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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 04 Mar 2016 15:31:35 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/04/t1457105544fxn9pmwoxf9832c.htm/, Retrieved Sat, 18 May 2024 14:21:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293393, Retrieved Sat, 18 May 2024 14:21:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten CPI ...] [2016-03-04 15:31:35] [25a5f245cb671e152cfd8b6d35402e87] [Current]
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Dataseries X:
110.27
110.91
110.27
109.41
111.47
110.77
110.83
110.52
110.44
109.99
110.55
109.99
111.2
111.81
110.36
111.24
112.6
111.75
112.49
111.94
113.22
112.85
114.37
113.68
118
118.27
119.2
117.98
117.59
117.41
118.31
118.4
117.92
118.94
118.81
117.44
120.21
119.74
118.79
118.19
119.16
118.88
119.59
119.44
119.84
119.31
118.15
118.23
119.89
118.83
118.95
119.86
119.07
119.52
119.92
119.68
119.81
120.09
119.98
118.96




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=293393&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=293393&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293393&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 Mean115.92150.500968205233992231.394924446064
Geometric Mean115.856965609004
Harmonic Mean115.791802677849
Quadratic Mean115.985349685495
Winsorized Mean ( 1 / 20 )115.9291666666670.498640937789834232.490270815928
Winsorized Mean ( 2 / 20 )115.92550.498128725733751232.721973279578
Winsorized Mean ( 3 / 20 )115.93650.494944945006584234.241204339318
Winsorized Mean ( 4 / 20 )115.93450.494673003046965234.365933224363
Winsorized Mean ( 5 / 20 )115.93950.492887744923776235.2249598292
Winsorized Mean ( 6 / 20 )115.94550.491090992581162236.097793996574
Winsorized Mean ( 7 / 20 )115.9513333333330.488856122853365237.189078570902
Winsorized Mean ( 8 / 20 )115.9460.486863082413269238.14908993568
Winsorized Mean ( 9 / 20 )115.970.47954604239808241.832878903693
Winsorized Mean ( 10 / 20 )115.9650.475760319232208243.746683597209
Winsorized Mean ( 11 / 20 )115.9668333333330.471437127972421245.985787823053
Winsorized Mean ( 12 / 20 )116.0088333333330.458977621629104252.754879250037
Winsorized Mean ( 13 / 20 )115.9893333333330.453908691051049255.5345064329
Winsorized Mean ( 14 / 20 )116.0173333333330.4413022502581262.897669942719
Winsorized Mean ( 15 / 20 )116.0773333333330.427967860524811271.229089939112
Winsorized Mean ( 16 / 20 )116.0693333333330.422318985839349274.838066071428
Winsorized Mean ( 17 / 20 )116.0750.412315050131537281.520162708031
Winsorized Mean ( 18 / 20 )116.2370.384286579444616302.474783709568
Winsorized Mean ( 19 / 20 )116.2686666666670.378165320218811307.454598426403
Winsorized Mean ( 20 / 20 )116.3320.36213247880215321.241553325454
Trimmed Mean ( 1 / 20 )115.9598275862070.500318923779414231.771820082769
Trimmed Mean ( 2 / 20 )115.9926785714290.501555081142862231.266082096354
Trimmed Mean ( 3 / 20 )116.030.502541062220124230.886605539064
Trimmed Mean ( 4 / 20 )116.0659615384620.504285574994432230.159194102951
Trimmed Mean ( 5 / 20 )116.10540.505528554271342229.671299512155
Trimmed Mean ( 6 / 20 )116.1468750.506574957544109229.278753855271
Trimmed Mean ( 7 / 20 )116.1906521739130.507258845602444229.055940928777
Trimmed Mean ( 8 / 20 )116.2372727272730.50749315116723229.042052015732
Trimmed Mean ( 9 / 20 )116.2892857142860.506952521086677229.388908975172
Trimmed Mean ( 10 / 20 )116.34250.506675153859415229.619508897966
Trimmed Mean ( 11 / 20 )116.4021052631580.50559728461472230.226919339292
Trimmed Mean ( 12 / 20 )116.4680555555560.503458486402667231.335966521784
Trimmed Mean ( 13 / 20 )116.5355882352940.501897325499349232.19009609057
Trimmed Mean ( 14 / 20 )116.6143750.498681312979866233.845488019537
Trimmed Mean ( 15 / 20 )116.6996666666670.495178241062202235.672040872263
Trimmed Mean ( 16 / 20 )116.7885714285710.49139627062543237.666784243046
Trimmed Mean ( 17 / 20 )116.8923076923080.484022665614331241.501722949163
Trimmed Mean ( 18 / 20 )117.01250.472300203137854247.750263968967
Trimmed Mean ( 19 / 20 )117.130.462026872777798253.513392621064
Trimmed Mean ( 20 / 20 )117.2660.442646585889917264.920150156005
Median118.075
Midrange114.81
Midmean - Weighted Average at Xnp116.530967741935
Midmean - Weighted Average at X(n+1)p116.699666666667
Midmean - Empirical Distribution Function116.530967741935
Midmean - Empirical Distribution Function - Averaging116.699666666667
Midmean - Empirical Distribution Function - Interpolation116.699666666667
Midmean - Closest Observation116.530967741935
Midmean - True Basic - Statistics Graphics Toolkit116.699666666667
Midmean - MS Excel (old versions)116.614375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 115.9215 & 0.500968205233992 & 231.394924446064 \tabularnewline
