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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 19 Apr 2008 12:50:32 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/19/t1208631127ost3hcpuuilfpjw.htm/, Retrieved Thu, 16 May 2024 09:31:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10299, Retrieved Thu, 16 May 2024 09:31:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact204
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [] [Maximumprijs 2005...] [-0001-11-30 00:00:00] [74be16979710d4c4e7c6647856088456]
- RM D    [Central Tendency] [Australische bier...] [2008-04-19 18:50:32] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
164
148
152
144
155
125
153
146
138
190
192
192
147
133
163
150
129
131
145
137
138
168
176
188
139
143
150
154
137
129
128
140
143
151
177
184
151
134
164
126
131
125
127
143
143
160
190
182
138
136
152
127
151
130
119
153




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10299&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10299&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10299&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean149.3035714285712.6195964350210156.9948750244708
Geometric Mean148.105134728873
Harmonic Mean146.971600010621
Quadratic Mean150.562220171121
Winsorized Mean ( 1 / 18 )149.4107142857142.5991727936985657.4839482191972
Winsorized Mean ( 2 / 18 )149.3392857142862.5782905826120357.9218210396564
Winsorized Mean ( 3 / 18 )149.3928571428572.5692586443266358.1462895815267
Winsorized Mean ( 4 / 18 )149.3214285714292.5170983014173659.3228434850347
Winsorized Mean ( 5 / 18 )148.9642857142862.4201486867645661.5517081776626
Winsorized Mean ( 6 / 18 )148.8571428571432.3469278857535563.4263812538695
Winsorized Mean ( 7 / 18 )148.3571428571432.1713046786255468.3262668374365
Winsorized Mean ( 8 / 18 )148.2142857142862.1372871331257469.34692274946
Winsorized Mean ( 9 / 18 )147.0892857142861.8230623561359480.6825313567704
Winsorized Mean ( 10 / 18 )146.5535714285711.6490689310994988.8704945346699
Winsorized Mean ( 11 / 18 )146.5535714285711.6490689310994988.8704945346699
Winsorized Mean ( 12 / 18 )146.7678571428571.5361427218740595.5431126632589
Winsorized Mean ( 13 / 18 )146.3035714285711.36774523973448106.966975412010
Winsorized Mean ( 14 / 18 )145.5535714285711.07053804983335135.963006126900
Winsorized Mean ( 15 / 18 )145.5535714285710.985254810095504147.731906444042
Winsorized Mean ( 16 / 18 )145.2678571428570.941638207548237154.271413350032
Winsorized Mean ( 17 / 18 )145.5714285714290.894012239833533162.829346272188
Winsorized Mean ( 18 / 18 )145.250.84640185721447171.608791689117
Trimmed Mean ( 1 / 18 )149.0740740740742.5349895077157858.8065842562012
Trimmed Mean ( 2 / 18 )148.7115384615382.4533869436085860.6147916654376
Trimmed Mean ( 3 / 18 )148.362.3638018494944762.7632980453623
Trimmed Mean ( 4 / 18 )147.9583333333332.2526498055783365.6819062452307
Trimmed Mean ( 5 / 18 )147.5434782608702.1306837082219169.2470110375966
Trimmed Mean ( 6 / 18 )147.1818181818182.0095629533562373.2407103425177
Trimmed Mean ( 7 / 18 )146.8095238095241.8750882581591478.2947272858789
Trimmed Mean ( 8 / 18 )146.51.7581312923174083.3271102335583
Trimmed Mean ( 9 / 18 )146.1842105263161.6093853748309190.8323219612175
Trimmed Mean ( 10 / 18 )146.0277777777781.5178755575187696.2053687829895
Trimmed Mean ( 11 / 18 )145.9411764705881.44842478607284100.758546714934
Trimmed Mean ( 12 / 18 )145.843751.34861740356918108.143161740326
Trimmed Mean ( 13 / 18 )145.71.24304964252966117.211730742704
Trimmed Mean ( 14 / 18 )145.6071428571431.15164856039138126.433660289263
Trimmed Mean ( 15 / 18 )145.6153846153851.12465642353828129.475439403319
Trimmed Mean ( 16 / 18 )145.6251.10796277994305131.434920591363
Trimmed Mean ( 17 / 18 )145.6818181818181.08987144012566133.668809749728
Trimmed Mean ( 18 / 18 )145.71.07139849581848135.990483996988
Median145.5
Midrange155.5
Midmean - Weighted Average at Xnp145.206896551724
Midmean - Weighted Average at X(n+1)p145.607142857143
Midmean - Empirical Distribution Function145.206896551724
Midmean - Empirical Distribution Function - Averaging145.607142857143
Midmean - Empirical Distribution Function - Interpolation145.607142857143
Midmean - Closest Observation145.206896551724
Midmean - True Basic - Statistics Graphics Toolkit145.607142857143
Midmean - MS Excel (old versions)145.7
Number of observations56

