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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 15 Nov 2011 15:39:07 -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/Nov/15/t132138961693gqg3k8f7anquc.htm/, Retrieved Thu, 28 Mar 2024 20:15:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143516, Retrieved Thu, 28 Mar 2024 20:15:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54
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]
- RM D  [Central Tendency] [WS VI-linear regr...] [2011-11-15 15:40:01] [74be16979710d4c4e7c6647856088456]
-    D      [Central Tendency] [WS VI-minitutoria...] [2011-11-15 20:39:07] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
122,0
126,0
127,4
123,5
137,4
153,2
107,4
84,6
98,0
100,2
104,4
93,9
122,0
126,0
127,4
123,5
137,4
153,2
93,8
99,3
95,0
95,6
107,7
106,7
117,4
118,9
118,0
95,2
95,8
107,8
106,7
117,3
119,0
118,3
105,9
116,3
131,9
93,7
99,3
95,0
95,6
107,7
106,8
117,3
118,9
117,9
116,4
123,0
138,7
98,8
108,5
103,9
310,1
420,9
90,8
96,1
86,8
84,0
127,3
135,8




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=143516&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=143516&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143516&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 Mean120.4566666666676.4107639737343618.7897522292494
Geometric Mean115.321625883887
Harmonic Mean112.35100729484
Quadratic Mean130.132948684541
Winsorized Mean ( 1 / 20 )118.625.0684343853545223.4036767532708
Winsorized Mean ( 2 / 20 )113.4633333333332.2622147623258850.1558628397761
Winsorized Mean ( 3 / 20 )113.6633333333332.2247985583498151.0892695910592
Winsorized Mean ( 4 / 20 )112.891.9342376124051958.3640806465464
Winsorized Mean ( 5 / 20 )112.791.9087439298739159.0912160791786
Winsorized Mean ( 6 / 20 )112.81.9070609208759459.1486086077361
Winsorized Mean ( 7 / 20 )112.7416666666671.8456427411772561.0853141571451
Winsorized Mean ( 8 / 20 )112.2216666666671.740613392217764.4724826135493
Winsorized Mean ( 9 / 20 )111.5766666666671.6144621232067769.1107366737379
Winsorized Mean ( 10 / 20 )111.6433333333331.6030767850941369.6431601851049
Winsorized Mean ( 11 / 20 )111.6251.6000275862734969.7644221622316
Winsorized Mean ( 12 / 20 )111.4051.550887161820871.8330789902255
Winsorized Mean ( 13 / 20 )111.471.5398460925367172.3903515684265
Winsorized Mean ( 14 / 20 )111.331.3753136262763780.9488089647036
Winsorized Mean ( 15 / 20 )111.531.3428136831186383.0569433437527
Winsorized Mean ( 16 / 20 )111.531.3014492139523485.6967746450104
Winsorized Mean ( 17 / 20 )111.2466666666671.2597808675618888.3063630597665
Winsorized Mean ( 18 / 20 )111.5166666666671.2167943590603491.6479155547573
Winsorized Mean ( 19 / 20 )111.7383333333330.902479608880136123.812585053292
Winsorized Mean ( 20 / 20 )111.8716666666670.873583087374143128.060705711389
Trimmed Mean ( 1 / 20 )115.9051724137933.9921932457177329.0329563926096
Trimmed Mean ( 2 / 20 )112.9964285714292.0954712520311653.9241129945829
Trimmed Mean ( 3 / 20 )112.7370370370371.9798130347748956.9432744692762
Trimmed Mean ( 4 / 20 )112.3807692307691.8516818787936960.6911859525145
Trimmed Mean ( 5 / 20 )112.2281.812669786558561.9130968211667
Trimmed Mean ( 6 / 20 )112.08751.7710202237633363.2897911023396
Trimmed Mean ( 7 / 20 )111.9326086956521.7171149107986965.1864403434643
Trimmed Mean ( 8 / 20 )111.7751.6651353518431267.1266752437136
Trimmed Mean ( 9 / 20 )111.6952380952381.6271539905473568.6445405561558
Trimmed Mean ( 10 / 20 )111.7151.6093618340263169.4157135070807
Trimmed Mean ( 11 / 20 )111.7263157894741.5855754671498370.464205649138
Trimmed Mean ( 12 / 20 )111.7416666666671.5512789142643872.031963845557
Trimmed Mean ( 13 / 20 )111.7911764705881.5148190602024373.798369328446
Trimmed Mean ( 14 / 20 )111.83751.4641051296423976.3862496863982
Trimmed Mean ( 15 / 20 )111.911.4379131590167677.8280658315441
Trimmed Mean ( 16 / 20 )111.9642857142861.4050759670448679.6855745456723
Trimmed Mean ( 17 / 20 )112.0269230769231.3645236722281582.0996552547838
Trimmed Mean ( 18 / 20 )112.1416666666671.3108371684254385.5496543490375
Trimmed Mean ( 19 / 20 )112.2363636363641.2383753051077390.6319458838043
Trimmed Mean ( 20 / 20 )112.3151.2493635221689189.8977743523514
Median112.4
Midrange252.45
Midmean - Weighted Average at Xnp111.8375
Midmean - Weighted Average at X(n+1)p112.283870967742
Midmean - Empirical Distribution Function111.8375
Midmean - Empirical Distribution Function - Averaging112.283870967742
Midmean - Empirical Distribution Function - Interpolation112.283870967742
Midmean - Closest Observation111.8375
Midmean - True Basic - Statistics Graphics Toolkit112.283870967742
