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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 11 Dec 2009 01:07:54 -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/11/t1260519069zt3his7fgzbv0jx.htm/, Retrieved Mon, 29 Apr 2024 04:47:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65864, Retrieved Mon, 29 Apr 2024 04:47:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2009-12-11 08:07:54] [5d37783481a916b2505b66314b556267] [Current]
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Dataseries X:
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




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=65864&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=65864&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65864&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 Mean19224.8142857143314.17403860060161.1916069556407
Geometric Mean19105.0467402478
Harmonic Mean18988.6851815106
Quadratic Mean19347.6443008877
Winsorized Mean ( 1 / 16 )19223.8020408163306.19379247477162.7831213867612
Winsorized Mean ( 2 / 16 )19247.5775510204298.50021902681964.4809495074143
Winsorized Mean ( 3 / 16 )19241.9448979592293.64779685442865.5272918921238
Winsorized Mean ( 4 / 16 )19215.7897959184276.27013353917969.5543508440563
Winsorized Mean ( 5 / 16 )19165.0857142857259.84941711466373.7545842014678
Winsorized Mean ( 6 / 16 )19169.2857142857258.68205774328374.1036540435648
Winsorized Mean ( 7 / 16 )19141.6857142857251.71955241841676.0436983554928
Winsorized Mean ( 8 / 16 )19091.1877551020228.8723526289283.414128162764
Winsorized Mean ( 9 / 16 )19129.1897959184221.30700223168886.4373454206925
Winsorized Mean ( 10 / 16 )19118.7408163265195.56312675687397.7625032560213
Winsorized Mean ( 11 / 16 )19103.4755102041175.877965058012108.617787929846
Winsorized Mean ( 12 / 16 )19001.9163265306154.165795805968123.256369723192
Winsorized Mean ( 13 / 16 )19039.6959183673137.910312315106138.058536731207
Winsorized Mean ( 14 / 16 )18926.4959183673113.496523402626166.758375948011
Winsorized Mean ( 15 / 16 )18839.924489795998.474524336437191.317750623801
Winsorized Mean ( 16 / 16 )18831.206122449094.389552957689199.505194509081
Trimmed Mean ( 1 / 16 )19224.8142857143295.26028936882565.111411787921
Trimmed Mean ( 2 / 16 )19204.5978723404281.06199590377668.328689585323
Trimmed Mean ( 3 / 16 )19147.2837209302267.96087059864771.4555213906926
Trimmed Mean ( 4 / 16 )19147.2837209302253.14301026621175.6382082238594
Trimmed Mean ( 5 / 16 )19076.2102564103241.32172638360279.0488719862999
Trimmed Mean ( 6 / 16 )19052.6702702703232.02187153767482.1158373734463
Trimmed Mean ( 7 / 16 )19025.46219.4149248885986.7099629146028
Trimmed Mean ( 8 / 16 )19025.46204.28613098604193.1314324088892
Trimmed Mean ( 9 / 16 )18982.9483870968191.53652414943499.108765137069
Trimmed Mean ( 10 / 16 )18955.4931034483175.365730775203108.091204704908
Trimmed Mean ( 11 / 16 )18925.8666666667161.541772446059117.157725708292
Trimmed Mean ( 12 / 16 )18894.22148.351997402574127.360738856302
Trimmed Mean ( 13 / 16 )18875.1137.677560093719137.096415618866
Trimmed Mean ( 14 / 16 )18845.5571428571126.938412808174148.462208766829
Trimmed Mean ( 15 / 16 )18830.6473684211121.633308901841154.814890250315
Trimmed Mean ( 16 / 16 )18830.6473684211119.376928669722157.741094349307
Median18883
Midrange19699.9
Midmean - Weighted Average at Xnp18829.8708333333
Midmean - Weighted Average at X(n+1)p18894.22
Midmean - Empirical Distribution Function18894.22
Midmean - Empirical Distribution Function - Averaging18894.22
Midmean - Empirical Distribution Function - Interpolation18894.22
Midmean - Closest Observation18851.2153846154
Midmean - True Basic - Statistics Graphics Toolkit18894.22
Midmean - MS Excel (old versions)18894.22
Number of observations49

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 19224.8142857143 & 314.174038600601 & 61.1916069556407 \tabularnewline
Geometric Mean & 19105.0467402478 &  &  \tabularnewline
Harmonic Mean & 18988.6851815106 &  &  \tabularnewline
Quadratic Mean & 19347.6443008877 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 19223.8020408163 & 306.193792474771 & 62.7831213867612 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 19247.5775510204 & 298.500219026819 & 64.4809495074143 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 19241.9448979592 & 293.647796854428 & 65.5272918921238 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 19215.7897959184 & 276.270133539179 & 69.5543508440563 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 19165.0857142857 & 259.849417114663 & 73.7545842014678 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 19169.2857142857 & 258.682057743283 & 74.1036540435648 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 19141.6857142857 & 251.719552418416 & 76.0436983554928 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 19091.1877551020 & 228.87235262892 & 83.414128162764 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 19129.1897959184 & 221.307002231688 & 86.4373454206925 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 19118.7408163265 & 195.563126756873 & 97.7625032560213 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 19103.4755102041 & 175.877965058012 & 108.617787929846 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 19001.9163265306 & 154.165795805968 & 123.256369723192 