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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 19 Oct 2011 06:54:27 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/19/t1319021761nwm1ivtl4277uet.htm/, Retrieved Wed, 15 May 2024 16:49:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132758, Retrieved Wed, 15 May 2024 16:49:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-10-19 10:54:27] [a7b46db3730015db727d65b06ff3f02a] [Current]
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Dataseries X:
99,42
99,42
99,42
99,42
99,42
109,26
110
110
109,26
100,07
100,07
100,05
100,05
100,05
100,05
100,05
100,05
108,77
111,32
111,6
108,52
103,13
102,87
102,75
102,75
102,75
102,75
102,75
102,75
115,22
115,53
115,4
111,99
107,93
107,43
106,98
106,98
106,98
106,98
106,98
106,98
113,71
118,77
118,54
116,16
110,52
110,06
109,9
109,9
110,72
110,09
110,07
112,45
113,06
119,83
119,84
113,73
110,5
110,12
109,86




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=132758&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=132758&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132758&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 Mean107.6996666666670.758731321651969141.947041848984
Geometric Mean107.542524047167
Harmonic Mean107.386018673521
Quadratic Mean107.857233971579
Winsorized Mean ( 1 / 20 )107.69950.758686138518202141.955275748611
Winsorized Mean ( 2 / 20 )107.6641666666670.74945921338225143.655805071482
Winsorized Mean ( 3 / 20 )107.6526666666670.746593804455424144.191749280842
Winsorized Mean ( 4 / 20 )107.4940.710505597015133151.292263497413
Winsorized Mean ( 5 / 20 )107.4940.690034683481041155.780575344012
Winsorized Mean ( 6 / 20 )107.4810.687482622276522156.339951756291
Winsorized Mean ( 7 / 20 )107.460.6834118047819157.240479675785
Winsorized Mean ( 8 / 20 )107.2613333333330.647410594864457165.677445170309
Winsorized Mean ( 9 / 20 )107.2583333333330.646903016101374165.802802991608
Winsorized Mean ( 10 / 20 )107.150.629114883565128170.318653713599
Winsorized Mean ( 11 / 20 )107.0418333333330.611111818652219175.159160838044
Winsorized Mean ( 12 / 20 )106.9498333333330.597633113634311178.955668441718
Winsorized Mean ( 13 / 20 )107.4460.47965643306987224.006168982933
Winsorized Mean ( 14 / 20 )107.3806666666670.470221420776892228.361920410291
Winsorized Mean ( 15 / 20 )107.2306666666670.449690720250566238.454257199077
Winsorized Mean ( 16 / 20 )107.1773333333330.442770736014061242.060562308548
Winsorized Mean ( 17 / 20 )107.1716666666670.442046611972435242.444266654281
Winsorized Mean ( 18 / 20 )107.0576666666670.427851772649943250.221393272708
Winsorized Mean ( 19 / 20 )107.0861666666670.42022667354216254.829532271285
Winsorized Mean ( 20 / 20 )107.1661666666670.404723180256005264.788803544386
Trimmed Mean ( 1 / 20 )107.6331034482760.742309968915543144.997518496915
Trimmed Mean ( 2 / 20 )107.5619642857140.7219163898976148.995044011913
Trimmed Mean ( 3 / 20 )107.5051851851850.702669649245434152.99534468385
Trimmed Mean ( 4 / 20 )107.4484615384620.679863484689487158.04417204071
Trimmed Mean ( 5 / 20 )107.43480.665608835302427161.40831416576
Trimmed Mean ( 6 / 20 )107.420.654145943114851164.214119388248
Trimmed Mean ( 7 / 20 )107.4067391304350.639803944483466167.874456005656
Trimmed Mean ( 8 / 20 )107.3963636363640.622082712979094172.640006538765
Trimmed Mean ( 9 / 20 )107.4204761904760.608720402756321176.469321061147
Trimmed Mean ( 10 / 20 )107.44750.590610044241524181.926299844742
Trimmed Mean ( 11 / 20 )107.4944736842110.570650435877393188.371841894652
Trimmed Mean ( 12 / 20 )107.5630555555560.547724849740203196.381551077288
Trimmed Mean ( 13 / 20 )107.6532352941180.51879380202303207.506787618366
Trimmed Mean ( 14 / 20 )107.6831250.514248284278192209.399094352149
Trimmed Mean ( 15 / 20 )107.7263333333330.508227816446485211.964654131985
Trimmed Mean ( 16 / 20 )107.7971428571430.502442146276816214.546378435684
Trimmed Mean ( 17 / 20 )107.8865384615380.49264652402421218.993808340027
Trimmed Mean ( 18 / 20 )107.9916666666670.474486628248335227.596859926991
Trimmed Mean ( 19 / 20 )108.1331818181820.445833227590861242.541773753604
Trimmed Mean ( 20 / 20 )108.29850.396543138291808273.106478317891
Median108.645
Midrange109.63
Midmean - Weighted Average at Xnp107.4153125
Midmean - Weighted Average at X(n+1)p107.4153125
Midmean - Empirical Distribution Function107.4153125
Midmean - Empirical Distribution Function - Averaging107.4153125
Midmean - Empirical Distribution Function - Interpolation107.4153125
Midmean - Closest Observation107.4153125
Midmean - True Basic - Statistics Graphics Toolkit107.4153125
Midmean - MS Excel (old versions)107.533636363636
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 107.699666666667 & 0.758731321651969 & 141.947041848984 \tabularnewline