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 149.303571428571 & 2.61959643502101 & 56.9948750244708 \tabularnewline
Geometric Mean & 148.105134728873 &  &  \tabularnewline
Harmonic Mean & 146.971600010621 &  &  \tabularnewline
Quadratic Mean & 150.562220171121 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & 149.410714285714 & 2.59917279369856 & 57.4839482191972 \tabularnewline
Winsorized Mean ( 2 / 18 ) & 149.339285714286 & 2.57829058261203 & 57.9218210396564 \tabularnewline
Winsorized Mean ( 3 / 18 ) & 149.392857142857 & 2.56925864432663 & 58.1462895815267 \tabularnewline
Winsorized Mean ( 4 / 18 ) & 149.321428571429 & 2.51709830141736 & 59.3228434850347 \tabularnewline
Winsorized Mean ( 5 / 18 ) & 148.964285714286 & 2.42014868676456 & 61.5517081776626 \tabularnewline
Winsorized Mean ( 6 / 18 ) & 148.857142857143 & 2.34692788575355 & 63.4263812538695 \tabularnewline
Winsorized Mean ( 7 / 18 ) & 148.357142857143 & 2.17130467862554 & 68.3262668374365 \tabularnewline
Winsorized Mean ( 8 / 18 ) & 148.214285714286 & 2.13728713312574 & 69.34692274946 \tabularnewline
Winsorized Mean ( 9 / 18 ) & 147.089285714286 & 1.82306235613594 & 80.6825313567704 \tabularnewline
Winsorized Mean ( 10 / 18 ) & 146.553571428571 & 1.64906893109949 & 88.8704945346699 \tabularnewline
Winsorized Mean ( 11 / 18 ) & 146.553571428571 & 1.64906893109949 & 88.8704945346699 \tabularnewline
Winsorized Mean ( 12 / 18 ) & 146.767857142857 & 1.53614272187405 & 95.5431126632589 \tabularnewline
Winsorized Mean ( 13 / 18 ) & 146.303571428571 & 1.36774523973448 & 106.966975412010 \tabularnewline
Winsorized Mean ( 14 / 18 ) & 145.553571428571 & 1.07053804983335 & 135.963006126900 \tabularnewline
Winsorized Mean ( 15 / 18 ) & 145.553571428571 & 0.985254810095504 & 147.731906444042 \tabularnewline
Winsorized Mean ( 16 / 18 ) & 145.267857142857 & 0.941638207548237 & 154.271413350032 \tabularnewline
Winsorized Mean ( 17 / 18 ) & 145.571428571429 & 0.894012239833533 & 162.829346272188 \tabularnewline
Winsorized Mean ( 18 / 18 ) & 145.25 & 0.84640185721447 & 171.608791689117 \tabularnewline
Trimmed Mean ( 1 / 18 ) & 149.074074074074 & 2.53498950771578 & 58.8065842562012 \tabularnewline
Trimmed Mean ( 2 / 18 ) & 148.711538461538 & 2.45338694360858 & 60.6147916654376 \tabularnewline
Trimmed Mean ( 3 / 18 ) & 148.36 & 2.36380184949447 & 62.7632980453623 \tabularnewline
Trimmed Mean ( 4 / 18 ) & 147.958333333333 & 2.25264980557833 & 65.6819062452307 \tabularnewline
Trimmed Mean ( 5 / 18 ) & 147.543478260870 & 2.13068370822191 & 69.2470110375966 \tabularnewline
Trimmed Mean ( 6 / 18 ) & 147.181818181818 & 2.00956295335623 & 73.2407103425177 \tabularnewline
Trimmed Mean ( 7 / 18 ) & 146.809523809524 & 1.87508825815914 & 78.2947272858789 \tabularnewline
Trimmed Mean ( 8 / 18 ) & 146.5 & 1.75813129231740 & 83.3271102335583 \tabularnewline
Trimmed Mean ( 9 / 18 ) & 146.184210526316 & 1.60938537483091 & 90.8323219612175 \tabularnewline
Trimmed Mean ( 10 / 18 ) & 146.027777777778 & 1.51787555751876 & 96.2053687829895 \tabularnewline
Trimmed Mean ( 11 / 18 ) & 145.941176470588 & 1.44842478607284 & 100.758546714934 \tabularnewline
Trimmed Mean ( 12 / 18 ) & 145.84375 & 1.34861740356918 & 108.143161740326 \tabularnewline
Trimmed Mean ( 13 / 18 ) & 145.7 & 1.24304964252966 & 117.211730742704 \tabularnewline
Trimmed Mean ( 14 / 18 ) & 145.607142857143 & 1.15164856039138 & 126.433660289263 \tabularnewline
Trimmed Mean ( 15 / 18 ) & 145.615384615385 & 1.12465642353828 & 129.475439403319 \tabularnewline
Trimmed Mean ( 16 / 18 ) & 145.625 & 1.10796277994305 & 131.434920591363 \tabularnewline
Trimmed Mean ( 17 / 18 ) & 145.681818181818 & 1.08987144012566 & 133.668809749728 \tabularnewline
Trimmed Mean ( 18 / 18 ) & 145.7 & 1.07139849581848 & 135.990483996988 \tabularnewline
Median & 145.5 &  &  \tabularnewline
Midrange & 155.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 145.206896551724 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 145.607142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 145.206896551724 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 145.607142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 145.607142857143 &  &  \tabularnewline
Midmean - Closest Observation & 145.206896551724 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 145.607142857143 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 145.7 &  &  \tabularnewline
