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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 09 Oct 2015 10:12:47 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/09/t1444381992fn2f1ijmpg8hgjl.htm/, Retrieved Tue, 14 May 2024 08:49:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=281765, Retrieved Tue, 14 May 2024 08:49:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Afzetprijsindex v...] [2015-10-09 09:12:47] [2d6a838730984919764007611a305b0c] [Current]
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Dataseries X:
98,4
98,1
97,5
97,7
98,2
98,9
99,9
100,9
101,8
102,1
103,1
103,4
105,5
106,7
106,9
107,2
107,7
107,3
107,2
107,1
106,6
106,6
106,5
106,7
106,3
108,9
109,9
110,8
110,5
111,2
111,4
112,2
113,2
114
114,2
114,6
115,9
116,1
116,4
116,7
117,9
118,1
118,3
118,8
118,4
118
117,9
117,9
117,9
117,3
117,8
117,8
117,8
117,6
117,3
116,3
114,3
113,8
113,5
114,7




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281765&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=281765&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281765&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean110.4283333333330.867065613306039127.358681556152
Geometric Mean110.223237778153
Harmonic Mean110.014063647343
Quadratic Mean110.628988816976
Winsorized Mean ( 1 / 20 )110.4250.865162618200881127.634964429728
Winsorized Mean ( 2 / 20 )110.4350.861364129646579128.20942525818
Winsorized Mean ( 3 / 20 )110.430.858622928492673128.612917656254
Winsorized Mean ( 4 / 20 )110.4366666666670.854416795401198129.25385743946
Winsorized Mean ( 5 / 20 )110.470.843349858036893130.989528186021
Winsorized Mean ( 6 / 20 )110.570.820697305829994134.726895305423
Winsorized Mean ( 7 / 20 )110.6866666666670.795671434711003139.111022261179
Winsorized Mean ( 8 / 20 )110.8066666666670.77127770822286143.666367490358
Winsorized Mean ( 9 / 20 )110.8366666666670.760106915861505145.817205913782
Winsorized Mean ( 10 / 20 )111.0033333333330.728530626551126152.366049261134
Winsorized Mean ( 11 / 20 )111.0583333333330.718505556975655154.568509951129
Winsorized Mean ( 12 / 20 )111.4383333333330.64086845943419173.886437525292
Winsorized Mean ( 13 / 20 )111.5466666666670.603925326821659184.702746701674
Winsorized Mean ( 14 / 20 )111.5933333333330.597115792207174186.88725836716
Winsorized Mean ( 15 / 20 )111.4683333333330.569663850065601195.673875603124
Winsorized Mean ( 16 / 20 )111.3883333333330.557339785530192199.857136033041
Winsorized Mean ( 17 / 20 )111.3883333333330.548918256531925202.923353355173
Winsorized Mean ( 18 / 20 )111.3283333333330.539873869275898206.21174624112
Winsorized Mean ( 19 / 20 )111.3283333333330.521260378599363213.575283877272
Winsorized Mean ( 20 / 20 )110.9950.454086436183051244.435841186976
Trimmed Mean ( 1 / 20 )110.5068965517240.856242378477932129.060298029353
Trimmed Mean ( 2 / 20 )110.5946428571430.844587118228956130.945216272127
Trimmed Mean ( 3 / 20 )110.6833333333330.831997881723369133.033191267348
Trimmed Mean ( 4 / 20 )110.7807692307690.816912290123727135.609135240199
Trimmed Mean ( 5 / 20 )110.8840.79894501866971138.788023467032
Trimmed Mean ( 6 / 20 )110.98750.779420730755806142.397418519232
Trimmed Mean ( 7 / 20 )111.0782608695650.761202411669321145.924735874089
Trimmed Mean ( 8 / 20 )111.1545454545450.74461743334747149.277387926366
Trimmed Mean ( 9 / 20 )111.2166666666670.729285497202918152.500861587436
Trimmed Mean ( 10 / 20 )111.280.711284500762979156.44935307972
Trimmed Mean ( 11 / 20 )111.3236842105260.695314886253626160.105423328905
Trimmed Mean ( 12 / 20 )111.3638888888890.675514533790023164.857872508048
Trimmed Mean ( 13 / 20 )111.3529411764710.66868102931684166.526245391221
Trimmed Mean ( 14 / 20 )111.3250.66656921330724167.011913808097
Trimmed Mean ( 15 / 20 )111.2866666666670.662401297498128168.004904409145
Trimmed Mean ( 16 / 20 )111.2607142857140.661134572460474168.28754525973
Trimmed Mean ( 17 / 20 )111.2423076923080.659024292231689168.798493475259
Trimmed Mean ( 18 / 20 )111.2208333333330.653972785817095170.069513205156
Trimmed Mean ( 19 / 20 )111.2045454545450.644372148957285172.578137702716
Trimmed Mean ( 20 / 20 )111.1850.630883882885124176.236868647737
Median111.3
Midrange108.15
Midmean - Weighted Average at Xnp111.132258064516
Midmean - Weighted Average at X(n+1)p111.286666666667
Midmean - Empirical Distribution Function111.132258064516
Midmean - Empirical Distribution Function - Averaging111.286666666667
Midmean - Empirical Distribution Function - Interpolation111.286666666667
Midmean - Closest Observation111.132258064516
Midmean - True Basic - Statistics Graphics Toolkit111.286666666667
Midmean - MS Excel (old versions)111.506060606061
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 110.428333333333 & 0.867065613306039 & 127.358681556152 \tabularnewline
