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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 20 Oct 2007 06:41:14 -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/qeb3g6g8a7dzbky1192887448.htm/, Retrieved Thu, 02 May 2024 23:13:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1162, Retrieved Thu, 02 May 2024 23:13:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact188
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [vrouwen boven de ...] [2007-10-20 13:41:14] [a1ee67c0c4cd462b4e85e70c1c0a96bd] [Current]
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Dataseries X:
7,9
7,3
7,3
7,4
7,7
7,7
7,7
7
7
7,1
7,3
7,3
7,4
7,9
7,7
7,8
8,6
8,6
8,6
7
7
7,1
8,7
8,9
8,9
7,9
7,8
7,9
8,2
8,2
8,2
7,9
7,9
7,9
8,5
8,5
8,5
8
7,8
7,9
8,3
8,2
8,1
7,9
8
8
7,7
7,7
7,6
7,8
7,6
7,6
8,1
8
7,8
7,4
7,3
7,2
7,4
7,5
7,2




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=1162&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=1162&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1162&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 Mean7.809836065573770.0626249534769757124.708053770373
Geometric Mean7.79488520292866
Harmonic Mean7.78005053210265
Quadratic Mean7.8248867377756
Winsorized Mean ( 1 / 20 )7.809836065573770.0626249534769757124.708053770373
Winsorized Mean ( 2 / 20 )7.803278688524590.0608665661055355128.203038019175
Winsorized Mean ( 3 / 20 )7.79836065573770.0597120505397777130.599444923479
Winsorized Mean ( 4 / 20 )7.804918032786890.0583201185425814133.828912351889
Winsorized Mean ( 5 / 20 )7.804918032786890.0583201185425814133.828912351889
Winsorized Mean ( 6 / 20 )7.804918032786890.0542422329313435143.890057820184
Winsorized Mean ( 7 / 20 )7.804918032786890.0542422329313435143.890057820184
Winsorized Mean ( 8 / 20 )7.818032786885250.0519303967085006150.548296997806
Winsorized Mean ( 9 / 20 )7.788524590163930.0459328543355233169.563261478843
Winsorized Mean ( 10 / 20 )7.772131147540980.0430485269158291180.543486719940
Winsorized Mean ( 11 / 20 )7.772131147540980.0430485269158291180.543486719940
Winsorized Mean ( 12 / 20 )7.772131147540980.0430485269158291180.543486719940
Winsorized Mean ( 13 / 20 )7.793442622950820.0393157911557465198.226778448326
Winsorized Mean ( 14 / 20 )7.770491803278690.0355552569487894218.546917393133
Winsorized Mean ( 15 / 20 )7.770491803278690.0355552569487894218.546917393133
Winsorized Mean ( 16 / 20 )7.744262295081970.031754229541779243.881284692889
Winsorized Mean ( 17 / 20 )7.772131147540980.0268705810997689289.243136152639
Winsorized Mean ( 18 / 20 )7.80163934426230.0221139378543155352.792858316721
Winsorized Mean ( 19 / 20 )7.80163934426230.0221139378543155352.792858316721
Winsorized Mean ( 20 / 20 )7.76885245901640.0175774606679435441.97808806278
Trimmed Mean ( 1 / 20 )7.805084745762710.060459168847107129.09679201017
Trimmed Mean ( 2 / 20 )7.80.0577892636870702134.973168065216
Trimmed Mean ( 3 / 20 )7.798181818181820.0556861641951308140.038049502855
Trimmed Mean ( 4 / 20 )7.798113207547170.0536403768564448145.377673770207
Trimmed Mean ( 5 / 20 )7.796078431372550.0516367997910083150.979116888071
Trimmed Mean ( 6 / 20 )7.793877551020410.0490910721119385158.763645113487
Trimmed Mean ( 7 / 20 )7.791489361702130.0472000277554092165.073830084967
Trimmed Mean ( 8 / 20 )7.788888888888890.0447464486737365174.067196833444
Trimmed Mean ( 9 / 20 )7.783720930232560.0422157922823952184.379363963247
Trimmed Mean ( 10 / 20 )7.782926829268290.0407105246511343191.177266713301
Trimmed Mean ( 11 / 20 )7.784615384615380.0394870042234574197.143732164693
Trimmed Mean ( 12 / 20 )7.786486486486490.0378002816619950205.990171081586
Trimmed Mean ( 13 / 20 )7.788571428571430.0354494381488060219.709305289335
Trimmed Mean ( 14 / 20 )7.787878787878790.0333591497822788233.455553834766
Trimmed Mean ( 15 / 20 )7.790322580645160.0315733788470765246.737057138453
Trimmed Mean ( 16 / 20 )7.793103448275860.0289091640416182269.572078841739
Trimmed Mean ( 17 / 20 )7.80.0261488180184246298.292641545178
Trimmed Mean ( 18 / 20 )7.8040.0241384893203089323.301093802672
Trimmed Mean ( 19 / 20 )7.804347826086960.023081108807362338.127075749397
Trimmed Mean ( 20 / 20 )7.80476190476190.02124257906971367.411220603189
Median7.8
Midrange7.95
Midmean - Weighted Average at Xnp7.75625
Midmean - Weighted Average at X(n+1)p7.7764705882353
Midmean - Empirical Distribution Function7.7764705882353
Midmean - Empirical Distribution Function - Averaging7.7764705882353
Midmean - Empirical Distribution Function - Interpolation7.7764705882353
Midmean - Closest Observation7.7764705882353
Midmean - True Basic - Statistics Graphics Toolkit7.7764705882353
Midmean - MS Excel (old versions)7.7764705882353
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.80983606557377 & 0.0626249534769757 & 124.708053770373 \tabularnewline