Midmean - MS Excel (old versions)111.8375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 120.456666666667 & 6.41076397373436 & 18.7897522292494 \tabularnewline
Geometric Mean & 115.321625883887 &  &  \tabularnewline
Harmonic Mean & 112.35100729484 &  &  \tabularnewline
Quadratic Mean & 130.132948684541 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 118.62 & 5.06843438535452 & 23.4036767532708 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 113.463333333333 & 2.26221476232588 & 50.1558628397761 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 113.663333333333 & 2.22479855834981 & 51.0892695910592 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 112.89 & 1.93423761240519 & 58.3640806465464 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 112.79 & 1.90874392987391 & 59.0912160791786 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 112.8 & 1.90706092087594 & 59.1486086077361 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 112.741666666667 & 1.84564274117725 & 61.0853141571451 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 112.221666666667 & 1.7406133922177 & 64.4724826135493 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 111.576666666667 & 1.61446212320677 & 69.1107366737379 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 111.643333333333 & 1.60307678509413 & 69.6431601851049 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 111.625 & 1.60002758627349 & 69.7644221622316 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 111.405 & 1.5508871618208 & 71.8330789902255 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 111.47 & 1.53984609253671 & 72.3903515684265 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 111.33 & 1.37531362627637 & 80.9488089647036 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 111.53 & 1.34281368311863 & 83.0569433437527 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 111.53 & 1.30144921395234 & 85.6967746450104 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 111.246666666667 & 1.25978086756188 & 88.3063630597665 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 111.516666666667 & 1.21679435906034 & 91.6479155547573 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 111.738333333333 & 0.902479608880136 & 123.812585053292 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 111.871666666667 & 0.873583087374143 & 128.060705711389 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 115.905172413793 & 3.99219324571773 & 29.0329563926096 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 112.996428571429 & 2.09547125203116 & 53.9241129945829 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 112.737037037037 & 1.97981303477489 & 56.9432744692762 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 112.380769230769 & 1.85168187879369 & 60.6911859525145 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 112.228 & 1.8126697865585 & 61.9130968211667 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 112.0875 & 1.77102022376333 & 63.2897911023396 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 111.932608695652 & 1.71711491079869 & 65.1864403434643 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 111.775 & 1.66513535184312 & 67.1266752437136 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 111.695238095238 & 1.62715399054735 & 68.6445405561558 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 111.715 & 1.60936183402631 & 69.4157135070807 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 111.726315789474 & 1.58557546714983 & 70.464205649138 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 111.741666666667 & 1.55127891426438 & 72.031963845557 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 111.791176470588 & 1.51481906020243 & 73.798369328446 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 111.8375 & 1.46410512964239 & 76.3862496863982 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 111.91 & 1.43791315901676 & 77.8280658315441 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 111.964285714286 & 1.40507596704486 & 79.6855745456723 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 112.026923076923 & 1.36452367222815 & 82.0996552547838 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 112.141666666667 & 1.31083716842543 & 85.5496543490375 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 112.236363636364 & 1.23837530510773 & 90.6319458838043 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 112.315 & 1.24936352216891 & 89.8977743523514 \tabularnewline
Median & 112.4 &  &  \tabularnewline
Midrange & 252.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.8375 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 112.283870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.8375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 112.283870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 112.283870967742 &  &  \tabularnewline
