Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 24 Feb 2014 15:15:09 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Feb/24/t1393272973ynp6deq1qyldarz.htm/, Retrieved Thu, 31 Oct 2024 23:36:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234017, Retrieved Thu, 31 Oct 2024 23:36:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-02-24 20:15:09] [3ace99d75142efe6ae27f9378c84deb8] [Current]
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Dataseries X:
80
80
80
80
80
80
80
80
80
80
80
80
80
80
85
85
85
85
85
85
85
85
85
85
85
85
85
85
85
85
85
85
85
85
85
85
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
110
110
110
110
110
110
110
110
110
110
110
110
110
120
120
120
120
120
120
120
120
120
120
120
120
120
120
120
120
120
120
120
120
120
200
210




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234017&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]3 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=234017&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234017&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean96.66666666666671.4253889806400367.8177451766612
Geometric Mean95.4340915168335
Harmonic Mean94.4385807594463
Quadratic Mean98.251045662915
Winsorized Mean ( 1 / 51 )96.60130718954251.3923145192234469.3818141345114
Winsorized Mean ( 2 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 3 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 4 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 5 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 6 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 7 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 8 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 9 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 10 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 11 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 12 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 13 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 14 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 15 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 16 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 17 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 18 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 19 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 20 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 21 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 22 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 23 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 24 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 25 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 26 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 27 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 28 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 29 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 30 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 31 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 32 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 33 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 34 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 35 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 36 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 37 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 38 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 39 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 40 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 41 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 42 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 43 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 44 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 45 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 46 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 47 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 48 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 49 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 50 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 51 / 51 )900Inf
Trimmed Mean ( 1 / 51 )96.02649006622521.2263820701097878.3006311056301
Trimmed Mean ( 2 / 51 )95.43624161073831.0200832111313593.5573103932295
Trimmed Mean ( 3 / 51 )95.37414965986391.0148561410760893.9779992450318
Trimmed Mean ( 4 / 51 )95.31034482758621.0090831372636794.4524205270529
Trimmed Mean ( 5 / 51 )95.24475524475521.0027155477675394.9868140140147
Trimmed Mean ( 6 / 51 )95.1773049645390.99569914483525695.5884169010576
Trimmed Mean ( 7 / 51 )95.1773049645390.98797327626189196.3359103443093
Trimmed Mean ( 8 / 51 )95.0364963503650.9794698467386697.0285064586806
Trimmed Mean ( 9 / 51 )94.9629629629630.97011208526520497.8886506057726
Trimmed Mean ( 10 / 51 )94.88721804511280.95981304044398698.8601050900708
Trimmed Mean ( 11 / 51 )94.80916030534350.94847372550028699.9597118574213
Trimmed Mean ( 12 / 51 )94.72868217054260.935980806431314101.207932384556
Trimmed Mean ( 13 / 51 )94.64566929133860.922203685433544102.62989704584
Trimmed Mean ( 14 / 51 )94.64566929133860.906990770661155104.351303621696
