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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 15 Oct 2011 10:01:15 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/15/t1318687311bd6p731ubeqb6q1.htm/, Retrieved Wed, 15 May 2024 23:07:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=129827, Retrieved Wed, 15 May 2024 23:07:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-10-15 14:01:15] [cc1ece1bb71b9752e72e266b4a37553b] [Current]
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Dataseries X:
117,87
117,74
117,61
117,55
117,06
117,08
117,21
117,58
117,27
117,14
116,52
116,16
114,79
114,97
114,66
114,3
114,48
114,96
115,44
116,38
116,5
116,2
116,37
116,46
115,07
115,03
115,15
114,71
114,67
115,49
114,65
114,92
114,17
112,8
112,28
112,05
111,03
110,4
109,08
107,89
107,26
107,76
107,32
107,15
108,04
106,52
106,62
106,47
105,46
106,13
105,15
105,39
104,57
104,29
104,09
104,51
103,39
102,71
102,62
101,94
101,65
101,86
101,27
101,21
102,15
102,07
102,8
103,39
102,71
102,65
101,12
100,29




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=129827&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=129827&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=129827&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean110.1701388888890.701285442060724157.097427497075
Geometric Mean110.010340741541
Harmonic Mean109.849463882518
Quadratic Mean110.328497647052
Winsorized Mean ( 1 / 24 )110.1798611111110.698811882740368157.667412121048
Winsorized Mean ( 2 / 24 )110.178750.697811410323688157.891872173446
Winsorized Mean ( 3 / 24 )110.180.697172946528257158.038260877259
Winsorized Mean ( 4 / 24 )110.1994444444440.693190072123883158.974354763624
Winsorized Mean ( 5 / 24 )110.1945833333330.687818099335766160.208903254726
Winsorized Mean ( 6 / 24 )110.196250.68596189268213160.644856770585
Winsorized Mean ( 7 / 24 )110.2020833333330.682853631506647161.384633907831
Winsorized Mean ( 8 / 24 )110.2043055555560.680415729104428161.966134587464
Winsorized Mean ( 9 / 24 )110.2605555555560.670445449312813164.45865307695
Winsorized Mean ( 10 / 24 )110.1897222222220.659345747123386167.119789128786
Winsorized Mean ( 11 / 24 )110.1958333333330.657459625553674167.608517771008
Winsorized Mean ( 12 / 24 )110.1891666666670.656561046711932167.827755268906
Winsorized Mean ( 13 / 24 )110.1909722222220.652023129327856168.99856349546
Winsorized Mean ( 14 / 24 )110.303750.633786143956712174.03938387068
Winsorized Mean ( 15 / 24 )110.2683333333330.629046898092662175.294296288049
Winsorized Mean ( 16 / 24 )110.4150.604409332842853182.682486851519
Winsorized Mean ( 17 / 24 )110.3040277777780.576843769777325191.219934333966
Winsorized Mean ( 18 / 24 )110.3465277777780.567238014911146194.533026484593
Winsorized Mean ( 19 / 24 )110.2858333333330.555382601208005198.576320348265
Winsorized Mean ( 20 / 24 )110.4247222222220.529654638865664208.484386087345
Winsorized Mean ( 21 / 24 )110.4830555555560.518461015586191213.098096547605
Winsorized Mean ( 22 / 24 )110.4861111111110.513246042954634215.269289705711
Winsorized Mean ( 23 / 24 )110.6969444444440.483849070758861228.784038524305
Winsorized Mean ( 24 / 24 )110.7969444444440.467266785447907237.117098614741
Trimmed Mean ( 1 / 24 )110.2012857142860.698581109181105157.750165680069
Trimmed Mean ( 2 / 24 )110.2239705882350.697697553524654157.982452470131
Trimmed Mean ( 3 / 24 )110.2486363636360.696634094989138158.259030324026
Trimmed Mean ( 4 / 24 )110.2743750.694994464227982158.66942929178
Trimmed Mean ( 5 / 24 )110.2961290322580.693739830672865158.987741737822
Trimmed Mean ( 6 / 24 )110.32050.693053320724482159.180393053563
Trimmed Mean ( 7 / 24 )110.3462068965520.691886862562065159.485911450809
Trimmed Mean ( 8 / 24 )110.3726785714290.690359472100531159.877111898822
Trimmed Mean ( 9 / 24 )110.4007407407410.68814285626283160.432880667113
Trimmed Mean ( 10 / 24 )110.4223076923080.686643563108998160.814596720801
Trimmed Mean ( 11 / 24 )110.45580.685927531722929161.031296881399
Trimmed Mean ( 12 / 24 )110.491250.68420844057902161.487703815076
Trimmed Mean ( 13 / 24 )110.5306521739130.680963114636222162.315182420651
Trimmed Mean ( 14 / 24 )110.5734090909090.676478487536417163.454435178852
Trimmed Mean ( 15 / 24 )110.6064285714290.673272454564515164.281826505097
Trimmed Mean ( 16 / 24 )110.6470.668496514384024165.516195850257
Trimmed Mean ( 17 / 24 )110.6744736842110.666047416003809166.166058188833
Trimmed Mean ( 18 / 24 )110.7180555555560.666493646529506166.12019654212
