Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 11 Oct 2016 17:44:37 +0100
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/Oct/11/t1476204330g7yp91u3e9bx2of.htm/, Retrieved Mon, 29 Apr 2024 03:15:39 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 29 Apr 2024 03:15:39 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
91.19
95.06
95.61
97.13
95.44
94.65
93.46
92.19
93.49
92.73
91.4
92.16
91.34
93.72
94.45
96.57
96.12
97.2
94.49
94.31
97.76
99.24
97.43
100.64
99.82
102.97
102.94
105.34
107.18
105.79
102.39
101.25
101.79
100.11
96.86
96.97
97.7
98.27
101.29
101.73
99.56
98.82
95.13
96.23
97.27
96.17
97.07
96.37
95.71
98.19
97.94
99.97
100.09
99.49
98.91
102.04
102.04
102.73
101.34
101.56




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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean97.94683333333330.481296829355097203.506084726498
Geometric Mean97.8773446357886
Harmonic Mean97.8081350885872
Quadratic Mean98.0165767187707
Winsorized Mean ( 1 / 20 )97.92616666666670.473675023383942206.737028199377
Winsorized Mean ( 2 / 20 )97.91316666666670.469080510097061208.73424616684
Winsorized Mean ( 3 / 20 )97.83266666666670.432380865448538226.265023465315
Winsorized Mean ( 4 / 20 )97.83266666666670.431534894705398226.708588035402
Winsorized Mean ( 5 / 20 )97.86016666666670.418385550008296233.899489752278
Winsorized Mean ( 6 / 20 )97.89916666666670.397255790858986246.438614412591
Winsorized Mean ( 7 / 20 )97.86183333333330.388959824778733251.598821006781
Winsorized Mean ( 8 / 20 )97.89250.383208328303752255.455043039683
Winsorized Mean ( 9 / 20 )97.94350.360636507688789271.585094442297
Winsorized Mean ( 10 / 20 )97.95683333333330.354884997021727276.024160377048
Winsorized Mean ( 11 / 20 )97.9330.348095407078833281.339535105733
Winsorized Mean ( 12 / 20 )97.9210.335073539444938292.237340382681
Winsorized Mean ( 13 / 20 )97.9990.318892034932676307.310905462689
Winsorized Mean ( 14 / 20 )98.0060.314719783891769311.407178754622
Winsorized Mean ( 15 / 20 )97.9310.276788146361259353.812116911185
Winsorized Mean ( 16 / 20 )97.8350.247080981258038395.963297141945
Winsorized Mean ( 17 / 20 )97.85766666666670.241901292689594404.535525952054
Winsorized Mean ( 18 / 20 )97.94466666666670.218259093774041448.754115913569
Winsorized Mean ( 19 / 20 )97.9130.208599486487172469.382747047277
Winsorized Mean ( 20 / 20 )97.84633333333330.192500637120769508.290958392764
Trimmed Mean ( 1 / 20 )97.90413793103450.456523995169943214.455623290051
Trimmed Mean ( 2 / 20 )97.88053571428570.435335101532325224.839521025891
Trimmed Mean ( 3 / 20 )97.86240740740740.41210398564136237.470179413828
Trimmed Mean ( 4 / 20 )97.87384615384620.401468284986043243.789733371464
Trimmed Mean ( 5 / 20 )97.88620.388330375860976252.06938752338
Trimmed Mean ( 6 / 20 )97.89270833333330.376274635109638260.162921438511
Trimmed Mean ( 7 / 20 )97.89130434782610.367479810966778266.385530378636
Trimmed Mean ( 8 / 20 )97.89704545454540.358342965206588273.193713732058
Trimmed Mean ( 9 / 20 )97.89785714285710.347831599774793281.451878455673
Trimmed Mean ( 10 / 20 )97.890250.339980672056214287.928867861684
Trimmed Mean ( 11 / 20 )97.87973684210530.330666271412864296.007622500736
Trimmed Mean ( 12 / 20 )97.87166666666670.31959212597329306.23929287559
Trimmed Mean ( 13 / 20 )97.86441176470590.307779463367315317.969271549191
Trimmed Mean ( 14 / 20 )97.8450.295588532668575331.017577429864
Trimmed Mean ( 15 / 20 )97.8220.278939864981437350.692074818743
Trimmed Mean ( 16 / 20 )97.80642857142860.267436000496006365.719007127049
Trimmed Mean ( 17 / 20 )97.80230769230770.259998406913645376.165026752612
Trimmed Mean ( 18 / 20 )97.79416666666670.249370887178076392.163527079374
Trimmed Mean ( 19 / 20 )97.77136363636360.240751255164827406.109465844429
Trimmed Mean ( 20 / 20 )97.7490.229454616542425426.005810965789
Median97.565
Midrange99.185
Midmean - Weighted Average at Xnp97.7351612903226
Midmean - Weighted Average at X(n+1)p97.822
Midmean - Empirical Distribution Function97.7351612903226
Midmean - Empirical Distribution Function - Averaging97.822
Midmean - Empirical Distribution Function - Interpolation97.822
Midmean - Closest Observation97.7351612903226
Midmean - True Basic - Statistics Graphics Toolkit97.822
Midmean - MS Excel (old versions)97.845
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 97.9468333333333 & 0.481296829355097 & 203.506084726498 \tabularnewline
Geometric Mean & 97.8773446357886 &  &  \tabularnewline
Harmonic Mean & 97.8081350885872 &  &  \tabularnewline