Trimmed Mean ( 15 / 51 )94.43089430894310.894626941148955105.553376458423
Trimmed Mean ( 16 / 51 )94.2975206611570.880821416353379107.056344124273
Trimmed Mean ( 17 / 51 )94.15966386554620.865386488719289108.806487151072
Trimmed Mean ( 18 / 51 )94.0170940170940.84809932135536110.856230691051
Trimmed Mean ( 19 / 51 )93.86956521739130.82869234653566113.274323830565
Trimmed Mean ( 20 / 51 )93.7168141592920.806839934903118116.15291968728
Trimmed Mean ( 21 / 51 )93.55855855855860.782139350175731119.618784731311
Trimmed Mean ( 22 / 51 )93.3944954128440.754082596349725123.851811280273
Trimmed Mean ( 23 / 51 )93.22429906542060.722013047654309129.117194444463
Trimmed Mean ( 24 / 51 )93.14285714285710.713736052246414130.500423580537
Trimmed Mean ( 25 / 51 )93.05825242718450.704318251944778132.125288774258
Trimmed Mean ( 26 / 51 )92.9702970297030.693599514306669134.040314492777
Trimmed Mean ( 27 / 51 )92.87878787878790.681388581761783136.308107245711
Trimmed Mean ( 28 / 51 )92.87878787878790.667454453592956139.15374656475
Trimmed Mean ( 29 / 51 )92.68421052631580.65151441427132142.25964690279
Trimmed Mean ( 30 / 51 )92.58064516129030.633216921828557146.206839978222
Trimmed Mean ( 31 / 51 )92.47252747252750.612116299160015151.070193032638
Trimmed Mean ( 32 / 51 )92.35955056179770.587633711342046157.171974274358
Trimmed Mean ( 33 / 51 )92.24137931034480.558993806506606165.013240284004
Trimmed Mean ( 34 / 51 )92.11764705882350.525114837301889175.423813069416
Trimmed Mean ( 35 / 51 )91.98795180722890.484400795256148189.900497084416
Trimmed Mean ( 36 / 51 )91.85185185185180.434297755539206211.495110624766
Trimmed Mean ( 37 / 51 )91.77215189873420.432360791812641212.258265866306
Trimmed Mean ( 38 / 51 )91.68831168831170.429698800970655213.378095263927
Trimmed Mean ( 39 / 51 )91.60.426170883122746214.937255517799
Trimmed Mean ( 40 / 51 )91.50684931506850.421602404397703217.045368718412
Trimmed Mean ( 41 / 51 )91.40845070422540.415774211665429219.851179172654
Trimmed Mean ( 42 / 51 )91.3043478260870.40840714635988223.562071917398
Trimmed Mean ( 43 / 51 )91.19402985074630.399139058759117228.476837456748
Trimmed Mean ( 44 / 51 )91.07692307692310.387489263069421235.043733484316
Trimmed Mean ( 45 / 51 )90.95238095238090.372800648218482243.970554737549
Trimmed Mean ( 46 / 51 )90.81967213114750.354138835978572256.452167636997
Trimmed Mean ( 47 / 51 )90.67796610169490.330099853803459274.698595158072
Trimmed Mean ( 48 / 51 )90.52631578947370.298393005007285303.37948366874
Trimmed Mean ( 49 / 51 )90.52631578947370.254737782079161355.370589516015
Trimmed Mean ( 50 / 51 )90.1886792452830.188679245283019478
Trimmed Mean ( 51 / 51 )900Inf
Median90
Midrange145
Midmean - Weighted Average at Xnp91.8518518518518
Midmean - Weighted Average at X(n+1)p91.8518518518518
Midmean - Empirical Distribution Function91.8518518518518
Midmean - Empirical Distribution Function - Averaging91.8518518518518
Midmean - Empirical Distribution Function - Interpolation91.8518518518518
Midmean - Closest Observation91.8518518518518
Midmean - True Basic - Statistics Graphics Toolkit91.8518518518518
Midmean - MS Excel (old versions)91.8518518518518
Number of observations153

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 96.6666666666667 & 1.42538898064003 & 67.8177451766612 \tabularnewline
Geometric Mean & 95.4340915168335 &  &  \tabularnewline
Harmonic Mean & 94.4385807594463 &  &  \tabularnewline
Quadratic Mean & 98.251045662915 &  &  \tabularnewline
Winsorized Mean ( 1 / 51 ) & 96.6013071895425 & 1.39231451922344 & 69.3818141345114 \tabularnewline
Winsorized Mean ( 2 / 51 ) & 95.5555555555556 & 1.02907044100813 & 92.8561852985929 \tabularnewline
Winsorized Mean ( 3 / 51 ) & 95.5555555555556 & 1.02907044100813 & 92.8561852985929 \tabularnewline
Winsorized Mean ( 4 / 51 ) & 95.5555555555556 & 1.02907044100813 & 92.8561852985929 \tabularnewline
Winsorized Mean ( 5 / 51 ) & 95.5555555555556 & 1.02907044100813 & 92.8561852985929 \tabularnewline
Winsorized Mean ( 6 / 51 ) & 95.5555555555556 & 1.02907044100813 & 92.8561852985929 \tabularnewline
Winsorized Mean ( 7 / 51 ) & 95.5555555555556 & 1.02907044100813 & 92.8561852985929 \tabularnewline
Winsorized Mean ( 8 / 51 ) & 95.5555555555556 & 1.02907044100813 & 92.8561852985929 \tabularnewline
Winsorized Mean ( 9 / 51 ) & 95.5555555555556 & 1.02907044100813 & 92.8561852985929 \tabularnewline
Winsorized Mean ( 10 / 51 ) & 95.5555555555556 & 1.02907044100813 & 92.8561852985929 \tabularnewline
Winsorized Mean ( 11 / 51 ) & 95.5555555555556 & 1.02907044100813 & 92.8561852985929 \tabularnewline
Winsorized Mean ( 12 / 51 ) & 95.5555555555556 & 1.02907044100813 & 92.8561852985929 \tabularnewline
Winsorized Mean ( 13 / 51 ) & 95.5555555555556 & 1.02907044100813 & 92.8561852985929 \tabularnewline
Winsorized Mean ( 14 / 51 ) & 96.0130718954248 & 0.98945189054175 & 97.0366248356504 \tabularnewline
Winsorized Mean ( 15 / 51 ) & 96.0130718954248 & 0.98945189054175 & 97.0366248356504 \tabularnewline
Winsorized Mean ( 16 / 51 ) & 96.0130718954248 & 0.98945189054175 & 97.0366248356504 \tabularnewline