Number of observations & 56 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10299&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]149.303571428571[/C][C]2.61959643502101[/C][C]56.9948750244708[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]148.105134728873[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]146.971600010621[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]150.562220171121[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]149.410714285714[/C][C]2.59917279369856[/C][C]57.4839482191972[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]149.339285714286[/C][C]2.57829058261203[/C][C]57.9218210396564[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]149.392857142857[/C][C]2.56925864432663[/C][C]58.1462895815267[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]149.321428571429[/C][C]2.51709830141736[/C][C]59.3228434850347[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]148.964285714286[/C][C]2.42014868676456[/C][C]61.5517081776626[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]148.857142857143[/C][C]2.34692788575355[/C][C]63.4263812538695[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]148.357142857143[/C][C]2.17130467862554[/C][C]68.3262668374365[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]148.214285714286[/C][C]2.13728713312574[/C][C]69.34692274946[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]147.089285714286[/C][C]1.82306235613594[/C][C]80.6825313567704[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]146.553571428571[/C][C]1.64906893109949[/C][C]88.8704945346699[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]146.553571428571[/C][C]1.64906893109949[/C][C]88.8704945346699[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]146.767857142857[/C][C]1.53614272187405[/C][C]95.5431126632589[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]146.303571428571[/C][C]1.36774523973448[/C][C]106.966975412010[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]145.553571428571[/C][C]1.07053804983335[/C][C]135.963006126900[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]145.553571428571[/C][C]0.985254810095504[/C][C]147.731906444042[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]145.267857142857[/C][C]0.941638207548237[/C][C]154.271413350032[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]145.571428571429[/C][C]0.894012239833533[/C][C]162.829346272188[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]145.25[/C][C]0.84640185721447[/C][C]171.608791689117[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]149.074074074074[/C][C]2.53498950771578[/C][C]58.8065842562012[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]148.711538461538[/C][C]2.45338694360858[/C][C]60.6147916654376[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]148.36[/C][C]2.36380184949447[/C][C]62.7632980453623[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]147.958333333333[/C][C]2.25264980557833[/C][C]65.6819062452307[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]147.543478260870[/C][C]2.13068370822191[/C][C]69.2470110375966[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]147.181818181818[/C][C]2.00956295335623[/C][C]73.2407103425177[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]146.809523809524[/C][C]1.87508825815914[/C][C]78.2947272858789[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]146.5[/C][C]1.75813129231740[/C][C]83.3271102335583[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]146.184210526316[/C][C]1.60938537483091[/C][C]90.8323219612175[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]146.027777777778[/C][C]1.51787555751876[/C][C]96.2053687829895[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]145.941176470588[/C][C]1.44842478607284[/C][C]100.758546714934[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]145.84375[/C][C]1.34861740356918[/C][C]108.143161740326[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]145.7[/C][C]1.24304964252966[/C][C]117.211730742704[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]145.607142857143[/C][C]1.15164856039138[/C][C]126.433660289263[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]145.615384615385[/C][C]1.12465642353828[/C][C]129.475439403319[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]145.625[/C][C]1.10796277994305[/C][C]131.434920591363[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]145.681818181818[/C][C]1.08987144012566[/C][C]133.668809749728[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]145.7[/C][C]1.07139849581848[/C][C]135.990483996988[/C][/ROW]