Geometric Mean & 110.223237778153 &  &  \tabularnewline
Harmonic Mean & 110.014063647343 &  &  \tabularnewline
Quadratic Mean & 110.628988816976 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 110.425 & 0.865162618200881 & 127.634964429728 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 110.435 & 0.861364129646579 & 128.20942525818 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 110.43 & 0.858622928492673 & 128.612917656254 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 110.436666666667 & 0.854416795401198 & 129.25385743946 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 110.47 & 0.843349858036893 & 130.989528186021 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 110.57 & 0.820697305829994 & 134.726895305423 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 110.686666666667 & 0.795671434711003 & 139.111022261179 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 110.806666666667 & 0.77127770822286 & 143.666367490358 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 110.836666666667 & 0.760106915861505 & 145.817205913782 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 111.003333333333 & 0.728530626551126 & 152.366049261134 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 111.058333333333 & 0.718505556975655 & 154.568509951129 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 111.438333333333 & 0.64086845943419 & 173.886437525292 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 111.546666666667 & 0.603925326821659 & 184.702746701674 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 111.593333333333 & 0.597115792207174 & 186.88725836716 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 111.468333333333 & 0.569663850065601 & 195.673875603124 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 111.388333333333 & 0.557339785530192 & 199.857136033041 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 111.388333333333 & 0.548918256531925 & 202.923353355173 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 111.328333333333 & 0.539873869275898 & 206.21174624112 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 111.328333333333 & 0.521260378599363 & 213.575283877272 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 110.995 & 0.454086436183051 & 244.435841186976 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 110.506896551724 & 0.856242378477932 & 129.060298029353 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 110.594642857143 & 0.844587118228956 & 130.945216272127 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 110.683333333333 & 0.831997881723369 & 133.033191267348 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 110.780769230769 & 0.816912290123727 & 135.609135240199 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 110.884 & 0.79894501866971 & 138.788023467032 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 110.9875 & 0.779420730755806 & 142.397418519232 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 111.078260869565 & 0.761202411669321 & 145.924735874089 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 111.154545454545 & 0.74461743334747 & 149.277387926366 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 111.216666666667 & 0.729285497202918 & 152.500861587436 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 111.28 & 0.711284500762979 & 156.44935307972 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 111.323684210526 & 0.695314886253626 & 160.105423328905 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 111.363888888889 & 0.675514533790023 & 164.857872508048 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 111.352941176471 & 0.66868102931684 & 166.526245391221 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 111.325 & 0.66656921330724 & 167.011913808097 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 111.286666666667 & 0.662401297498128 & 168.004904409145 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 111.260714285714 & 0.661134572460474 & 168.28754525973 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 111.242307692308 & 0.659024292231689 & 168.798493475259 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 111.220833333333 & 0.653972785817095 & 170.069513205156 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 111.204545454545 & 0.644372148957285 & 172.578137702716 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 111.185 & 0.630883882885124 & 176.236868647737 \tabularnewline
Median & 111.3 &  &  \tabularnewline
Midrange & 108.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.132258064516 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111.286666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.132258064516 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111.286666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111.286666666667 &  &  \tabularnewline
