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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 13 Mar 2017 21:48:14 +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/2017/Mar/13/t1489441727vdvfjtcoo9hv0w0.htm/, Retrieved Tue, 14 May 2024 14:52:39 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 14:52:39 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
99,49
99,84
100,9
101,31
100,09
99,28
99,57
101,04
101,87
101,39
100,3
99,95
99,87
100,51
100,27
100,04
99,23
99,32
99,95
100,23
101,02
99,83
99,61
100,12
99,83
100,03
100,07
100,46
100,43
100,68
101,8
101,21
100,63
100,55
99,76
98,8
96,59
97,59
98,79
98,79
99,65
99,78
100,05
99,22
97,72
97,55
98,14
97,95
97,24
97,02
97,57
98,07
98,86
99,57
100,14
99,88
99,79
100,59
100,55
101,42




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean99.69666666666670.155379009312197641.635360580461
Geometric Mean99.6894839878464
Harmonic Mean99.6822621008716
Quadratic Mean99.7038101578871
Winsorized Mean ( 1 / 20 )99.70266666666670.1528233104551652.404835163938
Winsorized Mean ( 2 / 20 )99.69733333333330.147972906870171673.753969169546
Winsorized Mean ( 3 / 20 )99.71133333333330.143513511768975694.787076870132
Winsorized Mean ( 4 / 20 )99.70733333333330.142135025058566701.497279029213
Winsorized Mean ( 5 / 20 )99.70066666666670.140152835596717711.371027508502
Winsorized Mean ( 6 / 20 )99.69666666666670.133866589011165744.746447960603
Winsorized Mean ( 7 / 20 )99.72116666666670.126930091454945785.638500087769
Winsorized Mean ( 8 / 20 )99.72116666666670.120462641996434827.818193374997
Winsorized Mean ( 9 / 20 )99.69866666666670.11283517969932883.577860489441
Winsorized Mean ( 10 / 20 )99.79866666666670.08810063155620721132.78037743687
Winsorized Mean ( 11 / 20 )99.79133333333330.08694321371185981147.7759916266
Winsorized Mean ( 12 / 20 )99.78533333333330.08532174621189981169.51817987307
Winsorized Mean ( 13 / 20 )99.79833333333330.08280061364256721205.28494829932
Winsorized Mean ( 14 / 20 )99.8730.0661108040949371510.69104917525
Winsorized Mean ( 15 / 20 )99.8630.06367657508604881568.28472424987
Winsorized Mean ( 16 / 20 )99.86833333333330.06017965883170031659.50314893986
Winsorized Mean ( 17 / 20 )99.84283333333330.0526506939592251896.32511606886
Winsorized Mean ( 18 / 20 )99.88483333333330.04301588963195622322.04504400462
Winsorized Mean ( 19 / 20 )99.89750.0372308609308162683.19070530316
Winsorized Mean ( 20 / 20 )99.86750.03284067427757353040.96983989755
Trimmed Mean ( 1 / 20 )99.71275862068970.146624820744255680.05374611581
Trimmed Mean ( 2 / 20 )99.72357142857140.138944403665038717.722835883201
Trimmed Mean ( 3 / 20 )99.73814814814810.132707670958021751.562795339074
Trimmed Mean ( 4 / 20 )99.74846153846150.127159293876853784.437051333919
Trimmed Mean ( 5 / 20 )99.76080.120694872488014826.553754467963
Trimmed Mean ( 6 / 20 )99.77583333333330.113116644643962882.061465378336
Trimmed Mean ( 7 / 20 )99.79304347826090.105473796258229946.14062467174
Trimmed Mean ( 8 / 20 )99.80704545454550.09785575285248761019.94049961477
Trimmed Mean ( 9 / 20 )99.8223809523810.08983001725727571111.23635506478
Trimmed Mean ( 10 / 20 )99.8430.08130600633819531227.99045847486
Trimmed Mean ( 11 / 20 )99.850.07812981137389281278.00129354165
Trimmed Mean ( 12 / 20 )99.85888888888890.07404715119197551348.58515528833
Trimmed Mean ( 13 / 20 )99.86970588235290.06876616360840911452.30881936448
Trimmed Mean ( 14 / 20 )99.880.06205486646196991609.5433878858
Trimmed Mean ( 15 / 20 )99.8810.05859926248015761704.47537686709
Trimmed Mean ( 16 / 20 )99.88357142857140.05429006526701671839.81306593224
Trimmed Mean ( 17 / 20 )99.88576923076920.04907191920475392035.4975075255
Trimmed Mean ( 18 / 20 )99.89208333333330.04408070318994272266.11819015002
Trimmed Mean ( 19 / 20 )99.89318181818180.04077382640031622449.93395609805
Trimmed Mean ( 20 / 20 )99.89250.03805034753282062625.27168546456
Median99.875
Midrange99.23
Midmean - Weighted Average at Xnp99.8596774193549
Midmean - Weighted Average at X(n+1)p99.881
Midmean - Empirical Distribution Function99.8596774193549
Midmean - Empirical Distribution Function - Averaging99.881
Midmean - Empirical Distribution Function - Interpolation99.881
Midmean - Closest Observation99.8596774193549
Midmean - True Basic - Statistics Graphics Toolkit99.881
Midmean - MS Excel (old versions)99.88
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 99.6966666666667 & 0.155379009312197 & 641.635360580461 \tabularnewline
Geometric Mean & 99.6894839878464 &  &  \tabularnewline
Harmonic Mean & 99.6822621008716 &  &  \tabularnewline