Midmean - Closest Observation & 111.8375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 112.283870967742 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111.8375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143516&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]120.456666666667[/C][C]6.41076397373436[/C][C]18.7897522292494[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]115.321625883887[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]112.35100729484[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]130.132948684541[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]118.62[/C][C]5.06843438535452[/C][C]23.4036767532708[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]113.463333333333[/C][C]2.26221476232588[/C][C]50.1558628397761[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]113.663333333333[/C][C]2.22479855834981[/C][C]51.0892695910592[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]112.89[/C][C]1.93423761240519[/C][C]58.3640806465464[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]112.79[/C][C]1.90874392987391[/C][C]59.0912160791786[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]112.8[/C][C]1.90706092087594[/C][C]59.1486086077361[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]112.741666666667[/C][C]1.84564274117725[/C][C]61.0853141571451[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]112.221666666667[/C][C]1.7406133922177[/C][C]64.4724826135493[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]111.576666666667[/C][C]1.61446212320677[/C][C]69.1107366737379[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]111.643333333333[/C][C]1.60307678509413[/C][C]69.6431601851049[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]111.625[/C][C]1.60002758627349[/C][C]69.7644221622316[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]111.405[/C][C]1.5508871618208[/C][C]71.8330789902255[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]111.47[/C][C]1.53984609253671[/C][C]72.3903515684265[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]111.33[/C][C]1.37531362627637[/C][C]80.9488089647036[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]111.53[/C][C]1.34281368311863[/C][C]83.0569433437527[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]111.53[/C][C]1.30144921395234[/C][C]85.6967746450104[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]111.246666666667[/C][C]1.25978086756188[/C][C]88.3063630597665[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]111.516666666667[/C][C]1.21679435906034[/C][C]91.6479155547573[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]111.738333333333[/C][C]0.902479608880136[/C][C]123.812585053292[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]111.871666666667[/C][C]0.873583087374143[/C][C]128.060705711389[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]115.905172413793[/C][C]3.99219324571773[/C][C]29.0329563926096[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]112.996428571429[/C][C]2.09547125203116[/C][C]53.9241129945829[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]112.737037037037[/C][C]1.97981303477489[/C][C]56.9432744692762[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]112.380769230769[/C][C]1.85168187879369[/C][C]60.6911859525145[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]112.228[/C][C]1.8126697865585[/C][C]61.9130968211667[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]112.0875[/C][C]1.77102022376333[/C][C]63.2897911023396[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]111.932608695652[/C][C]1.71711491079869[/C][C]65.1864403434643[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]111.775[/C][C]1.66513535184312[/C][C]67.1266752437136[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]111.695238095238[/C][C]1.62715399054735[/C][C]68.6445405561558[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]111.715[/C][C]1.60936183402631[/C][C]69.4157135070807[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]111.726315789474[/C][C]1.58557546714983[/C][C]70.464205649138[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]111.741666666667[/C][C]1.55127891426438[/C][C]72.031963845557[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]111.791176470588[/C][C]1.51481906020243[/C][C]73.798369328446[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]111.8375[/C][C]1.46410512964239[/C][C]76.3862496863982[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]111.91[/C][C]1.43791315901676[/C][C]77.8280658315441[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]111.964285714286[/C][C]1.40507596704486[/C][C]79.6855745456723[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]112.026923076923[/C][C]1.36452367222815[/C][C]82.0996552547838[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]112.141666666667[/C][C]1.31083716842543[/C][C]85.5496543490375[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]112.236363636364[/C][C]1.23837530510773[/C][C]90.6319458838043[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]112.315[/C][C]1.24936352216891[/C][C]89.8977743523514[/C][/ROW]
