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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 08 Oct 2012 03:38:36 -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/2012/Oct/08/t1349682084ina6x9bkqgs97sb.htm/, Retrieved Thu, 02 May 2024 06:22:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=173223, Retrieved Thu, 02 May 2024 06:22:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact58

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [robuustheid prijs...] [2012-10-08 07:38:36] [a4dec8ecbe2562b1daf91a8f6c837985] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
97,51
96,65
95,91
95,86
95,7
95,57
95,57
95,57
94,87
95,07
95,13
95,48
95,38
95,38
95,48
95,77
94,78
92,51
92,17
91,75
90,43
90,55
90,37
90,4
90,41
90,41
90,41
89,77
89,77
89,77
89,37
89,81
89,07
89,84
89,73
90,02
88,39
90,13
90,13
90,37
89,73
89,73
89,73
89,73
89,6
89,63
86,42
86,8
86,51
86,41
86,39
86,62
85,85
87,36
87,28
87,35
87,35
87,35
87,38
88,17
88,37
87,44
87,44
87,47
87,47
87,48
87,11
87,11
86,26
86,28
86,28
86,28

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173223&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173223&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173223&T=0

As an alternative you can also use a QR Code:  
QR Code


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

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






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean90.30055555555560.39599500720486228.034581023999
Geometric Mean90.2397902317547
Harmonic Mean90.1799243076288
Quadratic Mean90.3621822937499
Winsorized Mean ( 1 / 24 )90.29430555555560.392236466276242230.203750336573
Winsorized Mean ( 2 / 24 )90.27430555555560.387704705200517232.842945532133
Winsorized Mean ( 3 / 24 )90.27222222222220.387279758311808233.093055562026
Winsorized Mean ( 4 / 24 )90.26722222222220.386270094828643233.689388411667
Winsorized Mean ( 5 / 24 )90.270.384199979715181234.955764617478
Winsorized Mean ( 6 / 24 )90.26083333333330.381823970187445236.39383690087
Winsorized Mean ( 7 / 24 )90.26180555555560.381686005536916236.481831259663
Winsorized Mean ( 8 / 24 )90.27180555555550.380280522352008237.382143574514
Winsorized Mean ( 9 / 24 )90.27430555555560.376181749142182239.975240057261
Winsorized Mean ( 10 / 24 )90.29930555555560.37281876459732242.206975963475
Winsorized Mean ( 11 / 24 )90.33138888888890.363743862139222248.337905573551
Winsorized Mean ( 12 / 24 )90.33138888888890.363743862139222248.337905573551
Winsorized Mean ( 13 / 24 )90.31694444444440.351189942258294257.174063310782
Winsorized Mean ( 14 / 24 )90.31888888888890.347291586185883260.066446990014
Winsorized Mean ( 15 / 24 )90.27722222222220.339305088329723266.065040953629
Winsorized Mean ( 16 / 24 )90.25722222222220.335499896927131269.023099705529
Winsorized Mean ( 17 / 24 )89.72361111111110.239183396999985375.12474626789
Winsorized Mean ( 18 / 24 )89.64361111111110.224772037670278398.820120332809
Winsorized Mean ( 19 / 24 )89.54861111111110.205346600536602436.085189027268
Winsorized Mean ( 20 / 24 )89.21527777777780.159892982136158557.968689969182
Winsorized Mean ( 21 / 24 )89.18902777777780.154484371246409577.333662027969
Winsorized Mean ( 22 / 24 )89.18291666666670.153795287679823579.880684331051
Winsorized Mean ( 23 / 24 )89.18611111111110.153294360677344581.796425628673
Winsorized Mean ( 24 / 24 )89.41611111111110.118049244975403757.44754767167
Trimmed Mean ( 1 / 24 )90.26114285714290.388693971968972232.216471997019
Trimmed Mean ( 2 / 24 )90.22602941176470.384288799553235234.787039113966
Trimmed Mean ( 3 / 24 )90.1996969696970.381658750522865236.33598560527
Trimmed Mean ( 4 / 24 )90.17250.378438468714763238.275195188904
Trimmed Mean ( 5 / 24 )90.1450.37467248168923240.596799619701
Trimmed Mean ( 6 / 24 )90.1150.370487196420962243.233776687948
Trimmed Mean ( 7 / 24 )90.08482758620690.365796518084066246.270325529736
Trimmed Mean ( 8 / 24 )90.05232142857140.359829053124078250.264175854414
Trimmed Mean ( 9 / 24 )90.01574074074070.352550812793146255.326998192332
Trimmed Mean ( 10 / 24 )89.97596153846150.34423306010512261.380942059967
Trimmed Mean ( 11 / 24 )89.92940.334275263572904269.027983221937
Trimmed Mean ( 12 / 24 )89.87458333333330.323407576975484277.898817875087
Trimmed Mean ( 13 / 24 )89.8150.309155582050597290.51715451575
Trimmed Mean ( 14 / 24 )89.75181818181820.29351127071856305.786615832817
Trimmed Mean ( 15 / 24 )89.6823809523810.273425555146513327.995607083344
Trimmed Mean ( 16 / 24 )89.6110.24830729514155360.887504126354