Winsorized Mean ( 17 / 51 ) & 96.0130718954248 & 0.98945189054175 & 97.0366248356504 \tabularnewline
Winsorized Mean ( 18 / 51 ) & 96.0130718954248 & 0.98945189054175 & 97.0366248356504 \tabularnewline
Winsorized Mean ( 19 / 51 ) & 96.0130718954248 & 0.98945189054175 & 97.0366248356504 \tabularnewline
Winsorized Mean ( 20 / 51 ) & 96.0130718954248 & 0.98945189054175 & 97.0366248356504 \tabularnewline
Winsorized Mean ( 21 / 51 ) & 96.0130718954248 & 0.98945189054175 & 97.0366248356504 \tabularnewline
Winsorized Mean ( 22 / 51 ) & 96.0130718954248 & 0.98945189054175 & 97.0366248356504 \tabularnewline
Winsorized Mean ( 23 / 51 ) & 94.5098039215686 & 0.767195808729289 & 123.188634304593 \tabularnewline
Winsorized Mean ( 24 / 51 ) & 94.5098039215686 & 0.767195808729289 & 123.188634304593 \tabularnewline
Winsorized Mean ( 25 / 51 ) & 94.5098039215686 & 0.767195808729289 & 123.188634304593 \tabularnewline
Winsorized Mean ( 26 / 51 ) & 94.5098039215686 & 0.767195808729289 & 123.188634304593 \tabularnewline
Winsorized Mean ( 27 / 51 ) & 94.5098039215686 & 0.767195808729289 & 123.188634304593 \tabularnewline
Winsorized Mean ( 28 / 51 ) & 94.5098039215686 & 0.767195808729289 & 123.188634304593 \tabularnewline
Winsorized Mean ( 29 / 51 ) & 94.5098039215686 & 0.767195808729289 & 123.188634304593 \tabularnewline
Winsorized Mean ( 30 / 51 ) & 94.5098039215686 & 0.767195808729289 & 123.188634304593 \tabularnewline
Winsorized Mean ( 31 / 51 ) & 94.5098039215686 & 0.767195808729289 & 123.188634304593 \tabularnewline
Winsorized Mean ( 32 / 51 ) & 94.5098039215686 & 0.767195808729289 & 123.188634304593 \tabularnewline
Winsorized Mean ( 33 / 51 ) & 94.5098039215686 & 0.767195808729289 & 123.188634304593 \tabularnewline
Winsorized Mean ( 34 / 51 ) & 94.5098039215686 & 0.767195808729289 & 123.188634304593 \tabularnewline
Winsorized Mean ( 35 / 51 ) & 94.5098039215686 & 0.767195808729289 & 123.188634304593 \tabularnewline
Winsorized Mean ( 36 / 51 ) & 93.3333333333333 & 0.382359556450936 & 244.098340838278 \tabularnewline
Winsorized Mean ( 37 / 51 ) & 93.3333333333333 & 0.382359556450936 & 244.098340838278 \tabularnewline
Winsorized Mean ( 38 / 51 ) & 93.3333333333333 & 0.382359556450936 & 244.098340838278 \tabularnewline
Winsorized Mean ( 39 / 51 ) & 93.3333333333333 & 0.382359556450936 & 244.098340838278 \tabularnewline
Winsorized Mean ( 40 / 51 ) & 93.3333333333333 & 0.382359556450936 & 244.098340838278 \tabularnewline
Winsorized Mean ( 41 / 51 ) & 93.3333333333333 & 0.382359556450936 & 244.098340838278 \tabularnewline
Winsorized Mean ( 42 / 51 ) & 93.3333333333333 & 0.382359556450936 & 244.098340838278 \tabularnewline
Winsorized Mean ( 43 / 51 ) & 93.3333333333333 & 0.382359556450936 & 244.098340838278 \tabularnewline
Winsorized Mean ( 44 / 51 ) & 93.3333333333333 & 0.382359556450936 & 244.098340838278 \tabularnewline
Winsorized Mean ( 45 / 51 ) & 93.3333333333333 & 0.382359556450936 & 244.098340838278 \tabularnewline
Winsorized Mean ( 46 / 51 ) & 93.3333333333333 & 0.382359556450936 & 244.098340838278 \tabularnewline
Winsorized Mean ( 47 / 51 ) & 93.3333333333333 & 0.382359556450936 & 244.098340838278 \tabularnewline
Winsorized Mean ( 48 / 51 ) & 93.3333333333333 & 0.382359556450936 & 244.098340838278 \tabularnewline
Winsorized Mean ( 49 / 51 ) & 93.3333333333333 & 0.382359556450936 & 244.098340838278 \tabularnewline
Winsorized Mean ( 50 / 51 ) & 93.3333333333333 & 0.382359556450936 & 244.098340838278 \tabularnewline
Winsorized Mean ( 51 / 51 ) & 90 & 0 & Inf \tabularnewline
Trimmed Mean ( 1 / 51 ) & 96.0264900662252 & 1.22638207010978 & 78.3006311056301 \tabularnewline
Trimmed Mean ( 2 / 51 ) & 95.4362416107383 & 1.02008321113135 & 93.5573103932295 \tabularnewline
Trimmed Mean ( 3 / 51 ) & 95.3741496598639 & 1.01485614107608 & 93.9779992450318 \tabularnewline
Trimmed Mean ( 4 / 51 ) & 95.3103448275862 & 1.00908313726367 & 94.4524205270529 \tabularnewline
Trimmed Mean ( 5 / 51 ) & 95.2447552447552 & 1.00271554776753 & 94.9868140140147 \tabularnewline
Trimmed Mean ( 6 / 51 ) & 95.177304964539 & 0.995699144835256 & 95.5884169010576 \tabularnewline
Trimmed Mean ( 7 / 51 ) & 95.177304964539 & 0.987973276261891 & 96.3359103443093 \tabularnewline
Trimmed Mean ( 8 / 51 ) & 95.036496350365 & 0.97946984673866 & 97.0285064586806 \tabularnewline
Trimmed Mean ( 9 / 51 ) & 94.962962962963 & 0.970112085265204 & 97.8886506057726 \tabularnewline
Trimmed Mean ( 10 / 51 ) & 94.8872180451128 & 0.959813040443986 & 98.8601050900708 \tabularnewline
Trimmed Mean ( 11 / 51 ) & 94.8091603053435 & 0.948473725500286 & 99.9597118574213 \tabularnewline
Trimmed Mean ( 12 / 51 ) & 94.7286821705426 & 0.935980806431314 & 101.207932384556 \tabularnewline
Trimmed Mean ( 13 / 51 ) & 94.6456692913386 & 0.922203685433544 & 102.62989704584 \tabularnewline
Trimmed Mean ( 14 / 51 ) & 94.6456692913386 & 0.906990770661155 & 104.351303621696 \tabularnewline
Trimmed Mean ( 15 / 51 ) & 94.4308943089431 & 0.894626941148955 & 105.553376458423 \tabularnewline
Trimmed Mean ( 16 / 51 ) & 94.297520661157 & 0.880821416353379 & 107.056344124273 \tabularnewline