[ROW][C]Median[/C][C]112.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]252.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.8375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]112.283870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.8375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]112.283870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]112.283870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.8375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]112.283870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111.8375[/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=143516&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143516&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 Mean120.4566666666676.4107639737343618.7897522292494
Geometric Mean115.321625883887
Harmonic Mean112.35100729484
Quadratic Mean130.132948684541
Winsorized Mean ( 1 / 20 )118.625.0684343853545223.4036767532708
Winsorized Mean ( 2 / 20 )113.4633333333332.2622147623258850.1558628397761
Winsorized Mean ( 3 / 20 )113.6633333333332.2247985583498151.0892695910592
Winsorized Mean ( 4 / 20 )112.891.9342376124051958.3640806465464
Winsorized Mean ( 5 / 20 )112.791.9087439298739159.0912160791786
Winsorized Mean ( 6 / 20 )112.81.9070609208759459.1486086077361
Winsorized Mean ( 7 / 20 )112.7416666666671.8456427411772561.0853141571451
Winsorized Mean ( 8 / 20 )112.2216666666671.740613392217764.4724826135493
Winsorized Mean ( 9 / 20 )111.5766666666671.6144621232067769.1107366737379
Winsorized Mean ( 10 / 20 )111.6433333333331.6030767850941369.6431601851049
Winsorized Mean ( 11 / 20 )111.6251.6000275862734969.7644221622316
Winsorized Mean ( 12 / 20 )111.4051.550887161820871.8330789902255
Winsorized Mean ( 13 / 20 )111.471.5398460925367172.3903515684265
Winsorized Mean ( 14 / 20 )111.331.3753136262763780.9488089647036
Winsorized Mean ( 15 / 20 )111.531.3428136831186383.0569433437527
Winsorized Mean ( 16 / 20 )111.531.3014492139523485.6967746450104
Winsorized Mean ( 17 / 20 )111.2466666666671.2597808675618888.3063630597665
Winsorized Mean ( 18 / 20 )111.5166666666671.2167943590603491.6479155547573
Winsorized Mean ( 19 / 20 )111.7383333333330.902479608880136123.812585053292
Winsorized Mean ( 20 / 20 )111.8716666666670.873583087374143128.060705711389
Trimmed Mean ( 1 / 20 )115.9051724137933.9921932457177329.0329563926096
Trimmed Mean ( 2 / 20 )112.9964285714292.0954712520311653.9241129945829
Trimmed Mean ( 3 / 20 )112.7370370370371.9798130347748956.9432744692762
Trimmed Mean ( 4 / 20 )112.3807692307691.8516818787936960.6911859525145
Trimmed Mean ( 5 / 20 )112.2281.812669786558561.9130968211667
Trimmed Mean ( 6 / 20 )112.08751.7710202237633363.2897911023396
Trimmed Mean ( 7 / 20 )111.9326086956521.7171149107986965.1864403434643
Trimmed Mean ( 8 / 20 )111.7751.6651353518431267.1266752437136
Trimmed Mean ( 9 / 20 )111.6952380952381.6271539905473568.6445405561558
Trimmed Mean ( 10 / 20 )111.7151.6093618340263169.4157135070807
Trimmed Mean ( 11 / 20 )111.7263157894741.5855754671498370.464205649138
Trimmed Mean ( 12 / 20 )111.7416666666671.5512789142643872.031963845557
Trimmed Mean ( 13 / 20 )111.7911764705881.5148190602024373.798369328446
Trimmed Mean ( 14 / 20 )111.83751.4641051296423976.3862496863982
Trimmed Mean ( 15 / 20 )111.911.4379131590167677.8280658315441
Trimmed Mean ( 16 / 20 )111.9642857142861.4050759670448679.6855745456723
Trimmed Mean ( 17 / 20 )112.0269230769231.3645236722281582.0996552547838
Trimmed Mean ( 18 / 20 )112.1416666666671.3108371684254385.5496543490375
Trimmed Mean ( 19 / 20 )112.2363636363641.2383753051077390.6319458838043
Trimmed Mean ( 20 / 20 )112.3151.2493635221689189.8977743523514
Median112.4
Midrange252.45
Midmean - Weighted Average at Xnp111.8375
Midmean - Weighted Average at X(n+1)p112.283870967742
Midmean - Empirical Distribution Function111.8375
Midmean - Empirical Distribution Function - Averaging112.283870967742
Midmean - Empirical Distribution Function - Interpolation112.283870967742
Midmean - Closest Observation111.8375
Midmean - True Basic - Statistics Graphics Toolkit112.283870967742
Midmean - MS Excel (old versions)111.8375
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')