Quadratic Mean & 98.0165767187707 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 97.9261666666667 & 0.473675023383942 & 206.737028199377 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 97.9131666666667 & 0.469080510097061 & 208.73424616684 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 97.8326666666667 & 0.432380865448538 & 226.265023465315 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 97.8326666666667 & 0.431534894705398 & 226.708588035402 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 97.8601666666667 & 0.418385550008296 & 233.899489752278 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 97.8991666666667 & 0.397255790858986 & 246.438614412591 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 97.8618333333333 & 0.388959824778733 & 251.598821006781 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 97.8925 & 0.383208328303752 & 255.455043039683 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 97.9435 & 0.360636507688789 & 271.585094442297 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 97.9568333333333 & 0.354884997021727 & 276.024160377048 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 97.933 & 0.348095407078833 & 281.339535105733 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 97.921 & 0.335073539444938 & 292.237340382681 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 97.999 & 0.318892034932676 & 307.310905462689 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 98.006 & 0.314719783891769 & 311.407178754622 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 97.931 & 0.276788146361259 & 353.812116911185 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 97.835 & 0.247080981258038 & 395.963297141945 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 97.8576666666667 & 0.241901292689594 & 404.535525952054 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 97.9446666666667 & 0.218259093774041 & 448.754115913569 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 97.913 & 0.208599486487172 & 469.382747047277 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 97.8463333333333 & 0.192500637120769 & 508.290958392764 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 97.9041379310345 & 0.456523995169943 & 214.455623290051 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 97.8805357142857 & 0.435335101532325 & 224.839521025891 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 97.8624074074074 & 0.41210398564136 & 237.470179413828 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 97.8738461538462 & 0.401468284986043 & 243.789733371464 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 97.8862 & 0.388330375860976 & 252.06938752338 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 97.8927083333333 & 0.376274635109638 & 260.162921438511 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 97.8913043478261 & 0.367479810966778 & 266.385530378636 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 97.8970454545454 & 0.358342965206588 & 273.193713732058 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 97.8978571428571 & 0.347831599774793 & 281.451878455673 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 97.89025 & 0.339980672056214 & 287.928867861684 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 97.8797368421053 & 0.330666271412864 & 296.007622500736 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 97.8716666666667 & 0.31959212597329 & 306.23929287559 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 97.8644117647059 & 0.307779463367315 & 317.969271549191 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 97.845 & 0.295588532668575 & 331.017577429864 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 97.822 & 0.278939864981437 & 350.692074818743 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 97.8064285714286 & 0.267436000496006 & 365.719007127049 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 97.8023076923077 & 0.259998406913645 & 376.165026752612 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 97.7941666666667 & 0.249370887178076 & 392.163527079374 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 97.7713636363636 & 0.240751255164827 & 406.109465844429 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 97.749 & 0.229454616542425 & 426.005810965789 \tabularnewline
Median & 97.565 &  &  \tabularnewline
Midrange & 99.185 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.7351612903226 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 97.822 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.7351612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 97.822 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 97.822 &  &  \tabularnewline