Geometric Mean & 115.856965609004 &  &  \tabularnewline
Harmonic Mean & 115.791802677849 &  &  \tabularnewline
Quadratic Mean & 115.985349685495 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 115.929166666667 & 0.498640937789834 & 232.490270815928 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 115.9255 & 0.498128725733751 & 232.721973279578 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 115.9365 & 0.494944945006584 & 234.241204339318 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 115.9345 & 0.494673003046965 & 234.365933224363 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 115.9395 & 0.492887744923776 & 235.2249598292 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 115.9455 & 0.491090992581162 & 236.097793996574 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 115.951333333333 & 0.488856122853365 & 237.189078570902 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 115.946 & 0.486863082413269 & 238.14908993568 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 115.97 & 0.47954604239808 & 241.832878903693 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 115.965 & 0.475760319232208 & 243.746683597209 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 115.966833333333 & 0.471437127972421 & 245.985787823053 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 116.008833333333 & 0.458977621629104 & 252.754879250037 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 115.989333333333 & 0.453908691051049 & 255.5345064329 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 116.017333333333 & 0.4413022502581 & 262.897669942719 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 116.077333333333 & 0.427967860524811 & 271.229089939112 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 116.069333333333 & 0.422318985839349 & 274.838066071428 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 116.075 & 0.412315050131537 & 281.520162708031 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 116.237 & 0.384286579444616 & 302.474783709568 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 116.268666666667 & 0.378165320218811 & 307.454598426403 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 116.332 & 0.36213247880215 & 321.241553325454 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 115.959827586207 & 0.500318923779414 & 231.771820082769 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 115.992678571429 & 0.501555081142862 & 231.266082096354 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 116.03 & 0.502541062220124 & 230.886605539064 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 116.065961538462 & 0.504285574994432 & 230.159194102951 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 116.1054 & 0.505528554271342 & 229.671299512155 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 116.146875 & 0.506574957544109 & 229.278753855271 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 116.190652173913 & 0.507258845602444 & 229.055940928777 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 116.237272727273 & 0.50749315116723 & 229.042052015732 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 116.289285714286 & 0.506952521086677 & 229.388908975172 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 116.3425 & 0.506675153859415 & 229.619508897966 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 116.402105263158 & 0.50559728461472 & 230.226919339292 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 116.468055555556 & 0.503458486402667 & 231.335966521784 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 116.535588235294 & 0.501897325499349 & 232.19009609057 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 116.614375 & 0.498681312979866 & 233.845488019537 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 116.699666666667 & 0.495178241062202 & 235.672040872263 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 116.788571428571 & 0.49139627062543 & 237.666784243046 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 116.892307692308 & 0.484022665614331 & 241.501722949163 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 117.0125 & 0.472300203137854 & 247.750263968967 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 117.13 & 0.462026872777798 & 253.513392621064 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 117.266 & 0.442646585889917 & 264.920150156005 \tabularnewline
Median & 118.075 &  &  \tabularnewline
Midrange & 114.81 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 116.530967741935 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 116.699666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 116.530967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 116.699666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 116.699666666667 &  &  \tabularnewline
