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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, 21 Oct 2009 07:22:22 -0600
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/Oct/21/t1256131394kmlff1m2dhdx9lf.htm/, Retrieved Thu, 02 May 2024 06:53:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49351, Retrieved Thu, 02 May 2024 06:53:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [] [2009-10-21 13:22:22] [91df150cd527c563f0151b3a845ecd72] [Current]
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Post a new message
Dataseries X:
9.55
9.5
8.85
8.35
8.4
8.65
8.7
8.65
8.3
8.2
8.05
8.8
8.9
8.9
8.65
8.45
8.6
8.75
8.8
8.7
8.6
8.45
8.15
8.35
8.35
8.25
8.1
8
8.05
8.15
8.1
8
8.1
7.8
7.35
7.55
7.35
7.05
7.1
7.05
7.25
7.35
7.2
6.75
6.45
6.15
6.5
7.7
8
7.6
7
6.65
7
7.7
8.05
8.05
7.7
7.3
7.4
8.05
8.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49351&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49351&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49351&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.96393442622950.095092212562771583.7495964348545
Geometric Mean7.92882052556376
Harmonic Mean7.89261055706515
Quadratic Mean7.99792493579982
Winsorized Mean ( 1 / 20 )7.968032786885250.093417454188770385.2949039992473
Winsorized Mean ( 2 / 20 )7.950.088498402319560389.8321302038111
Winsorized Mean ( 3 / 20 )7.957377049180330.086561801302727791.9271194617524
Winsorized Mean ( 4 / 20 )7.960655737704920.084366125350710294.358437164353
Winsorized Mean ( 5 / 20 )7.977049180327870.0790791760193974100.874207115805
Winsorized Mean ( 6 / 20 )7.977049180327870.0790791760193974100.874207115805
Winsorized Mean ( 7 / 20 )7.977049180327870.0769338457790518103.687123652149
Winsorized Mean ( 8 / 20 )7.970491803278690.0758591685636244105.069590851021
Winsorized Mean ( 9 / 20 )7.977868852459020.0743875227338249107.247406006591
Winsorized Mean ( 10 / 20 )7.98606557377050.0699251272834196114.208809966144
Winsorized Mean ( 11 / 20 )7.995081967213120.0682600391747047117.126829458016
Winsorized Mean ( 12 / 20 )8.004918032786890.0664960752984673120.381811961937
Winsorized Mean ( 13 / 20 )8.004918032786890.0629283671822149127.206828831390
Winsorized Mean ( 14 / 20 )8.004918032786880.0629283671822149127.206828831390
Winsorized Mean ( 15 / 20 )7.968032786885250.0574269884155273138.750664221334
Winsorized Mean ( 16 / 20 )7.98114754098360.055097577803541144.854780539385
Winsorized Mean ( 17 / 20 )8.009016393442620.0459494286745866174.300674120725
Winsorized Mean ( 18 / 20 )8.009016393442620.0414476461644096193.232116527761
Winsorized Mean ( 19 / 20 )8.040163934426230.0364552962288058220.548583228166
Winsorized Mean ( 20 / 20 )8.040163934426230.0364552962288058220.548583228166
Trimmed Mean ( 1 / 20 )7.96779661016950.089300177985431389.2248681908494
Trimmed Mean ( 2 / 20 )7.967543859649120.084213626457137694.6111003033978
Trimmed Mean ( 3 / 20 )7.977272727272730.081255076835102698.175683760187
Trimmed Mean ( 4 / 20 )7.984905660377360.078522561372651101.689317322225
Trimmed Mean ( 5 / 20 )7.99215686274510.075969195886016105.202599152642
Trimmed Mean ( 6 / 20 )7.995918367346940.0745712908040981107.225157042709
Trimmed Mean ( 7 / 20 )80.0727419882513814109.977747272368
Trimmed Mean ( 8 / 20 )8.004444444444450.070974853674358112.778597348998
Trimmed Mean ( 9 / 20 )8.010465116279070.0689173944103477116.232849265647
Trimmed Mean ( 10 / 20 )8.015853658536590.0665902794577627120.375732371283
Trimmed Mean ( 11 / 20 )8.020512820512820.0646989798345075123.966604126191
Trimmed Mean ( 12 / 20 )8.024324324324320.062559929874537128.26619755516
Trimmed Mean ( 13 / 20 )8.027142857142860.0600889696509225133.587626876868
Trimmed Mean ( 14 / 20 )8.030303030303030.0576504698666837139.292932891493
Trimmed Mean ( 15 / 20 )8.033870967741930.0541000217028455148.500328001151
Trimmed Mean ( 16 / 20 )8.043103448275860.0505952339318603158.969587117791
Trimmed Mean ( 17 / 20 )8.051851851851850.0461850515308886174.338916704830
Trimmed Mean ( 18 / 20 )8.0580.043270467218801186.22401184748
Trimmed Mean ( 19 / 20 )8.065217391304350.0404318074471771199.477042965277
Trimmed Mean ( 20 / 20 )8.069047619047620.0381844194223418211.317802944685
Median8.05
Midrange7.85
Midmean - Weighted Average at Xnp7.99242424242424
Midmean - Weighted Average at X(n+1)p7.99242424242424
Midmean - Empirical Distribution Function7.99242424242424
Midmean - Empirical Distribution Function - Averaging7.99242424242424
Midmean - Empirical Distribution Function - Interpolation7.99242424242424
Midmean - Closest Observation7.99242424242424
Midmean - True Basic - Statistics Graphics Toolkit7.99242424242424
Midmean - MS Excel (old versions)7.99242424242424
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.9639344262295 & 0.0950922125627715 & 83.7495964348545 \tabularnewline
