Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Oct 2016 16:10:05 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/13/t1476371429nskzdwbffmmvooq.htm/, Retrieved Tue, 30 Apr 2024 19:30:16 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 19:30:16 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
100,55
100,41
100,54
100,66
100,86
100,88
100,88
101,37
101,84
102,25
102,58
102,59
102,59
101,95
101,94
102,18
102,47
102,5
102,5
102,87
103,08
103,47
103,65
103,68
99,76
99,13
99,19
99,37
99,61
99,65
99,66
99,98
100,38
100,92
101,16
101,19
101,52
101,14
101,38
101,46
101,52
101,53
100,79
101,2
101,28
101,59
101,75
101,76
103,03
102,97
103,11
103,17
103,17
103,2
102,17
102,22
102,18
102,44
102,61
102,63




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean101.6351666666670.15384772933968660.621818098247
Geometric Mean101.628278564327
Harmonic Mean101.621372510852
Quadratic Mean101.642036489174
Winsorized Mean ( 1 / 20 )101.6356666666670.153462737093025662.282379370426
Winsorized Mean ( 2 / 20 )101.6356666666670.150599811425867674.872469655762
Winsorized Mean ( 3 / 20 )101.6341666666670.145016517988959700.845449029499
Winsorized Mean ( 4 / 20 )101.6348333333330.144025949416976705.670288894161
Winsorized Mean ( 5 / 20 )101.6356666666670.143831619750056706.629507776416
Winsorized Mean ( 6 / 20 )101.6396666666670.140458282739777723.628857509041
Winsorized Mean ( 7 / 20 )101.6618333333330.134193235254044757.57792962421
Winsorized Mean ( 8 / 20 )101.70850.122380767524505831.082383754734
Winsorized Mean ( 9 / 20 )101.7040.119926342742601848.053877689642
Winsorized Mean ( 10 / 20 )101.7090.113102798099132899.261571856552
Winsorized Mean ( 11 / 20 )101.6668333333330.105532411725832963.370699775716
Winsorized Mean ( 12 / 20 )101.6848333333330.1010469185832941006.31305495489
Winsorized Mean ( 13 / 20 )101.7086666666670.09565547484683371063.28118520686
Winsorized Mean ( 14 / 20 )101.7250.09303862875536161093.36306178242
Winsorized Mean ( 15 / 20 )101.72750.09186013225717191107.41730389853
Winsorized Mean ( 16 / 20 )101.7061666666670.08856071097947581148.43439649256
Winsorized Mean ( 17 / 20 )101.71750.08678196101184931172.1041886356
Winsorized Mean ( 18 / 20 )101.77450.07552319395297551347.59263575862
Winsorized Mean ( 19 / 20 )101.7713333333330.07314619161924471391.34151868212
Winsorized Mean ( 20 / 20 )101.7180.06219651742389631635.42918820917
Trimmed Mean ( 1 / 20 )101.6431034482760.148930286719229682.487798065539
Trimmed Mean ( 2 / 20 )101.6510714285710.143335651525169709.182051687413
Trimmed Mean ( 3 / 20 )101.659629629630.138327830196154734.918125191965
Trimmed Mean ( 4 / 20 )101.6694230769230.134792845213608754.26424092322
Trimmed Mean ( 5 / 20 )101.67980.130695623960594777.989322968131
Trimmed Mean ( 6 / 20 )101.6908333333330.125518722761162810.164659871752
Trimmed Mean ( 7 / 20 )101.7019565217390.119974481813819847.69656833829
Trimmed Mean ( 8 / 20 )101.7097727272730.11478562086118886.084615513633
Trimmed Mean ( 9 / 20 )101.710.111523084489193912.008491029996
Trimmed Mean ( 10 / 20 )101.7110.107832847856871943.228357791341
Trimmed Mean ( 11 / 20 )101.7113157894740.104741890340608971.066260678708
Trimmed Mean ( 12 / 20 )101.7180555555560.102472465867778992.637921749673
Trimmed Mean ( 13 / 20 )101.7229411764710.1004220411458971012.95432771262
Trimmed Mean ( 14 / 20 )101.7250.09884718574158951029.11377027904
Trimmed Mean ( 15 / 20 )101.7250.09706112542601981048.05090146554
Trimmed Mean ( 16 / 20 )101.7246428571430.09449879221934331076.46500519316
Trimmed Mean ( 17 / 20 )101.7273076923080.09145248062801671112.35154031615
Trimmed Mean ( 18 / 20 )101.728750.087097547553621167.98638833513
Trimmed Mean ( 19 / 20 )101.7218181818180.08439147174767561205.35660861513
Trimmed Mean ( 20 / 20 )101.7140.08042125929981741264.76507437917
Median101.67
Midrange101.405
Midmean - Weighted Average at Xnp101.697096774194
Midmean - Weighted Average at X(n+1)p101.725
Midmean - Empirical Distribution Function101.697096774194
Midmean - Empirical Distribution Function - Averaging101.725
Midmean - Empirical Distribution Function - Interpolation101.725
Midmean - Closest Observation101.697096774194
Midmean - True Basic - Statistics Graphics Toolkit101.725
Midmean - MS Excel (old versions)101.751212121212
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.635166666667 & 0.15384772933968 & 660.621818098247 \tabularnewline
Geometric Mean & 101.628278564327 &  &  \tabularnewline
Harmonic Mean & 101.621372510852 &  &  \tabularnewline
