FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Dec 2007 08:16:09 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/13/t1197558044a73qkfg7jio23du.htm/, Retrieved Sun, 05 May 2024 09:28:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3601, Retrieved Sun, 05 May 2024 09:28:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact193

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-12-13 15:16:09] [919a0fafa615dc0e3c6b6d22cd1007a0] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
-9,65
-1,45
-15,65
-14,45
-21,25
-15,95
-8,55
-16,45
-12,65
2,35
-13,25
-34,25
-8,85
-5,25
-17,55
-0,25
-21,25
-13,85
6,35
1,75
-5,45
3,35
-6,45
-9,35
1,45
-3,55
-8,95
7,95
-15,25
-6,85
9,85
0,25
-4,45
17,95
-15,05
-18,25
3,95
-1,85
15,75
23,15
0,25
2,05
26,15
5,95
19,45
32,55
-2,35
-7,65
13,65
22,95
20,25
36,25
22,65
17,65
46,55
25,05
31,25
39,85
27,35
5,75

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3601&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3601&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3601&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.561666666666672.245900334943861.14059676950478
Geometric MeanNaN
Harmonic Mean15.7283044577963
Quadratic Mean17.4402456022462
Winsorized Mean ( 1 / 20 )2.666666666666672.160422336126241.23432655831922
Winsorized Mean ( 2 / 20 )2.546666666666672.126792984577181.19742103962834
Winsorized Mean ( 3 / 20 )2.511666666666672.051851983718251.2240973942551
Winsorized Mean ( 4 / 20 )2.471666666666672.022731122976281.22194523957777
Winsorized Mean ( 5 / 20 )2.238333333333331.932471693343631.15827483581945
Winsorized Mean ( 6 / 20 )2.168333333333331.898263392609491.14227211132834
Winsorized Mean ( 7 / 20 )2.0751.865476757044551.11231619057393
Winsorized Mean ( 8 / 20 )1.8751.805131769764941.03870533520340
Winsorized Mean ( 9 / 20 )1.8751.79433922338771.04495291389775
Winsorized Mean ( 10 / 20 )1.9251.768555580638591.08845886500492
Winsorized Mean ( 11 / 20 )1.5951.665767709540230.957516459747104
Winsorized Mean ( 12 / 20 )1.5551.616829612034080.96175873352771
Winsorized Mean ( 13 / 20 )1.361.536452918452590.885155661892785
Winsorized Mean ( 14 / 20 )1.991.420599459685511.40081708917484
Winsorized Mean ( 15 / 20 )1.591.322619810770201.20215952237559
Winsorized Mean ( 16 / 20 )1.136666666666671.207533945591250.94131239193455
Winsorized Mean ( 17 / 20 )0.08833333333333351.021036063116560.086513431331416
Winsorized Mean ( 18 / 20 )-0.3916666666666670.917354005277198-0.426952588001528
Winsorized Mean ( 19 / 20 )-0.6133333333333330.797938610649559-0.768647268283022
Winsorized Mean ( 20 / 20 )-0.480.738812224333666-0.649691469889947
Trimmed Mean ( 1 / 20 )2.437931034482762.098961339062931.16149401568833
Trimmed Mean ( 2 / 20 )2.192857142857142.022671592487891.08413899270713
Trimmed Mean ( 3 / 20 )1.996296296296301.950591146510541.02343143506394
Trimmed Mean ( 4 / 20 )1.798076923076921.897035653691620.947835070773644
Trimmed Mean ( 5 / 20 )1.5961.840592650784650.867112013796004
Trimmed Mean ( 6 / 20 )1.435416666666671.800056612543860.797428623446525
Trimmed Mean ( 7 / 20 )1.276086956521741.757752833038310.725976333268655
Trimmed Mean ( 8 / 20 )1.120454545454551.711624167001620.654614819687506
Trimmed Mean ( 9 / 20 )0.9857142857142861.667628600785450.591087419135183
Trimmed Mean ( 10 / 20 )0.83751.610940907970980.519882508325431
Trimmed Mean ( 11 / 20 )0.665789473684211.540766681722990.432115700308160
Trimmed Mean ( 12 / 20 )0.5251.475414254445920.355832267729552
Trimmed Mean ( 13 / 20 )0.3735294117647061.398414296935630.267109262672177
Trimmed Mean ( 14 / 20 )0.231251.314830400414760.175878196858738
Trimmed Mean ( 15 / 20 )-0.021.22802663867172-0.0162862916570220
Trimmed Mean ( 16 / 20 )-0.251.13551377551817-0.220164656202358
Trimmed Mean ( 17 / 20 )-0.451.04133050986189-0.432139455953981
Trimmed Mean ( 18 / 20 )-0.5291666666666670.978055953444195-0.541039257317766
Trimmed Mean ( 19 / 20 )-0.550.920897360215539-0.597243540660461
Trimmed Mean ( 20 / 20 )-0.540.87926105338517-0.614152074541446
Median0
Midrange6.15
Midmean - Weighted Average at Xnp-0.330645161290322
Midmean - Weighted Average at X(n+1)p-0.0200000000000000
Midmean - Empirical Distribution Function-0.330645161290322
Midmean - Empirical Distribution Function - Averaging-0.0200000000000000
Midmean - Empirical Distribution Function - Interpolation-0.0200000000000000
Midmean - Closest Observation-0.330645161290322
Midmean - True Basic - Statistics Graphics Toolkit-0.0200000000000000
Midmean - MS Excel (old versions)0.23125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.56166666666667 & 2.24590033494386 & 1.14059676950478 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 15.7283044577963 &  &  \tabularnewline
