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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 30 Nov 2010 19:29:46 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/30/t1291145321c6jyvj0vjriayfv.htm/, Retrieved Mon, 29 Apr 2024 13:17:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=103789, Retrieved Mon, 29 Apr 2024 13:17:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Minitutorial Test...] [2010-11-26 13:56:53] [b9eaf9df71639055b3e2389f5099ca2c]
-    D    [Central Tendency] [] [2010-11-30 19:29:46] [1d208f56d63f78e3037c4c685f0bba30] [Current]
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Dataseries X:
112,3
117,3
111,1
102,2
104,3
122,9
107,6
121,3
131,5
89
104,4
128,9
135,9
133,3
121,3
120,5
120,4
137,9
126,1
133,2
151,1
105
119
140,4
156,6
137,1
122,7
125,8
139,3
134,9
149,2
132,3
149
117,2
119,6
152
149,4
127,3
114,1
102,1
107,7
104,4
102,1
96
109,3
90
83,9
112
114,3
103,6
91,7
80,8
87,2
109,2
102,7
95,1
117,5
85,1
92,1
113,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103789&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]2 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=103789&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103789&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean117.0616666666672.4488808601161747.8021077191618
Geometric Mean115.536166516681
Harmonic Mean113.999953921588
Quadratic Mean118.563307280682
Winsorized Mean ( 1 / 20 )117.0366666666672.4164922594381948.4324608156935
Winsorized Mean ( 2 / 20 )117.0466666666672.4000452757813548.7685244306741
Winsorized Mean ( 3 / 20 )117.0666666666672.3568132590915549.6715920173457
Winsorized Mean ( 4 / 20 )117.1733333333332.3285138281389450.3210811623068
Winsorized Mean ( 5 / 20 )117.242.3077457389149850.8028237353056
Winsorized Mean ( 6 / 20 )116.552.0892616217922055.7852586695301
Winsorized Mean ( 7 / 20 )116.4683333333332.0553698330614756.6653900723326
Winsorized Mean ( 8 / 20 )116.6816666666671.9425891215828260.0650262941834
Winsorized Mean ( 9 / 20 )116.6966666666671.8953257500181261.5707704417308
Winsorized Mean ( 10 / 20 )117.5133333333331.6847948569428869.7493423897113
Winsorized Mean ( 11 / 20 )117.331.6513037136766471.0529498772602
Winsorized Mean ( 12 / 20 )117.031.5915637408671273.5314565134787
Winsorized Mean ( 13 / 20 )117.1166666666671.5708254094721474.5574052726984
Winsorized Mean ( 14 / 20 )117.1166666666671.5022585006038577.9603953777529
Winsorized Mean ( 15 / 20 )117.0916666666671.4416784232563381.2189908497005
Winsorized Mean ( 16 / 20 )116.4251.3233680387940887.9762821732435
Winsorized Mean ( 17 / 20 )115.9716666666671.2523606898780492.602448802478
Winsorized Mean ( 18 / 20 )115.7916666666671.1696836495072898.9940029643425
Winsorized Mean ( 19 / 20 )116.521.03031397770552113.091739529233
Winsorized Mean ( 20 / 20 )115.5866666666670.883279925898518130.860742192330
Trimmed Mean ( 1 / 20 )117.0051724137932.3560215196751449.6621832341863
Trimmed Mean ( 2 / 20 )116.9714285714292.2813767691668751.2722975671157
Trimmed Mean ( 3 / 20 )116.9296296296302.1998167600927253.1542589141384
Trimmed Mean ( 4 / 20 )116.8769230769232.1193154209742655.1484323287726
Trimmed Mean ( 5 / 20 )116.7882.0292908985703457.551137731056
Trimmed Mean ( 6 / 20 )116.6751.9219396323388060.7069015263599
Trimmed Mean ( 7 / 20 )116.7021739130431.8580897393616762.8076090410658
Trimmed Mean ( 8 / 20 )116.7477272727271.7853422713178565.3923503343424
Trimmed Mean ( 9 / 20 )116.7595238095241.7234127998125167.7490174276447
Trimmed Mean ( 10 / 20 )116.771.6544237512553970.5804664079527
Trimmed Mean ( 11 / 20 )116.6526315789471.6196286073154272.024309185488
Trimmed Mean ( 12 / 20 )116.551.5794036447393373.7936754725142
Trimmed Mean ( 13 / 20 )116.4794117647061.5386973876736175.7000126846342
Trimmed Mean ( 14 / 20 )116.38751.4847052900785078.3909781811621
Trimmed Mean ( 15 / 20 )116.2833333333331.4262166279116981.5327286595997
Trimmed Mean ( 16 / 20 )116.1678571428571.3579771523608585.5447802939089
Trimmed Mean ( 17 / 20 )116.1307692307691.2970471699004489.5347308299382
Trimmed Mean ( 18 / 20 )116.1541666666671.2270646482423894.6601850465204
Trimmed Mean ( 19 / 20 )116.2090909090911.14693095258436101.321784582794
Trimmed Mean ( 20 / 20 )116.161.07799521530039107.755580313621