Trimmed Mean ( 17 / 24 )89.53447368421050.213570439164318419.22690253647
Trimmed Mean ( 18 / 24 )89.51222222222220.200259795991738446.980492409545
Trimmed Mean ( 19 / 24 )89.49676470588240.186229938846256480.571304809199
Trimmed Mean ( 20 / 24 )89.4906250.172751066415176518.032257959701
Trimmed Mean ( 21 / 24 )89.52366666666670.166933453141597536.283560795514
Trimmed Mean ( 22 / 24 )89.56464285714290.1591898156048562.627970368993
Trimmed Mean ( 23 / 24 )89.61269230769230.146738446215139610.696750709135
Trimmed Mean ( 24 / 24 )89.66833333333330.125812816256133712.712233949077
Median89.75
Midrange91.68
Midmean - Weighted Average at Xnp89.454054054054
Midmean - Weighted Average at X(n+1)p89.5122222222222
Midmean - Empirical Distribution Function89.454054054054
Midmean - Empirical Distribution Function - Averaging89.5122222222222
Midmean - Empirical Distribution Function - Interpolation89.5122222222222
Midmean - Closest Observation89.454054054054
Midmean - True Basic - Statistics Graphics Toolkit89.5122222222222
Midmean - MS Excel (old versions)89.5344736842105
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 90.3005555555556 & 0.39599500720486 & 228.034581023999 \tabularnewline
Geometric Mean & 90.2397902317547 &  &  \tabularnewline
Harmonic Mean & 90.1799243076288 &  &  \tabularnewline
Quadratic Mean & 90.3621822937499 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 90.2943055555556 & 0.392236466276242 & 230.203750336573 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 90.2743055555556 & 0.387704705200517 & 232.842945532133 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 90.2722222222222 & 0.387279758311808 & 233.093055562026 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 90.2672222222222 & 0.386270094828643 & 233.689388411667 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 90.27 & 0.384199979715181 & 234.955764617478 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 90.2608333333333 & 0.381823970187445 & 236.39383690087 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 90.2618055555556 & 0.381686005536916 & 236.481831259663 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 90.2718055555555 & 0.380280522352008 & 237.382143574514 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 90.2743055555556 & 0.376181749142182 & 239.975240057261 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 90.2993055555556 & 0.37281876459732 & 242.206975963475 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 90.3313888888889 & 0.363743862139222 & 248.337905573551 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 90.3313888888889 & 0.363743862139222 & 248.337905573551 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 90.3169444444444 & 0.351189942258294 & 257.174063310782 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 90.3188888888889 & 0.347291586185883 & 260.066446990014 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 90.2772222222222 & 0.339305088329723 & 266.065040953629 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 90.2572222222222 & 0.335499896927131 & 269.023099705529 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 89.7236111111111 & 0.239183396999985 & 375.12474626789 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 89.6436111111111 & 0.224772037670278 & 398.820120332809 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 89.5486111111111 & 0.205346600536602 & 436.085189027268 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 89.2152777777778 & 0.159892982136158 & 557.968689969182 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 89.1890277777778 & 0.154484371246409 & 577.333662027969 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 89.1829166666667 & 0.153795287679823 & 579.880684331051 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 89.1861111111111 & 0.153294360677344 & 581.796425628673 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 89.4161111111111 & 0.118049244975403 & 757.44754767167 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 90.2611428571429 & 0.388693971968972 & 232.216471997019 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 90.2260294117647 & 0.384288799553235 & 234.787039113966 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 90.199696969697 & 0.381658750522865 & 236.33598560527 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 90.1725 & 0.378438468714763 & 238.275195188904 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 90.145 & 0.37467248168923 & 240.596799619701 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 90.115 & 