Midmean - Closest Observation & 97.7351612903226 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 97.822 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.845 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]97.9468333333333[/C][C]0.481296829355097[/C][C]203.506084726498[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]97.8773446357886[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]97.8081350885872[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]98.0165767187707[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]97.9261666666667[/C][C]0.473675023383942[/C][C]206.737028199377[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]97.9131666666667[/C][C]0.469080510097061[/C][C]208.73424616684[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]97.8326666666667[/C][C]0.432380865448538[/C][C]226.265023465315[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]97.8326666666667[/C][C]0.431534894705398[/C][C]226.708588035402[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]97.8601666666667[/C][C]0.418385550008296[/C][C]233.899489752278[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]97.8991666666667[/C][C]0.397255790858986[/C][C]246.438614412591[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]97.8618333333333[/C][C]0.388959824778733[/C][C]251.598821006781[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]97.8925[/C][C]0.383208328303752[/C][C]255.455043039683[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]97.9435[/C][C]0.360636507688789[/C][C]271.585094442297[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]97.9568333333333[/C][C]0.354884997021727[/C][C]276.024160377048[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]97.933[/C][C]0.348095407078833[/C][C]281.339535105733[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]97.921[/C][C]0.335073539444938[/C][C]292.237340382681[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]97.999[/C][C]0.318892034932676[/C][C]307.310905462689[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]98.006[/C][C]0.314719783891769[/C][C]311.407178754622[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]97.931[/C][C]0.276788146361259[/C][C]353.812116911185[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]97.835[/C][C]0.247080981258038[/C][C]395.963297141945[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]97.8576666666667[/C][C]0.241901292689594[/C][C]404.535525952054[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]97.9446666666667[/C][C]0.218259093774041[/C][C]448.754115913569[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]97.913[/C][C]0.208599486487172[/C][C]469.382747047277[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]97.8463333333333[/C][C]0.192500637120769[/C][C]508.290958392764[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]97.9041379310345[/C][C]0.456523995169943[/C][C]214.455623290051[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]97.8805357142857[/C][C]0.435335101532325[/C][C]224.839521025891[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]97.8624074074074[/C][C]0.41210398564136[/C][C]237.470179413828[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]97.8738461538462[/C][C]0.401468284986043[/C][C]243.789733371464[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]97.8862[/C][C]0.388330375860976[/C][C]252.06938752338[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]97.8927083333333[/C][C]0.376274635109638[/C][C]260.162921438511[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]97.8913043478261[/C][C]0.367479810966778[/C][C]266.385530378636[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]97.8970454545454[/C][C]0.358342965206588[/C][C]273.193713732058[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]97.8978571428571[/C][C]0.347831599774793[/C][C]281.451878455673[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]97.89025[/C][C]0.339980672056214[/C][C]287.928867861684[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]97.8797368421053[/C][C]0.330666271412864[/C][C]296.007622500736[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]97.8716666666667[/C][C]0.31959212597329[/C][C]306.23929287559[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]97.8644117647059[/C][C]0.307779463367315[/C][C]317.969271549191[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]97.845[/C][C]0.295588532668575[/C][C]331.017577429864[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]97.822[/C][C]0.278939864981437[/C][C]350.692074818743[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]97.8064285714286[/C][C]0.267436000496006[/C][C]365.719007127049[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]97.8023076923077[/C][C]0.259998406913645[/C][C]376.165026752612[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]97.7941666666667[/C][C]0.249370887178076[/C][C]392.163527079374[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]97.7713636363636[/C][C]0.240751255164827[/C][C]406.109465844429[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]97.749[/C][C]0.229454616542425[/C][C]426.005810965789[/C][/ROW]