Quadratic Mean & 101.642036489174 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 101.635666666667 & 0.153462737093025 & 662.282379370426 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 101.635666666667 & 0.150599811425867 & 674.872469655762 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 101.634166666667 & 0.145016517988959 & 700.845449029499 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 101.634833333333 & 0.144025949416976 & 705.670288894161 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 101.635666666667 & 0.143831619750056 & 706.629507776416 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 101.639666666667 & 0.140458282739777 & 723.628857509041 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 101.661833333333 & 0.134193235254044 & 757.57792962421 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 101.7085 & 0.122380767524505 & 831.082383754734 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 101.704 & 0.119926342742601 & 848.053877689642 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 101.709 & 0.113102798099132 & 899.261571856552 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 101.666833333333 & 0.105532411725832 & 963.370699775716 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 101.684833333333 & 0.101046918583294 & 1006.31305495489 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 101.708666666667 & 0.0956554748468337 & 1063.28118520686 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 101.725 & 0.0930386287553616 & 1093.36306178242 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 101.7275 & 0.0918601322571719 & 1107.41730389853 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 101.706166666667 & 0.0885607109794758 & 1148.43439649256 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 101.7175 & 0.0867819610118493 & 1172.1041886356 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 101.7745 & 0.0755231939529755 & 1347.59263575862 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 101.771333333333 & 0.0731461916192447 & 1391.34151868212 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 101.718 & 0.0621965174238963 & 1635.42918820917 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 101.643103448276 & 0.148930286719229 & 682.487798065539 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 101.651071428571 & 0.143335651525169 & 709.182051687413 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 101.65962962963 & 0.138327830196154 & 734.918125191965 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 101.669423076923 & 0.134792845213608 & 754.26424092322 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 101.6798 & 0.130695623960594 & 777.989322968131 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 101.690833333333 & 0.125518722761162 & 810.164659871752 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 101.701956521739 & 0.119974481813819 & 847.69656833829 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 101.709772727273 & 0.11478562086118 & 886.084615513633 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 101.71 & 0.111523084489193 & 912.008491029996 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 101.711 & 0.107832847856871 & 943.228357791341 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 101.711315789474 & 0.104741890340608 & 971.066260678708 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 101.718055555556 & 0.102472465867778 & 992.637921749673 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 101.722941176471 & 0.100422041145897 & 1012.95432771262 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 101.725 & 0.0988471857415895 & 1029.11377027904 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 101.725 & 0.0970611254260198 & 1048.05090146554 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 101.724642857143 & 0.0944987922193433 & 1076.46500519316 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 101.727307692308 & 0.0914524806280167 & 1112.35154031615 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 101.72875 & 0.08709754755362 & 1167.98638833513 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 101.721818181818 & 0.0843914717476756 & 1205.35660861513 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 101.714 & 0.0804212592998174 & 1264.76507437917 \tabularnewline
Median & 101.67 &  &  \tabularnewline
Midrange & 101.405 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 101.697096774194 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.725 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 101.697096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.725 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.725 &  &  \tabularnewline