Trimmed Mean ( 19 / 24 )110.7617647058820.666760929689013166.119158717868
Trimmed Mean ( 20 / 24 )110.8181250.666834940750442166.185240496378
Trimmed Mean ( 21 / 24 )110.8653333333330.670253466094925165.408071634846
Trimmed Mean ( 22 / 24 )110.9121428571430.674020425236266164.553088755826
Trimmed Mean ( 23 / 24 )110.9657692307690.676173207913913164.108497544755
Trimmed Mean ( 24 / 24 )111.0008333333330.683419820437031162.419687012225
Median111.54
Midrange109.08
Midmean - Weighted Average at Xnp110.544324324324
Midmean - Weighted Average at X(n+1)p110.718055555556
Midmean - Empirical Distribution Function110.544324324324
Midmean - Empirical Distribution Function - Averaging110.718055555556
Midmean - Empirical Distribution Function - Interpolation110.718055555556
Midmean - Closest Observation110.544324324324
Midmean - True Basic - Statistics Graphics Toolkit110.718055555556
Midmean - MS Excel (old versions)110.674473684211
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 110.170138888889 & 0.701285442060724 & 157.097427497075 \tabularnewline
Geometric Mean & 110.010340741541 &  &  \tabularnewline
Harmonic Mean & 109.849463882518 &  &  \tabularnewline
Quadratic Mean & 110.328497647052 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 110.179861111111 & 0.698811882740368 & 157.667412121048 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 110.17875 & 0.697811410323688 & 157.891872173446 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 110.18 & 0.697172946528257 & 158.038260877259 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 110.199444444444 & 0.693190072123883 & 158.974354763624 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 110.194583333333 & 0.687818099335766 & 160.208903254726 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 110.19625 & 0.68596189268213 & 160.644856770585 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 110.202083333333 & 0.682853631506647 & 161.384633907831 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 110.204305555556 & 0.680415729104428 & 161.966134587464 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 110.260555555556 & 0.670445449312813 & 164.45865307695 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 110.189722222222 & 0.659345747123386 & 167.119789128786 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 110.195833333333 & 0.657459625553674 & 167.608517771008 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 110.189166666667 & 0.656561046711932 & 167.827755268906 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 110.190972222222 & 0.652023129327856 & 168.99856349546 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 110.30375 & 0.633786143956712 & 174.03938387068 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 110.268333333333 & 0.629046898092662 & 175.294296288049 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 110.415 & 0.604409332842853 & 182.682486851519 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 110.304027777778 & 0.576843769777325 & 191.219934333966 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 110.346527777778 & 0.567238014911146 & 194.533026484593 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 110.285833333333 & 0.555382601208005 & 198.576320348265 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 110.424722222222 & 0.529654638865664 & 208.484386087345 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 110.483055555556 & 0.518461015586191 & 213.098096547605 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 110.486111111111 & 0.513246042954634 & 215.269289705711 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 110.696944444444 & 0.483849070758861 & 228.784038524305 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 110.796944444444 & 0.467266785447907 & 237.117098614741 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 110.201285714286 & 0.698581109181105 & 157.750165680069 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 110.223970588235 & 0.697697553524654 & 157.982452470131 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 110.248636363636 & 0.696634094989138 & 158.259030324026 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 110.274375 & 0.694994464227982 & 158.66942929178 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 110.296129032258 & 0.693739830672865 & 158.987741737822 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 110.3205 & 0.693053320724482 & 159.180393053563 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 110.346206896552 & 0.691886862562065 & 159.485911450809 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 110.372678571429 & 0.690359472100531 & 159.877111898822 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 110.400740740741 & 0.68814285626283 & 160.432880667113 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 110.422307692308 & 0.686643563108998 & 160.814596720801 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 110.4558 & 0.685927531722929 & 161.031296881399 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 110.49125 & 0.68420844057902 & 161.487703815076 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 110.530652173913 & 0.680963114636222 & 162.315182420651 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 110.573409090909 & 0.676478487536417 & 163.454435178852 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 110.606428571429 & 0.673272454564515 & 164.281826505097 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 110.647 & 0.668496514384024 & 165.516195850257 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 110.674473684211 & 0.666047416003809 & 166.166058188833 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 110.718055555556 & 0.666493646529506 & 166.12019654212 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 110.761764705882 & 0.666760929689013 & 166.119158717868 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 110.818125 & 0.666834940750442 & 166.185240496378 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 110.865333333333 & 0.670253466094925 & 165.408071634846 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 110.912142857143 & 0.674020425236266 & 164.553088755826 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 110.965769230769 & 0.676173207913913 & 164.108497544755 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 111.000833333333 & 0.683419820437031 & 162.419687012225 \tabularnewline
Median & 111.54 &  &  \tabularnewline
Midrange & 109.08 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 110.544324324324 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 110.718055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 110.544324324324 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 110.718055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 110.718055555556 &  &  \tabularnewline
Midmean - Closest Observation & 110.544324324324 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 110.718055555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 110.674473684211 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=129827&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]110.170138888889[/C][C]0.701285442060724[/C][C]157.097427497075[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]110.010340741541[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]109.849463882518[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]110.328497647052[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]110.179861111111[/C][C]0.698811882740368[/C][C]157.667412121048[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]110.17875[/C][C]0.697811410323688[/C][C]157.891872173446[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]110.18[/C][C]0.697172946528257[/C][C]158.038260877259[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]110.199444444444[/C][C]0.693190072123883[/C][C]158.974354763624[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]110.194583333333[/C][C]0.687818099335766[/C][C]160.208903254726[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]110.19625[/C][C]0.68596189268213[/C][C]160.644856770585[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]110.202083333333[/C][C]0.682853631506647[/C][C]161.384633907831[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]110.204305555556[/C][C]0.680415729104428[/C][C]161.966134587464[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]110.260555555556[/C][C]0.670445449312813[/C][C]164.45865307695[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]110.189722222222[/C][C]0.659345747123386[/C][C]167.119789128786[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]110.195833333333[/C][C]0.657459625553674[/C][C]167.608517771008[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]110.189166666667[/C][C]0.656561046711932[/C][C]167.827755268906[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]110.190972222222[/C][C]0.652023129327856[/C][C]168.99856349546[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]110.30375[/C][C]0.633786143956712[/C][C]