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 19039.6959183673 & 137.910312315106 & 138.058536731207 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 18926.4959183673 & 113.496523402626 & 166.758375948011 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 18839.9244897959 & 98.474524336437 & 191.317750623801 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 18831.2061224490 & 94.389552957689 & 199.505194509081 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 19224.8142857143 & 295.260289368825 & 65.111411787921 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 19204.5978723404 & 281.061995903776 & 68.328689585323 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 19147.2837209302 & 267.960870598647 & 71.4555213906926 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 19147.2837209302 & 253.143010266211 & 75.6382082238594 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 19076.2102564103 & 241.321726383602 & 79.0488719862999 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 19052.6702702703 & 232.021871537674 & 82.1158373734463 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 19025.46 & 219.41492488859 & 86.7099629146028 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 19025.46 & 204.286130986041 & 93.1314324088892 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 18982.9483870968 & 191.536524149434 & 99.108765137069 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 18955.4931034483 & 175.365730775203 & 108.091204704908 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 18925.8666666667 & 161.541772446059 & 117.157725708292 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 18894.22 & 148.351997402574 & 127.360738856302 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 18875.1 & 137.677560093719 & 137.096415618866 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 18845.5571428571 & 126.938412808174 & 148.462208766829 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 18830.6473684211 & 121.633308901841 & 154.814890250315 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 18830.6473684211 & 119.376928669722 & 157.741094349307 \tabularnewline
Median & 18883 &  &  \tabularnewline
Midrange & 19699.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18829.8708333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 18894.22 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18894.22 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 18894.22 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 18894.22 &  &  \tabularnewline
Midmean - Closest Observation & 18851.2153846154 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 18894.22 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 18894.22 &  &  \tabularnewline
Number of observations & 49 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65864&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]19224.8142857143[/C][C]314.174038600601[/C][C]61.1916069556407[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]19105.0467402478[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]18988.6851815106[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]19347.6443008877[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]19223.8020408163[/C][C]306.193792474771[/C][C]62.7831213867612[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]19247.5775510204[/C][C]298.500219026819[/C][C]64.4809495074143[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]19241.9448979592[/C][C]293.647796854428[/C][C]65.5272918921238[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]19215.7897959184[/C][C]276.270133539179[/C][C]69.5543508440563[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]19165.0857142857[/C][C]259.849417114663[/C][C]73.7545842014678[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]19169.2857142857[/C][C]258.682057743283[/C][C]74.1036540435648[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]19141.6857142857[/C][C]251.719552418416[/C][C]76.0436983554928[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]19091.1877551020[/C][C]228.87235262892[/C][C]83.414128162764[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]19129.1897959184[/C][C]221.307002231688[/C][C]86.4373454206925[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]19118.7408163265[/C][C]195.563126756873[/C][C]97.7625032560213[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]19103.4755102041[/C][C]175.877965058012[/C][C]108.617787929846[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]19001.9163265306[/C][C]154.165795805968[/C][C]123.256369723192[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]19039.6959183673[/C][C]137.910312315106[/C][C]138.058536731207[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]18926.4959183673[/C][C]113.496523402626[/C][C]166.758375948011[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]18839.9244897959[/C][C]98.474524336437[/C][C]191.317750623801[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]18831.2061224490[/C][C]94.389552957689[/C][C]199.505194509081[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]19224.8142857143[/C][C]295.260289368825[/C][C]65.111411787921[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]19204.5978723404[/C][C]281.061995903776[/C][C]68.328689585323[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]19147.2837209302[/C][C]267.960870598