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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 21 Dec 2011 06:40:29 -0500
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/Dec/21/t1324467646xm5hizd7yfsrdti.htm/, Retrieved Tue, 07 May 2024 13:08:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158525, Retrieved Tue, 07 May 2024 13:08:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RMPD    [Central Tendency] [] [2011-12-21 11:40:29] [46e17293cd0520480fa187e99449b207] [Current]
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Dataseries X:
-1
1
-1
2
2
1
-1
-2
-2
-1
-8
-4
-6
-3
-3
-7
-9
-11
-13
-11
-9
-17
-22
-25
-20
-24
-24
-22
-19
-18
-17
-11
-11
-12
-10
-15
-15
-15
-13
-8
-13
-9
-7
-4
-4
-2
0
-2
-3
1
-2
-1
1
-3
-4
-9
-9
-7
-14
-12




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158525&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158525&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158525&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-8.450.954745802830575-8.85052332772549
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean11.1885357993499
Winsorized Mean ( 1 / 20 )-8.433333333333330.949982654217697-8.87735507158087
Winsorized Mean ( 2 / 20 )-8.466666666666670.944046664874885-8.96848321347415
Winsorized Mean ( 3 / 20 )-8.366666666666670.917490641485136-9.11907575768141
Winsorized Mean ( 4 / 20 )-8.366666666666670.917490641485136-9.11907575768141
Winsorized Mean ( 5 / 20 )-8.20.877464245895443-9.34511011515003
Winsorized Mean ( 6 / 20 )-8.20.837942058053758-9.78587949033814
Winsorized Mean ( 7 / 20 )-8.20.794330190775474-10.3231629556906
Winsorized Mean ( 8 / 20 )-8.066666666666670.767219157350034-10.5141622043548
Winsorized Mean ( 9 / 20 )-8.066666666666670.767219157350034-10.5141622043548
Winsorized Mean ( 10 / 20 )-7.733333333333330.705053055929894-10.9684416914325
Winsorized Mean ( 11 / 20 )-7.733333333333330.705053055929894-10.9684416914325
Winsorized Mean ( 12 / 20 )-7.933333333333330.673915394221514-11.7720019476594
Winsorized Mean ( 13 / 20 )-7.716666666666670.636503365929768-12.1235284520367
Winsorized Mean ( 14 / 20 )-7.483333333333330.598723532336301-12.4988127727874
Winsorized Mean ( 15 / 20 )-7.483333333333330.598723532336301-12.4988127727874
Winsorized Mean ( 16 / 20 )-7.483333333333330.598723532336301-12.4988127727874
Winsorized Mean ( 17 / 20 )-7.483333333333330.512274018893351-14.6080672791084
Winsorized Mean ( 18 / 20 )-7.483333333333330.512274018893351-14.6080672791084
Winsorized Mean ( 19 / 20 )-7.166666666666670.466485033256539-15.3631224063848
Winsorized Mean ( 20 / 20 )-7.166666666666670.466485033256539-15.3631224063848
Trimmed Mean ( 1 / 20 )-8.34482758620690.927352626682711-8.99854849827479
Trimmed Mean ( 2 / 20 )-8.250.899224052227194-9.17457665813813
Trimmed Mean ( 3 / 20 )-8.129629629629630.867958357008708-9.36638211267095
Trimmed Mean ( 4 / 20 )-8.038461538461540.841944142154304-9.54749981144036
Trimmed Mean ( 5 / 20 )-7.940.808833879667487-9.81660165281918
Trimmed Mean ( 6 / 20 )-7.8750.781334215319135-10.0789135373823
Trimmed Mean ( 7 / 20 )-7.804347826086960.758602557858692-10.2877952957558
Trimmed Mean ( 8 / 20 )-7.727272727272730.741665199994807-10.4188152920305
Trimmed Mean ( 9 / 20 )-7.666666666666670.726682969268054-10.5502220237649
Trimmed Mean ( 10 / 20 )-7.60.706018086497462-10.7645967509181
Trimmed Mean ( 11 / 20 )-7.578947368421050.695066519476351-10.903916612371
Trimmed Mean ( 12 / 20 )-7.555555555555560.67898669183541-11.1276931439285
Trimmed Mean ( 13 / 20 )-7.50.663875619216176-11.2972969377232
Trimmed Mean ( 14 / 20 )-7.468750.652205277340135-11.4515326071257
Trimmed Mean ( 15 / 20 )-7.466666666666670.644576548753571-11.5838323331885
Trimmed Mean ( 16 / 20 )-7.464285714285710.630952380952381-11.8301886792453
