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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 26 Nov 2010 14:51:47 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/26/t1290783062yo13jrn60e6ghlg.htm/, Retrieved Fri, 03 May 2024 17:29:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=101954, Retrieved Fri, 03 May 2024 17:29:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWorkshop 3
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Minitutorial test...] [2010-11-26 14:51:47] [f76239c595e4d455b3b05a43389f68d5] [Current]
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Dataseries X:
2
3
1
1
0
1
-1
2
2
0
1
1
3
3
1
1
-2
1
1
-1
-4
-2
-1
-5
-4
-5
0
-2
-4
-6
-2
-2
-2
1
-2
0
-1
2
3
2
3
4
5
5
4
5
6
4
6
6
3
5
5
5
3
5
5
6
6
5
4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101954&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101954&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101954&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.409836065573770.4071606664392593.46260378710745
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean3.4546238911795
Winsorized Mean ( 1 / 20 )1.426229508196720.4024915682471843.54350158043764
Winsorized Mean ( 2 / 20 )1.426229508196720.4024915682471843.54350158043764
Winsorized Mean ( 3 / 20 )1.475409836065570.3901845978823583.78131234311411
Winsorized Mean ( 4 / 20 )1.475409836065570.3901845978823583.78131234311411
Winsorized Mean ( 5 / 20 )1.393442622950820.3756805762461363.70911543224922
Winsorized Mean ( 6 / 20 )1.590163934426230.3341877431018734.75829520157323
Winsorized Mean ( 7 / 20 )1.590163934426230.3341877431018734.75829520157323
Winsorized Mean ( 8 / 20 )1.590163934426230.3341877431018734.75829520157323
Winsorized Mean ( 9 / 20 )1.590163934426230.3341877431018734.75829520157323
Winsorized Mean ( 10 / 20 )1.590163934426230.3341877431018734.75829520157323
Winsorized Mean ( 11 / 20 )1.590163934426230.3341877431018734.75829520157323
Winsorized Mean ( 12 / 20 )1.590163934426230.3341877431018734.75829520157323
Winsorized Mean ( 13 / 20 )1.803278688524590.2982825815100866.0455380243637
Winsorized Mean ( 14 / 20 )1.573770491803280.2597382208770886.05906395481168
Winsorized Mean ( 15 / 20 )1.573770491803280.2597382208770886.05906395481168
Winsorized Mean ( 16 / 20 )1.573770491803280.2597382208770886.05906395481168
Winsorized Mean ( 17 / 20 )1.852459016393440.2165755153877018.55340924885842
Winsorized Mean ( 18 / 20 )1.557377049180330.1710216650768189.10631438701524
Winsorized Mean ( 19 / 20 )1.557377049180330.1710216650768189.10631438701524
Winsorized Mean ( 20 / 20 )1.557377049180330.1710216650768189.10631438701524
Trimmed Mean ( 1 / 20 )1.457627118644070.3937872533179433.70155993207628
Trimmed Mean ( 2 / 20 )1.491228070175440.3830058591016993.89348631290644
Trimmed Mean ( 3 / 20 )1.527272727272730.3695976021451964.13225821382018
Trimmed Mean ( 4 / 20 )1.547169811320750.3589676757886964.31005328800548
Trimmed Mean ( 5 / 20 )1.568627450980390.3455656368636894.53930392274261
Trimmed Mean ( 6 / 20 )1.612244897959180.3335241713881934.83396717919636
Trimmed Mean ( 7 / 20 )1.617021276595740.3311645019808324.8828339599313
Trimmed Mean ( 8 / 20 )1.622222222222220.3276621949953654.95089835507318
Trimmed Mean ( 9 / 20 )1.627906976744190.3226812775502395.04493780706174
Trimmed Mean ( 10 / 20 )1.634146341463410.3157571186864835.17532699899623
Trimmed Mean ( 11 / 20 )1.641025641025640.3062268294954035.35885651733947
Trimmed Mean ( 12 / 20 )1.648648648648650.2931044772071615.62478152622491
Trimmed Mean ( 13 / 20 )1.657142857142860.2748348844042086.02959431709422
Trimmed Mean ( 14 / 20 )1.636363636363640.2604562642071386.28268105336202
Trimmed Mean ( 15 / 20 )1.645161290322580.2520811744015936.52631555778797
Trimmed Mean ( 16 / 20 )1.655172413793100.2394362326997986.91279007830172
Trimmed Mean ( 17 / 20 )1.666666666666670.2200750972578427.57317246446102
Trimmed Mean ( 18 / 20 )1.640.2072036035722677.91492026067978
Trimmed Mean ( 19 / 20 )1.652173913043480.2047720766322318.06835551123881
Trimmed Mean ( 20 / 20 )1.666666666666670.1992047682223998.36660026534076
Median1
Midrange0
Midmean - Weighted Average at Xnp1.55882352941176
Midmean - Weighted Average at X(n+1)p1.55882352941176
Midmean - Empirical Distribution Function1.55882352941176
Midmean - Empirical Distribution Function - Averaging1.55882352941176
Midmean - Empirical Distribution Function - Interpolation1.55882352941176
Midmean - Closest Observation1.55882352941176
Midmean - True Basic - Statistics Graphics Toolkit1.55882352941176
Midmean - MS Excel (old versions)1.55882352941176