0.370487196420962 & 243.233776687948 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 90.0848275862069 & 0.365796518084066 & 246.270325529736 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 90.0523214285714 & 0.359829053124078 & 250.264175854414 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 90.0157407407407 & 0.352550812793146 & 255.326998192332 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 89.9759615384615 & 0.34423306010512 & 261.380942059967 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 89.9294 & 0.334275263572904 & 269.027983221937 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 89.8745833333333 & 0.323407576975484 & 277.898817875087 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 89.815 & 0.309155582050597 & 290.51715451575 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 89.7518181818182 & 0.29351127071856 & 305.786615832817 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 89.682380952381 & 0.273425555146513 & 327.995607083344 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 89.611 & 0.24830729514155 & 360.887504126354 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 89.5344736842105 & 0.213570439164318 & 419.22690253647 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 89.5122222222222 & 0.200259795991738 & 446.980492409545 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 89.4967647058824 & 0.186229938846256 & 480.571304809199 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 89.490625 & 0.172751066415176 & 518.032257959701 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 89.5236666666667 & 0.166933453141597 & 536.283560795514 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 89.5646428571429 & 0.1591898156048 & 562.627970368993 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 89.6126923076923 & 0.146738446215139 & 610.696750709135 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 89.6683333333333 & 0.125812816256133 & 712.712233949077 \tabularnewline
Median & 89.75 &  &  \tabularnewline
Midrange & 91.68 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 89.454054054054 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 89.5122222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 89.454054054054 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 89.5122222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 89.5122222222222 &  &  \tabularnewline
Midmean - Closest Observation & 89.454054054054 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 89.5122222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 89.5344736842105 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173223&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]90.3005555555556[/C][C]0.39599500720486[/C][C]228.034581023999[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]90.2397902317547[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]90.1799243076288[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]90.3621822937499[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]90.2943055555556[/C][C]0.392236466276242[/C][C]230.203750336573[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]90.2743055555556[/C][C]0.387704705200517[/C][C]232.842945532133[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]90.2722222222222[/C][C]0.387279758311808[/C][C]233.093055562026[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]90.2672222222222[/C][C]0.386270094828643[/C][C]233.689388411667[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]90.27[/C][C]0.384199979715181[/C][C]234.955764617478[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]90.2608333333333[/C][C]0.381823970187445[/C][C]236.39383690087[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]90.2618055555556[/C][C]0.381686005536916[/C][C]236.481831259663[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]90.2718055555555[/C][C]0.380280522352008[/C][C]237.382143574514[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]90.2743055555556[/C][C]0.376181749142182[/C][C]239.975240057261[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]90.2993055555556[/C][C]0.37281876459732[/C][C]242.206975963475[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]90.3313888888889[/C][C]0.363743862139222[/C][C]248.337905573551[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]90.3313888888889[/C][C]0.363743862139222[/C][C]248.337905573551[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]90.3169444444444[/C][C]0.351189942258294[/C][C]257.174063310782[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