Quadratic Mean & 17.4402456022462 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.66666666666667 & 2.16042233612624 & 1.23432655831922 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.54666666666667 & 2.12679298457718 & 1.19742103962834 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.51166666666667 & 2.05185198371825 & 1.2240973942551 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.47166666666667 & 2.02273112297628 & 1.22194523957777 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.23833333333333 & 1.93247169334363 & 1.15827483581945 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.16833333333333 & 1.89826339260949 & 1.14227211132834 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.075 & 1.86547675704455 & 1.11231619057393 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.875 & 1.80513176976494 & 1.03870533520340 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.875 & 1.7943392233877 & 1.04495291389775 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.925 & 1.76855558063859 & 1.08845886500492 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.595 & 1.66576770954023 & 0.957516459747104 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.555 & 1.61682961203408 & 0.96175873352771 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.36 & 1.53645291845259 & 0.885155661892785 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.99 & 1.42059945968551 & 1.40081708917484 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.59 & 1.32261981077020 & 1.20215952237559 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.13666666666667 & 1.20753394559125 & 0.94131239193455 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.0883333333333335 & 1.02103606311656 & 0.086513431331416 \tabularnewline
Winsorized Mean ( 18 / 20 ) & -0.391666666666667 & 0.917354005277198 & -0.426952588001528 \tabularnewline
Winsorized Mean ( 19 / 20 ) & -0.613333333333333 & 0.797938610649559 & -0.768647268283022 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -0.48 & 0.738812224333666 & -0.649691469889947 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.43793103448276 & 2.09896133906293 & 1.16149401568833 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.19285714285714 & 2.02267159248789 & 1.08413899270713 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.99629629629630 & 1.95059114651054 & 1.02343143506394 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.79807692307692 & 1.89703565369162 & 0.947835070773644 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.596 & 1.84059265078465 & 0.867112013796004 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.43541666666667 & 1.80005661254386 & 0.797428623446525 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.27608695652174 & 1.75775283303831 & 0.725976333268655 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.12045454545455 & 1.71162416700162 & 0.654614819687506 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.985714285714286 & 1.66762860078545 & 0.591087419135183 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.8375 & 1.61094090797098 & 0.519882508325431 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.66578947368421 & 1.54076668172299 & 0.432115700308160 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.525 & 1.47541425444592 & 0.355832267729552 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.373529411764706 & 1.39841429693563 & 0.267109262672177 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.23125 & 1.31483040041476 & 0.175878196858738 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -0.02 & 1.22802663867172 & -0.0162862916570220 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -0.25 & 1.13551377551817 & -0.220164656202358 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -0.45 & 1.04133050986189 & -0.432139455953981 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -0.529166666666667 & 0.978055953444195 & -0.541039257317766 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -0.55 & 0.920897360215539 & -0.597243540660461 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -0.54 & 0.87926105338517 & -0.614152074541446 \tabularnewline
Median & 0 &  &  \tabularnewline
Midrange & 6.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.330645161290322 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -0.0200000000000000 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.330645161290322 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -0.0200000000000000 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -0.0200000000000000 &  &  \tabularnewline