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.40983606557377 & 0.407160666439259 & 3.46260378710745 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 3.4546238911795 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.42622950819672 & 0.402491568247184 & 3.54350158043764 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.42622950819672 & 0.402491568247184 & 3.54350158043764 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.47540983606557 & 0.390184597882358 & 3.78131234311411 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.47540983606557 & 0.390184597882358 & 3.78131234311411 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.39344262295082 & 0.375680576246136 & 3.70911543224922 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.59016393442623 & 0.334187743101873 & 4.75829520157323 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.59016393442623 & 0.334187743101873 & 4.75829520157323 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.59016393442623 & 0.334187743101873 & 4.75829520157323 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.59016393442623 & 0.334187743101873 & 4.75829520157323 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.59016393442623 & 0.334187743101873 & 4.75829520157323 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.59016393442623 & 0.334187743101873 & 4.75829520157323 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.59016393442623 & 0.334187743101873 & 4.75829520157323 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.80327868852459 & 0.298282581510086 & 6.0455380243637 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.57377049180328 & 0.259738220877088 & 6.05906395481168 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.57377049180328 & 0.259738220877088 & 6.05906395481168 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.57377049180328 & 0.259738220877088 & 6.05906395481168 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.85245901639344 & 0.216575515387701 & 8.55340924885842 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.55737704918033 & 0.171021665076818 & 9.10631438701524 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.55737704918033 & 0.171021665076818 & 9.10631438701524 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.55737704918033 & 0.171021665076818 & 9.10631438701524 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.45762711864407 & 0.393787253317943 & 3.70155993207628 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.49122807017544 & 0.383005859101699 & 3.89348631290644 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.52727272727273 & 0.369597602145196 & 4.13225821382018 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.54716981132075 & 0.358967675788696 & 4.31005328800548 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.56862745098039 & 0.345565636863689 & 4.53930392274261 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.61224489795918 & 0.333524171388193 & 4.83396717919636 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.61702127659574 & 0.331164501980832 & 4.8828339599313 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.62222222222222 & 0.327662194995365 & 4.95089835507318 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.62790697674419 & 0.322681277550239 & 5.04493780706174 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.63414634146341 & 0.315757118686483 & 5.17532699899623 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.64102564102564 & 0.306226829495403 & 5.35885651733947 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.64864864864865 & 0.293104477207161 & 5.62478152622491 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.65714285714286 & 0.274834884404208 & 6.02959431709422 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.63636363636364 & 0.260456264207138 & 6.28268105336202 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.64516129032258 & 0.252081174401593 & 6.52631555778797 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.65517241379310 & 0.239436232699798 & 6.91279007830172 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.66666666666667 & 0.220075097257842 & 7.57317246446102 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.64 & 0.207203603572267 & 7.91492026067978 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.65217391304348 & 0.204772076632231 & 8.06835551123881 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.66666666666667 & 0.199204768222399 & 8.36660026534076 \tabularnewline
Median & 1 &  &  \tabularnewline
Midrange & 0 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.55882352941176 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.55882352941176 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.55882352941176 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.55882352941176 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.55882352941176 &  &  \tabularnewline