Trimmed Mean ( 17 / 51 ) & 94.1596638655462 & 0.865386488719289 & 108.806487151072 \tabularnewline
Trimmed Mean ( 18 / 51 ) & 94.017094017094 & 0.84809932135536 & 110.856230691051 \tabularnewline
Trimmed Mean ( 19 / 51 ) & 93.8695652173913 & 0.82869234653566 & 113.274323830565 \tabularnewline
Trimmed Mean ( 20 / 51 ) & 93.716814159292 & 0.806839934903118 & 116.15291968728 \tabularnewline
Trimmed Mean ( 21 / 51 ) & 93.5585585585586 & 0.782139350175731 & 119.618784731311 \tabularnewline
Trimmed Mean ( 22 / 51 ) & 93.394495412844 & 0.754082596349725 & 123.851811280273 \tabularnewline
Trimmed Mean ( 23 / 51 ) & 93.2242990654206 & 0.722013047654309 & 129.117194444463 \tabularnewline
Trimmed Mean ( 24 / 51 ) & 93.1428571428571 & 0.713736052246414 & 130.500423580537 \tabularnewline
Trimmed Mean ( 25 / 51 ) & 93.0582524271845 & 0.704318251944778 & 132.125288774258 \tabularnewline
Trimmed Mean ( 26 / 51 ) & 92.970297029703 & 0.693599514306669 & 134.040314492777 \tabularnewline
Trimmed Mean ( 27 / 51 ) & 92.8787878787879 & 0.681388581761783 & 136.308107245711 \tabularnewline
Trimmed Mean ( 28 / 51 ) & 92.8787878787879 & 0.667454453592956 & 139.15374656475 \tabularnewline
Trimmed Mean ( 29 / 51 ) & 92.6842105263158 & 0.65151441427132 & 142.25964690279 \tabularnewline
Trimmed Mean ( 30 / 51 ) & 92.5806451612903 & 0.633216921828557 & 146.206839978222 \tabularnewline
Trimmed Mean ( 31 / 51 ) & 92.4725274725275 & 0.612116299160015 & 151.070193032638 \tabularnewline
Trimmed Mean ( 32 / 51 ) & 92.3595505617977 & 0.587633711342046 & 157.171974274358 \tabularnewline
Trimmed Mean ( 33 / 51 ) & 92.2413793103448 & 0.558993806506606 & 165.013240284004 \tabularnewline
Trimmed Mean ( 34 / 51 ) & 92.1176470588235 & 0.525114837301889 & 175.423813069416 \tabularnewline
Trimmed Mean ( 35 / 51 ) & 91.9879518072289 & 0.484400795256148 & 189.900497084416 \tabularnewline
Trimmed Mean ( 36 / 51 ) & 91.8518518518518 & 0.434297755539206 & 211.495110624766 \tabularnewline
Trimmed Mean ( 37 / 51 ) & 91.7721518987342 & 0.432360791812641 & 212.258265866306 \tabularnewline
Trimmed Mean ( 38 / 51 ) & 91.6883116883117 & 0.429698800970655 & 213.378095263927 \tabularnewline
Trimmed Mean ( 39 / 51 ) & 91.6 & 0.426170883122746 & 214.937255517799 \tabularnewline
Trimmed Mean ( 40 / 51 ) & 91.5068493150685 & 0.421602404397703 & 217.045368718412 \tabularnewline
Trimmed Mean ( 41 / 51 ) & 91.4084507042254 & 0.415774211665429 & 219.851179172654 \tabularnewline
Trimmed Mean ( 42 / 51 ) & 91.304347826087 & 0.40840714635988 & 223.562071917398 \tabularnewline
Trimmed Mean ( 43 / 51 ) & 91.1940298507463 & 0.399139058759117 & 228.476837456748 \tabularnewline
Trimmed Mean ( 44 / 51 ) & 91.0769230769231 & 0.387489263069421 & 235.043733484316 \tabularnewline
Trimmed Mean ( 45 / 51 ) & 90.9523809523809 & 0.372800648218482 & 243.970554737549 \tabularnewline
Trimmed Mean ( 46 / 51 ) & 90.8196721311475 & 0.354138835978572 & 256.452167636997 \tabularnewline
Trimmed Mean ( 47 / 51 ) & 90.6779661016949 & 0.330099853803459 & 274.698595158072 \tabularnewline
Trimmed Mean ( 48 / 51 ) & 90.5263157894737 & 0.298393005007285 & 303.37948366874 \tabularnewline
Trimmed Mean ( 49 / 51 ) & 90.5263157894737 & 0.254737782079161 & 355.370589516015 \tabularnewline
Trimmed Mean ( 50 / 51 ) & 90.188679245283 & 0.188679245283019 & 478 \tabularnewline
Trimmed Mean ( 51 / 51 ) & 90 & 0 & Inf \tabularnewline
Median & 90 &  &  \tabularnewline
Midrange & 145 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 91.8518518518518 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 91.8518518518518 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 91.8518518518518 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 91.8518518518518 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 91.8518518518518 &  &  \tabularnewline
Midmean - Closest Observation & 91.8518518518518 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 91.8518518518518 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 91.8518518518518 &  &  \tabularnewline
Number of observations & 153 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234017&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]96.6666666666667[/C][C]1.42538898064003[/C][C]67.8177451766612[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]95.4340915168335[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]94.4385807594463[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]98.251045662915[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 51 )[/C][C]96.6013071895425[/C][C]1.39231451922344[/C][C]69.3818141345114[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 51 )[/C][C]95.5555555555556[/C][C]1.02907044100813[/C][C]92.8561852985929[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 51 )[/C][C]95.5555555555556[/C][C]1.02907044100813[/C][C]92.8561852985929[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 51 )[/C][C]95.5555555555556[/C][C]1.02907044100813[/C][C]92.8561852985929[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 51 )[/C][C]95.5555555555556[/C][C]1.02907044100813[/C][C]92.8561852985929[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 51 )[/C][C]95.5555555555556[/C][C]1.02907044100813[/C][C]92.8561852985929[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 51 )[/C][C]95.5555555555556[/C][C]1.02907044100813[/C][C]92.8561852985929[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 51 )[/C][C]95.5555555555556[/C][C]1.02907044100813[/C][C]92.8561852985929[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 51 )[/C][C]95.5555555555556[/C][C]1.02907044100813[/C][C]92.8561852985929[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 51 )[/C][C]95.5555555555556[/C][C]1.02907044100813[/C][C]92.8561852985929[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 51 )[/C][C]95.5555555555556[/C][C]1.02907044100813[/C][C]92.8561852985929[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 51 )[/C][C]95.5555555555556[/C][C]1.02907044100813[/C][C]92.8561852985929[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 51 )[/C][C]95.5555555555556[/C][C]1.02907044100813[/C][C]92.8561852985929[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 51 )[/C][C]96.0130718954248[/C][C]0.98945189054175[/C][C]97.0366248356504[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 51 )[/C][C]96.0130718954248[/C][C]0.98945189054175[/C][C]97.0366248356504[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 51 )[/C][C]96.0130718954248[/C][C]0.98945189054175[/C][C]97.0366248356504[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 51 )[/C][C]96.0130718954248[/C][C]0.98945189054175[/C][C]97.0366248356504[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 51 )[/C][C]96.0130718954248[/C][C]0.98945189054175[/C][C]97.0366248356504[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 51 )[/C][C]96.0130718954248[/C][C]0.98945189054175[/C][C]97.0366248356504[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 51 )[/C][C]96.0130718954248[/C][C]0.98945189054175[/C][C]97.0366248356504[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 51 )[/C][C]96.0130718954248[/C][C]0.98945189054175[/C][C]97.0366248356504[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 51 )[/C][C]96.0130718954248[/C][C]0.98945189054175[/C][C]97.0366248356504[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 51 )[/C][C]94.5098039215686[/C][C]0.767195808729289[/C][C]123.188634304593[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 51 )[/C][C]94.5098039215686[/C][C]0.767195808729289[/C][C]123.188634304593[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 51 )[/C][C]94.5098039215686[/C][C]0.767195808729289[/C][C]123.188634304593[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 51 )[/C][C]94.5098039215686[/C][C]0.767195808729289[/C][C]123.188634304593[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 51 )[/C][C]94.5098039215686[/C][C]0.767195808729289[/C][C]123.188634304593[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 51 )[/C][C]94.5098039215686[/C][C]0.767195808729289[/C][C]123.188634304593[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 51 )[/C][C]94.5098039215686[/C][C]0.767195808729289[/C][C]123.188634304593[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 51 )[/C][C]94.5098039215686[/C][C]0.767195808729289[/C][C]123.188634304593[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 51 )[/C][C]94.5098039215686[/C][C]0.767195808729289[/C][C]123.188634304593[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 51 )[/C][C]94.5098039215686[/C][C]0.767195808729289[/C][C]123.188634304593[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 51 )[/C][C]94.5098039215686[/C][C]0.767195808729289[/C][C]123.188634304593[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 51 )[/C][C]94.5098039215686[/C][C]0.767195808729289[/C][C]123.188634304593[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 51 )[/C][C]94.5098039215686[/C][C]0.767195808729289[/C][C]123.188634304593[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 51 )[/C][C]93.3333333333333[/C][C]0.382359556450936[/C][C]244.098340838278[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 51 )[/C][C]93.3333333333333[/C][C]0.382359556450936[/C][C]244.098340838278[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 51 )[/C][C]93.3333333333333[/C][C]0.382359556450936[/C][C]244.098340838278[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 51 )[/C][C]93.3333333333333[/C][C]0.382359556450936[/C][C]244.098340838278[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 51 )[/C][C]93.3333333333333[/C][C]0.382359556450936[/C][C]244.098340838278[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 51 )[/C][C]93.3333333333333[/C][C]0.382359556450936[/C][C]244.098340838278[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 51 )[/C][C]93.3333333333333[/C][C]0.382359556450936[/C][C]244.098340838278[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 51 )[/C][C]93.3333333333333[/C][C]0.382359556450936[/C][C]244.098340838278[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 51 )[/C][C]93.3333333333333[/C][C]0.382359556450936[/C][C]244.098340838278[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 51 )[/C][C]93.3333333333333[/C][C]0.382359556450936[/C][C]244.098340838278[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 51 )[/C][C]93.3333333333333[/C][C]0.382359556450936[/C][C]244.098340838278[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 51 )[/C][C]93.3333333333333[/C][C]0.382359556450936[/C][C]244.098340838278[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 51 )[/C][C]93.3333333333333[/C][C]0.382359556450936[/C][C]244.098340838278[/C][/ROW]
