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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 16 Dec 2009 07:52:58 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/16/t1260975288v5b3r8q8136ud7a.htm/, Retrieved Tue, 30 Apr 2024 18:47:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68393, Retrieved Tue, 30 Apr 2024 18:47:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central tendency] [2009-12-16 14:52:58] [29af64a72952b0c5025d716b5179273f] [Current]
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Dataseries X:
9.9
9.8
9.3
8.3
8
8.5
10.4
11.1
10.9
10
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9
9
9
9.8
10
9.8
9.3
9
9
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.7
7.9
7.9
8
7.9
7.6
7.1
6.8
6.5
6.9
8.2
8.7
8.3
7.9
7.5
7.8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68393&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68393&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68393&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.893333333333330.12731176792564869.8547626683432
Geometric Mean8.83771872661975
Harmonic Mean8.78008237500377
Quadratic Mean8.94693616086908
Winsorized Mean ( 1 / 20 )8.8950.12485980839090171.2398978873352
Winsorized Mean ( 2 / 20 )8.881666666666670.11985140674469374.1056522230598
Winsorized Mean ( 3 / 20 )8.886666666666670.11609139850146776.5488811520725
Winsorized Mean ( 4 / 20 )8.906666666666670.10829616920119382.2435985719846
Winsorized Mean ( 5 / 20 )8.906666666666670.10485035520596684.9464615467497
Winsorized Mean ( 6 / 20 )8.906666666666670.10089617269640888.2755651541551
Winsorized Mean ( 7 / 20 )8.918333333333330.098591540722678490.4573888181656
Winsorized Mean ( 8 / 20 )8.918333333333330.093654361135500295.2260335258728
Winsorized Mean ( 9 / 20 )8.903333333333330.091069187911265297.7644968351804
Winsorized Mean ( 10 / 20 )8.903333333333330.091069187911265297.7644968351804
Winsorized Mean ( 11 / 20 )8.903333333333330.091069187911265297.7644968351804
Winsorized Mean ( 12 / 20 )8.883333333333330.0809954545235965109.676936632849
Winsorized Mean ( 13 / 20 )8.883333333333330.0809954545235965109.676936632849
Winsorized Mean ( 14 / 20 )8.883333333333330.0733063638132317121.180929884424
Winsorized Mean ( 15 / 20 )8.908333333333330.068860444586317129.367932299169
Winsorized Mean ( 16 / 20 )8.908333333333330.0604732590978307147.310289973323
Winsorized Mean ( 17 / 20 )8.908333333333330.0604732590978307147.310289973323
Winsorized Mean ( 18 / 20 )8.878333333333330.0565031705858384157.129825482015
Winsorized Mean ( 19 / 20 )8.910.0510732275881522174.455393182688
Winsorized Mean ( 20 / 20 )8.943333333333330.0454958039082508196.574905047704
Trimmed Mean ( 1 / 20 )8.896551724137930.11895302283214074.7904635991658
Trimmed Mean ( 2 / 20 )8.898214285714290.11161422055480179.7229442761321
Trimmed Mean ( 3 / 20 )8.90740740740740.10593340246199984.0849741478167
Trimmed Mean ( 4 / 20 )8.915384615384620.10072829122434388.5092411180511
Trimmed Mean ( 5 / 20 )8.9180.097423544068030691.5384477675394
Trimmed Mean ( 6 / 20 )8.920833333333330.094435535318910994.4647933980305
Trimmed Mean ( 7 / 20 )8.923913043478260.09185079176528797.1566262192077
Trimmed Mean ( 8 / 20 )8.9250.089166032744251100.094169554442
Trimmed Mean ( 9 / 20 )8.926190476190480.0870246019528866102.570885426433
Trimmed Mean ( 10 / 20 )8.930.084822590121216105.278558309037
Trimmed Mean ( 11 / 20 )8.934210526315790.0817897519542857109.23386259087
Trimmed Mean ( 12 / 20 )8.938888888888890.0775904774244163115.206004468739
Trimmed Mean ( 13 / 20 )8.947058823529410.0747229337565889119.736450025833
Trimmed Mean ( 14 / 20 )8.956250.0705590435665922126.932701285091
Trimmed Mean ( 15 / 20 )8.966666666666670.0670106070405178133.809661823314
Trimmed Mean ( 16 / 20 )8.9750.0633343776020842141.708189766827
Trimmed Mean ( 17 / 20 )8.984615384615380.0606864089948185148.049876956511
Trimmed Mean ( 18 / 20 )8.995833333333330.0562986236435189159.787802101427
Trimmed Mean ( 19 / 20 )9.013636363636360.0502355725645232179.427363987126
Trimmed Mean ( 20 / 20 )9.030.0429810239646827210.092714576086
Median9.05
Midrange8.8
Midmean - Weighted Average at Xnp8.95625
Midmean - Weighted Average at X(n+1)p8.98387096774193
Midmean - Empirical Distribution Function8.95625
Midmean - Empirical Distribution Function - Averaging8.98387096774193
Midmean - Empirical Distribution Function - Interpolation8.98387096774193
Midmean - Closest Observation8.95625
Midmean - True Basic - Statistics Graphics Toolkit8.98387096774193
Midmean - MS Excel (old versions)8.95625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.89333333333333 & 0.127311767925648 & 69.8547626683432 \tabularnewline
Geometric Mean & 8.83771872661975 &  &  \tabularnewline