Geometric Mean & 7.92882052556376 &  &  \tabularnewline
Harmonic Mean & 7.89261055706515 &  &  \tabularnewline
Quadratic Mean & 7.99792493579982 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.96803278688525 & 0.0934174541887703 & 85.2949039992473 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.95 & 0.0884984023195603 & 89.8321302038111 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.95737704918033 & 0.0865618013027277 & 91.9271194617524 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.96065573770492 & 0.0843661253507102 & 94.358437164353 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.97704918032787 & 0.0790791760193974 & 100.874207115805 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.97704918032787 & 0.0790791760193974 & 100.874207115805 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.97704918032787 & 0.0769338457790518 & 103.687123652149 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.97049180327869 & 0.0758591685636244 & 105.069590851021 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.97786885245902 & 0.0743875227338249 & 107.247406006591 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.9860655737705 & 0.0699251272834196 & 114.208809966144 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.99508196721312 & 0.0682600391747047 & 117.126829458016 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.00491803278689 & 0.0664960752984673 & 120.381811961937 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.00491803278689 & 0.0629283671822149 & 127.206828831390 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.00491803278688 & 0.0629283671822149 & 127.206828831390 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.96803278688525 & 0.0574269884155273 & 138.750664221334 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.9811475409836 & 0.055097577803541 & 144.854780539385 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8.00901639344262 & 0.0459494286745866 & 174.300674120725 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8.00901639344262 & 0.0414476461644096 & 193.232116527761 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8.04016393442623 & 0.0364552962288058 & 220.548583228166 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8.04016393442623 & 0.0364552962288058 & 220.548583228166 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.9677966101695 & 0.0893001779854313 & 89.2248681908494 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.96754385964912 & 0.0842136264571376 & 94.6111003033978 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.97727272727273 & 0.0812550768351026 & 98.175683760187 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.98490566037736 & 0.078522561372651 & 101.689317322225 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.9921568627451 & 0.075969195886016 & 105.202599152642 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.99591836734694 & 0.0745712908040981 & 107.225157042709 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8 & 0.0727419882513814 & 109.977747272368 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8.00444444444445 & 0.070974853674358 & 112.778597348998 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8.01046511627907 & 0.0689173944103477 & 116.232849265647 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8.01585365853659 & 0.0665902794577627 & 120.375732371283 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8.02051282051282 & 0.0646989798345075 & 123.966604126191 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8.02432432432432 & 0.062559929874537 & 128.26619755516 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.02714285714286 & 0.0600889696509225 & 133.587626876868 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8.03030303030303 & 0.0576504698666837 & 139.292932891493 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8.03387096774193 & 0.0541000217028455 & 148.500328001151 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8.04310344827586 & 0.0505952339318603 & 158.969587117791 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8.05185185185185 & 0.0461850515308886 & 174.338916704830 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8.058 & 0.043270467218801 & 186.22401184748 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8.06521739130435 & 0.0404318074471771 & 199.477042965277 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8.06904761904762 & 0.0381844194223418 & 211.317802944685 \tabularnewline
Median & 8.05 &  &  \tabularnewline
Midrange & 7.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.99242424242424 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.99242424242424 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.99242424242424 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.99242424242424 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.99242424242424 &  &  \tabularnewline