174.03938387068[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]110.268333333333[/C][C]0.629046898092662[/C][C]175.294296288049[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]110.415[/C][C]0.604409332842853[/C][C]182.682486851519[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]110.304027777778[/C][C]0.576843769777325[/C][C]191.219934333966[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]110.346527777778[/C][C]0.567238014911146[/C][C]194.533026484593[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]110.285833333333[/C][C]0.555382601208005[/C][C]198.576320348265[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]110.424722222222[/C][C]0.529654638865664[/C][C]208.484386087345[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]110.483055555556[/C][C]0.518461015586191[/C][C]213.098096547605[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]110.486111111111[/C][C]0.513246042954634[/C][C]215.269289705711[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]110.696944444444[/C][C]0.483849070758861[/C][C]228.784038524305[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]110.796944444444[/C][C]0.467266785447907[/C][C]237.117098614741[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]110.201285714286[/C][C]0.698581109181105[/C][C]157.750165680069[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]110.223970588235[/C][C]0.697697553524654[/C][C]157.982452470131[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]110.248636363636[/C][C]0.696634094989138[/C][C]158.259030324026[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]110.274375[/C][C]0.694994464227982[/C][C]158.66942929178[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]110.296129032258[/C][C]0.693739830672865[/C][C]158.987741737822[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]110.3205[/C][C]0.693053320724482[/C][C]159.180393053563[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]110.346206896552[/C][C]0.691886862562065[/C][C]159.485911450809[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]110.372678571429[/C][C]0.690359472100531[/C][C]159.877111898822[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]110.400740740741[/C][C]0.68814285626283[/C][C]160.432880667113[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]110.422307692308[/C][C]0.686643563108998[/C][C]160.814596720801[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]110.4558[/C][C]0.685927531722929[/C][C]161.031296881399[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]110.49125[/C][C]0.68420844057902[/C][C]161.487703815076[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]110.530652173913[/C][C]0.680963114636222[/C][C]162.315182420651[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]110.573409090909[/C][C]0.676478487536417[/C][C]163.454435178852[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]110.606428571429[/C][C]0.673272454564515[/C][C]164.281826505097[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]110.647[/C][C]0.668496514384024[/C][C]165.516195850257[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]110.674473684211[/C][C]0.666047416003809[/C][C]166.166058188833[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]110.718055555556[/C][C]0.666493646529506[/C][C]166.12019654212[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]110.761764705882[/C][C]0.666760929689013[/C][C]166.119158717868[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]110.818125[/C][C]0.666834940750442[/C][C]166.185240496378[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]110.865333333333[/C][C]0.670253466094925[/C][C]165.408071634846[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]110.912142857143[/C][C]0.674020425236266[/C][C]164.553088755826[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]110.965769230769[/C][C]0.676173207913913[/C][C]164.108497544755[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]111.000833333333[/C][C]0.683419820437031[/C][C]162.419687012225[/C][/ROW]
[ROW][C]Median[/C][C]111.54[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]109.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]110.544324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]110.718055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]110.544324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]110.718055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]110.718055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]110.544324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]110.718055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]110.674473684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=129827&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=129827&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 Mean110.1701388888890.701285442060724157.097427497075