Quadratic Mean & 99.7038101578871 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 99.7026666666667 & 0.1528233104551 & 652.404835163938 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 99.6973333333333 & 0.147972906870171 & 673.753969169546 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 99.7113333333333 & 0.143513511768975 & 694.787076870132 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 99.7073333333333 & 0.142135025058566 & 701.497279029213 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 99.7006666666667 & 0.140152835596717 & 711.371027508502 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 99.6966666666667 & 0.133866589011165 & 744.746447960603 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 99.7211666666667 & 0.126930091454945 & 785.638500087769 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 99.7211666666667 & 0.120462641996434 & 827.818193374997 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 99.6986666666667 & 0.11283517969932 & 883.577860489441 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 99.7986666666667 & 0.0881006315562072 & 1132.78037743687 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 99.7913333333333 & 0.0869432137118598 & 1147.7759916266 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 99.7853333333333 & 0.0853217462118998 & 1169.51817987307 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 99.7983333333333 & 0.0828006136425672 & 1205.28494829932 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 99.873 & 0.066110804094937 & 1510.69104917525 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 99.863 & 0.0636765750860488 & 1568.28472424987 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 99.8683333333333 & 0.0601796588317003 & 1659.50314893986 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 99.8428333333333 & 0.052650693959225 & 1896.32511606886 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 99.8848333333333 & 0.0430158896319562 & 2322.04504400462 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 99.8975 & 0.037230860930816 & 2683.19070530316 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 99.8675 & 0.0328406742775735 & 3040.96983989755 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 99.7127586206897 & 0.146624820744255 & 680.05374611581 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 99.7235714285714 & 0.138944403665038 & 717.722835883201 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 99.7381481481481 & 0.132707670958021 & 751.562795339074 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 99.7484615384615 & 0.127159293876853 & 784.437051333919 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 99.7608 & 0.120694872488014 & 826.553754467963 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 99.7758333333333 & 0.113116644643962 & 882.061465378336 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 99.7930434782609 & 0.105473796258229 & 946.14062467174 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 99.8070454545455 & 0.0978557528524876 & 1019.94049961477 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 99.822380952381 & 0.0898300172572757 & 1111.23635506478 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 99.843 & 0.0813060063381953 & 1227.99045847486 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 99.85 & 0.0781298113738928 & 1278.00129354165 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 99.8588888888889 & 0.0740471511919755 & 1348.58515528833 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 99.8697058823529 & 0.0687661636084091 & 1452.30881936448 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 99.88 & 0.0620548664619699 & 1609.5433878858 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 99.881 & 0.0585992624801576 & 1704.47537686709 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 99.8835714285714 & 0.0542900652670167 & 1839.81306593224 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 99.8857692307692 & 0.0490719192047539 & 2035.4975075255 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 99.8920833333333 & 0.0440807031899427 & 2266.11819015002 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 99.8931818181818 & 0.0407738264003162 & 2449.93395609805 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 99.8925 & 0.0380503475328206 & 2625.27168546456 \tabularnewline
Median & 99.875 &  &  \tabularnewline
Midrange & 99.23 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.8596774193549 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.881 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.8596774193549 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.881 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.881 &  &  \tabularnewline