Midmean - Closest Observation & 111.132258064516 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111.286666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111.506060606061 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281765&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]110.428333333333[/C][C]0.867065613306039[/C][C]127.358681556152[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]110.223237778153[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]110.014063647343[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]110.628988816976[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]110.425[/C][C]0.865162618200881[/C][C]127.634964429728[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]110.435[/C][C]0.861364129646579[/C][C]128.20942525818[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]110.43[/C][C]0.858622928492673[/C][C]128.612917656254[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]110.436666666667[/C][C]0.854416795401198[/C][C]129.25385743946[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]110.47[/C][C]0.843349858036893[/C][C]130.989528186021[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]110.57[/C][C]0.820697305829994[/C][C]134.726895305423[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]110.686666666667[/C][C]0.795671434711003[/C][C]139.111022261179[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]110.806666666667[/C][C]0.77127770822286[/C][C]143.666367490358[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]110.836666666667[/C][C]0.760106915861505[/C][C]145.817205913782[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]111.003333333333[/C][C]0.728530626551126[/C][C]152.366049261134[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]111.058333333333[/C][C]0.718505556975655[/C][C]154.568509951129[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]111.438333333333[/C][C]0.64086845943419[/C][C]173.886437525292[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]111.546666666667[/C][C]0.603925326821659[/C][C]184.702746701674[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]111.593333333333[/C][C]0.597115792207174[/C][C]186.88725836716[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]111.468333333333[/C][C]0.569663850065601[/C][C]195.673875603124[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]111.388333333333[/C][C]0.557339785530192[/C][C]199.857136033041[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]111.388333333333[/C][C]0.548918256531925[/C][C]202.923353355173[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]111.328333333333[/C][C]0.539873869275898[/C][C]206.21174624112[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]111.328333333333[/C][C]0.521260378599363[/C][C]213.575283877272[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]110.995[/C][C]0.454086436183051[/C][C]244.435841186976[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]110.506896551724[/C][C]0.856242378477932[/C][C]129.060298029353[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]110.594642857143[/C][C]0.844587118228956[/C][C]130.945216272127[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]110.683333333333[/C][C]0.831997881723369[/C][C]133.033191267348[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]110.780769230769[/C][C]0.816912290123727[/C][C]135.609135240199[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]110.884[/C][C]0.79894501866971[/C][C]138.788023467032[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]110.9875[/C][C]0.779420730755806[/C][C]142.397418519232[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]111.078260869565[/C][C]0.761202411669321[/C][C]145.924735874089[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]111.154545454545[/C][C]0.74461743334747[/C][C]149.277387926366[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]111.216666666667[/C][C]0.729285497202918[/C][C]152.500861587436[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]111.28[/C][C]0.711284500762979[/C][C]156.44935307972[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]111.323684210526[/C][C]0.695314886253626[/C][C]160.105423328905[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]111.363888888889[/C][C]0.675514533790023[/C][C]164.857872508048[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]111.352941176471[/C][C]0.66868102931684[/C][C]166.526245391221[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]111.325[/C][C]0.66656921330724[/C][C]167.011913808097[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]111.286666666667[/C][C]0.662401297498128[/C][C]168.004904409145[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]111.260714285714[/C][C]0.661134572460474[/C][C]168.28754525973[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]111.242307692308[/C][C]0.659024292231689[/C][C]168.798493475259[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]111.220833333333[/C][C]0.653972785817095[/C][C]170.069513205156[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]111.204545454545[/C][C]0.644372148957285[/C][C]172.578137702716[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]111.185[/C][C]0.630883882885124[/C][C]176.236868647737[/C][/ROW]