Harmonic Mean & 8.78008237500377 &  &  \tabularnewline
Quadratic Mean & 8.94693616086908 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8.895 & 0.124859808390901 & 71.2398978873352 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8.88166666666667 & 0.119851406744693 & 74.1056522230598 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8.88666666666667 & 0.116091398501467 & 76.5488811520725 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8.90666666666667 & 0.108296169201193 & 82.2435985719846 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8.90666666666667 & 0.104850355205966 & 84.9464615467497 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8.90666666666667 & 0.100896172696408 & 88.2755651541551 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8.91833333333333 & 0.0985915407226784 & 90.4573888181656 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8.91833333333333 & 0.0936543611355002 & 95.2260335258728 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8.90333333333333 & 0.0910691879112652 & 97.7644968351804 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8.90333333333333 & 0.0910691879112652 & 97.7644968351804 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8.90333333333333 & 0.0910691879112652 & 97.7644968351804 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.88333333333333 & 0.0809954545235965 & 109.676936632849 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.88333333333333 & 0.0809954545235965 & 109.676936632849 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.88333333333333 & 0.0733063638132317 & 121.180929884424 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8.90833333333333 & 0.068860444586317 & 129.367932299169 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8.90833333333333 & 0.0604732590978307 & 147.310289973323 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8.90833333333333 & 0.0604732590978307 & 147.310289973323 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8.87833333333333 & 0.0565031705858384 & 157.129825482015 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8.91 & 0.0510732275881522 & 174.455393182688 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8.94333333333333 & 0.0454958039082508 & 196.574905047704 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8.89655172413793 & 0.118953022832140 & 74.7904635991658 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8.89821428571429 & 0.111614220554801 & 79.7229442761321 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8.9074074074074 & 0.105933402461999 & 84.0849741478167 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8.91538461538462 & 0.100728291224343 & 88.5092411180511 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8.918 & 0.0974235440680306 & 91.5384477675394 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8.92083333333333 & 0.0944355353189109 & 94.4647933980305 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8.92391304347826 & 0.091850791765287 & 97.1566262192077 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8.925 & 0.089166032744251 & 100.094169554442 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8.92619047619048 & 0.0870246019528866 & 102.570885426433 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8.93 & 0.084822590121216 & 105.278558309037 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8.93421052631579 & 0.0817897519542857 & 109.23386259087 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8.93888888888889 & 0.0775904774244163 & 115.206004468739 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.94705882352941 & 0.0747229337565889 & 119.736450025833 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8.95625 & 0.0705590435665922 & 126.932701285091 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8.96666666666667 & 0.0670106070405178 & 133.809661823314 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8.975 & 0.0633343776020842 & 141.708189766827 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8.98461538461538 & 0.0606864089948185 & 148.049876956511 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8.99583333333333 & 0.0562986236435189 & 159.787802101427 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 9.01363636363636 & 0.0502355725645232 & 179.427363987126 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 9.03 & 0.0429810239646827 & 210.092714576086 \tabularnewline
Median & 9.05 &  &  \tabularnewline
Midrange & 8.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.95625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.98387096774193 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.95625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.98387096774193 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.98387096774193 &  &  \tabularnewline