Trimmed Mean ( 17 / 20 )-7.461538461538460.608227612331409-12.2676746505103
Trimmed Mean ( 18 / 20 )-7.458333333333330.601866561197682-12.3920048299272
Trimmed Mean ( 19 / 20 )-7.454545454545450.587485922193947-12.688892061799
Trimmed Mean ( 20 / 20 )-7.50.578109441469165-12.9733221117096
Median-8
Midrange-11.5
Midmean - Weighted Average at Xnp-7.14705882352941
Midmean - Weighted Average at X(n+1)p-7.14705882352941
Midmean - Empirical Distribution Function-7.14705882352941
Midmean - Empirical Distribution Function - Averaging-7.14705882352941
Midmean - Empirical Distribution Function - Interpolation-7.14705882352941
Midmean - Closest Observation-7.14705882352941
Midmean - True Basic - Statistics Graphics Toolkit-7.14705882352941
Midmean - MS Excel (old versions)-7.14705882352941
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -8.45 & 0.954745802830575 & -8.85052332772549 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 11.1885357993499 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & -8.43333333333333 & 0.949982654217697 & -8.87735507158087 \tabularnewline
Winsorized Mean ( 2 / 20 ) & -8.46666666666667 & 0.944046664874885 & -8.96848321347415 \tabularnewline
Winsorized Mean ( 3 / 20 ) & -8.36666666666667 & 0.917490641485136 & -9.11907575768141 \tabularnewline
Winsorized Mean ( 4 / 20 ) & -8.36666666666667 & 0.917490641485136 & -9.11907575768141 \tabularnewline
Winsorized Mean ( 5 / 20 ) & -8.2 & 0.877464245895443 & -9.34511011515003 \tabularnewline
Winsorized Mean ( 6 / 20 ) & -8.2 & 0.837942058053758 & -9.78587949033814 \tabularnewline
Winsorized Mean ( 7 / 20 ) & -8.2 & 0.794330190775474 & -10.3231629556906 \tabularnewline
Winsorized Mean ( 8 / 20 ) & -8.06666666666667 & 0.767219157350034 & -10.5141622043548 \tabularnewline
Winsorized Mean ( 9 / 20 ) & -8.06666666666667 & 0.767219157350034 & -10.5141622043548 \tabularnewline
Winsorized Mean ( 10 / 20 ) & -7.73333333333333 & 0.705053055929894 & -10.9684416914325 \tabularnewline
Winsorized Mean ( 11 / 20 ) & -7.73333333333333 & 0.705053055929894 & -10.9684416914325 \tabularnewline
Winsorized Mean ( 12 / 20 ) & -7.93333333333333 & 0.673915394221514 & -11.7720019476594 \tabularnewline
Winsorized Mean ( 13 / 20 ) & -7.71666666666667 & 0.636503365929768 & -12.1235284520367 \tabularnewline
Winsorized Mean ( 14 / 20 ) & -7.48333333333333 & 0.598723532336301 & -12.4988127727874 \tabularnewline
Winsorized Mean ( 15 / 20 ) & -7.48333333333333 & 0.598723532336301 & -12.4988127727874 \tabularnewline
Winsorized Mean ( 16 / 20 ) & -7.48333333333333 & 0.598723532336301 & -12.4988127727874 \tabularnewline
Winsorized Mean ( 17 / 20 ) & -7.48333333333333 & 0.512274018893351 & -14.6080672791084 \tabularnewline
Winsorized Mean ( 18 / 20 ) & -7.48333333333333 & 0.512274018893351 & -14.6080672791084 \tabularnewline
Winsorized Mean ( 19 / 20 ) & -7.16666666666667 & 0.466485033256539 & -15.3631224063848 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -7.16666666666667 & 0.466485033256539 & -15.3631224063848 \tabularnewline
Trimmed Mean ( 1 / 20 ) & -8.3448275862069 & 0.927352626682711 & -8.99854849827479 \tabularnewline
Trimmed Mean ( 2 / 20 ) & -8.25 & 0.899224052227194 & -9.17457665813813 \tabularnewline
Trimmed Mean ( 3 / 20 ) & -8.12962962962963 & 0.867958357008708 & -9.36638211267095 \tabularnewline
Trimmed Mean ( 4 / 20 ) & -8.03846153846154 & 0.841944142154304 & -9.54749981144036 \tabularnewline
Trimmed Mean ( 5 / 20 ) & -7.94 & 0.808833879667487 & -9.81660165281918 \tabularnewline
Trimmed Mean ( 6 / 20 ) & -7.875 & 0.781334215319135 & -10.0789135373823 \tabularnewline
Trimmed Mean ( 7 / 20 ) & -7.80434782608696 & 0.758602557858692 & -10.2877952957558 \tabularnewline