Midmean - Closest Observation & 101.697096774194 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.725 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.751212121212 &  &  \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]101.635166666667[/C][C]0.15384772933968[/C][C]660.621818098247[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.628278564327[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.621372510852[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.642036489174[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]101.635666666667[/C][C]0.153462737093025[/C][C]662.282379370426[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]101.635666666667[/C][C]0.150599811425867[/C][C]674.872469655762[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]101.634166666667[/C][C]0.145016517988959[/C][C]700.845449029499[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]101.634833333333[/C][C]0.144025949416976[/C][C]705.670288894161[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]101.635666666667[/C][C]0.143831619750056[/C][C]706.629507776416[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]101.639666666667[/C][C]0.140458282739777[/C][C]723.628857509041[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]101.661833333333[/C][C]0.134193235254044[/C][C]757.57792962421[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]101.7085[/C][C]0.122380767524505[/C][C]831.082383754734[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]101.704[/C][C]0.119926342742601[/C][C]848.053877689642[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]101.709[/C][C]0.113102798099132[/C][C]899.261571856552[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]101.666833333333[/C][C]0.105532411725832[/C][C]963.370699775716[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]101.684833333333[/C][C]0.101046918583294[/C][C]1006.31305495489[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]101.708666666667[/C][C]0.0956554748468337[/C][C]1063.28118520686[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]101.725[/C][C]0.0930386287553616[/C][C]1093.36306178242[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]101.7275[/C][C]0.0918601322571719[/C][C]1107.41730389853[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]101.706166666667[/C][C]0.0885607109794758[/C][C]1148.43439649256[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]101.7175[/C][C]0.0867819610118493[/C][C]1172.1041886356[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]101.7745[/C][C]0.0755231939529755[/C][C]1347.59263575862[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]101.771333333333[/C][C]0.0731461916192447[/C][C]1391.34151868212[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]101.718[/C][C]0.0621965174238963[/C][C]1635.42918820917[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]101.643103448276[/C][C]0.148930286719229[/C][C]682.487798065539[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]101.651071428571[/C][C]0.143335651525169[/C][C]709.182051687413[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]101.65962962963[/C][C]0.138327830196154[/C][C]734.918125191965[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]101.669423076923[/C][C]0.134792845213608[/C][C]754.26424092322[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]101.6798[/C][C]0.130695623960594[/C][C]777.989322968131[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]101.690833333333[/C][C]0.125518722761162[/C][C]810.164659871752[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]101.701956521739[/C][C]0.119974481813819[/C][C]847.69656833829[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]101.709772727273[/C][C]0.11478562086118[/C][C]886.084615513633[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]101.71[/C][C]0.111523084489193[/C][C]912.008491029996[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]101.711[/C][C]0.107832847856871[/C][C]943.228357791341[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]101.711315789474[/C][C]0.104741890340608[/C][C]971.066260678708[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]101.718055555556[/C][C]0.102472465867778[/C][C]992.637921749673[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]101.722941176471[/C][C]0.100422041145897[/C][C]1012.95432771262[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]101.725[/C][C]0.0988471857415895[/C][C]1029.11377027904[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]101.725[/C][C]0.0970611254260198[/C][C]1048.05090146554[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]101.724642857143[/C][C]0.0944987922193433[/C][C]1076.46500519316[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]101.727307692308[/C][C]0.0914524806280167[/C][C]1112.35154031615[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]101.72875[/C][C]0.08709754755362[/C][C]1167.98638833513[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]101.721818181818[/C][C]0.0843914717476756[/C][C]1205.35660861513[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]101.714[/C][C]0.0804212592998174[/C][C]1264.76507437917[/C][/ROW]