[ROW][C]Winsorized Mean ( 49 / 51 )[/C][C]93.3333333333333[/C][C]0.382359556450936[/C][C]244.098340838278[/C][/ROW]
[ROW][C]Winsorized Mean ( 50 / 51 )[/C][C]93.3333333333333[/C][C]0.382359556450936[/C][C]244.098340838278[/C][/ROW]
[ROW][C]Winsorized Mean ( 51 / 51 )[/C][C]90[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 51 )[/C][C]96.0264900662252[/C][C]1.22638207010978[/C][C]78.3006311056301[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 51 )[/C][C]95.4362416107383[/C][C]1.02008321113135[/C][C]93.5573103932295[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 51 )[/C][C]95.3741496598639[/C][C]1.01485614107608[/C][C]93.9779992450318[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 51 )[/C][C]95.3103448275862[/C][C]1.00908313726367[/C][C]94.4524205270529[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 51 )[/C][C]95.2447552447552[/C][C]1.00271554776753[/C][C]94.9868140140147[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 51 )[/C][C]95.177304964539[/C][C]0.995699144835256[/C][C]95.5884169010576[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 51 )[/C][C]95.177304964539[/C][C]0.987973276261891[/C][C]96.3359103443093[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 51 )[/C][C]95.036496350365[/C][C]0.97946984673866[/C][C]97.0285064586806[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 51 )[/C][C]94.962962962963[/C][C]0.970112085265204[/C][C]97.8886506057726[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 51 )[/C][C]94.8872180451128[/C][C]0.959813040443986[/C][C]98.8601050900708[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 51 )[/C][C]94.8091603053435[/C][C]0.948473725500286[/C][C]99.9597118574213[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 51 )[/C][C]94.7286821705426[/C][C]0.935980806431314[/C][C]101.207932384556[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 51 )[/C][C]94.6456692913386[/C][C]0.922203685433544[/C][C]102.62989704584[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 51 )[/C][C]94.6456692913386[/C][C]0.906990770661155[/C][C]104.351303621696[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 51 )[/C][C]94.4308943089431[/C][C]0.894626941148955[/C][C]105.553376458423[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 51 )[/C][C]94.297520661157[/C][C]0.880821416353379[/C][C]107.056344124273[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 51 )[/C][C]94.1596638655462[/C][C]0.865386488719289[/C][C]108.806487151072[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 51 )[/C][C]94.017094017094[/C][C]0.84809932135536[/C][C]110.856230691051[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 51 )[/C][C]93.8695652173913[/C][C]0.82869234653566[/C][C]113.274323830565[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 51 )[/C][C]93.716814159292[/C][C]0.806839934903118[/C][C]116.15291968728[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 51 )[/C][C]93.5585585585586[/C][C]0.782139350175731[/C][C]119.618784731311[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 51 )[/C][C]93.394495412844[/C][C]0.754082596349725[/C][C]123.851811280273[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 51 )[/C][C]93.2242990654206[/C][C]0.722013047654309[/C][C]129.117194444463[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 51 )[/C][C]93.1428571428571[/C][C]0.713736052246414[/C][C]130.500423580537[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 51 )[/C][C]93.0582524271845[/C][C]0.704318251944778[/C][C]132.125288774258[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 51 )[/C][C]92.970297029703[/C][C]0.693599514306669[/C][C]134.040314492777[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 51 )[/C][C]92.8787878787879[/C][C]0.681388581761783[/C][C]136.308107245711[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 51 )[/C][C]92.8787878787879[/C][C]0.667454453592956[/C][C]139.15374656475[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 51 )[/C][C]92.6842105263158[/C][C]0.65151441427132[/C][C]142.25964690279[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 51 )[/C][C]92.5806451612903[/C][C]0.633216921828557[/C][C]146.206839978222[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 51 )[/C][C]92.4725274725275[/C][C]0.612116299160015[/C][C]151.070193032638[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 51 )[/C][C]92.3595505617977[/C][C]0.587633711342046[/C][C]157.171974274358[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 51 )[/C][C]92.2413793103448[/C][C]0.558993806506606[/C][C]165.013240284004[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 51 )[/C][C]92.1176470588235[/C][C]0.525114837301889[/C][C]175.423813069416[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 51 )[/C][C]91.9879518072289[/C][C]0.484400795256148[/C][C]189.900497084416[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 