Trimmed Mean ( 8 / 20 ) & -7.72727272727273 & 0.741665199994807 & -10.4188152920305 \tabularnewline
Trimmed Mean ( 9 / 20 ) & -7.66666666666667 & 0.726682969268054 & -10.5502220237649 \tabularnewline
Trimmed Mean ( 10 / 20 ) & -7.6 & 0.706018086497462 & -10.7645967509181 \tabularnewline
Trimmed Mean ( 11 / 20 ) & -7.57894736842105 & 0.695066519476351 & -10.903916612371 \tabularnewline
Trimmed Mean ( 12 / 20 ) & -7.55555555555556 & 0.67898669183541 & -11.1276931439285 \tabularnewline
Trimmed Mean ( 13 / 20 ) & -7.5 & 0.663875619216176 & -11.2972969377232 \tabularnewline
Trimmed Mean ( 14 / 20 ) & -7.46875 & 0.652205277340135 & -11.4515326071257 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -7.46666666666667 & 0.644576548753571 & -11.5838323331885 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -7.46428571428571 & 0.630952380952381 & -11.8301886792453 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -7.46153846153846 & 0.608227612331409 & -12.2676746505103 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -7.45833333333333 & 0.601866561197682 & -12.3920048299272 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -7.45454545454545 & 0.587485922193947 & -12.688892061799 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -7.5 & 0.578109441469165 & -12.9733221117096 \tabularnewline
Median & -8 &  &  \tabularnewline
Midrange & -11.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -7.14705882352941 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -7.14705882352941 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -7.14705882352941 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -7.14705882352941 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -7.14705882352941 &  &  \tabularnewline
Midmean - Closest Observation & -7.14705882352941 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -7.14705882352941 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -7.14705882352941 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158525&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]-8.45[/C][C]0.954745802830575[/C][C]-8.85052332772549[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]11.1885357993499[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]-8.43333333333333[/C][C]0.949982654217697[/C][C]-8.87735507158087[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]-8.46666666666667[/C][C]0.944046664874885[/C][C]-8.96848321347415[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]-8.36666666666667[/C][C]0.917490641485136[/C][C]-9.11907575768141[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]-8.36666666666667[/C][C]0.917490641485136[/C][C]-9.11907575768141[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]-8.2[/C][C]0.877464245895443[/C][C]-9.34511011515003[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]-8.2[/C][C]0.837942058053758[/C][C]-9.78587949033814[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]-8.2[/C][C]0.794330190775474[/C][C]-10.3231629556906[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]-8.06666666666667[/C][C]0.767219157350034[/C][C]-10.5141622043548[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]-8.06666666666667[/C][C]0.767219157350034[/C][C]-10.5141622043548[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]-7.73333333333333[/C][C]0.705053055929894[/C][C]-10.9684416914325[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]-7.73333333333333[/C][C]0.705053055929894[/C][C]-10.9684416914325[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]-7.93333333333333[/C][C]0.673915394221514[/C][C]-11.7720019476594[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]-7.71666666666667[/C][C]0.636503365929768[/C][C]-12.1235284520367[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]-7.48333333333333[/C][C]0.598723532336301[/C][C]-12.4988