Midmean - Closest Observation & 1.55882352941176 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.55882352941176 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.55882352941176 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101954&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]1.40983606557377[/C][C]0.407160666439259[/C][C]3.46260378710745[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.4546238911795[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.42622950819672[/C][C]0.402491568247184[/C][C]3.54350158043764[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.42622950819672[/C][C]0.402491568247184[/C][C]3.54350158043764[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.47540983606557[/C][C]0.390184597882358[/C][C]3.78131234311411[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.47540983606557[/C][C]0.390184597882358[/C][C]3.78131234311411[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.39344262295082[/C][C]0.375680576246136[/C][C]3.70911543224922[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.59016393442623[/C][C]0.334187743101873[/C][C]4.75829520157323[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.59016393442623[/C][C]0.334187743101873[/C][C]4.75829520157323[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.59016393442623[/C][C]0.334187743101873[/C][C]4.75829520157323[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.59016393442623[/C][C]0.334187743101873[/C][C]4.75829520157323[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.59016393442623[/C][C]0.334187743101873[/C][C]4.75829520157323[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.59016393442623[/C][C]0.334187743101873[/C][C]4.75829520157323[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.59016393442623[/C][C]0.334187743101873[/C][C]4.75829520157323[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.80327868852459[/C][C]0.298282581510086[/C][C]6.0455380243637[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.57377049180328[/C][C]0.259738220877088[/C][C]6.05906395481168[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.57377049180328[/C][C]0.259738220877088[/C][C]6.05906395481168[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.57377049180328[/C][C]0.259738220877088[/C][C]6.05906395481168[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.85245901639344[/C][C]0.216575515387701[/C][C]8.55340924885842[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.55737704918033[/C][C]0.171021665076818[/C][C]9.10631438701524[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.55737704918033[/C][C]0.171021665076818[/C][C]9.10631438701524[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.55737704918033[/C][C]0.171021665076818[/C][C]9.10631438701524[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.45762711864407[/C][C]0.393787253317943[/C][C]3.70155993207628[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.49122807017544[/C][C]0.383005859101699[/C][C]3.89348631290644[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.52727272727273[/C][C]0.369597602145196[/C][C]4.13225821382018[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.54716981132075[/C][C]0.358967675788696[/C][C]4.31005328800548[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.56862745098039[/C][C]0.345565636863689[/C][C]4.53930392274261[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.61224489795918[/C][C]0.333524171388193[/C][C]4.83396717919636[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.61702127659574[/C][C]0.331164501980832[/C][C]4.8828339599313[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.62222222222222[/C][C]0.327662194995365[/C][C]4.95089835507318[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.62790697674419[/C][C]0.322681277550239[/C][C]5.04493780706174[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.63414634146341[/C][C]0.315757118686483[/C][C]5.17532699899623[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.64102564102564[/C][C]0.306226829495403[/C][C]5.35885651733947[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.64864864864865[/C][C]0.293104477207161[/C][C]5.62478152622491[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.65714285714286[/C][C]0.274834884404208[/C][C]6.02959431709422[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.63636363636364[/C][C]0.260456264207138[/C][C]6.28268105336202[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.64516129032258[/C][C]0.252081174401593[/C][C]6.52631555778797[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.65517241379310[/C][C]0.239436232699798[/C][C]6.91279007830172[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.66666666666667[/C][C]0.220075097257842[/C][C]7.57317246446102[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.64[/C][C]0.207203603572267[/C][C]7.91492026067978[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.65217391304348[/C][C]0.204772076632231[/C][C]8.06835551123881[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.66666666666667[/C][C]0.199204768222399[/C][C]8.36660026534076[/C][/ROW]