Midmean - Closest Observation & 99.8596774193549 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.881 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.88 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]99.6966666666667[/C][C]0.155379009312197[/C][C]641.635360580461[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]99.6894839878464[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.6822621008716[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]99.7038101578871[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]99.7026666666667[/C][C]0.1528233104551[/C][C]652.404835163938[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]99.6973333333333[/C][C]0.147972906870171[/C][C]673.753969169546[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]99.7113333333333[/C][C]0.143513511768975[/C][C]694.787076870132[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]99.7073333333333[/C][C]0.142135025058566[/C][C]701.497279029213[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]99.7006666666667[/C][C]0.140152835596717[/C][C]711.371027508502[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]99.6966666666667[/C][C]0.133866589011165[/C][C]744.746447960603[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]99.7211666666667[/C][C]0.126930091454945[/C][C]785.638500087769[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]99.7211666666667[/C][C]0.120462641996434[/C][C]827.818193374997[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]99.6986666666667[/C][C]0.11283517969932[/C][C]883.577860489441[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]99.7986666666667[/C][C]0.0881006315562072[/C][C]1132.78037743687[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]99.7913333333333[/C][C]0.0869432137118598[/C][C]1147.7759916266[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]99.7853333333333[/C][C]0.0853217462118998[/C][C]1169.51817987307[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]99.7983333333333[/C][C]0.0828006136425672[/C][C]1205.28494829932[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]99.873[/C][C]0.066110804094937[/C][C]1510.69104917525[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]99.863[/C][C]0.0636765750860488[/C][C]1568.28472424987[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]99.8683333333333[/C][C]0.0601796588317003[/C][C]1659.50314893986[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]99.8428333333333[/C][C]0.052650693959225[/C][C]1896.32511606886[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]99.8848333333333[/C][C]0.0430158896319562[/C][C]2322.04504400462[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]99.8975[/C][C]0.037230860930816[/C][C]2683.19070530316[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]99.8675[/C][C]0.0328406742775735[/C][C]3040.96983989755[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]99.7127586206897[/C][C]0.146624820744255[/C][C]680.05374611581[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]99.7235714285714[/C][C]0.138944403665038[/C][C]717.722835883201[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]99.7381481481481[/C][C]0.132707670958021[/C][C]751.562795339074[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]99.7484615384615[/C][C]0.127159293876853[/C][C]784.437051333919[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]99.7608[/C][C]0.120694872488014[/C][C]826.553754467963[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]99.7758333333333[/C][C]0.113116644643962[/C][C]882.061465378336[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]99.7930434782609[/C][C]0.105473796258229[/C][C]946.14062467174[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]99.8070454545455[/C][C]0.0978557528524876[/C][C]1019.94049961477[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]99.822380952381[/C][C]0.0898300172572757[/C][C]1111.23635506478[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]99.843[/C][C]0.0813060063381953[/C][C]1227.99045847486[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]99.85[/C][C]0.0781298113738928[/C][C]1278.00129354165[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]99.8588888888889[/C][C]0.0740471511919755[/C][C]1348.58515528833[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]99.8697058823529[/C][C]0.0687661636084091[/C][C]1452.30881936448[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]99.88[/C][C]0.0620548664619699[/C][C]1609.5433878858[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]99.881[/C][C]0.0585992624801576[/C][C]1704.47537686709[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]99.8835714285714[/C][C]0.0542900652670167[/C][C]1839.81306593224[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]99.8857692307692[/C][C]0.0490719192047539[/C][C]2035.4975075255[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]99.8920833333333[/C][C]0.0440807031899427[/C][C]2266.11819015002[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]99.8931818181818[/C][C]0.0407738264003162[/C][C]2449.93395609805[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]99.8925[/C][C]0.0380503475328206[/C][C]2625.27168546456[/C][/ROW]