51 )[/C][C]91.8518518518518[/C][C]0.434297755539206[/C][C]211.495110624766[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 51 )[/C][C]91.7721518987342[/C][C]0.432360791812641[/C][C]212.258265866306[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 51 )[/C][C]91.6883116883117[/C][C]0.429698800970655[/C][C]213.378095263927[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 51 )[/C][C]91.6[/C][C]0.426170883122746[/C][C]214.937255517799[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 51 )[/C][C]91.5068493150685[/C][C]0.421602404397703[/C][C]217.045368718412[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 51 )[/C][C]91.4084507042254[/C][C]0.415774211665429[/C][C]219.851179172654[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 51 )[/C][C]91.304347826087[/C][C]0.40840714635988[/C][C]223.562071917398[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 51 )[/C][C]91.1940298507463[/C][C]0.399139058759117[/C][C]228.476837456748[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 51 )[/C][C]91.0769230769231[/C][C]0.387489263069421[/C][C]235.043733484316[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 51 )[/C][C]90.9523809523809[/C][C]0.372800648218482[/C][C]243.970554737549[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 51 )[/C][C]90.8196721311475[/C][C]0.354138835978572[/C][C]256.452167636997[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 51 )[/C][C]90.6779661016949[/C][C]0.330099853803459[/C][C]274.698595158072[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 51 )[/C][C]90.5263157894737[/C][C]0.298393005007285[/C][C]303.37948366874[/C][/ROW]
[ROW][C]Trimmed Mean ( 49 / 51 )[/C][C]90.5263157894737[/C][C]0.254737782079161[/C][C]355.370589516015[/C][/ROW]
[ROW][C]Trimmed Mean ( 50 / 51 )[/C][C]90.188679245283[/C][C]0.188679245283019[/C][C]478[/C][/ROW]
[ROW][C]Trimmed Mean ( 51 / 51 )[/C][C]90[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Median[/C][C]90[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]145[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]91.8518518518518[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]91.8518518518518[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]91.8518518518518[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]91.8518518518518[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]91.8518518518518[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]91.8518518518518[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]91.8518518518518[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]91.8518518518518[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]153[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234017&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234017&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 Mean96.66666666666671.4253889806400367.8177451766612
Geometric Mean95.4340915168335
Harmonic Mean94.4385807594463
Quadratic Mean98.251045662915
Winsorized Mean ( 1 / 51 )96.60130718954251.3923145192234469.3818141345114
Winsorized Mean ( 2 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 3 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 4 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 5 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 6 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 7 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 8 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 9 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 10 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 11 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 12 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 13 / 51 )95.55555555555561.0290704410081392.8561852985929
Winsorized Mean ( 14 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 15 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 16 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 17 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 18 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 19 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 20 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 21 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 22 / 51 )96.01307189542480.9894518905417597.0366248356504
Winsorized Mean ( 23 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 24 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 25 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 26 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 27 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 28 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 29 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 30 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 31 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 32 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 33 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 34 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 35 / 51 )94.50980392156860.767195808729289123.188634304593