Geometric Mean & 7.79488520292866 &  &  \tabularnewline
Harmonic Mean & 7.78005053210265 &  &  \tabularnewline
Quadratic Mean & 7.8248867377756 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.80983606557377 & 0.0626249534769757 & 124.708053770373 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.80327868852459 & 0.0608665661055355 & 128.203038019175 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.7983606557377 & 0.0597120505397777 & 130.599444923479 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.80491803278689 & 0.0583201185425814 & 133.828912351889 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.80491803278689 & 0.0583201185425814 & 133.828912351889 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.80491803278689 & 0.0542422329313435 & 143.890057820184 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.80491803278689 & 0.0542422329313435 & 143.890057820184 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.81803278688525 & 0.0519303967085006 & 150.548296997806 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.78852459016393 & 0.0459328543355233 & 169.563261478843 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.77213114754098 & 0.0430485269158291 & 180.543486719940 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.77213114754098 & 0.0430485269158291 & 180.543486719940 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.77213114754098 & 0.0430485269158291 & 180.543486719940 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.79344262295082 & 0.0393157911557465 & 198.226778448326 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.77049180327869 & 0.0355552569487894 & 218.546917393133 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.77049180327869 & 0.0355552569487894 & 218.546917393133 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.74426229508197 & 0.031754229541779 & 243.881284692889 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.77213114754098 & 0.0268705810997689 & 289.243136152639 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.8016393442623 & 0.0221139378543155 & 352.792858316721 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.8016393442623 & 0.0221139378543155 & 352.792858316721 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.7688524590164 & 0.0175774606679435 & 441.97808806278 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.80508474576271 & 0.060459168847107 & 129.09679201017 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.8 & 0.0577892636870702 & 134.973168065216 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.79818181818182 & 0.0556861641951308 & 140.038049502855 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.79811320754717 & 0.0536403768564448 & 145.377673770207 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.79607843137255 & 0.0516367997910083 & 150.979116888071 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.79387755102041 & 0.0490910721119385 & 158.763645113487 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.79148936170213 & 0.0472000277554092 & 165.073830084967 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.78888888888889 & 0.0447464486737365 & 174.067196833444 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.78372093023256 & 0.0422157922823952 & 184.379363963247 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.78292682926829 & 0.0407105246511343 & 191.177266713301 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.78461538461538 & 0.0394870042234574 & 197.143732164693 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.78648648648649 & 0.0378002816619950 & 205.990171081586 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.78857142857143 & 0.0354494381488060 & 219.709305289335 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.78787878787879 & 0.0333591497822788 & 233.455553834766 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.79032258064516 & 0.0315733788470765 & 246.737057138453 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.79310344827586 & 0.0289091640416182 & 269.572078841739 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.8 & 0.0261488180184246 & 298.292641545178 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.804 & 0.0241384893203089 & 323.301093802672 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.80434782608696 & 0.023081108807362 & 338.127075749397 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.8047619047619 & 0.02124257906971 & 367.411220603189 \tabularnewline
Median & 7.8 &  &  \tabularnewline
Midrange & 7.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.75625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.7764705882353 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.7764705882353 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.7764705882353 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.7764705882353 &  &  \tabularnewline
