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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 20 Oct 2007 05:33:07 -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/2007/Oct/20/jd2q97z7cakm2fh1192883366.htm/, Retrieved Fri, 03 May 2024 03:44:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1140, Retrieved Fri, 03 May 2024 03:44:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact193
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-10-20 12:33:07] [d9ccf6bb4f7743d5d52b9a9a992ccbd5] [Current]
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Dataseries X:
110.40
96.40
101.90
106.20
81.00
94.70
101.00
109.40
102.30
90.70
96.20
96.10
106.00
103.10
102.00
104.70
86.00
92.10
106.90
112.60
101.70
92.00
97.40
97.00
105.40
102.70
98.10
104.50
87.40
89.90
109.80
111.70
98.60
96.90
95.10
97.00
112.70
102.90
97.40
111.40
87.40
96.80
114.10
110.30
103.90
101.60
94.60
95.90
104.70
102.80
98.10
113.90
80.90
95.70
113.20
105.90
108.80
102.30
99.00
100.70
115.50




Summary of compuational 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 compuational 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=1140&T=0

[TABLE]
[ROW][C]Summary of compuational 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=1140&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1140&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 compuational 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 Mean100.9081967213111.0346570802309197.5281556076446
Geometric Mean100.582005686654
Harmonic Mean100.247309303102
Quadratic Mean101.225960513928
Winsorized Mean ( 1 / 20 )100.8868852459021.0289749671949598.0460054542679
Winsorized Mean ( 2 / 20 )101.0442622950820.980051087633946103.101015416476
Winsorized Mean ( 3 / 20 )101.0786885245900.955619316121645105.772965049320
Winsorized Mean ( 4 / 20 )101.0459016393440.94879726502134106.498938566261
Winsorized Mean ( 5 / 20 )101.2426229508200.900960201253411112.371914774894
Winsorized Mean ( 6 / 20 )101.2327868852460.86651024642905116.828147505968
Winsorized Mean ( 7 / 20 )101.3475409836070.830443974210547122.040190706365
Winsorized Mean ( 8 / 20 )101.2295081967210.802235075390877126.184345838280
Winsorized Mean ( 9 / 20 )101.5836065573770.734933104750562138.221568603655
Winsorized Mean ( 10 / 20 )101.5180327868850.716333668462015141.718918510206
Winsorized Mean ( 11 / 20 )101.5180327868850.691223308545919146.8672012818
Winsorized Mean ( 12 / 20 )101.5180327868850.651066834459338155.925670628252
Winsorized Mean ( 13 / 20 )101.1557377049180.572810750798555176.595389601010
Winsorized Mean ( 14 / 20 )101.0409836065570.539552420508328187.268149981356
Winsorized Mean ( 15 / 20 )101.0163934426230.52801918912736191.311974115125
Winsorized Mean ( 16 / 20 )101.0426229508200.515976759634602195.827856708846
Winsorized Mean ( 17 / 20 )101.0147540983610.477818563466615211.408182565135
Winsorized Mean ( 18 / 20 )100.8377049180330.442614956414346227.822633322032
Winsorized Mean ( 19 / 20 )100.8688524590160.438013030868906230.287332454284
Winsorized Mean ( 20 / 20 )100.8032786885250.42851865319638235.236617908273
Trimmed Mean ( 1 / 20 )1010.982657925465633102.782461101243
Trimmed Mean ( 2 / 20 )101.1210526315790.925125260238302109.305255166777
Trimmed Mean ( 3 / 20 )101.1636363636360.887596397330812113.974816333028
Trimmed Mean ( 4 / 20 )101.1962264150940.853040163215748118.630084231450
Trimmed Mean ( 5 / 20 )101.2411764705880.81233228239694124.630251270893
Trimmed Mean ( 6 / 20 )101.2408163265310.778390752121095130.064258922208
Trimmed Mean ( 7 / 20 )101.2425531914890.746423756608607135.636831350984
Trimmed Mean ( 8 / 20 )101.2222222222220.716309910420451141.310654438395
Trimmed Mean ( 9 / 20 )101.2209302325580.685432651393394147.674508978802
Trimmed Mean ( 10 / 20 )101.1609756097560.66354441879714152.455469059839
Trimmed Mean ( 11 / 20 )101.1051282051280.639236098570714158.165548583993
Trimmed Mean ( 12 / 20 )101.0432432432430.613028475700867164.826345346718
Trimmed Mean ( 13 / 20 )100.9742857142860.588179685246656171.672514789323
Trimmed Mean ( 14 / 20 )100.9484848484850.576367300756283175.146099919313
Trimmed Mean ( 15 / 20 )100.9354838709680.567688169497152177.800928915560
Trimmed Mean ( 16 / 20 )100.9241379310340.55668032526955181.296398219510
Trimmed Mean ( 17 / 20 )100.9074074074070.542231485294439186.096547589105
Trimmed Mean ( 18 / 20 )100.8920.531253862731055189.912972079558
Trimmed Mean ( 19 / 20 )100.90.523933133952945192.581826689857
Trimmed Mean ( 20 / 20 )100.9047619047620.510017562278202197.845661341601
Median101.7
Midrange98.2
Midmean - Weighted Average at Xnp100.766666666667
Midmean - Weighted Average at X(n+1)p100.935483870968
Midmean - Empirical Distribution Function100.935483870968
Midmean - Empirical Distribution Function - Averaging100.935483870968
Midmean - Empirical Distribution Function - Interpolation100.935483870968
Midmean - Closest Observation100.784375