[ROW][C]Median[/C][C]97.565[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]99.185[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.7351612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]97.822[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.7351612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]97.822[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]97.822[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.7351612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]97.822[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.845[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean97.94683333333330.481296829355097203.506084726498
Geometric Mean97.8773446357886
Harmonic Mean97.8081350885872
Quadratic Mean98.0165767187707
Winsorized Mean ( 1 / 20 )97.92616666666670.473675023383942206.737028199377
Winsorized Mean ( 2 / 20 )97.91316666666670.469080510097061208.73424616684
Winsorized Mean ( 3 / 20 )97.83266666666670.432380865448538226.265023465315
Winsorized Mean ( 4 / 20 )97.83266666666670.431534894705398226.708588035402
Winsorized Mean ( 5 / 20 )97.86016666666670.418385550008296233.899489752278
Winsorized Mean ( 6 / 20 )97.89916666666670.397255790858986246.438614412591
Winsorized Mean ( 7 / 20 )97.86183333333330.388959824778733251.598821006781
Winsorized Mean ( 8 / 20 )97.89250.383208328303752255.455043039683
Winsorized Mean ( 9 / 20 )97.94350.360636507688789271.585094442297
Winsorized Mean ( 10 / 20 )97.95683333333330.354884997021727276.024160377048
Winsorized Mean ( 11 / 20 )97.9330.348095407078833281.339535105733
Winsorized Mean ( 12 / 20 )97.9210.335073539444938292.237340382681
Winsorized Mean ( 13 / 20 )97.9990.318892034932676307.310905462689
Winsorized Mean ( 14 / 20 )98.0060.314719783891769311.407178754622
Winsorized Mean ( 15 / 20 )97.9310.276788146361259353.812116911185
Winsorized Mean ( 16 / 20 )97.8350.247080981258038395.963297141945
Winsorized Mean ( 17 / 20 )97.85766666666670.241901292689594404.535525952054
Winsorized Mean ( 18 / 20 )97.94466666666670.218259093774041448.754115913569
Winsorized Mean ( 19 / 20 )97.9130.208599486487172469.382747047277
Winsorized Mean ( 20 / 20 )97.84633333333330.192500637120769508.290958392764
Trimmed Mean ( 1 / 20 )97.90413793103450.456523995169943214.455623290051
Trimmed Mean ( 2 / 20 )97.88053571428570.435335101532325224.839521025891
Trimmed Mean ( 3 / 20 )97.86240740740740.41210398564136237.470179413828
Trimmed Mean ( 4 / 20 )97.87384615384620.401468284986043243.789733371464
Trimmed Mean ( 5 / 20 )97.88620.388330375860976252.06938752338
Trimmed Mean ( 6 / 20 )97.89270833333330.376274635109638260.162921438511
Trimmed Mean ( 7 / 20 )97.89130434782610.367479810966778266.385530378636
Trimmed Mean ( 8 / 20 )97.89704545454540.358342965206588273.193713732058
Trimmed Mean ( 9 / 20 )97.89785714285710.347831599774793281.451878455673
Trimmed Mean ( 10 / 20 )97.890250.339980672056214287.928867861684
Trimmed Mean ( 11 / 20 )97.87973684210530.330666271412864296.007622500736
Trimmed Mean ( 12 / 20 )97.87166666666670.31959212597329306.23929287559
Trimmed Mean ( 13 / 20 )97.86441176470590.307779463367315317.969271549191
Trimmed Mean ( 14 / 20 )97.8450.295588532668575331.017577429864
Trimmed Mean ( 15 / 20 )97.8220.278939864981437350.692074818743
Trimmed Mean ( 16 / 20 )97.80642857142860.267436000496006365.719007127049
Trimmed Mean ( 17 / 20 )97.80230769230770.259998406913645376.165026752612
Trimmed Mean ( 18 / 20 )97.79416666666670.249370887178076392.163527079374
Trimmed Mean ( 19 / 20 )97.77136363636360.240751255164827406.109465844429
Trimmed Mean ( 20 / 20 )97.7490.229454616542425426.005810965789
Median97.565
Midrange99.185
Midmean - Weighted Average at Xnp97.7351612903226
Midmean - Weighted Average at X(n+1)p97.822
Midmean - Empirical Distribution Function97.7351612903226
Midmean - Empirical Distribution Function - Averaging97.822
Midmean - Empirical Distribution Function - Interpolation97.822
Midmean - Closest Observation97.7351612903226
Midmean - True Basic - Statistics Graphics Toolkit97.822
Midmean - MS Excel (old versions)97.845
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')