Midmean - Closest Observation & 7.99242424242424 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.99242424242424 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.99242424242424 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49351&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]7.9639344262295[/C][C]0.0950922125627715[/C][C]83.7495964348545[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.92882052556376[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.89261055706515[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.99792493579982[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.96803278688525[/C][C]0.0934174541887703[/C][C]85.2949039992473[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.95[/C][C]0.0884984023195603[/C][C]89.8321302038111[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.95737704918033[/C][C]0.0865618013027277[/C][C]91.9271194617524[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.96065573770492[/C][C]0.0843661253507102[/C][C]94.358437164353[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.97704918032787[/C][C]0.0790791760193974[/C][C]100.874207115805[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.97704918032787[/C][C]0.0790791760193974[/C][C]100.874207115805[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.97704918032787[/C][C]0.0769338457790518[/C][C]103.687123652149[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.97049180327869[/C][C]0.0758591685636244[/C][C]105.069590851021[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.97786885245902[/C][C]0.0743875227338249[/C][C]107.247406006591[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.9860655737705[/C][C]0.0699251272834196[/C][C]114.208809966144[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.99508196721312[/C][C]0.0682600391747047[/C][C]117.126829458016[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.00491803278689[/C][C]0.0664960752984673[/C][C]120.381811961937[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.00491803278689[/C][C]0.0629283671822149[/C][C]127.206828831390[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.00491803278688[/C][C]0.0629283671822149[/C][C]127.206828831390[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.96803278688525[/C][C]0.0574269884155273[/C][C]138.750664221334[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.9811475409836[/C][C]0.055097577803541[/C][C]144.854780539385[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8.00901639344262[/C][C]0.0459494286745866[/C][C]174.300674120725[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8.00901639344262[/C][C]0.0414476461644096[/C][C]193.232116527761[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8.04016393442623[/C][C]0.0364552962288058[/C][C]220.548583228166[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8.04016393442623[/C][C]0.0364552962288058[/C][C]220.548583228166[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.9677966101695[/C][C]0.0893001779854313[/C][C]89.2248681908494[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.96754385964912[/C][C]0.0842136264571376[/C][C]94.6111003033978[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.97727272727273[/C][C]0.0812550768351026[/C][C]98.175683760187[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.98490566037736[/C][C]0.078522561372651[/C][C]101.689317322225[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.9921568627451[/C][C]0.075969195886016[/C][C]105.202599152642[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.99591836734694[/C][C]0.0745712908040981[/C][C]107.225157042709[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8[/C][C]0.0727419882513814[/C][C]109.977747272368[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8.00444444444445[/C][C]0.070974853674358[/C][C]112.778597348998[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8.01046511627907[/C][C]0.0689173944103477[/C][C]116.232849265647[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8.01585365853659[/C][C]0.0665902794577627[/C][C]120.375732371283[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8.02051282051282[/C][C]0.0646989798345075[/C][C]123.966604126191[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8.02432432432432[/C][C]0.062559929874537[/C][C]128.26619755516[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.02714285714286[/C][C]0.0600889696509225[/C][C]133.587626876868[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8.03030303030303[/C][C]0.0576504698666837[/C][C]139.292932891493[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8.03387096774193[/C][C]0.0541000217028455[/C][C]148.500328001151[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8.04310344827586[/C][C]0.0505952339318603[/C][C]158.969587117791[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8.05185185185185[/C][C]0.0461850515308886[/C][C]174.338916704830[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8.058[/C][C]0.043270467218801[/C][C]186.22401184748[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8.06521739130435[/C][C]0.0404318074471771[/C][C]199.477042965277[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8.06904761904762[/C][C]0.0381844194223418[/C][C]211.317802944685[/C][/ROW]