127727874[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]-7.48333333333333[/C][C]0.598723532336301[/C][C]-12.4988127727874[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]-7.48333333333333[/C][C]0.598723532336301[/C][C]-12.4988127727874[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]-7.48333333333333[/C][C]0.512274018893351[/C][C]-14.6080672791084[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]-7.48333333333333[/C][C]0.512274018893351[/C][C]-14.6080672791084[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]-7.16666666666667[/C][C]0.466485033256539[/C][C]-15.3631224063848[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-7.16666666666667[/C][C]0.466485033256539[/C][C]-15.3631224063848[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]-8.3448275862069[/C][C]0.927352626682711[/C][C]-8.99854849827479[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]-8.25[/C][C]0.899224052227194[/C][C]-9.17457665813813[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]-8.12962962962963[/C][C]0.867958357008708[/C][C]-9.36638211267095[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]-8.03846153846154[/C][C]0.841944142154304[/C][C]-9.54749981144036[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]-7.94[/C][C]0.808833879667487[/C][C]-9.81660165281918[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]-7.875[/C][C]0.781334215319135[/C][C]-10.0789135373823[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]-7.80434782608696[/C][C]0.758602557858692[/C][C]-10.2877952957558[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]-7.72727272727273[/C][C]0.741665199994807[/C][C]-10.4188152920305[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]-7.66666666666667[/C][C]0.726682969268054[/C][C]-10.5502220237649[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]-7.6[/C][C]0.706018086497462[/C][C]-10.7645967509181[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]-7.57894736842105[/C][C]0.695066519476351[/C][C]-10.903916612371[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]-7.55555555555556[/C][C]0.67898669183541[/C][C]-11.1276931439285[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]-7.5[/C][C]0.663875619216176[/C][C]-11.2972969377232[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]-7.46875[/C][C]0.652205277340135[/C][C]-11.4515326071257[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-7.46666666666667[/C][C]0.644576548753571[/C][C]-11.5838323331885[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-7.46428571428571[/C][C]0.630952380952381[/C][C]-11.8301886792453[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-7.46153846153846[/C][C]0.608227612331409[/C][C]-12.2676746505103[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-7.45833333333333[/C][C]0.601866561197682[/C][C]-12.3920048299272[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-7.45454545454545[/C][C]0.587485922193947[/C][C]-12.688892061799[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-7.5[/C][C]0.578109441469165[/C][C]-12.9733221117096[/C][/ROW]
[ROW][C]Median[/C][C]-8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-11.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-7.14705882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-7.14705882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-7.14705882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-7.14705882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-7.14705882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-7.14705882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-7.14705882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-7.14705882352941[/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=158525&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158525&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 Mean-8.450.954745802830575-8.85052332772549