Geometric Mean110.010340741541
Harmonic Mean109.849463882518
Quadratic Mean110.328497647052
Winsorized Mean ( 1 / 24 )110.1798611111110.698811882740368157.667412121048
Winsorized Mean ( 2 / 24 )110.178750.697811410323688157.891872173446
Winsorized Mean ( 3 / 24 )110.180.697172946528257158.038260877259
Winsorized Mean ( 4 / 24 )110.1994444444440.693190072123883158.974354763624
Winsorized Mean ( 5 / 24 )110.1945833333330.687818099335766160.208903254726
Winsorized Mean ( 6 / 24 )110.196250.68596189268213160.644856770585
Winsorized Mean ( 7 / 24 )110.2020833333330.682853631506647161.384633907831
Winsorized Mean ( 8 / 24 )110.2043055555560.680415729104428161.966134587464
Winsorized Mean ( 9 / 24 )110.2605555555560.670445449312813164.45865307695
Winsorized Mean ( 10 / 24 )110.1897222222220.659345747123386167.119789128786
Winsorized Mean ( 11 / 24 )110.1958333333330.657459625553674167.608517771008
Winsorized Mean ( 12 / 24 )110.1891666666670.656561046711932167.827755268906
Winsorized Mean ( 13 / 24 )110.1909722222220.652023129327856168.99856349546
Winsorized Mean ( 14 / 24 )110.303750.633786143956712174.03938387068
Winsorized Mean ( 15 / 24 )110.2683333333330.629046898092662175.294296288049
Winsorized Mean ( 16 / 24 )110.4150.604409332842853182.682486851519
Winsorized Mean ( 17 / 24 )110.3040277777780.576843769777325191.219934333966
Winsorized Mean ( 18 / 24 )110.3465277777780.567238014911146194.533026484593
Winsorized Mean ( 19 / 24 )110.2858333333330.555382601208005198.576320348265
Winsorized Mean ( 20 / 24 )110.4247222222220.529654638865664208.484386087345
Winsorized Mean ( 21 / 24 )110.4830555555560.518461015586191213.098096547605
Winsorized Mean ( 22 / 24 )110.4861111111110.513246042954634215.269289705711
Winsorized Mean ( 23 / 24 )110.6969444444440.483849070758861228.784038524305
Winsorized Mean ( 24 / 24 )110.7969444444440.467266785447907237.117098614741
Trimmed Mean ( 1 / 24 )110.2012857142860.698581109181105157.750165680069
Trimmed Mean ( 2 / 24 )110.2239705882350.697697553524654157.982452470131
Trimmed Mean ( 3 / 24 )110.2486363636360.696634094989138158.259030324026
Trimmed Mean ( 4 / 24 )110.2743750.694994464227982158.66942929178
Trimmed Mean ( 5 / 24 )110.2961290322580.693739830672865158.987741737822
Trimmed Mean ( 6 / 24 )110.32050.693053320724482159.180393053563
Trimmed Mean ( 7 / 24 )110.3462068965520.691886862562065159.485911450809
Trimmed Mean ( 8 / 24 )110.3726785714290.690359472100531159.877111898822
Trimmed Mean ( 9 / 24 )110.4007407407410.68814285626283160.432880667113
Trimmed Mean ( 10 / 24 )110.4223076923080.686643563108998160.814596720801
Trimmed Mean ( 11 / 24 )110.45580.685927531722929161.031296881399
Trimmed Mean ( 12 / 24 )110.491250.68420844057902161.487703815076
Trimmed Mean ( 13 / 24 )110.5306521739130.680963114636222162.315182420651
Trimmed Mean ( 14 / 24 )110.5734090909090.676478487536417163.454435178852
Trimmed Mean ( 15 / 24 )110.6064285714290.673272454564515164.281826505097
Trimmed Mean ( 16 / 24 )110.6470.668496514384024165.516195850257
Trimmed Mean ( 17 / 24 )110.6744736842110.666047416003809166.166058188833
Trimmed Mean ( 18 / 24 )110.7180555555560.666493646529506166.12019654212
Trimmed Mean ( 19 / 24 )110.7617647058820.666760929689013166.119158717868
Trimmed Mean ( 20 / 24 )110.8181250.666834940750442166.185240496378
Trimmed Mean ( 21 / 24 )110.8653333333330.670253466094925165.408071634846
Trimmed Mean ( 22 / 24 )110.9121428571430.674020425236266164.553088755826
Trimmed Mean ( 23 / 24 )110.9657692307690.676173207913913164.108497544755
Trimmed Mean ( 24 / 24 )111.0008333333330.683419820437031162.419687012225
Median111.54
Midrange109.08
Midmean - Weighted Average at Xnp110.544324324324
Midmean - Weighted Average at X(n+1)p110.718055555556
Midmean - Empirical Distribution Function110.544324324324
Midmean - Empirical Distribution Function - Averaging110.718055555556
Midmean - Empirical Distribution Function - Interpolation110.718055555556
Midmean - Closest Observation110.544324324324
Midmean - True Basic - Statistics Graphics Toolkit110.718055555556
Midmean - MS Excel (old versions)110.674473684211
Number of observations72



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')