Midmean - Closest Observation & 116.530967741935 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 116.699666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 116.614375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293393&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]115.9215[/C][C]0.500968205233992[/C][C]231.394924446064[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]115.856965609004[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]115.791802677849[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]115.985349685495[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]115.929166666667[/C][C]0.498640937789834[/C][C]232.490270815928[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]115.9255[/C][C]0.498128725733751[/C][C]232.721973279578[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]115.9365[/C][C]0.494944945006584[/C][C]234.241204339318[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]115.9345[/C][C]0.494673003046965[/C][C]234.365933224363[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]115.9395[/C][C]0.492887744923776[/C][C]235.2249598292[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]115.9455[/C][C]0.491090992581162[/C][C]236.097793996574[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]115.951333333333[/C][C]0.488856122853365[/C][C]237.189078570902[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]115.946[/C][C]0.486863082413269[/C][C]238.14908993568[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]115.97[/C][C]0.47954604239808[/C][C]241.832878903693[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]115.965[/C][C]0.475760319232208[/C][C]243.746683597209[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]115.966833333333[/C][C]0.471437127972421[/C][C]245.985787823053[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]116.008833333333[/C][C]0.458977621629104[/C][C]252.754879250037[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]115.989333333333[/C][C]0.453908691051049[/C][C]255.5345064329[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]116.017333333333[/C][C]0.4413022502581[/C][C]262.897669942719[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]116.077333333333[/C][C]0.427967860524811[/C][C]271.229089939112[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]116.069333333333[/C][C]0.422318985839349[/C][C]274.838066071428[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]116.075[/C][C]0.412315050131537[/C][C]281.520162708031[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]116.237[/C][C]0.384286579444616[/C][C]302.474783709568[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]116.268666666667[/C][C]0.378165320218811[/C][C]307.454598426403[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]116.332[/C][C]0.36213247880215[/C][C]321.241553325454[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]115.959827586207[/C][C]0.500318923779414[/C][C]231.771820082769[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]115.992678571429[/C][C]0.501555081142862[/C][C]231.266082096354[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]116.03[/C][C]0.502541062220124[/C][C]230.886605539064[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]116.065961538462[/C][C]0.504285574994432[/C][C]230.159194102951[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]116.1054[/C][C]0.505528554271342[/C][C]229.671299512155[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]116.146875[/C][C]0.506574957544109[/C][C]229.278753855271[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]116.190652173913[/C][C]0.507258845602444[/C][C]229.055940928777[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]116.237272727273[/C][C]0.50749315116723[/C][C]229.042052015732[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]116.289285714286[/C][C]0.506952521086677[/C][C]229.388908975172[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]116.3425[/C][C]0.506675153859415[/C][C]229.619508897966[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]116.402105263158[/C][C]0.50559728461472[/C][C]230.226919339292[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]116.468055555556[/C][C]0.503458486402667[/C][C]231.335966521784[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]116.535588235294[/C][C]0.501897325499349[/C][C]232.19009609057[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]116.614375[/C][C]0.498681312979866[/C][C]233.845488019537[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]116.699666666667[/C][C]0.495178241062202[/C][C]235.672040872263[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]116.788571428571[/C][C]0.49139627062543[/C][C]237.666784243046[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]116.892307692308[/C][C]0.484022665614331[/C][C]241.501722949163[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]117.0125[/C][C]0.472300203137854[/C][C]247.750263968967[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]117.13[/C][C]0.462026872777798[/C][C]253.513392621064[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]117.266[/C][C]0.442646585889917[/C][C]264.920150156005[/C][/ROW]