[ROW][C]Median[/C][C]111.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]108.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.132258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111.286666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.132258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111.286666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111.286666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.132258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111.286666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111.506060606061[/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=281765&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281765&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean110.4283333333330.867065613306039127.358681556152
Geometric Mean110.223237778153
Harmonic Mean110.014063647343
Quadratic Mean110.628988816976
Winsorized Mean ( 1 / 20 )110.4250.865162618200881127.634964429728
Winsorized Mean ( 2 / 20 )110.4350.861364129646579128.20942525818
Winsorized Mean ( 3 / 20 )110.430.858622928492673128.612917656254
Winsorized Mean ( 4 / 20 )110.4366666666670.854416795401198129.25385743946
Winsorized Mean ( 5 / 20 )110.470.843349858036893130.989528186021
Winsorized Mean ( 6 / 20 )110.570.820697305829994134.726895305423
Winsorized Mean ( 7 / 20 )110.6866666666670.795671434711003139.111022261179
Winsorized Mean ( 8 / 20 )110.8066666666670.77127770822286143.666367490358
Winsorized Mean ( 9 / 20 )110.8366666666670.760106915861505145.817205913782
Winsorized Mean ( 10 / 20 )111.0033333333330.728530626551126152.366049261134
Winsorized Mean ( 11 / 20 )111.0583333333330.718505556975655154.568509951129
Winsorized Mean ( 12 / 20 )111.4383333333330.64086845943419173.886437525292
Winsorized Mean ( 13 / 20 )111.5466666666670.603925326821659184.702746701674
Winsorized Mean ( 14 / 20 )111.5933333333330.597115792207174186.88725836716
Winsorized Mean ( 15 / 20 )111.4683333333330.569663850065601195.673875603124
Winsorized Mean ( 16 / 20 )111.3883333333330.557339785530192199.857136033041
Winsorized Mean ( 17 / 20 )111.3883333333330.548918256531925202.923353355173
Winsorized Mean ( 18 / 20 )111.3283333333330.539873869275898206.21174624112
Winsorized Mean ( 19 / 20 )111.3283333333330.521260378599363213.575283877272
Winsorized Mean ( 20 / 20 )110.9950.454086436183051244.435841186976
Trimmed Mean ( 1 / 20 )110.5068965517240.856242378477932129.060298029353
Trimmed Mean ( 2 / 20 )110.5946428571430.844587118228956130.945216272127
Trimmed Mean ( 3 / 20 )110.6833333333330.831997881723369133.033191267348
Trimmed Mean ( 4 / 20 )110.7807692307690.816912290123727135.609135240199
Trimmed Mean ( 5 / 20 )110.8840.79894501866971138.788023467032
Trimmed Mean ( 6 / 20 )110.98750.779420730755806142.397418519232
Trimmed Mean ( 7 / 20 )111.0782608695650.761202411669321145.924735874089
Trimmed Mean ( 8 / 20 )111.1545454545450.74461743334747149.277387926366
Trimmed Mean ( 9 / 20 )111.2166666666670.729285497202918152.500861587436
Trimmed Mean ( 10 / 20 )111.280.711284500762979156.44935307972
Trimmed Mean ( 11 / 20 )111.3236842105260.695314886253626160.105423328905
Trimmed Mean ( 12 / 20 )111.3638888888890.675514533790023164.857872508048
Trimmed Mean ( 13 / 20 )111.3529411764710.66868102931684166.526245391221
Trimmed Mean ( 14 / 20 )111.3250.66656921330724167.011913808097
Trimmed Mean ( 15 / 20 )111.2866666666670.662401297498128168.004904409145
Trimmed Mean ( 16 / 20 )111.2607142857140.661134572460474168.28754525973
Trimmed Mean ( 17 / 20 )111.2423076923080.659024292231689168.798493475259
Trimmed Mean ( 18 / 20 )111.2208333333330.653972785817095170.069513205156
Trimmed Mean ( 19 / 20 )111.2045454545450.644372148957285172.578137702716
Trimmed Mean ( 20 / 20 )111.1850.630883882885124176.236868647737
Median111.3
Midrange108.15
Midmean - Weighted Average at Xnp111.132258064516
Midmean - Weighted Average at X(n+1)p111.286666666667
Midmean - Empirical Distribution Function111.132258064516
Midmean - Empirical Distribution Function - Averaging111.286666666667
Midmean - Empirical Distribution Function - Interpolation111.286666666667
Midmean - Closest Observation111.132258064516
Midmean - True Basic - Statistics Graphics Toolkit111.286666666667
Midmean - MS Excel (old versions)111.506060606061
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')