Midmean - Closest Observation & 8.95625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.98387096774193 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.95625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68393&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]8.89333333333333[/C][C]0.127311767925648[/C][C]69.8547626683432[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.83771872661975[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.78008237500377[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.94693616086908[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8.895[/C][C]0.124859808390901[/C][C]71.2398978873352[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8.88166666666667[/C][C]0.119851406744693[/C][C]74.1056522230598[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8.88666666666667[/C][C]0.116091398501467[/C][C]76.5488811520725[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8.90666666666667[/C][C]0.108296169201193[/C][C]82.2435985719846[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8.90666666666667[/C][C]0.104850355205966[/C][C]84.9464615467497[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8.90666666666667[/C][C]0.100896172696408[/C][C]88.2755651541551[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8.91833333333333[/C][C]0.0985915407226784[/C][C]90.4573888181656[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8.91833333333333[/C][C]0.0936543611355002[/C][C]95.2260335258728[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8.90333333333333[/C][C]0.0910691879112652[/C][C]97.7644968351804[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8.90333333333333[/C][C]0.0910691879112652[/C][C]97.7644968351804[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8.90333333333333[/C][C]0.0910691879112652[/C][C]97.7644968351804[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.88333333333333[/C][C]0.0809954545235965[/C][C]109.676936632849[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.88333333333333[/C][C]0.0809954545235965[/C][C]109.676936632849[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.88333333333333[/C][C]0.0733063638132317[/C][C]121.180929884424[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8.90833333333333[/C][C]0.068860444586317[/C][C]129.367932299169[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8.90833333333333[/C][C]0.0604732590978307[/C][C]147.310289973323[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8.90833333333333[/C][C]0.0604732590978307[/C][C]147.310289973323[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8.87833333333333[/C][C]0.0565031705858384[/C][C]157.129825482015[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8.91[/C][C]0.0510732275881522[/C][C]174.455393182688[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8.94333333333333[/C][C]0.0454958039082508[/C][C]196.574905047704[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8.89655172413793[/C][C]0.118953022832140[/C][C]74.7904635991658[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8.89821428571429[/C][C]0.111614220554801[/C][C]79.7229442761321[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8.9074074074074[/C][C]0.105933402461999[/C][C]84.0849741478167[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8.91538461538462[/C][C]0.100728291224343[/C][C]88.5092411180511[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8.918[/C][C]0.0974235440680306[/C][C]91.5384477675394[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8.92083333333333[/C][C]0.0944355353189109[/C][C]94.4647933980305[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8.92391304347826[/C][C]0.091850791765287[/C][C]97.1566262192077[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8.925[/C][C]0.089166032744251[/C][C]100.094169554442[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8.92619047619048[/C][C]0.0870246019528866[/C][C]102.570885426433[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8.93[/C][C]0.084822590121216[/C][C]105.278558309037[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8.93421052631579[/C][C]0.0817897519542857[/C][C]109.23386259087[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8.93888888888889[/C][C]0.0775904774244163[/C][C]115.206004468739[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.94705882352941[/C][C]0.0747229337565889[/C][C]119.736450025833[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8.95625[/C][C]0.0705590435665922[/C][C]126.932701285091[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8.96666666666667[/C][C]0.0670106070405178[/C][C]133.809661823314[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8.975[/C][C]0.0633343776020842[/C][C]141.708189766827[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8.98461538461538[/C][C]0.0606864089948185[/C][C]148.049876956511[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8.99583333333333[/C][C]0.0562986236435189[/C][C]159.787802101427[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]9.01363636363636[/C][C]0.0502355725645232[/C][C]179.427363987126[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]9.03[/C][C]0.0429810239646827[/C][C]210.092714576086[/C][/ROW]