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean11.1885357993499
Winsorized Mean ( 1 / 20 )-8.433333333333330.949982654217697-8.87735507158087
Winsorized Mean ( 2 / 20 )-8.466666666666670.944046664874885-8.96848321347415
Winsorized Mean ( 3 / 20 )-8.366666666666670.917490641485136-9.11907575768141
Winsorized Mean ( 4 / 20 )-8.366666666666670.917490641485136-9.11907575768141
Winsorized Mean ( 5 / 20 )-8.20.877464245895443-9.34511011515003
Winsorized Mean ( 6 / 20 )-8.20.837942058053758-9.78587949033814
Winsorized Mean ( 7 / 20 )-8.20.794330190775474-10.3231629556906
Winsorized Mean ( 8 / 20 )-8.066666666666670.767219157350034-10.5141622043548
Winsorized Mean ( 9 / 20 )-8.066666666666670.767219157350034-10.5141622043548
Winsorized Mean ( 10 / 20 )-7.733333333333330.705053055929894-10.9684416914325
Winsorized Mean ( 11 / 20 )-7.733333333333330.705053055929894-10.9684416914325
Winsorized Mean ( 12 / 20 )-7.933333333333330.673915394221514-11.7720019476594
Winsorized Mean ( 13 / 20 )-7.716666666666670.636503365929768-12.1235284520367
Winsorized Mean ( 14 / 20 )-7.483333333333330.598723532336301-12.4988127727874
Winsorized Mean ( 15 / 20 )-7.483333333333330.598723532336301-12.4988127727874
Winsorized Mean ( 16 / 20 )-7.483333333333330.598723532336301-12.4988127727874
Winsorized Mean ( 17 / 20 )-7.483333333333330.512274018893351-14.6080672791084
Winsorized Mean ( 18 / 20 )-7.483333333333330.512274018893351-14.6080672791084
Winsorized Mean ( 19 / 20 )-7.166666666666670.466485033256539-15.3631224063848
Winsorized Mean ( 20 / 20 )-7.166666666666670.466485033256539-15.3631224063848
Trimmed Mean ( 1 / 20 )-8.34482758620690.927352626682711-8.99854849827479
Trimmed Mean ( 2 / 20 )-8.250.899224052227194-9.17457665813813
Trimmed Mean ( 3 / 20 )-8.129629629629630.867958357008708-9.36638211267095
Trimmed Mean ( 4 / 20 )-8.038461538461540.841944142154304-9.54749981144036
Trimmed Mean ( 5 / 20 )-7.940.808833879667487-9.81660165281918
Trimmed Mean ( 6 / 20 )-7.8750.781334215319135-10.0789135373823
Trimmed Mean ( 7 / 20 )-7.804347826086960.758602557858692-10.2877952957558
Trimmed Mean ( 8 / 20 )-7.727272727272730.741665199994807-10.4188152920305
Trimmed Mean ( 9 / 20 )-7.666666666666670.726682969268054-10.5502220237649
Trimmed Mean ( 10 / 20 )-7.60.706018086497462-10.7645967509181
Trimmed Mean ( 11 / 20 )-7.578947368421050.695066519476351-10.903916612371
Trimmed Mean ( 12 / 20 )-7.555555555555560.67898669183541-11.1276931439285
Trimmed Mean ( 13 / 20 )-7.50.663875619216176-11.2972969377232
Trimmed Mean ( 14 / 20 )-7.468750.652205277340135-11.4515326071257
Trimmed Mean ( 15 / 20 )-7.466666666666670.644576548753571-11.5838323331885
Trimmed Mean ( 16 / 20 )-7.464285714285710.630952380952381-11.8301886792453
Trimmed Mean ( 17 / 20 )-7.461538461538460.608227612331409-12.2676746505103
Trimmed Mean ( 18 / 20 )-7.458333333333330.601866561197682-12.3920048299272
Trimmed Mean ( 19 / 20 )-7.454545454545450.587485922193947-12.688892061799
Trimmed Mean ( 20 / 20 )-7.50.578109441469165-12.9733221117096
Median-8
Midrange-11.5
Midmean - Weighted Average at Xnp-7.14705882352941
Midmean - Weighted Average at X(n+1)p-7.14705882352941
Midmean - Empirical Distribution Function-7.14705882352941
Midmean - Empirical Distribution Function - Averaging-7.14705882352941
Midmean - Empirical Distribution Function - Interpolation-7.14705882352941
Midmean - Closest Observation-7.14705882352941
Midmean - True Basic - Statistics Graphics Toolkit-7.14705882352941
Midmean - MS Excel (old versions)-7.14705882352941
Number of observations60



Parameters (Session):
par1 = 0 ; par2 = 36 ;
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')