Midmean - Closest Observation & 7.7764705882353 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.7764705882353 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.7764705882353 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1162&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]7.80983606557377[/C][C]0.0626249534769757[/C][C]124.708053770373[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.79488520292866[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.78005053210265[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.8248867377756[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.80983606557377[/C][C]0.0626249534769757[/C][C]124.708053770373[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.80327868852459[/C][C]0.0608665661055355[/C][C]128.203038019175[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.7983606557377[/C][C]0.0597120505397777[/C][C]130.599444923479[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.80491803278689[/C][C]0.0583201185425814[/C][C]133.828912351889[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.80491803278689[/C][C]0.0583201185425814[/C][C]133.828912351889[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.80491803278689[/C][C]0.0542422329313435[/C][C]143.890057820184[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.80491803278689[/C][C]0.0542422329313435[/C][C]143.890057820184[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.81803278688525[/C][C]0.0519303967085006[/C][C]150.548296997806[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.78852459016393[/C][C]0.0459328543355233[/C][C]169.563261478843[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.77213114754098[/C][C]0.0430485269158291[/C][C]180.543486719940[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.77213114754098[/C][C]0.0430485269158291[/C][C]180.543486719940[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.77213114754098[/C][C]0.0430485269158291[/C][C]180.543486719940[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.79344262295082[/C][C]0.0393157911557465[/C][C]198.226778448326[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.77049180327869[/C][C]0.0355552569487894[/C][C]218.546917393133[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.77049180327869[/C][C]0.0355552569487894[/C][C]218.546917393133[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.74426229508197[/C][C]0.031754229541779[/C][C]243.881284692889[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.77213114754098[/C][C]0.0268705810997689[/C][C]289.243136152639[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.8016393442623[/C][C]0.0221139378543155[/C][C]352.792858316721[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.8016393442623[/C][C]0.0221139378543155[/C][C]352.792858316721[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.7688524590164[/C][C]0.0175774606679435[/C][C]441.97808806278[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.80508474576271[/C][C]0.060459168847107[/C][C]129.09679201017[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.8[/C][C]0.0577892636870702[/C][C]134.973168065216[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.79818181818182[/C][C]0.0556861641951308[/C][C]140.038049502855[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.79811320754717[/C][C]0.0536403768564448[/C][C]145.377673770207[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.79607843137255[/C][C]0.0516367997910083[/C][C]150.979116888071[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.79387755102041[/C][C]0.0490910721119385[/C][C]158.763645113487[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.79148936170213[/C][C]0.0472000277554092[/C][C]165.073830084967[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.78888888888889[/C][C]0.0447464486737365[/C][C]174.067196833444[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.78372093023256[/C][C]0.0422157922823952[/C][C]184.379363963247[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.78292682926829[/C][C]0.0407105246511343[/C][C]191.177266713301[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.78461538461538[/C][C]0.0394870042234574[/C][C]197.143732164693[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.78648648648649[/C][C]0.0378002816619950[/C][C]205.990171081586[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.78857142857143[/C][C]0.0354494381488060[/C][C]219.709305289335[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.78787878787879[/C][C]0.0333591497822788[/C][C]233.455553834766[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.79032258064516[/C][C]0.0315733788470765[/C][C]246.737057138453[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.79310344827586[/C][C]0.0289091640416182[/C][C]269.572078841739[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.8[/C][C]0.0261488180184246[/C][C]298.292641545178[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.804[/C][C]0.0241384893203089[/C][C]323.301093802672[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.80434782608696[/C][C]0.023081108807362[/C][C]338.127075749397[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.8047619047619[/C][C]0.02124257906971[/C][C]367.411220603189[/C][/ROW]