[ROW][C]Median[/C][C]118.075[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]114.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]116.530967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]116.699666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]116.530967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]116.699666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]116.699666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]116.530967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]116.699666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]116.614375[/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=293393&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293393&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 Mean115.92150.500968205233992231.394924446064
Geometric Mean115.856965609004
Harmonic Mean115.791802677849
Quadratic Mean115.985349685495
Winsorized Mean ( 1 / 20 )115.9291666666670.498640937789834232.490270815928
Winsorized Mean ( 2 / 20 )115.92550.498128725733751232.721973279578
Winsorized Mean ( 3 / 20 )115.93650.494944945006584234.241204339318
Winsorized Mean ( 4 / 20 )115.93450.494673003046965234.365933224363
Winsorized Mean ( 5 / 20 )115.93950.492887744923776235.2249598292
Winsorized Mean ( 6 / 20 )115.94550.491090992581162236.097793996574
Winsorized Mean ( 7 / 20 )115.9513333333330.488856122853365237.189078570902
Winsorized Mean ( 8 / 20 )115.9460.486863082413269238.14908993568
Winsorized Mean ( 9 / 20 )115.970.47954604239808241.832878903693
Winsorized Mean ( 10 / 20 )115.9650.475760319232208243.746683597209
Winsorized Mean ( 11 / 20 )115.9668333333330.471437127972421245.985787823053
Winsorized Mean ( 12 / 20 )116.0088333333330.458977621629104252.754879250037
Winsorized Mean ( 13 / 20 )115.9893333333330.453908691051049255.5345064329
Winsorized Mean ( 14 / 20 )116.0173333333330.4413022502581262.897669942719
Winsorized Mean ( 15 / 20 )116.0773333333330.427967860524811271.229089939112
Winsorized Mean ( 16 / 20 )116.0693333333330.422318985839349274.838066071428
Winsorized Mean ( 17 / 20 )116.0750.412315050131537281.520162708031
Winsorized Mean ( 18 / 20 )116.2370.384286579444616302.474783709568
Winsorized Mean ( 19 / 20 )116.2686666666670.378165320218811307.454598426403
Winsorized Mean ( 20 / 20 )116.3320.36213247880215321.241553325454
Trimmed Mean ( 1 / 20 )115.9598275862070.500318923779414231.771820082769
Trimmed Mean ( 2 / 20 )115.9926785714290.501555081142862231.266082096354
Trimmed Mean ( 3 / 20 )116.030.502541062220124230.886605539064
Trimmed Mean ( 4 / 20 )116.0659615384620.504285574994432230.159194102951
Trimmed Mean ( 5 / 20 )116.10540.505528554271342229.671299512155
Trimmed Mean ( 6 / 20 )116.1468750.506574957544109229.278753855271
Trimmed Mean ( 7 / 20 )116.1906521739130.507258845602444229.055940928777
Trimmed Mean ( 8 / 20 )116.2372727272730.50749315116723229.042052015732
Trimmed Mean ( 9 / 20 )116.2892857142860.506952521086677229.388908975172
Trimmed Mean ( 10 / 20 )116.34250.506675153859415229.619508897966
Trimmed Mean ( 11 / 20 )116.4021052631580.50559728461472230.226919339292
Trimmed Mean ( 12 / 20 )116.4680555555560.503458486402667231.335966521784
Trimmed Mean ( 13 / 20 )116.5355882352940.501897325499349232.19009609057
Trimmed Mean ( 14 / 20 )116.6143750.498681312979866233.845488019537
Trimmed Mean ( 15 / 20 )116.6996666666670.495178241062202235.672040872263
Trimmed Mean ( 16 / 20 )116.7885714285710.49139627062543237.666784243046
Trimmed Mean ( 17 / 20 )116.8923076923080.484022665614331241.501722949163
Trimmed Mean ( 18 / 20 )117.01250.472300203137854247.750263968967
Trimmed Mean ( 19 / 20 )117.130.462026872777798253.513392621064
Trimmed Mean ( 20 / 20 )117.2660.442646585889917264.920150156005
Median118.075
Midrange114.81
Midmean - Weighted Average at Xnp116.530967741935
Midmean - Weighted Average at X(n+1)p116.699666666667
Midmean - Empirical Distribution Function116.530967741935
Midmean - Empirical Distribution Function - Averaging116.699666666667
Midmean - Empirical Distribution Function - Interpolation116.699666666667
Midmean - Closest Observation116.530967741935
Midmean - True Basic - Statistics Graphics Toolkit116.699666666667
Midmean - MS Excel (old versions)116.614375
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')