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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, 07 Mar 2016 18:22:13 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/07/t14573749512xnfmrve1q1cqkf.htm/, Retrieved Wed, 01 May 2024 07:27:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293608, Retrieved Wed, 01 May 2024 07:27:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-07 18:22:13] [b787349f7d799cee4daf21043f8c3664] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
92,88
91,69
91,66
90,26
91,11
92,33
91,82
92,24
93,35
93,53
93,34
92,59
92,42
92,64
94,44
93,59
93,39
93,33
93,72
95,43
97,06
97,7
97,59
96,97
97,75
99,27
100,63
99,8
99,5
99,72
99,77
100,18
101,11
100,67
101,13
100,46
101,6
102,3
103,26
104,56
104,61
104,62
105,03
104,93
104,73
104,33
104,6
104,41
104,63
105,55
106,12
106,62
106,72
106,52
106,79
106,95
106,92
106,74
108,13
107,86

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'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293608&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293608&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293608&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'Gertrude Mary Cox' @ cox.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean99.560.72164935849079137.961738382493
Geometric Mean99.4048269094261
Harmonic Mean99.2490156430674
Quadratic Mean99.7141890103911
Winsorized Mean ( 1 / 20 )99.56966666666670.717793502506852138.716310915222
Winsorized Mean ( 2 / 20 )99.55766666666660.708577367068982140.503593952606
Winsorized Mean ( 3 / 20 )99.55766666666670.708029627147778140.612289160447
Winsorized Mean ( 4 / 20 )99.55766666666670.704889916743693141.238602371535
Winsorized Mean ( 5 / 20 )99.58850.697785473038943142.72079865217
Winsorized Mean ( 6 / 20 )99.59550.695838616306614143.130170798274
Winsorized Mean ( 7 / 20 )99.59433333333330.691970753385206143.928529993653
Winsorized Mean ( 8 / 20 )99.60366666666670.685727374409878145.252574687402
Winsorized Mean ( 9 / 20 )99.55116666666670.674342789143106147.626946219989
Winsorized Mean ( 10 / 20 )99.49616666666670.652106196148152.576631313108
Winsorized Mean ( 11 / 20 )99.48333333333330.623412001440853159.578790757001
Winsorized Mean ( 12 / 20 )99.46533333333330.620075513292178160.408419944275
Winsorized Mean ( 13 / 20 )99.42416666666670.613298541677792162.11381555657
Winsorized Mean ( 14 / 20 )99.41016666666670.608324897008293163.416238847958
Winsorized Mean ( 15 / 20 )99.44266666666670.602112799212505165.156207934338
Winsorized Mean ( 16 / 20 )99.4560.599064817333844166.018763115871
Winsorized Mean ( 17 / 20 )99.490.592555034512874167.900016378712
Winsorized Mean ( 18 / 20 )99.6940.555637832702151179.422627712683
Winsorized Mean ( 19 / 20 )99.960.499244796899915200.222417180322
Winsorized Mean ( 20 / 20 )100.4466666666670.419304621186554239.555353295228
Trimmed Mean ( 1 / 20 )99.57258620689650.71362365087235139.530950361828
Trimmed Mean ( 2 / 20 )99.57571428571430.707866781487839140.670132982395
Trimmed Mean ( 3 / 20 )99.58574074074070.705936720124287141.068934228563
Trimmed Mean ( 4 / 20 )99.59653846153850.702862059194088141.701400948768
Trimmed Mean ( 5 / 20 )99.60820.699241787034137142.451726780363
Trimmed Mean ( 6 / 20 )99.6131250.695969472577463143.128583831546
Trimmed Mean ( 7 / 20 )99.61695652173910.6912826326611144.104526593215
Trimmed Mean ( 8 / 20 )99.62136363636360.685224118126524145.385080590478
Trimmed Mean ( 9 / 20 )99.62452380952380.677891724091159146.962295406526
Trimmed Mean ( 10 / 20 )99.636750.670027878055678148.705379676337
Trimmed Mean ( 11 / 20 )99.65894736842110.663894795933347150.112559970159
Trimmed Mean ( 12 / 20 )99.68555555555560.661152246285951150.775492506519
Trimmed Mean ( 13 / 20 )99.71794117647060.656089095973961151.988414055929
Trimmed Mean ( 14 / 20 )99.76031250.6485399987004153.822914083801
Trimmed Mean ( 15 / 20 )99.81033333333330.636865074097618156.721317266072
Trimmed Mean ( 16 / 20 )99.86285714285710.619584230183242161.177209292952
Trimmed Mean ( 17 / 20 )99.92153846153850.592573446874586168.623044094458
Trimmed Mean ( 18 / 20 )99.9850.55134782151547181.346504145377
Trimmed Mean ( 19 / 20 )100.0290909090910.501251640793984199.558630373049
Trimmed Mean ( 20 / 20 )100.040.44642615939198224.090810754127
Median99.99
Midrange99.195
Midmean - Weighted Average at Xnp99.6032258064516
Midmean - Weighted Average at X(n+1)p99.8103333333333
Midmean - Empirical Distribution Function99.6032258064516
Midmean - Empirical Distribution Function - Averaging99.8103333333333
Midmean - Empirical Distribution Function - Interpolation99.8103333333333
Midmean - Closest Observation99.6032258064516
Midmean - True Basic - Statistics Graphics Toolkit99.8103333333333
Midmean - MS Excel (old versions)99.7603125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 99.56 & 0.72164935849079 & 137.961738382493 \tabularnewline