Geometric Mean & 107.542524047167 &  &  \tabularnewline
Harmonic Mean & 107.386018673521 &  &  \tabularnewline
Quadratic Mean & 107.857233971579 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 107.6995 & 0.758686138518202 & 141.955275748611 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 107.664166666667 & 0.74945921338225 & 143.655805071482 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 107.652666666667 & 0.746593804455424 & 144.191749280842 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 107.494 & 0.710505597015133 & 151.292263497413 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 107.494 & 0.690034683481041 & 155.780575344012 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 107.481 & 0.687482622276522 & 156.339951756291 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 107.46 & 0.6834118047819 & 157.240479675785 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 107.261333333333 & 0.647410594864457 & 165.677445170309 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 107.258333333333 & 0.646903016101374 & 165.802802991608 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 107.15 & 0.629114883565128 & 170.318653713599 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 107.041833333333 & 0.611111818652219 & 175.159160838044 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 106.949833333333 & 0.597633113634311 & 178.955668441718 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 107.446 & 0.47965643306987 & 224.006168982933 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 107.380666666667 & 0.470221420776892 & 228.361920410291 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 107.230666666667 & 0.449690720250566 & 238.454257199077 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 107.177333333333 & 0.442770736014061 & 242.060562308548 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 107.171666666667 & 0.442046611972435 & 242.444266654281 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 107.057666666667 & 0.427851772649943 & 250.221393272708 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 107.086166666667 & 0.42022667354216 & 254.829532271285 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 107.166166666667 & 0.404723180256005 & 264.788803544386 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 107.633103448276 & 0.742309968915543 & 144.997518496915 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 107.561964285714 & 0.7219163898976 & 148.995044011913 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 107.505185185185 & 0.702669649245434 & 152.99534468385 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 107.448461538462 & 0.679863484689487 & 158.04417204071 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 107.4348 & 0.665608835302427 & 161.40831416576 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 107.42 & 0.654145943114851 & 164.214119388248 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 107.406739130435 & 0.639803944483466 & 167.874456005656 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 107.396363636364 & 0.622082712979094 & 172.640006538765 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 107.420476190476 & 0.608720402756321 & 176.469321061147 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 107.4475 & 0.590610044241524 & 181.926299844742 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 107.494473684211 & 0.570650435877393 & 188.371841894652 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 107.563055555556 & 0.547724849740203 & 196.381551077288 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 107.653235294118 & 0.51879380202303 & 207.506787618366 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 107.683125 & 0.514248284278192 & 209.399094352149 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 107.726333333333 & 0.508227816446485 & 211.964654131985 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 107.797142857143 & 0.502442146276816 & 214.546378435684 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 107.886538461538 & 0.49264652402421 & 218.993808340027 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 107.991666666667 & 0.474486628248335 & 227.596859926991 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 108.133181818182 & 0.445833227590861 & 242.541773753604 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 108.2985 & 0.396543138291808 & 273.106478317891 \tabularnewline
Median & 108.645 &  &  \tabularnewline
Midrange & 109.63 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 107.4153125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 107.4153125 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 107.4153125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 107.4153125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 107.4153125 &  &  \tabularnewline