[ROW][C]Median[/C][C]7.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.75625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.7764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.7764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.7764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.7764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.7764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.7764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.7764705882353[/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=1162&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1162&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 Mean7.809836065573770.0626249534769757124.708053770373
Geometric Mean7.79488520292866
Harmonic Mean7.78005053210265
Quadratic Mean7.8248867377756
Winsorized Mean ( 1 / 20 )7.809836065573770.0626249534769757124.708053770373
Winsorized Mean ( 2 / 20 )7.803278688524590.0608665661055355128.203038019175
Winsorized Mean ( 3 / 20 )7.79836065573770.0597120505397777130.599444923479
Winsorized Mean ( 4 / 20 )7.804918032786890.0583201185425814133.828912351889
Winsorized Mean ( 5 / 20 )7.804918032786890.0583201185425814133.828912351889
Winsorized Mean ( 6 / 20 )7.804918032786890.0542422329313435143.890057820184
Winsorized Mean ( 7 / 20 )7.804918032786890.0542422329313435143.890057820184
Winsorized Mean ( 8 / 20 )7.818032786885250.0519303967085006150.548296997806
Winsorized Mean ( 9 / 20 )7.788524590163930.0459328543355233169.563261478843
Winsorized Mean ( 10 / 20 )7.772131147540980.0430485269158291180.543486719940
Winsorized Mean ( 11 / 20 )7.772131147540980.0430485269158291180.543486719940
Winsorized Mean ( 12 / 20 )7.772131147540980.0430485269158291180.543486719940
Winsorized Mean ( 13 / 20 )7.793442622950820.0393157911557465198.226778448326
Winsorized Mean ( 14 / 20 )7.770491803278690.0355552569487894218.546917393133
Winsorized Mean ( 15 / 20 )7.770491803278690.0355552569487894218.546917393133
Winsorized Mean ( 16 / 20 )7.744262295081970.031754229541779243.881284692889
Winsorized Mean ( 17 / 20 )7.772131147540980.0268705810997689289.243136152639
Winsorized Mean ( 18 / 20 )7.80163934426230.0221139378543155352.792858316721
Winsorized Mean ( 19 / 20 )7.80163934426230.0221139378543155352.792858316721
Winsorized Mean ( 20 / 20 )7.76885245901640.0175774606679435441.97808806278
Trimmed Mean ( 1 / 20 )7.805084745762710.060459168847107129.09679201017
Trimmed Mean ( 2 / 20 )7.80.0577892636870702134.973168065216
Trimmed Mean ( 3 / 20 )7.798181818181820.0556861641951308140.038049502855
Trimmed Mean ( 4 / 20 )7.798113207547170.0536403768564448145.377673770207
Trimmed Mean ( 5 / 20 )7.796078431372550.0516367997910083150.979116888071
Trimmed Mean ( 6 / 20 )7.793877551020410.0490910721119385158.763645113487
Trimmed Mean ( 7 / 20 )7.791489361702130.0472000277554092165.073830084967
Trimmed Mean ( 8 / 20 )7.788888888888890.0447464486737365174.067196833444
Trimmed Mean ( 9 / 20 )7.783720930232560.0422157922823952184.379363963247
Trimmed Mean ( 10 / 20 )7.782926829268290.0407105246511343191.177266713301
Trimmed Mean ( 11 / 20 )7.784615384615380.0394870042234574197.143732164693
Trimmed Mean ( 12 / 20 )7.786486486486490.0378002816619950205.990171081586
Trimmed Mean ( 13 / 20 )7.788571428571430.0354494381488060219.709305289335
Trimmed Mean ( 14 / 20 )7.787878787878790.0333591497822788233.455553834766
Trimmed Mean ( 15 / 20 )7.790322580645160.0315733788470765246.737057138453
Trimmed Mean ( 16 / 20 )7.793103448275860.0289091640416182269.572078841739
Trimmed Mean ( 17 / 20 )7.80.0261488180184246298.292641545178
Trimmed Mean ( 18 / 20 )7.8040.0241384893203089323.301093802672
Trimmed Mean ( 19 / 20 )7.804347826086960.023081108807362338.127075749397
Trimmed Mean ( 20 / 20 )7.80476190476190.02124257906971367.411220603189
Median7.8
Midrange7.95
Midmean - Weighted Average at Xnp7.75625
Midmean - Weighted Average at X(n+1)p7.7764705882353
Midmean - Empirical Distribution Function7.7764705882353
Midmean - Empirical Distribution Function - Averaging7.7764705882353
Midmean - Empirical Distribution Function - Interpolation7.7764705882353
Midmean - Closest Observation7.7764705882353
Midmean - True Basic - Statistics Graphics Toolkit7.7764705882353
Midmean - MS Excel (old versions)7.7764705882353
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')