Winsorized Mean ( 36 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 37 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 38 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 39 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 40 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 41 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 42 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 43 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 44 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 45 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 46 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 47 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 48 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 49 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 50 / 51 )93.33333333333330.382359556450936244.098340838278
Winsorized Mean ( 51 / 51 )900Inf
Trimmed Mean ( 1 / 51 )96.02649006622521.2263820701097878.3006311056301
Trimmed Mean ( 2 / 51 )95.43624161073831.0200832111313593.5573103932295
Trimmed Mean ( 3 / 51 )95.37414965986391.0148561410760893.9779992450318
Trimmed Mean ( 4 / 51 )95.31034482758621.0090831372636794.4524205270529
Trimmed Mean ( 5 / 51 )95.24475524475521.0027155477675394.9868140140147
Trimmed Mean ( 6 / 51 )95.1773049645390.99569914483525695.5884169010576
Trimmed Mean ( 7 / 51 )95.1773049645390.98797327626189196.3359103443093
Trimmed Mean ( 8 / 51 )95.0364963503650.9794698467386697.0285064586806
Trimmed Mean ( 9 / 51 )94.9629629629630.97011208526520497.8886506057726
Trimmed Mean ( 10 / 51 )94.88721804511280.95981304044398698.8601050900708
Trimmed Mean ( 11 / 51 )94.80916030534350.94847372550028699.9597118574213
Trimmed Mean ( 12 / 51 )94.72868217054260.935980806431314101.207932384556
Trimmed Mean ( 13 / 51 )94.64566929133860.922203685433544102.62989704584
Trimmed Mean ( 14 / 51 )94.64566929133860.906990770661155104.351303621696
Trimmed Mean ( 15 / 51 )94.43089430894310.894626941148955105.553376458423
Trimmed Mean ( 16 / 51 )94.2975206611570.880821416353379107.056344124273
Trimmed Mean ( 17 / 51 )94.15966386554620.865386488719289108.806487151072
Trimmed Mean ( 18 / 51 )94.0170940170940.84809932135536110.856230691051
Trimmed Mean ( 19 / 51 )93.86956521739130.82869234653566113.274323830565
Trimmed Mean ( 20 / 51 )93.7168141592920.806839934903118116.15291968728
Trimmed Mean ( 21 / 51 )93.55855855855860.782139350175731119.618784731311
Trimmed Mean ( 22 / 51 )93.3944954128440.754082596349725123.851811280273
Trimmed Mean ( 23 / 51 )93.22429906542060.722013047654309129.117194444463
Trimmed Mean ( 24 / 51 )93.14285714285710.713736052246414130.500423580537
Trimmed Mean ( 25 / 51 )93.05825242718450.704318251944778132.125288774258
Trimmed Mean ( 26 / 51 )92.9702970297030.693599514306669134.040314492777
Trimmed Mean ( 27 / 51 )92.87878787878790.681388581761783136.308107245711
Trimmed Mean ( 28 / 51 )92.87878787878790.667454453592956139.15374656475
Trimmed Mean ( 29 / 51 )92.68421052631580.65151441427132142.25964690279
Trimmed Mean ( 30 / 51 )92.58064516129030.633216921828557146.206839978222
Trimmed Mean ( 31 / 51 )92.47252747252750.612116299160015151.070193032638
Trimmed Mean ( 32 / 51 )92.35955056179770.587633711342046157.171974274358
Trimmed Mean ( 33 / 51 )92.24137931034480.558993806506606165.013240284004
Trimmed Mean ( 34 / 51 )92.11764705882350.525114837301889175.423813069416
Trimmed Mean ( 35 / 51 )91.98795180722890.484400795256148189.900497084416
Trimmed Mean ( 36 / 51 )91.85185185185180.434297755539206211.495110624766
Trimmed Mean ( 37 / 51 )91.77215189873420.432360791812641212.258265866306
Trimmed Mean ( 38 / 51 )91.68831168831170.429698800970655213.378095263927
Trimmed Mean ( 39 / 51 )91.60.426170883122746214.937255517799
Trimmed Mean ( 40 / 51 )91.50684931506850.421602404397703217.045368718412
Trimmed Mean ( 41 / 51 )91.40845070422540.415774211665429219.851179172654
Trimmed Mean ( 42 / 51 )91.3043478260870.40840714635988223.562071917398
Trimmed Mean ( 43 / 51 )91.19402985074630.399139058759117228.476837456748
Trimmed Mean ( 44 / 51 )91.07692307692310.387489263069421235.043733484316
Trimmed Mean ( 45 / 51 )90.95238095238090.372800648218482243.970554737549
Trimmed Mean ( 46 / 51 )90.81967213114750.354138835978572256.452167636997
Trimmed Mean ( 47 / 51 )90.67796610169490.330099853803459274.698595158072
Trimmed Mean ( 48 / 51 )90.52631578947370.298393005007285303.37948366874
Trimmed Mean ( 49 / 51 )90.52631578947370.254737782079161355.370589516015
Trimmed Mean ( 50 / 51 )90.1886792452830.188679245283019478
Trimmed Mean ( 51 / 51 )900Inf
Median90
Midrange145
Midmean - Weighted Average at Xnp91.8518518518518
Midmean - Weighted Average at X(n+1)p91.8518518518518
Midmean - Empirical Distribution Function91.8518518518518
Midmean - Empirical Distribution Function - Averaging91.8518518518518
Midmean - Empirical Distribution Function - Interpolation91.8518518518518
Midmean - Closest Observation91.8518518518518
Midmean - True Basic - Statistics Graphics Toolkit91.8518518518518
Midmean - MS Excel (old versions)91.8518518518518
Number of observations153



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')