Midmean - Closest Observation & 107.4153125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 107.4153125 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 107.533636363636 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132758&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]107.699666666667[/C][C]0.758731321651969[/C][C]141.947041848984[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]107.542524047167[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]107.386018673521[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]107.857233971579[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]107.6995[/C][C]0.758686138518202[/C][C]141.955275748611[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]107.664166666667[/C][C]0.74945921338225[/C][C]143.655805071482[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]107.652666666667[/C][C]0.746593804455424[/C][C]144.191749280842[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]107.494[/C][C]0.710505597015133[/C][C]151.292263497413[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]107.494[/C][C]0.690034683481041[/C][C]155.780575344012[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]107.481[/C][C]0.687482622276522[/C][C]156.339951756291[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]107.46[/C][C]0.6834118047819[/C][C]157.240479675785[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]107.261333333333[/C][C]0.647410594864457[/C][C]165.677445170309[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]107.258333333333[/C][C]0.646903016101374[/C][C]165.802802991608[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]107.15[/C][C]0.629114883565128[/C][C]170.318653713599[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]107.041833333333[/C][C]0.611111818652219[/C][C]175.159160838044[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]106.949833333333[/C][C]0.597633113634311[/C][C]178.955668441718[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]107.446[/C][C]0.47965643306987[/C][C]224.006168982933[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]107.380666666667[/C][C]0.470221420776892[/C][C]228.361920410291[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]107.230666666667[/C][C]0.449690720250566[/C][C]238.454257199077[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]107.177333333333[/C][C]0.442770736014061[/C][C]242.060562308548[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]107.171666666667[/C][C]0.442046611972435[/C][C]242.444266654281[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]107.057666666667[/C][C]0.427851772649943[/C][C]250.221393272708[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]107.086166666667[/C][C]0.42022667354216[/C][C]254.829532271285[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]107.166166666667[/C][C]0.404723180256005[/C][C]264.788803544386[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]107.633103448276[/C][C]0.742309968915543[/C][C]144.997518496915[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]107.561964285714[/C][C]0.7219163898976[/C][C]148.995044011913[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]107.505185185185[/C][C]0.702669649245434[/C][C]152.99534468385[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]107.448461538462[/C][C]0.679863484689487[/C][C]158.04417204071[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]107.4348[/C][C]0.665608835302427[/C][C]161.40831416576[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]107.42[/C][C]0.654145943114851[/C][C]164.214119388248[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]107.406739130435[/C][C]0.639803944483466[/C][C]167.874456005656[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]107.396363636364[/C][C]0.622082712979094[/C][C]172.640006538765[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]107.420476190476[/C][C]0.608720402756321[/C][C]176.469321061147[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]107.4475[/C][C]0.590610044241524[/C][C]181.926299844742[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]107.494473684211[/C][C]0.570650435877393[/C][C]188.371841894652[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]107.563055555556[/C][C]0.547724849740203[/C][C]196.381551077288[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]107.653235294118[/C][C]0.51879380202303[/C][C]207.506787618366[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]107.683125[/C][C]0.514248284278192[/C][C]209.399094352149[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]107.726333333333[/C][C]0.508227816446485[/C][C]211.964654131985[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]107.797142857143[/C][C]0.502442146276816[/C][C]214.546378435684[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]107.886538461538[/C][C]0.49264652402421[/C][C]218.993808340027[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]107.991666666667[/C][C]0.474486628248335[/C][C]227.596859926991[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]108.133181818182[/C][C]0.445833227590861[/C][C]242.541773753604[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]108.2985[/C][C]0.396543138291808[/C][C]273.106478317891[/C][/ROW]