Midmean - True Basic - Statistics Graphics Toolkit100.935483870968
Midmean - MS Excel (old versions)100.935483870968
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 100.908196721311 & 1.03465708023091 & 97.5281556076446 \tabularnewline
Geometric Mean & 100.582005686654 &  &  \tabularnewline
Harmonic Mean & 100.247309303102 &  &  \tabularnewline
Quadratic Mean & 101.225960513928 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 100.886885245902 & 1.02897496719495 & 98.0460054542679 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 101.044262295082 & 0.980051087633946 & 103.101015416476 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 101.078688524590 & 0.955619316121645 & 105.772965049320 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 101.045901639344 & 0.94879726502134 & 106.498938566261 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 101.242622950820 & 0.900960201253411 & 112.371914774894 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 101.232786885246 & 0.86651024642905 & 116.828147505968 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 101.347540983607 & 0.830443974210547 & 122.040190706365 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 101.229508196721 & 0.802235075390877 & 126.184345838280 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 101.583606557377 & 0.734933104750562 & 138.221568603655 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 101.518032786885 & 0.716333668462015 & 141.718918510206 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 101.518032786885 & 0.691223308545919 & 146.8672012818 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 101.518032786885 & 0.651066834459338 & 155.925670628252 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 101.155737704918 & 0.572810750798555 & 176.595389601010 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 101.040983606557 & 0.539552420508328 & 187.268149981356 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 101.016393442623 & 0.52801918912736 & 191.311974115125 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 101.042622950820 & 0.515976759634602 & 195.827856708846 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 101.014754098361 & 0.477818563466615 & 211.408182565135 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 100.837704918033 & 0.442614956414346 & 227.822633322032 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 100.868852459016 & 0.438013030868906 & 230.287332454284 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 100.803278688525 & 0.42851865319638 & 235.236617908273 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 101 & 0.982657925465633 & 102.782461101243 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 101.121052631579 & 0.925125260238302 & 109.305255166777 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 101.163636363636 & 0.887596397330812 & 113.974816333028 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 101.196226415094 & 0.853040163215748 & 118.630084231450 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 101.241176470588 & 0.81233228239694 & 124.630251270893 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 101.240816326531 & 0.778390752121095 & 130.064258922208 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 101.242553191489 & 0.746423756608607 & 135.636831350984 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 101.222222222222 & 0.716309910420451 & 141.310654438395 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 101.220930232558 & 0.685432651393394 & 147.674508978802 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 101.160975609756 & 0.66354441879714 & 152.455469059839 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 101.105128205128 & 0.639236098570714 & 158.165548583993 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 101.043243243243 & 0.613028475700867 & 164.826345346718 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 100.974285714286 & 0.588179685246656 & 171.672514789323 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 100.948484848485 & 0.576367300756283 & 175.146099919313 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 100.935483870968 & 0.567688169497152 & 177.800928915560 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 100.924137931034 & 0.55668032526955 & 181.296398219510 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 100.907407407407 & 0.542231485294439 & 186.096547589105 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 100.892 & 0.531253862731055 & 189.912972079558 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 100.9 & 0.523933133952945 & 192.581826689857 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 100.904761904762 & 0.510017562278202 & 197.845661341601 \tabularnewline
Median & 101.7 &  &  \tabularnewline