Midmean - Closest Observation & -0.330645161290322 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -0.0200000000000000 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.23125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3601&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]2.56166666666667[/C][C]2.24590033494386[/C][C]1.14059676950478[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]15.7283044577963[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17.4402456022462[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.66666666666667[/C][C]2.16042233612624[/C][C]1.23432655831922[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.54666666666667[/C][C]2.12679298457718[/C][C]1.19742103962834[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.51166666666667[/C][C]2.05185198371825[/C][C]1.2240973942551[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.47166666666667[/C][C]2.02273112297628[/C][C]1.22194523957777[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.23833333333333[/C][C]1.93247169334363[/C][C]1.15827483581945[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.16833333333333[/C][C]1.89826339260949[/C][C]1.14227211132834[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.075[/C][C]1.86547675704455[/C][C]1.11231619057393[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.875[/C][C]1.80513176976494[/C][C]1.03870533520340[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.875[/C][C]1.7943392233877[/C][C]1.04495291389775[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.925[/C][C]1.76855558063859[/C][C]1.08845886500492[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.595[/C][C]1.66576770954023[/C][C]0.957516459747104[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.555[/C][C]1.61682961203408[/C][C]0.96175873352771[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.36[/C][C]1.53645291845259[/C][C]0.885155661892785[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.99[/C][C]1.42059945968551[/C][C]1.40081708917484[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.59[/C][C]1.32261981077020[/C][C]1.20215952237559[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.13666666666667[/C][C]1.20753394559125[/C][C]0.94131239193455[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.0883333333333335[/C][C]1.02103606311656[/C][C]0.086513431331416[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]-0.391666666666667[/C][C]0.917354005277198[/C][C]-0.426952588001528[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]-0.613333333333333[/C][C]0.797938610649559[/C][C]-0.768647268283022[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-0.48[/C][C]0.738812224333666[/C][C]-0.649691469889947[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.43793103448276[/C][C]2.09896133906293[/C][C]1.16149401568833[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.19285714285714[/C][C]2.02267159248789[/C][C]1.08413899270713[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.99629629629630[/C][C]1.95059114651054[/C][C]1.02343143506394[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.79807692307692[/C][C]1.89703565369162[/C][C]0.947835070773644[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.596[/C][C]1.84059265078465[/C][C]0.867112013796004[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.43541666666667[/C][C]1.80005661254386[/C][C]0.797428623446525[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.27608695652174[/C][C]1.75775283303831[/C][C]0.725976333268655[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.12045454545455[/C][C]1.71162416700162[/C][C]0.654614819687506[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.985714285714286[/C][C]1.66762860078545[/C][C]0.591087419135183[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.8375[/C][C]1.61094090797098[/C][C]0.519882508325431[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.66578947368421[/C][C]1.54076668172299[/C][C]0.432115700308160[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.525[/C][C]1.47541425444592[/C][C]0.355832267729552[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.373529411764706[/C][C]1.39841429693563[/C][C]0.267109262672177[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.23125[/C][C]1.31483040041476[/C][C]0.175878196858738[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-0.02[/C][C]1.22802663867172[/C][C]-0.0162862916570220[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-0.25[/C][C]1.13551377551817[/C][C]-0.220164656202358[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-0.45[/C][C]1.04133050986189[/C][C]-0.432139455953981[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-0.529166666666667[/C][C]0.978055953444195[/C][C]-0.541039257317766[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-0.55[/C][C]0.920897360215539[/C][C]-0.597243540660461[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-0.54[/C][C]0.87926105338517[/C][C]-0.614152074541446[/C][/ROW]