[ROW][C]Median[/C][C]8.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.99242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.99242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.99242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.99242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.99242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.99242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.99242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.99242424242424[/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=49351&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49351&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 Mean7.96393442622950.095092212562771583.7495964348545
Geometric Mean7.92882052556376
Harmonic Mean7.89261055706515
Quadratic Mean7.99792493579982
Winsorized Mean ( 1 / 20 )7.968032786885250.093417454188770385.2949039992473
Winsorized Mean ( 2 / 20 )7.950.088498402319560389.8321302038111
Winsorized Mean ( 3 / 20 )7.957377049180330.086561801302727791.9271194617524
Winsorized Mean ( 4 / 20 )7.960655737704920.084366125350710294.358437164353
Winsorized Mean ( 5 / 20 )7.977049180327870.0790791760193974100.874207115805
Winsorized Mean ( 6 / 20 )7.977049180327870.0790791760193974100.874207115805
Winsorized Mean ( 7 / 20 )7.977049180327870.0769338457790518103.687123652149
Winsorized Mean ( 8 / 20 )7.970491803278690.0758591685636244105.069590851021
Winsorized Mean ( 9 / 20 )7.977868852459020.0743875227338249107.247406006591
Winsorized Mean ( 10 / 20 )7.98606557377050.0699251272834196114.208809966144
Winsorized Mean ( 11 / 20 )7.995081967213120.0682600391747047117.126829458016
Winsorized Mean ( 12 / 20 )8.004918032786890.0664960752984673120.381811961937
Winsorized Mean ( 13 / 20 )8.004918032786890.0629283671822149127.206828831390
Winsorized Mean ( 14 / 20 )8.004918032786880.0629283671822149127.206828831390
Winsorized Mean ( 15 / 20 )7.968032786885250.0574269884155273138.750664221334
Winsorized Mean ( 16 / 20 )7.98114754098360.055097577803541144.854780539385
Winsorized Mean ( 17 / 20 )8.009016393442620.0459494286745866174.300674120725
Winsorized Mean ( 18 / 20 )8.009016393442620.0414476461644096193.232116527761
Winsorized Mean ( 19 / 20 )8.040163934426230.0364552962288058220.548583228166
Winsorized Mean ( 20 / 20 )8.040163934426230.0364552962288058220.548583228166
Trimmed Mean ( 1 / 20 )7.96779661016950.089300177985431389.2248681908494
Trimmed Mean ( 2 / 20 )7.967543859649120.084213626457137694.6111003033978
Trimmed Mean ( 3 / 20 )7.977272727272730.081255076835102698.175683760187
Trimmed Mean ( 4 / 20 )7.984905660377360.078522561372651101.689317322225
Trimmed Mean ( 5 / 20 )7.99215686274510.075969195886016105.202599152642
Trimmed Mean ( 6 / 20 )7.995918367346940.0745712908040981107.225157042709
Trimmed Mean ( 7 / 20 )80.0727419882513814109.977747272368
Trimmed Mean ( 8 / 20 )8.004444444444450.070974853674358112.778597348998
Trimmed Mean ( 9 / 20 )8.010465116279070.0689173944103477116.232849265647
Trimmed Mean ( 10 / 20 )8.015853658536590.0665902794577627120.375732371283
Trimmed Mean ( 11 / 20 )8.020512820512820.0646989798345075123.966604126191
Trimmed Mean ( 12 / 20 )8.024324324324320.062559929874537128.26619755516
Trimmed Mean ( 13 / 20 )8.027142857142860.0600889696509225133.587626876868
Trimmed Mean ( 14 / 20 )8.030303030303030.0576504698666837139.292932891493
Trimmed Mean ( 15 / 20 )8.033870967741930.0541000217028455148.500328001151
Trimmed Mean ( 16 / 20 )8.043103448275860.0505952339318603158.969587117791
Trimmed Mean ( 17 / 20 )8.051851851851850.0461850515308886174.338916704830
Trimmed Mean ( 18 / 20 )8.0580.043270467218801186.22401184748
Trimmed Mean ( 19 / 20 )8.065217391304350.0404318074471771199.477042965277
Trimmed Mean ( 20 / 20 )8.069047619047620.0381844194223418211.317802944685
Median8.05
Midrange7.85
Midmean - Weighted Average at Xnp7.99242424242424
Midmean - Weighted Average at X(n+1)p7.99242424242424
Midmean - Empirical Distribution Function7.99242424242424
Midmean - Empirical Distribution Function - Averaging7.99242424242424
Midmean - Empirical Distribution Function - Interpolation7.99242424242424
Midmean - Closest Observation7.99242424242424
Midmean - True Basic - Statistics Graphics Toolkit7.99242424242424
Midmean - MS Excel (old versions)7.99242424242424
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')