]90.3188888888889[/C][C]0.347291586185883[/C][C]260.066446990014[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]90.2772222222222[/C][C]0.339305088329723[/C][C]266.065040953629[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]90.2572222222222[/C][C]0.335499896927131[/C][C]269.023099705529[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]89.7236111111111[/C][C]0.239183396999985[/C][C]375.12474626789[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]89.6436111111111[/C][C]0.224772037670278[/C][C]398.820120332809[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]89.5486111111111[/C][C]0.205346600536602[/C][C]436.085189027268[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]89.2152777777778[/C][C]0.159892982136158[/C][C]557.968689969182[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]89.1890277777778[/C][C]0.154484371246409[/C][C]577.333662027969[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]89.1829166666667[/C][C]0.153795287679823[/C][C]579.880684331051[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]89.1861111111111[/C][C]0.153294360677344[/C][C]581.796425628673[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]89.4161111111111[/C][C]0.118049244975403[/C][C]757.44754767167[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]90.2611428571429[/C][C]0.388693971968972[/C][C]232.216471997019[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]90.2260294117647[/C][C]0.384288799553235[/C][C]234.787039113966[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]90.199696969697[/C][C]0.381658750522865[/C][C]236.33598560527[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]90.1725[/C][C]0.378438468714763[/C][C]238.275195188904[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]90.145[/C][C]0.37467248168923[/C][C]240.596799619701[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]90.115[/C][C]0.370487196420962[/C][C]243.233776687948[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]90.0848275862069[/C][C]0.365796518084066[/C][C]246.270325529736[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]90.0523214285714[/C][C]0.359829053124078[/C][C]250.264175854414[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]90.0157407407407[/C][C]0.352550812793146[/C][C]255.326998192332[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]89.9759615384615[/C][C]0.34423306010512[/C][C]261.380942059967[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]89.9294[/C][C]0.334275263572904[/C][C]269.027983221937[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]89.8745833333333[/C][C]0.323407576975484[/C][C]277.898817875087[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]89.815[/C][C]0.309155582050597[/C][C]290.51715451575[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]89.7518181818182[/C][C]0.29351127071856[/C][C]305.786615832817[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]89.682380952381[/C][C]0.273425555146513[/C][C]327.995607083344[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]89.611[/C][C]0.24830729514155[/C][C]360.887504126354[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]89.5344736842105[/C][C]0.213570439164318[/C][C]419.22690253647[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]89.5122222222222[/C][C]0.200259795991738[/C][C]446.980492409545[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]89.4967647058824[/C][C]0.186229938846256[/C][C]480.571304809199[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]89.490625[/C][C]0.172751066415176[/C][C]518.032257959701[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]89.5236666666667[/C][C]0.166933453141597[/C][C]536.283560795514[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]89.5646428571429[/C][C]0.1591898156048[/C][C]562.627970368993[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]89.6126923076923[/C][C]0.146738446215139[/C][C]610.696750709135[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]89.6683333333333[/C][C]0.125812816256133[/C][C]712.712233949077[/C][/ROW]
[ROW][C]Median[/C][C]89.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]91.68[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]89.454054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]89.5122222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]89.454054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]89.5122222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]89.5122222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]89.454054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]89.5122222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]89.5344736842105[/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=173223&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173223&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean90.30055555555560.39599500720486228.034581023999