[ROW][C]Median[/C][C]108.645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]109.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]107.4153125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]107.4153125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]107.4153125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]107.4153125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]107.4153125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]107.4153125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]107.4153125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]107.533636363636[/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=132758&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132758&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 Mean107.6996666666670.758731321651969141.947041848984
Geometric Mean107.542524047167
Harmonic Mean107.386018673521
Quadratic Mean107.857233971579
Winsorized Mean ( 1 / 20 )107.69950.758686138518202141.955275748611
Winsorized Mean ( 2 / 20 )107.6641666666670.74945921338225143.655805071482
Winsorized Mean ( 3 / 20 )107.6526666666670.746593804455424144.191749280842
Winsorized Mean ( 4 / 20 )107.4940.710505597015133151.292263497413
Winsorized Mean ( 5 / 20 )107.4940.690034683481041155.780575344012
Winsorized Mean ( 6 / 20 )107.4810.687482622276522156.339951756291
Winsorized Mean ( 7 / 20 )107.460.6834118047819157.240479675785
Winsorized Mean ( 8 / 20 )107.2613333333330.647410594864457165.677445170309
Winsorized Mean ( 9 / 20 )107.2583333333330.646903016101374165.802802991608
Winsorized Mean ( 10 / 20 )107.150.629114883565128170.318653713599
Winsorized Mean ( 11 / 20 )107.0418333333330.611111818652219175.159160838044
Winsorized Mean ( 12 / 20 )106.9498333333330.597633113634311178.955668441718
Winsorized Mean ( 13 / 20 )107.4460.47965643306987224.006168982933
Winsorized Mean ( 14 / 20 )107.3806666666670.470221420776892228.361920410291
Winsorized Mean ( 15 / 20 )107.2306666666670.449690720250566238.454257199077
Winsorized Mean ( 16 / 20 )107.1773333333330.442770736014061242.060562308548
Winsorized Mean ( 17 / 20 )107.1716666666670.442046611972435242.444266654281
Winsorized Mean ( 18 / 20 )107.0576666666670.427851772649943250.221393272708
Winsorized Mean ( 19 / 20 )107.0861666666670.42022667354216254.829532271285
Winsorized Mean ( 20 / 20 )107.1661666666670.404723180256005264.788803544386
Trimmed Mean ( 1 / 20 )107.6331034482760.742309968915543144.997518496915
Trimmed Mean ( 2 / 20 )107.5619642857140.7219163898976148.995044011913
Trimmed Mean ( 3 / 20 )107.5051851851850.702669649245434152.99534468385
Trimmed Mean ( 4 / 20 )107.4484615384620.679863484689487158.04417204071
Trimmed Mean ( 5 / 20 )107.43480.665608835302427161.40831416576
Trimmed Mean ( 6 / 20 )107.420.654145943114851164.214119388248
Trimmed Mean ( 7 / 20 )107.4067391304350.639803944483466167.874456005656
Trimmed Mean ( 8 / 20 )107.3963636363640.622082712979094172.640006538765
Trimmed Mean ( 9 / 20 )107.4204761904760.608720402756321176.469321061147
Trimmed Mean ( 10 / 20 )107.44750.590610044241524181.926299844742
Trimmed Mean ( 11 / 20 )107.4944736842110.570650435877393188.371841894652
Trimmed Mean ( 12 / 20 )107.5630555555560.547724849740203196.381551077288
Trimmed Mean ( 13 / 20 )107.6532352941180.51879380202303207.506787618366
Trimmed Mean ( 14 / 20 )107.6831250.514248284278192209.399094352149
Trimmed Mean ( 15 / 20 )107.7263333333330.508227816446485211.964654131985
Trimmed Mean ( 16 / 20 )107.7971428571430.502442146276816214.546378435684
Trimmed Mean ( 17 / 20 )107.8865384615380.49264652402421218.993808340027
Trimmed Mean ( 18 / 20 )107.9916666666670.474486628248335227.596859926991
Trimmed Mean ( 19 / 20 )108.1331818181820.445833227590861242.541773753604
Trimmed Mean ( 20 / 20 )108.29850.396543138291808273.106478317891
Median108.645
Midrange109.63
Midmean - Weighted Average at Xnp107.4153125
Midmean - Weighted Average at X(n+1)p107.4153125
Midmean - Empirical Distribution Function107.4153125
Midmean - Empirical Distribution Function - Averaging107.4153125
Midmean - Empirical Distribution Function - Interpolation107.4153125
Midmean - Closest Observation107.4153125
Midmean - True Basic - Statistics Graphics Toolkit107.4153125
Midmean - MS Excel (old versions)107.533636363636
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')