[ROW][C]Median[/C][C]145.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]155.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]145.206896551724[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]145.607142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]145.206896551724[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]145.607142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]145.607142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]145.206896551724[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]145.607142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]145.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]56[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10299&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10299&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 Mean149.3035714285712.6195964350210156.9948750244708
Geometric Mean148.105134728873
Harmonic Mean146.971600010621
Quadratic Mean150.562220171121
Winsorized Mean ( 1 / 18 )149.4107142857142.5991727936985657.4839482191972
Winsorized Mean ( 2 / 18 )149.3392857142862.5782905826120357.9218210396564
Winsorized Mean ( 3 / 18 )149.3928571428572.5692586443266358.1462895815267
Winsorized Mean ( 4 / 18 )149.3214285714292.5170983014173659.3228434850347
Winsorized Mean ( 5 / 18 )148.9642857142862.4201486867645661.5517081776626
Winsorized Mean ( 6 / 18 )148.8571428571432.3469278857535563.4263812538695
Winsorized Mean ( 7 / 18 )148.3571428571432.1713046786255468.3262668374365
Winsorized Mean ( 8 / 18 )148.2142857142862.1372871331257469.34692274946
Winsorized Mean ( 9 / 18 )147.0892857142861.8230623561359480.6825313567704
Winsorized Mean ( 10 / 18 )146.5535714285711.6490689310994988.8704945346699
Winsorized Mean ( 11 / 18 )146.5535714285711.6490689310994988.8704945346699
Winsorized Mean ( 12 / 18 )146.7678571428571.5361427218740595.5431126632589
Winsorized Mean ( 13 / 18 )146.3035714285711.36774523973448106.966975412010
Winsorized Mean ( 14 / 18 )145.5535714285711.07053804983335135.963006126900
Winsorized Mean ( 15 / 18 )145.5535714285710.985254810095504147.731906444042
Winsorized Mean ( 16 / 18 )145.2678571428570.941638207548237154.271413350032
Winsorized Mean ( 17 / 18 )145.5714285714290.894012239833533162.829346272188
Winsorized Mean ( 18 / 18 )145.250.84640185721447171.608791689117
Trimmed Mean ( 1 / 18 )149.0740740740742.5349895077157858.8065842562012
Trimmed Mean ( 2 / 18 )148.7115384615382.4533869436085860.6147916654376
Trimmed Mean ( 3 / 18 )148.362.3638018494944762.7632980453623
Trimmed Mean ( 4 / 18 )147.9583333333332.2526498055783365.6819062452307
Trimmed Mean ( 5 / 18 )147.5434782608702.1306837082219169.2470110375966
Trimmed Mean ( 6 / 18 )147.1818181818182.0095629533562373.2407103425177
Trimmed Mean ( 7 / 18 )146.8095238095241.8750882581591478.2947272858789
Trimmed Mean ( 8 / 18 )146.51.7581312923174083.3271102335583
Trimmed Mean ( 9 / 18 )146.1842105263161.6093853748309190.8323219612175
Trimmed Mean ( 10 / 18 )146.0277777777781.5178755575187696.2053687829895
Trimmed Mean ( 11 / 18 )145.9411764705881.44842478607284100.758546714934
Trimmed Mean ( 12 / 18 )145.843751.34861740356918108.143161740326
Trimmed Mean ( 13 / 18 )145.71.24304964252966117.211730742704
Trimmed Mean ( 14 / 18 )145.6071428571431.15164856039138126.433660289263
Trimmed Mean ( 15 / 18 )145.6153846153851.12465642353828129.475439403319
Trimmed Mean ( 16 / 18 )145.6251.10796277994305131.434920591363
Trimmed Mean ( 17 / 18 )145.6818181818181.08987144012566133.668809749728
Trimmed Mean ( 18 / 18 )145.71.07139849581848135.990483996988
Median145.5
Midrange155.5
Midmean - Weighted Average at Xnp145.206896551724
Midmean - Weighted Average at X(n+1)p145.607142857143
Midmean - Empirical Distribution Function145.206896551724
Midmean - Empirical Distribution Function - Averaging145.607142857143
Midmean - Empirical Distribution Function - Interpolation145.607142857143
Midmean - Closest Observation145.206896551724
Midmean - True Basic - Statistics Graphics Toolkit145.607142857143
Midmean - MS Excel (old versions)145.7
Number of observations56



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')