[ROW][C]Median[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.330645161290322[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-0.0200000000000000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.330645161290322[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-0.0200000000000000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-0.0200000000000000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.330645161290322[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-0.0200000000000000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.23125[/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=3601&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3601&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.561666666666672.245900334943861.14059676950478
Geometric MeanNaN
Harmonic Mean15.7283044577963
Quadratic Mean17.4402456022462
Winsorized Mean ( 1 / 20 )2.666666666666672.160422336126241.23432655831922
Winsorized Mean ( 2 / 20 )2.546666666666672.126792984577181.19742103962834
Winsorized Mean ( 3 / 20 )2.511666666666672.051851983718251.2240973942551
Winsorized Mean ( 4 / 20 )2.471666666666672.022731122976281.22194523957777
Winsorized Mean ( 5 / 20 )2.238333333333331.932471693343631.15827483581945
Winsorized Mean ( 6 / 20 )2.168333333333331.898263392609491.14227211132834
Winsorized Mean ( 7 / 20 )2.0751.865476757044551.11231619057393
Winsorized Mean ( 8 / 20 )1.8751.805131769764941.03870533520340
Winsorized Mean ( 9 / 20 )1.8751.79433922338771.04495291389775
Winsorized Mean ( 10 / 20 )1.9251.768555580638591.08845886500492
Winsorized Mean ( 11 / 20 )1.5951.665767709540230.957516459747104
Winsorized Mean ( 12 / 20 )1.5551.616829612034080.96175873352771
Winsorized Mean ( 13 / 20 )1.361.536452918452590.885155661892785
Winsorized Mean ( 14 / 20 )1.991.420599459685511.40081708917484
Winsorized Mean ( 15 / 20 )1.591.322619810770201.20215952237559
Winsorized Mean ( 16 / 20 )1.136666666666671.207533945591250.94131239193455
Winsorized Mean ( 17 / 20 )0.08833333333333351.021036063116560.086513431331416
Winsorized Mean ( 18 / 20 )-0.3916666666666670.917354005277198-0.426952588001528
Winsorized Mean ( 19 / 20 )-0.6133333333333330.797938610649559-0.768647268283022
Winsorized Mean ( 20 / 20 )-0.480.738812224333666-0.649691469889947
Trimmed Mean ( 1 / 20 )2.437931034482762.098961339062931.16149401568833
Trimmed Mean ( 2 / 20 )2.192857142857142.022671592487891.08413899270713
Trimmed Mean ( 3 / 20 )1.996296296296301.950591146510541.02343143506394
Trimmed Mean ( 4 / 20 )1.798076923076921.897035653691620.947835070773644
Trimmed Mean ( 5 / 20 )1.5961.840592650784650.867112013796004
Trimmed Mean ( 6 / 20 )1.435416666666671.800056612543860.797428623446525
Trimmed Mean ( 7 / 20 )1.276086956521741.757752833038310.725976333268655
Trimmed Mean ( 8 / 20 )1.120454545454551.711624167001620.654614819687506
Trimmed Mean ( 9 / 20 )0.9857142857142861.667628600785450.591087419135183
Trimmed Mean ( 10 / 20 )0.83751.610940907970980.519882508325431
Trimmed Mean ( 11 / 20 )0.665789473684211.540766681722990.432115700308160
Trimmed Mean ( 12 / 20 )0.5251.475414254445920.355832267729552
Trimmed Mean ( 13 / 20 )0.3735294117647061.398414296935630.267109262672177
Trimmed Mean ( 14 / 20 )0.231251.314830400414760.175878196858738
Trimmed Mean ( 15 / 20 )-0.021.22802663867172-0.0162862916570220
Trimmed Mean ( 16 / 20 )-0.251.13551377551817-0.220164656202358
Trimmed Mean ( 17 / 20 )-0.451.04133050986189-0.432139455953981
Trimmed Mean ( 18 / 20 )-0.5291666666666670.978055953444195-0.541039257317766
Trimmed Mean ( 19 / 20 )-0.550.920897360215539-0.597243540660461
Trimmed Mean ( 20 / 20 )-0.540.87926105338517-0.614152074541446
Median0
Midrange6.15
Midmean - Weighted Average at Xnp-0.330645161290322
Midmean - Weighted Average at X(n+1)p-0.0200000000000000
Midmean - Empirical Distribution Function-0.330645161290322
Midmean - Empirical Distribution Function - Averaging-0.0200000000000000
Midmean - Empirical Distribution Function - Interpolation-0.0200000000000000
Midmean - Closest Observation-0.330645161290322
Midmean - True Basic - Statistics Graphics Toolkit-0.0200000000000000
Midmean - MS Excel (old versions)0.23125
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')