[ROW][C]Median[/C][C]9.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.95625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.98387096774193[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.95625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.98387096774193[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.98387096774193[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.95625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.98387096774193[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.95625[/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=68393&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68393&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 Mean8.893333333333330.12731176792564869.8547626683432
Geometric Mean8.83771872661975
Harmonic Mean8.78008237500377
Quadratic Mean8.94693616086908
Winsorized Mean ( 1 / 20 )8.8950.12485980839090171.2398978873352
Winsorized Mean ( 2 / 20 )8.881666666666670.11985140674469374.1056522230598
Winsorized Mean ( 3 / 20 )8.886666666666670.11609139850146776.5488811520725
Winsorized Mean ( 4 / 20 )8.906666666666670.10829616920119382.2435985719846
Winsorized Mean ( 5 / 20 )8.906666666666670.10485035520596684.9464615467497
Winsorized Mean ( 6 / 20 )8.906666666666670.10089617269640888.2755651541551
Winsorized Mean ( 7 / 20 )8.918333333333330.098591540722678490.4573888181656
Winsorized Mean ( 8 / 20 )8.918333333333330.093654361135500295.2260335258728
Winsorized Mean ( 9 / 20 )8.903333333333330.091069187911265297.7644968351804
Winsorized Mean ( 10 / 20 )8.903333333333330.091069187911265297.7644968351804
Winsorized Mean ( 11 / 20 )8.903333333333330.091069187911265297.7644968351804
Winsorized Mean ( 12 / 20 )8.883333333333330.0809954545235965109.676936632849
Winsorized Mean ( 13 / 20 )8.883333333333330.0809954545235965109.676936632849
Winsorized Mean ( 14 / 20 )8.883333333333330.0733063638132317121.180929884424
Winsorized Mean ( 15 / 20 )8.908333333333330.068860444586317129.367932299169
Winsorized Mean ( 16 / 20 )8.908333333333330.0604732590978307147.310289973323
Winsorized Mean ( 17 / 20 )8.908333333333330.0604732590978307147.310289973323
Winsorized Mean ( 18 / 20 )8.878333333333330.0565031705858384157.129825482015
Winsorized Mean ( 19 / 20 )8.910.0510732275881522174.455393182688
Winsorized Mean ( 20 / 20 )8.943333333333330.0454958039082508196.574905047704
Trimmed Mean ( 1 / 20 )8.896551724137930.11895302283214074.7904635991658
Trimmed Mean ( 2 / 20 )8.898214285714290.11161422055480179.7229442761321
Trimmed Mean ( 3 / 20 )8.90740740740740.10593340246199984.0849741478167
Trimmed Mean ( 4 / 20 )8.915384615384620.10072829122434388.5092411180511
Trimmed Mean ( 5 / 20 )8.9180.097423544068030691.5384477675394
Trimmed Mean ( 6 / 20 )8.920833333333330.094435535318910994.4647933980305
Trimmed Mean ( 7 / 20 )8.923913043478260.09185079176528797.1566262192077
Trimmed Mean ( 8 / 20 )8.9250.089166032744251100.094169554442
Trimmed Mean ( 9 / 20 )8.926190476190480.0870246019528866102.570885426433
Trimmed Mean ( 10 / 20 )8.930.084822590121216105.278558309037
Trimmed Mean ( 11 / 20 )8.934210526315790.0817897519542857109.23386259087
Trimmed Mean ( 12 / 20 )8.938888888888890.0775904774244163115.206004468739
Trimmed Mean ( 13 / 20 )8.947058823529410.0747229337565889119.736450025833
Trimmed Mean ( 14 / 20 )8.956250.0705590435665922126.932701285091
Trimmed Mean ( 15 / 20 )8.966666666666670.0670106070405178133.809661823314
Trimmed Mean ( 16 / 20 )8.9750.0633343776020842141.708189766827
Trimmed Mean ( 17 / 20 )8.984615384615380.0606864089948185148.049876956511
Trimmed Mean ( 18 / 20 )8.995833333333330.0562986236435189159.787802101427
Trimmed Mean ( 19 / 20 )9.013636363636360.0502355725645232179.427363987126
Trimmed Mean ( 20 / 20 )9.030.0429810239646827210.092714576086
Median9.05
Midrange8.8
Midmean - Weighted Average at Xnp8.95625
Midmean - Weighted Average at X(n+1)p8.98387096774193
Midmean - Empirical Distribution Function8.95625
Midmean - Empirical Distribution Function - Averaging8.98387096774193
Midmean - Empirical Distribution Function - Interpolation8.98387096774193
Midmean - Closest Observation8.95625
Midmean - True Basic - Statistics Graphics Toolkit8.98387096774193
Midmean - MS Excel (old versions)8.95625
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')