[ROW][C]Median[/C][C]1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.55882352941176[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.55882352941176[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.55882352941176[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.55882352941176[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.55882352941176[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.55882352941176[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.55882352941176[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.55882352941176[/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=101954&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101954&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 Mean1.409836065573770.4071606664392593.46260378710745
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean3.4546238911795
Winsorized Mean ( 1 / 20 )1.426229508196720.4024915682471843.54350158043764
Winsorized Mean ( 2 / 20 )1.426229508196720.4024915682471843.54350158043764
Winsorized Mean ( 3 / 20 )1.475409836065570.3901845978823583.78131234311411
Winsorized Mean ( 4 / 20 )1.475409836065570.3901845978823583.78131234311411
Winsorized Mean ( 5 / 20 )1.393442622950820.3756805762461363.70911543224922
Winsorized Mean ( 6 / 20 )1.590163934426230.3341877431018734.75829520157323
Winsorized Mean ( 7 / 20 )1.590163934426230.3341877431018734.75829520157323
Winsorized Mean ( 8 / 20 )1.590163934426230.3341877431018734.75829520157323
Winsorized Mean ( 9 / 20 )1.590163934426230.3341877431018734.75829520157323
Winsorized Mean ( 10 / 20 )1.590163934426230.3341877431018734.75829520157323
Winsorized Mean ( 11 / 20 )1.590163934426230.3341877431018734.75829520157323
Winsorized Mean ( 12 / 20 )1.590163934426230.3341877431018734.75829520157323
Winsorized Mean ( 13 / 20 )1.803278688524590.2982825815100866.0455380243637
Winsorized Mean ( 14 / 20 )1.573770491803280.2597382208770886.05906395481168
Winsorized Mean ( 15 / 20 )1.573770491803280.2597382208770886.05906395481168
Winsorized Mean ( 16 / 20 )1.573770491803280.2597382208770886.05906395481168
Winsorized Mean ( 17 / 20 )1.852459016393440.2165755153877018.55340924885842
Winsorized Mean ( 18 / 20 )1.557377049180330.1710216650768189.10631438701524
Winsorized Mean ( 19 / 20 )1.557377049180330.1710216650768189.10631438701524
Winsorized Mean ( 20 / 20 )1.557377049180330.1710216650768189.10631438701524
Trimmed Mean ( 1 / 20 )1.457627118644070.3937872533179433.70155993207628
Trimmed Mean ( 2 / 20 )1.491228070175440.3830058591016993.89348631290644
Trimmed Mean ( 3 / 20 )1.527272727272730.3695976021451964.13225821382018
Trimmed Mean ( 4 / 20 )1.547169811320750.3589676757886964.31005328800548
Trimmed Mean ( 5 / 20 )1.568627450980390.3455656368636894.53930392274261
Trimmed Mean ( 6 / 20 )1.612244897959180.3335241713881934.83396717919636
Trimmed Mean ( 7 / 20 )1.617021276595740.3311645019808324.8828339599313
Trimmed Mean ( 8 / 20 )1.622222222222220.3276621949953654.95089835507318
Trimmed Mean ( 9 / 20 )1.627906976744190.3226812775502395.04493780706174
Trimmed Mean ( 10 / 20 )1.634146341463410.3157571186864835.17532699899623
Trimmed Mean ( 11 / 20 )1.641025641025640.3062268294954035.35885651733947
Trimmed Mean ( 12 / 20 )1.648648648648650.2931044772071615.62478152622491
Trimmed Mean ( 13 / 20 )1.657142857142860.2748348844042086.02959431709422
Trimmed Mean ( 14 / 20 )1.636363636363640.2604562642071386.28268105336202
Trimmed Mean ( 15 / 20 )1.645161290322580.2520811744015936.52631555778797
Trimmed Mean ( 16 / 20 )1.655172413793100.2394362326997986.91279007830172
Trimmed Mean ( 17 / 20 )1.666666666666670.2200750972578427.57317246446102
Trimmed Mean ( 18 / 20 )1.640.2072036035722677.91492026067978
Trimmed Mean ( 19 / 20 )1.652173913043480.2047720766322318.06835551123881
Trimmed Mean ( 20 / 20 )1.666666666666670.1992047682223998.36660026534076
Median1
Midrange0
Midmean - Weighted Average at Xnp1.55882352941176
Midmean - Weighted Average at X(n+1)p1.55882352941176
Midmean - Empirical Distribution Function1.55882352941176
Midmean - Empirical Distribution Function - Averaging1.55882352941176
Midmean - Empirical Distribution Function - Interpolation1.55882352941176
Midmean - Closest Observation1.55882352941176
Midmean - True Basic - Statistics Graphics Toolkit1.55882352941176
Midmean - MS Excel (old versions)1.55882352941176
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')