[ROW][C]Median[/C][C]101.67[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]101.697096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]101.697096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]101.697096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.751212121212[/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 Mean101.6351666666670.15384772933968660.621818098247
Geometric Mean101.628278564327
Harmonic Mean101.621372510852
Quadratic Mean101.642036489174
Winsorized Mean ( 1 / 20 )101.6356666666670.153462737093025662.282379370426
Winsorized Mean ( 2 / 20 )101.6356666666670.150599811425867674.872469655762
Winsorized Mean ( 3 / 20 )101.6341666666670.145016517988959700.845449029499
Winsorized Mean ( 4 / 20 )101.6348333333330.144025949416976705.670288894161
Winsorized Mean ( 5 / 20 )101.6356666666670.143831619750056706.629507776416
Winsorized Mean ( 6 / 20 )101.6396666666670.140458282739777723.628857509041
Winsorized Mean ( 7 / 20 )101.6618333333330.134193235254044757.57792962421
Winsorized Mean ( 8 / 20 )101.70850.122380767524505831.082383754734
Winsorized Mean ( 9 / 20 )101.7040.119926342742601848.053877689642
Winsorized Mean ( 10 / 20 )101.7090.113102798099132899.261571856552
Winsorized Mean ( 11 / 20 )101.6668333333330.105532411725832963.370699775716
Winsorized Mean ( 12 / 20 )101.6848333333330.1010469185832941006.31305495489
Winsorized Mean ( 13 / 20 )101.7086666666670.09565547484683371063.28118520686
Winsorized Mean ( 14 / 20 )101.7250.09303862875536161093.36306178242
Winsorized Mean ( 15 / 20 )101.72750.09186013225717191107.41730389853
Winsorized Mean ( 16 / 20 )101.7061666666670.08856071097947581148.43439649256
Winsorized Mean ( 17 / 20 )101.71750.08678196101184931172.1041886356
Winsorized Mean ( 18 / 20 )101.77450.07552319395297551347.59263575862
Winsorized Mean ( 19 / 20 )101.7713333333330.07314619161924471391.34151868212
Winsorized Mean ( 20 / 20 )101.7180.06219651742389631635.42918820917
Trimmed Mean ( 1 / 20 )101.6431034482760.148930286719229682.487798065539
Trimmed Mean ( 2 / 20 )101.6510714285710.143335651525169709.182051687413
Trimmed Mean ( 3 / 20 )101.659629629630.138327830196154734.918125191965
Trimmed Mean ( 4 / 20 )101.6694230769230.134792845213608754.26424092322
Trimmed Mean ( 5 / 20 )101.67980.130695623960594777.989322968131
Trimmed Mean ( 6 / 20 )101.6908333333330.125518722761162810.164659871752
Trimmed Mean ( 7 / 20 )101.7019565217390.119974481813819847.69656833829
Trimmed Mean ( 8 / 20 )101.7097727272730.11478562086118886.084615513633
Trimmed Mean ( 9 / 20 )101.710.111523084489193912.008491029996
Trimmed Mean ( 10 / 20 )101.7110.107832847856871943.228357791341
Trimmed Mean ( 11 / 20 )101.7113157894740.104741890340608971.066260678708
Trimmed Mean ( 12 / 20 )101.7180555555560.102472465867778992.637921749673
Trimmed Mean ( 13 / 20 )101.7229411764710.1004220411458971012.95432771262
Trimmed Mean ( 14 / 20 )101.7250.09884718574158951029.11377027904
Trimmed Mean ( 15 / 20 )101.7250.09706112542601981048.05090146554
Trimmed Mean ( 16 / 20 )101.7246428571430.09449879221934331076.46500519316
Trimmed Mean ( 17 / 20 )101.7273076923080.09145248062801671112.35154031615
Trimmed Mean ( 18 / 20 )101.728750.087097547553621167.98638833513
Trimmed Mean ( 19 / 20 )101.7218181818180.08439147174767561205.35660861513
Trimmed Mean ( 20 / 20 )101.7140.08042125929981741264.76507437917
Median101.67
Midrange101.405
Midmean - Weighted Average at Xnp101.697096774194
Midmean - Weighted Average at X(n+1)p101.725
Midmean - Empirical Distribution Function101.697096774194
Midmean - Empirical Distribution Function - Averaging101.725
Midmean - Empirical Distribution Function - Interpolation101.725
Midmean - Closest Observation101.697096774194
Midmean - True Basic - Statistics Graphics Toolkit101.725
Midmean - MS Excel (old versions)101.751212121212
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')