trimmed Mean ( 7 / 20 )19211.2826086957391.5289201663349.0673399056558
Trimmed Mean ( 8 / 20 )19160.1590909091376.37531865097350.9070551161115
Trimmed Mean ( 9 / 20 )19110.5476190476359.26130691490253.1940046178542
Trimmed Mean ( 10 / 20 )19067.475344.6009099864155.3320506343178
Trimmed Mean ( 11 / 20 )19016326.20028275060158.2954736876756
Trimmed Mean ( 12 / 20 )18956.8333333333308.35409325221761.4774823755223
Trimmed Mean ( 13 / 20 )18892.2058823529283.58050279872766.6202566675107
Trimmed Mean ( 14 / 20 )18845.59375268.47097991252570.1960180431434
Trimmed Mean ( 15 / 20 )18800.7666666667250.09347072568175.174960034397
Trimmed Mean ( 16 / 20 )18762.5714285714233.63901421739280.3058148974794
Trimmed Mean ( 17 / 20 )18719.5769230769208.94764285729989.5897970759186
Trimmed Mean ( 18 / 20 )18702197.75870049934294.569796184832
Trimmed Mean ( 19 / 20 )18690.3636363636184.286732468381101.42001752389
Trimmed Mean ( 20 / 20 )18677.8165.281109819477113.006259580422
Median18713.5
Midrange14871.5
Midmean - Weighted Average at Xnp18732.3225806452
Midmean - Weighted Average at X(n+1)p18800.7666666667
Midmean - Empirical Distribution Function18732.3225806452
Midmean - Empirical Distribution Function - Averaging18800.7666666667
Midmean - Empirical Distribution Function - Interpolation18800.7666666667
Midmean - Closest Observation18732.3225806452
Midmean - True Basic - Statistics Graphics Toolkit18800.7666666667
Midmean - MS Excel (old versions)18845.59375
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')