Geometric Mean & 99.4048269094261 &  &  \tabularnewline
Harmonic Mean & 99.2490156430674 &  &  \tabularnewline
Quadratic Mean & 99.7141890103911 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 99.5696666666667 & 0.717793502506852 & 138.716310915222 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 99.5576666666666 & 0.708577367068982 & 140.503593952606 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 99.5576666666667 & 0.708029627147778 & 140.612289160447 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 99.5576666666667 & 0.704889916743693 & 141.238602371535 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 99.5885 & 0.697785473038943 & 142.72079865217 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 99.5955 & 0.695838616306614 & 143.130170798274 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 99.5943333333333 & 0.691970753385206 & 143.928529993653 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 99.6036666666667 & 0.685727374409878 & 145.252574687402 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 99.5511666666667 & 0.674342789143106 & 147.626946219989 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 99.4961666666667 & 0.652106196148 & 152.576631313108 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 99.4833333333333 & 0.623412001440853 & 159.578790757001 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 99.4653333333333 & 0.620075513292178 & 160.408419944275 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 99.4241666666667 & 0.613298541677792 & 162.11381555657 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 99.4101666666667 & 0.608324897008293 & 163.416238847958 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 99.4426666666667 & 0.602112799212505 & 165.156207934338 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 99.456 & 0.599064817333844 & 166.018763115871 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 99.49 & 0.592555034512874 & 167.900016378712 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 99.694 & 0.555637832702151 & 179.422627712683 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 99.96 & 0.499244796899915 & 200.222417180322 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 100.446666666667 & 0.419304621186554 & 239.555353295228 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 99.5725862068965 & 0.71362365087235 & 139.530950361828 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 99.5757142857143 & 0.707866781487839 & 140.670132982395 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 99.5857407407407 & 0.705936720124287 & 141.068934228563 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 99.5965384615385 & 0.702862059194088 & 141.701400948768 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 99.6082 & 0.699241787034137 & 142.451726780363 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 99.613125 & 0.695969472577463 & 143.128583831546 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 99.6169565217391 & 0.6912826326611 & 144.104526593215 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 99.6213636363636 & 0.685224118126524 & 145.385080590478 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 99.6245238095238 & 0.677891724091159 & 146.962295406526 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 99.63675 & 0.670027878055678 & 148.705379676337 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 99.6589473684211 & 0.663894795933347 & 150.112559970159 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 99.6855555555556 & 0.661152246285951 & 150.775492506519 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 99.7179411764706 & 0.656089095973961 & 151.988414055929 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 99.7603125 & 0.6485399987004 & 153.822914083801 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 99.8103333333333 & 0.636865074097618 & 156.721317266072 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 99.8628571428571 & 0.619584230183242 & 161.177209292952 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 99.9215384615385 & 0.592573446874586 & 168.623044094458 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 99.985 & 0.55134782151547 & 181.346504145377 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 100.029090909091 & 0.501251640793984 & 199.558630373049 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 100.04 & 0.44642615939198 & 224.090810754127 \tabularnewline
Median & 99.99 &  &  \tabularnewline
Midrange & 99.195 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.6032258064516 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.8103333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.6032258064516 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.8103333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.8103333333333 &  &  \tabularnewline