Midrange & 98.2 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 100.766666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 100.935483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 100.935483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 100.935483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 100.935483870968 &  &  \tabularnewline
Midmean - Closest Observation & 100.784375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 100.935483870968 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 100.935483870968 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1140&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]100.908196721311[/C][C]1.03465708023091[/C][C]97.5281556076446[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]100.582005686654[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]100.247309303102[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.225960513928[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]100.886885245902[/C][C]1.02897496719495[/C][C]98.0460054542679[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]101.044262295082[/C][C]0.980051087633946[/C][C]103.101015416476[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]101.078688524590[/C][C]0.955619316121645[/C][C]105.772965049320[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]101.045901639344[/C][C]0.94879726502134[/C][C]106.498938566261[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]101.242622950820[/C][C]0.900960201253411[/C][C]112.371914774894[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]101.232786885246[/C][C]0.86651024642905[/C][C]116.828147505968[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]101.347540983607[/C][C]0.830443974210547[/C][C]122.040190706365[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]101.229508196721[/C][C]0.802235075390877[/C][C]126.184345838280[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]101.583606557377[/C][C]0.734933104750562[/C][C]138.221568603655[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]101.518032786885[/C][C]0.716333668462015[/C][C]141.718918510206[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]101.518032786885[/C][C]0.691223308545919[/C][C]146.8672012818[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]101.518032786885[/C][C]0.651066834459338[/C][C]155.925670628252[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]101.155737704918[/C][C]0.572810750798555[/C][C]176.595389601010[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]101.040983606557[/C][C]0.539552420508328[/C][C]187.268149981356[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]101.016393442623[/C][C]0.52801918912736[/C][C]191.311974115125[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]101.042622950820[/C][C]0.515976759634602[/C][C]195.827856708846[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]101.014754098361[/C][C]0.477818563466615[/C][C]211.408182565135[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]100.837704918033[/C][C]0.442614956414346[/C][C]227.822633322032[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]100.868852459016[/C][C]0.438013030868906[/C][C]230.287332454284[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]100.803278688525[/C][C]0.42851865319638[/C][C]235.236617908273[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]101[/C][C]0.982657925465633[/C][C]102.782461101243[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]101.121052631579[/C][C]0.925125260238302[/C][C]109.305255166777[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]101.163636363636[/C][C]0.887596397330812[/C][C]113.974816333028[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]101.196226415094[/C][C]0.853040163215748[/C][C]118.630084231450[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]101.241176470588[/C][C]0.81233228239694[/C][C]124.630251270893[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]101.240816326531[/C][C]0.778390752121095[/C][C]130.064258922208[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]101.242553191489[/C][C]0.746423756608607[/C][C]135.636831350984[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]101.222222222222[/C][C]0.716309910420451[/C][C]141.310654438395[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]101.220930232558[/C][C]0.685432651393394[/C][C]147.674508978802[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]101.160975609756[/C][C]0.66354441879714[/C][C]152.455469059839[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]101.105128205128[/C][C]0.639236098570714[/C][C]158.165548583993[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]101.043243243243[/C][C]0.613028475700867[/C][C]164.826345346718[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]100.974285714286[/C][C]0.588179685246656[/C][C]171.672514789323[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]100.948484848485[/C][C]0.576367300756283[/C][C]175.146099919313[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]100.935483870968[/C][C]0.567688169497152[/C][C]177.800928915560[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]100.924137931034[/C][C]0.55668032526955[/C][C]181.296398219510[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]100.907407407407[/C][C]0.542231485294439[/C][C]186.096547589105[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]100.892[/C][C]0.531253862731055[/C][C]189.912972079558[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]100.9[/C][C]0.523933133952945[/C][C]192.581826689857[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]100.904761904762[/C][C]0.510017562278202[/C][C]197.845661341601[/C][/ROW]