Geometric Mean90.2397902317547
Harmonic Mean90.1799243076288
Quadratic Mean90.3621822937499
Winsorized Mean ( 1 / 24 )90.29430555555560.392236466276242230.203750336573
Winsorized Mean ( 2 / 24 )90.27430555555560.387704705200517232.842945532133
Winsorized Mean ( 3 / 24 )90.27222222222220.387279758311808233.093055562026
Winsorized Mean ( 4 / 24 )90.26722222222220.386270094828643233.689388411667
Winsorized Mean ( 5 / 24 )90.270.384199979715181234.955764617478
Winsorized Mean ( 6 / 24 )90.26083333333330.381823970187445236.39383690087
Winsorized Mean ( 7 / 24 )90.26180555555560.381686005536916236.481831259663
Winsorized Mean ( 8 / 24 )90.27180555555550.380280522352008237.382143574514
Winsorized Mean ( 9 / 24 )90.27430555555560.376181749142182239.975240057261
Winsorized Mean ( 10 / 24 )90.29930555555560.37281876459732242.206975963475
Winsorized Mean ( 11 / 24 )90.33138888888890.363743862139222248.337905573551
Winsorized Mean ( 12 / 24 )90.33138888888890.363743862139222248.337905573551
Winsorized Mean ( 13 / 24 )90.31694444444440.351189942258294257.174063310782
Winsorized Mean ( 14 / 24 )90.31888888888890.347291586185883260.066446990014
Winsorized Mean ( 15 / 24 )90.27722222222220.339305088329723266.065040953629
Winsorized Mean ( 16 / 24 )90.25722222222220.335499896927131269.023099705529
Winsorized Mean ( 17 / 24 )89.72361111111110.239183396999985375.12474626789
Winsorized Mean ( 18 / 24 )89.64361111111110.224772037670278398.820120332809
Winsorized Mean ( 19 / 24 )89.54861111111110.205346600536602436.085189027268
Winsorized Mean ( 20 / 24 )89.21527777777780.159892982136158557.968689969182
Winsorized Mean ( 21 / 24 )89.18902777777780.154484371246409577.333662027969
Winsorized Mean ( 22 / 24 )89.18291666666670.153795287679823579.880684331051
Winsorized Mean ( 23 / 24 )89.18611111111110.153294360677344581.796425628673
Winsorized Mean ( 24 / 24 )89.41611111111110.118049244975403757.44754767167
Trimmed Mean ( 1 / 24 )90.26114285714290.388693971968972232.216471997019
Trimmed Mean ( 2 / 24 )90.22602941176470.384288799553235234.787039113966
Trimmed Mean ( 3 / 24 )90.1996969696970.381658750522865236.33598560527
Trimmed Mean ( 4 / 24 )90.17250.378438468714763238.275195188904
Trimmed Mean ( 5 / 24 )90.1450.37467248168923240.596799619701
Trimmed Mean ( 6 / 24 )90.1150.370487196420962243.233776687948
Trimmed Mean ( 7 / 24 )90.08482758620690.365796518084066246.270325529736
Trimmed Mean ( 8 / 24 )90.05232142857140.359829053124078250.264175854414
Trimmed Mean ( 9 / 24 )90.01574074074070.352550812793146255.326998192332
Trimmed Mean ( 10 / 24 )89.97596153846150.34423306010512261.380942059967
Trimmed Mean ( 11 / 24 )89.92940.334275263572904269.027983221937
Trimmed Mean ( 12 / 24 )89.87458333333330.323407576975484277.898817875087
Trimmed Mean ( 13 / 24 )89.8150.309155582050597290.51715451575
Trimmed Mean ( 14 / 24 )89.75181818181820.29351127071856305.786615832817
Trimmed Mean ( 15 / 24 )89.6823809523810.273425555146513327.995607083344
Trimmed Mean ( 16 / 24 )89.6110.24830729514155360.887504126354
Trimmed Mean ( 17 / 24 )89.53447368421050.213570439164318419.22690253647
Trimmed Mean ( 18 / 24 )89.51222222222220.200259795991738446.980492409545
Trimmed Mean ( 19 / 24 )89.49676470588240.186229938846256480.571304809199
Trimmed Mean ( 20 / 24 )89.4906250.172751066415176518.032257959701
Trimmed Mean ( 21 / 24 )89.52366666666670.166933453141597536.283560795514
Trimmed Mean ( 22 / 24 )89.56464285714290.1591898156048562.627970368993
Trimmed Mean ( 23 / 24 )89.61269230769230.146738446215139610.696750709135
Trimmed Mean ( 24 / 24 )89.66833333333330.125812816256133712.712233949077
Median89.75
Midrange91.68
Midmean - Weighted Average at Xnp89.454054054054
Midmean - Weighted Average at X(n+1)p89.5122222222222
Midmean - Empirical Distribution Function89.454054054054
Midmean - Empirical Distribution Function - Averaging89.5122222222222
Midmean - Empirical Distribution Function - Interpolation89.5122222222222
Midmean - Closest Observation89.454054054054
Midmean - True Basic - Statistics Graphics Toolkit89.5122222222222
Midmean - MS Excel (old versions)89.5344736842105
Number of observations72


Figures (Output of Computation)

Input Parameters & R Code

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')