Midmean - Closest Observation & 99.6032258064516 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.8103333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.7603125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293608&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]99.56[/C][C]0.72164935849079[/C][C]137.961738382493[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]99.4048269094261[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.2490156430674[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]99.7141890103911[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]99.5696666666667[/C][C]0.717793502506852[/C][C]138.716310915222[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]99.5576666666666[/C][C]0.708577367068982[/C][C]140.503593952606[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]99.5576666666667[/C][C]0.708029627147778[/C][C]140.612289160447[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]99.5576666666667[/C][C]0.704889916743693[/C][C]141.238602371535[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]99.5885[/C][C]0.697785473038943[/C][C]142.72079865217[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]99.5955[/C][C]0.695838616306614[/C][C]143.130170798274[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]99.5943333333333[/C][C]0.691970753385206[/C][C]143.928529993653[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]99.6036666666667[/C][C]0.685727374409878[/C][C]145.252574687402[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]99.5511666666667[/C][C]0.674342789143106[/C][C]147.626946219989[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]99.4961666666667[/C][C]0.652106196148[/C][C]152.576631313108[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]99.4833333333333[/C][C]0.623412001440853[/C][C]159.578790757001[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]99.4653333333333[/C][C]0.620075513292178[/C][C]160.408419944275[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]99.4241666666667[/C][C]0.613298541677792[/C][C]162.11381555657[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]99.4101666666667[/C][C]0.608324897008293[/C][C]163.416238847958[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]99.4426666666667[/C][C]0.602112799212505[/C][C]165.156207934338[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]99.456[/C][C]0.599064817333844[/C][C]166.018763115871[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]99.49[/C][C]0.592555034512874[/C][C]167.900016378712[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]99.694[/C][C]0.555637832702151[/C][C]179.422627712683[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]99.96[/C][C]0.499244796899915[/C][C]200.222417180322[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]100.446666666667[/C][C]0.419304621186554[/C][C]239.555353295228[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]99.5725862068965[/C][C]0.71362365087235[/C][C]139.530950361828[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]99.5757142857143[/C][C]0.707866781487839[/C][C]140.670132982395[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]99.5857407407407[/C][C]0.705936720124287[/C][C]141.068934228563[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]99.5965384615385[/C][C]0.702862059194088[/C][C]141.701400948768[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]99.6082[/C][C]0.699241787034137[/C][C]142.451726780363[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]99.613125[/C][C]0.695969472577463[/C][C]143.128583831546[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]99.6169565217391[/C][C]0.6912826326611[/C][C]144.104526593215[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]99.6213636363636[/C][C]0.685224118126524[/C][C]145.385080590478[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]99.6245238095238[/C][C]0.677891724091159[/C][C]146.962295406526[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]99.63675[/C][C]0.670027878055678[/C][C]148.705379676337[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]99.6589473684211[/C][C]0.663894795933347[/C][C]150.112559970159[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]99.6855555555556[/C][C]0.661152246285951[/C][C]150.775492506519[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]99.7179411764706[/C][C]0.656089095973961[/C][C]151.988414055929[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]99.7603125[/C][C]0.6485399987004[/C][C]153.822914083801[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]99.8103333333333[/C][C]0.636865074097618[/C][C]156.721317266072[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]99.8628571428571[/C][C]0.619584230183242[/C][C]161.177209292952[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]99.9215384615385[/C][C]0.592573446874586[/C][C]168.623044094458[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]99.985[/C][C]0.55134782151547[/C][C]181.346504145377[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]100.029090909091[/C][C]0.501251640793984[/C][C]199.558630373049[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]100.04[/C][C]0.44642615939198[/C][C]224.090810754127[/C][/ROW]