[ROW][C]Median[/C][C]101.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]98.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]100.766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]100.935483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]100.935483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]100.935483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]100.935483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]100.784375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]100.935483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]100.935483870968[/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=1140&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1140&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 Mean100.9081967213111.0346570802309197.5281556076446
Geometric Mean100.582005686654
Harmonic Mean100.247309303102
Quadratic Mean101.225960513928
Winsorized Mean ( 1 / 20 )100.8868852459021.0289749671949598.0460054542679
Winsorized Mean ( 2 / 20 )101.0442622950820.980051087633946103.101015416476
Winsorized Mean ( 3 / 20 )101.0786885245900.955619316121645105.772965049320
Winsorized Mean ( 4 / 20 )101.0459016393440.94879726502134106.498938566261
Winsorized Mean ( 5 / 20 )101.2426229508200.900960201253411112.371914774894
Winsorized Mean ( 6 / 20 )101.2327868852460.86651024642905116.828147505968
Winsorized Mean ( 7 / 20 )101.3475409836070.830443974210547122.040190706365
Winsorized Mean ( 8 / 20 )101.2295081967210.802235075390877126.184345838280
Winsorized Mean ( 9 / 20 )101.5836065573770.734933104750562138.221568603655
Winsorized Mean ( 10 / 20 )101.5180327868850.716333668462015141.718918510206
Winsorized Mean ( 11 / 20 )101.5180327868850.691223308545919146.8672012818
Winsorized Mean ( 12 / 20 )101.5180327868850.651066834459338155.925670628252
Winsorized Mean ( 13 / 20 )101.1557377049180.572810750798555176.595389601010
Winsorized Mean ( 14 / 20 )101.0409836065570.539552420508328187.268149981356
Winsorized Mean ( 15 / 20 )101.0163934426230.52801918912736191.311974115125
Winsorized Mean ( 16 / 20 )101.0426229508200.515976759634602195.827856708846
Winsorized Mean ( 17 / 20 )101.0147540983610.477818563466615211.408182565135
Winsorized Mean ( 18 / 20 )100.8377049180330.442614956414346227.822633322032
Winsorized Mean ( 19 / 20 )100.8688524590160.438013030868906230.287332454284
Winsorized Mean ( 20 / 20 )100.8032786885250.42851865319638235.236617908273
Trimmed Mean ( 1 / 20 )1010.982657925465633102.782461101243
Trimmed Mean ( 2 / 20 )101.1210526315790.925125260238302109.305255166777
Trimmed Mean ( 3 / 20 )101.1636363636360.887596397330812113.974816333028
Trimmed Mean ( 4 / 20 )101.1962264150940.853040163215748118.630084231450
Trimmed Mean ( 5 / 20 )101.2411764705880.81233228239694124.630251270893
Trimmed Mean ( 6 / 20 )101.2408163265310.778390752121095130.064258922208
Trimmed Mean ( 7 / 20 )101.2425531914890.746423756608607135.636831350984
Trimmed Mean ( 8 / 20 )101.2222222222220.716309910420451141.310654438395
Trimmed Mean ( 9 / 20 )101.2209302325580.685432651393394147.674508978802
Trimmed Mean ( 10 / 20 )101.1609756097560.66354441879714152.455469059839
Trimmed Mean ( 11 / 20 )101.1051282051280.639236098570714158.165548583993
Trimmed Mean ( 12 / 20 )101.0432432432430.613028475700867164.826345346718
Trimmed Mean ( 13 / 20 )100.9742857142860.588179685246656171.672514789323
Trimmed Mean ( 14 / 20 )100.9484848484850.576367300756283175.146099919313
Trimmed Mean ( 15 / 20 )100.9354838709680.567688169497152177.800928915560
Trimmed Mean ( 16 / 20 )100.9241379310340.55668032526955181.296398219510
Trimmed Mean ( 17 / 20 )100.9074074074070.542231485294439186.096547589105
Trimmed Mean ( 18 / 20 )100.8920.531253862731055189.912972079558
Trimmed Mean ( 19 / 20 )100.90.523933133952945192.581826689857
Trimmed Mean ( 20 / 20 )100.9047619047620.510017562278202197.845661341601
Median101.7
Midrange98.2
Midmean - Weighted Average at Xnp100.766666666667
Midmean - Weighted Average at X(n+1)p100.935483870968
Midmean - Empirical Distribution Function100.935483870968
Midmean - Empirical Distribution Function - Averaging100.935483870968
Midmean - Empirical Distribution Function - Interpolation100.935483870968
Midmean - Closest Observation100.784375
Midmean - True Basic - Statistics Graphics Toolkit100.935483870968
Midmean - MS Excel (old versions)100.935483870968
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')