647[/C][C]71.4555213906926[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]19147.2837209302[/C][C]253.143010266211[/C][C]75.6382082238594[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]19076.2102564103[/C][C]241.321726383602[/C][C]79.0488719862999[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]19052.6702702703[/C][C]232.021871537674[/C][C]82.1158373734463[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]19025.46[/C][C]219.41492488859[/C][C]86.7099629146028[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]19025.46[/C][C]204.286130986041[/C][C]93.1314324088892[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]18982.9483870968[/C][C]191.536524149434[/C][C]99.108765137069[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]18955.4931034483[/C][C]175.365730775203[/C][C]108.091204704908[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]18925.8666666667[/C][C]161.541772446059[/C][C]117.157725708292[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]18894.22[/C][C]148.351997402574[/C][C]127.360738856302[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]18875.1[/C][C]137.677560093719[/C][C]137.096415618866[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]18845.5571428571[/C][C]126.938412808174[/C][C]148.462208766829[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]18830.6473684211[/C][C]121.633308901841[/C][C]154.814890250315[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]18830.6473684211[/C][C]119.376928669722[/C][C]157.741094349307[/C][/ROW]
[ROW][C]Median[/C][C]18883[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19699.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18829.8708333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]18894.22[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18894.22[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]18894.22[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]18894.22[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18851.2153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]18894.22[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]18894.22[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]49[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65864&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65864&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 Mean19224.8142857143314.17403860060161.1916069556407
Geometric Mean19105.0467402478
Harmonic Mean18988.6851815106
Quadratic Mean19347.6443008877
Winsorized Mean ( 1 / 16 )19223.8020408163306.19379247477162.7831213867612
Winsorized Mean ( 2 / 16 )19247.5775510204298.50021902681964.4809495074143
Winsorized Mean ( 3 / 16 )19241.9448979592293.64779685442865.5272918921238
Winsorized Mean ( 4 / 16 )19215.7897959184276.27013353917969.5543508440563
Winsorized Mean ( 5 / 16 )19165.0857142857259.84941711466373.7545842014678
Winsorized Mean ( 6 / 16 )19169.2857142857258.68205774328374.1036540435648
Winsorized Mean ( 7 / 16 )19141.6857142857251.71955241841676.0436983554928
Winsorized Mean ( 8 / 16 )19091.1877551020228.8723526289283.414128162764
Winsorized Mean ( 9 / 16 )19129.1897959184221.30700223168886.4373454206925
Winsorized Mean ( 10 / 16 )19118.7408163265195.56312675687397.7625032560213
Winsorized Mean ( 11 / 16 )19103.4755102041175.877965058012108.617787929846
Winsorized Mean ( 12 / 16 )19001.9163265306154.165795805968123.256369723192
Winsorized Mean ( 13 / 16 )19039.6959183673137.910312315106138.058536731207
Winsorized Mean ( 14 / 16 )18926.4959183673113.496523402626166.758375948011
Winsorized Mean ( 15 / 16 )18839.924489795998.474524336437191.317750623801
Winsorized Mean ( 16 / 16 )18831.206122449094.389552957689199.505194509081
Trimmed Mean ( 1 / 16 )19224.8142857143295.26028936882565.111411787921
Trimmed Mean ( 2 / 16 )19204.5978723404281.06199590377668.328689585323
Trimmed Mean ( 3 / 16 )19147.2837209302267.96087059864771.4555213906926
Trimmed Mean ( 4 / 16 )19147.2837209302253.14301026621175.6382082238594
Trimmed Mean ( 5 / 16 )19076.2102564103241.32172638360279.0488719862999
Trimmed Mean ( 6 / 16 )19052.6702702703232.02187153767482.1158373734463
Trimmed Mean ( 7 / 16 )19025.46219.4149248885986.7099629146028
Trimmed Mean ( 8 / 16 )19025.46204.28613098604193.1314324088892
Trimmed Mean ( 9 / 16 )18982.9483870968191.53652414943499.108765137069
Trimmed Mean ( 10 / 16 )18955.4931034483175.365730775203108.091204704908
Trimmed Mean ( 11 / 16 )18925.8666666667161.541772446059117.157725708292
Trimmed Mean ( 12 / 16 )18894.22148.351997402574127.360738856302
Trimmed Mean ( 13 / 16 )18875.1137.677560093719137.096415618866
Trimmed Mean ( 14 / 16 )18845.5571428571126.938412808174148.462208766829
Trimmed Mean ( 15 / 16 )18830.6473684211121.633308901841154.814890250315
Trimmed Mean ( 16 / 16 )18830.6473684211119.376928669722157.741094349307
Median18883
Midrange19699.9
Midmean - Weighted Average at Xnp18829.8708333333
Midmean - Weighted Average at X(n+1)p18894.22
Midmean - Empirical Distribution Function18894.22
Midmean - Empirical Distribution Function - Averaging18894.22
Midmean - Empirical Distribution Function - Interpolation18894.22
Midmean - Closest Observation18851.2153846154
Midmean - True Basic - Statistics Graphics Toolkit18894.22
Midmean - MS Excel (old versions)18894.22
Number of observations49



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')