[ROW][C]Median[/C][C]99.99[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]99.195[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.6032258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.8103333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.6032258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.8103333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.8103333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.6032258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.8103333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.7603125[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293608&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293608&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 Mean99.560.72164935849079137.961738382493
Geometric Mean99.4048269094261
Harmonic Mean99.2490156430674
Quadratic Mean99.7141890103911
Winsorized Mean ( 1 / 20 )99.56966666666670.717793502506852138.716310915222
Winsorized Mean ( 2 / 20 )99.55766666666660.708577367068982140.503593952606
Winsorized Mean ( 3 / 20 )99.55766666666670.708029627147778140.612289160447
Winsorized Mean ( 4 / 20 )99.55766666666670.704889916743693141.238602371535
Winsorized Mean ( 5 / 20 )99.58850.697785473038943142.72079865217
Winsorized Mean ( 6 / 20 )99.59550.695838616306614143.130170798274
Winsorized Mean ( 7 / 20 )99.59433333333330.691970753385206143.928529993653
Winsorized Mean ( 8 / 20 )99.60366666666670.685727374409878145.252574687402
Winsorized Mean ( 9 / 20 )99.55116666666670.674342789143106147.626946219989
Winsorized Mean ( 10 / 20 )99.49616666666670.652106196148152.576631313108
Winsorized Mean ( 11 / 20 )99.48333333333330.623412001440853159.578790757001
Winsorized Mean ( 12 / 20 )99.46533333333330.620075513292178160.408419944275
Winsorized Mean ( 13 / 20 )99.42416666666670.613298541677792162.11381555657
Winsorized Mean ( 14 / 20 )99.41016666666670.608324897008293163.416238847958
Winsorized Mean ( 15 / 20 )99.44266666666670.602112799212505165.156207934338
Winsorized Mean ( 16 / 20 )99.4560.599064817333844166.018763115871
Winsorized Mean ( 17 / 20 )99.490.592555034512874167.900016378712
Winsorized Mean ( 18 / 20 )99.6940.555637832702151179.422627712683
Winsorized Mean ( 19 / 20 )99.960.499244796899915200.222417180322
Winsorized Mean ( 20 / 20 )100.4466666666670.419304621186554239.555353295228
Trimmed Mean ( 1 / 20 )99.57258620689650.71362365087235139.530950361828
Trimmed Mean ( 2 / 20 )99.57571428571430.707866781487839140.670132982395
Trimmed Mean ( 3 / 20 )99.58574074074070.705936720124287141.068934228563
Trimmed Mean ( 4 / 20 )99.59653846153850.702862059194088141.701400948768
Trimmed Mean ( 5 / 20 )99.60820.699241787034137142.451726780363
Trimmed Mean ( 6 / 20 )99.6131250.695969472577463143.128583831546
Trimmed Mean ( 7 / 20 )99.61695652173910.6912826326611144.104526593215
Trimmed Mean ( 8 / 20 )99.62136363636360.685224118126524145.385080590478
Trimmed Mean ( 9 / 20 )99.62452380952380.677891724091159146.962295406526
Trimmed Mean ( 10 / 20 )99.636750.670027878055678148.705379676337
Trimmed Mean ( 11 / 20 )99.65894736842110.663894795933347150.112559970159
Trimmed Mean ( 12 / 20 )99.68555555555560.661152246285951150.775492506519
Trimmed Mean ( 13 / 20 )99.71794117647060.656089095973961151.988414055929
Trimmed Mean ( 14 / 20 )99.76031250.6485399987004153.822914083801
Trimmed Mean ( 15 / 20 )99.81033333333330.636865074097618156.721317266072
Trimmed Mean ( 16 / 20 )99.86285714285710.619584230183242161.177209292952
Trimmed Mean ( 17 / 20 )99.92153846153850.592573446874586168.623044094458
Trimmed Mean ( 18 / 20 )99.9850.55134782151547181.346504145377
Trimmed Mean ( 19 / 20 )100.0290909090910.501251640793984199.558630373049
Trimmed Mean ( 20 / 20 )100.040.44642615939198224.090810754127
Median99.99
Midrange99.195
Midmean - Weighted Average at Xnp99.6032258064516
Midmean - Weighted Average at X(n+1)p99.8103333333333
Midmean - Empirical Distribution Function99.6032258064516
Midmean - Empirical Distribution Function - Averaging99.8103333333333
Midmean - Empirical Distribution Function - Interpolation99.8103333333333
Midmean - Closest Observation99.6032258064516
Midmean - True Basic - Statistics Graphics Toolkit99.8103333333333
Midmean - MS Excel (old versions)99.7603125
Number of observations60


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')