[ROW][C]Median[/C][C]99.875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]99.23[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.8596774193549[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.881[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.8596774193549[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.881[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.881[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.8596774193549[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.881[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.88[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean99.69666666666670.155379009312197641.635360580461
Geometric Mean99.6894839878464
Harmonic Mean99.6822621008716
Quadratic Mean99.7038101578871
Winsorized Mean ( 1 / 20 )99.70266666666670.1528233104551652.404835163938
Winsorized Mean ( 2 / 20 )99.69733333333330.147972906870171673.753969169546
Winsorized Mean ( 3 / 20 )99.71133333333330.143513511768975694.787076870132
Winsorized Mean ( 4 / 20 )99.70733333333330.142135025058566701.497279029213
Winsorized Mean ( 5 / 20 )99.70066666666670.140152835596717711.371027508502
Winsorized Mean ( 6 / 20 )99.69666666666670.133866589011165744.746447960603
Winsorized Mean ( 7 / 20 )99.72116666666670.126930091454945785.638500087769
Winsorized Mean ( 8 / 20 )99.72116666666670.120462641996434827.818193374997
Winsorized Mean ( 9 / 20 )99.69866666666670.11283517969932883.577860489441
Winsorized Mean ( 10 / 20 )99.79866666666670.08810063155620721132.78037743687
Winsorized Mean ( 11 / 20 )99.79133333333330.08694321371185981147.7759916266
Winsorized Mean ( 12 / 20 )99.78533333333330.08532174621189981169.51817987307
Winsorized Mean ( 13 / 20 )99.79833333333330.08280061364256721205.28494829932
Winsorized Mean ( 14 / 20 )99.8730.0661108040949371510.69104917525
Winsorized Mean ( 15 / 20 )99.8630.06367657508604881568.28472424987
Winsorized Mean ( 16 / 20 )99.86833333333330.06017965883170031659.50314893986
Winsorized Mean ( 17 / 20 )99.84283333333330.0526506939592251896.32511606886
Winsorized Mean ( 18 / 20 )99.88483333333330.04301588963195622322.04504400462
Winsorized Mean ( 19 / 20 )99.89750.0372308609308162683.19070530316
Winsorized Mean ( 20 / 20 )99.86750.03284067427757353040.96983989755
Trimmed Mean ( 1 / 20 )99.71275862068970.146624820744255680.05374611581
Trimmed Mean ( 2 / 20 )99.72357142857140.138944403665038717.722835883201
Trimmed Mean ( 3 / 20 )99.73814814814810.132707670958021751.562795339074
Trimmed Mean ( 4 / 20 )99.74846153846150.127159293876853784.437051333919
Trimmed Mean ( 5 / 20 )99.76080.120694872488014826.553754467963
Trimmed Mean ( 6 / 20 )99.77583333333330.113116644643962882.061465378336
Trimmed Mean ( 7 / 20 )99.79304347826090.105473796258229946.14062467174
Trimmed Mean ( 8 / 20 )99.80704545454550.09785575285248761019.94049961477
Trimmed Mean ( 9 / 20 )99.8223809523810.08983001725727571111.23635506478
Trimmed Mean ( 10 / 20 )99.8430.08130600633819531227.99045847486
Trimmed Mean ( 11 / 20 )99.850.07812981137389281278.00129354165
Trimmed Mean ( 12 / 20 )99.85888888888890.07404715119197551348.58515528833
Trimmed Mean ( 13 / 20 )99.86970588235290.06876616360840911452.30881936448
Trimmed Mean ( 14 / 20 )99.880.06205486646196991609.5433878858
Trimmed Mean ( 15 / 20 )99.8810.05859926248015761704.47537686709
Trimmed Mean ( 16 / 20 )99.88357142857140.05429006526701671839.81306593224
Trimmed Mean ( 17 / 20 )99.88576923076920.04907191920475392035.4975075255
Trimmed Mean ( 18 / 20 )99.89208333333330.04408070318994272266.11819015002
Trimmed Mean ( 19 / 20 )99.89318181818180.04077382640031622449.93395609805
Trimmed Mean ( 20 / 20 )99.89250.03805034753282062625.27168546456
Median99.875
Midrange99.23
Midmean - Weighted Average at Xnp99.8596774193549
Midmean - Weighted Average at X(n+1)p99.881
Midmean - Empirical Distribution Function99.8596774193549
Midmean - Empirical Distribution Function - Averaging99.881
Midmean - Empirical Distribution Function - Interpolation99.881
Midmean - Closest Observation99.8596774193549
Midmean - True Basic - Statistics Graphics Toolkit99.881
Midmean - MS Excel (old versions)99.88
Number of observations60



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')