Median117.25
Midrange118.7
Midmean - Weighted Average at Xnp115.874193548387
Midmean - Weighted Average at X(n+1)p116.283333333333
Midmean - Empirical Distribution Function115.874193548387
Midmean - Empirical Distribution Function - Averaging116.283333333333
Midmean - Empirical Distribution Function - Interpolation116.283333333333
Midmean - Closest Observation115.874193548387
Midmean - True Basic - Statistics Graphics Toolkit116.283333333333
Midmean - MS Excel (old versions)116.3875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 117.061666666667 & 2.44888086011617 & 47.8021077191618 \tabularnewline
Geometric Mean & 115.536166516681 &  &  \tabularnewline
Harmonic Mean & 113.999953921588 &  &  \tabularnewline
Quadratic Mean & 118.563307280682 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 117.036666666667 & 2.41649225943819 & 48.4324608156935 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 117.046666666667 & 2.40004527578135 & 48.7685244306741 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 117.066666666667 & 2.35681325909155 & 49.6715920173457 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 117.173333333333 & 2.32851382813894 & 50.3210811623068 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 117.24 & 2.30774573891498 & 50.8028237353056 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 116.55 & 2.08926162179220 & 55.7852586695301 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 116.468333333333 & 2.05536983306147 & 56.6653900723326 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 116.681666666667 & 1.94258912158282 & 60.0650262941834 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 116.696666666667 & 1.89532575001812 & 61.5707704417308 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 117.513333333333 & 1.68479485694288 & 69.7493423897113 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 117.33 & 1.65130371367664 & 71.0529498772602 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 117.03 & 1.59156374086712 & 73.5314565134787 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 117.116666666667 & 1.57082540947214 & 74.5574052726984 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 117.116666666667 & 1.50225850060385 & 77.9603953777529 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 117.091666666667 & 1.44167842325633 & 81.2189908497005 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 116.425 & 1.32336803879408 & 87.9762821732435 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 115.971666666667 & 1.25236068987804 & 92.602448802478 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 115.791666666667 & 1.16968364950728 & 98.9940029643425 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 116.52 & 1.03031397770552 & 113.091739529233 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 115.586666666667 & 0.883279925898518 & 130.860742192330 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 117.005172413793 & 2.35602151967514 & 49.6621832341863 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 116.971428571429 & 2.28137676916687 & 51.2722975671157 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 116.929629629630 & 2.19981676009272 & 53.1542589141384 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 116.876923076923 & 2.11931542097426 & 55.1484323287726 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 116.788 & 2.02929089857034 & 57.551137731056 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 116.675 & 1.92193963233880 & 60.7069015263599 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 116.702173913043 & 1.85808973936167 & 62.8076090410658 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 116.747727272727 & 1.78534227131785 & 65.3923503343424 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 116.759523809524 & 1.72341279981251 & 67.7490174276447 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 116.77 & 1.65442375125539 & 70.5804664079527 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 116.652631578947 & 1.61962860731542 & 72.024309185488 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 116.55 & 1.57940364473933 & 73.7936754725142 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 116.479411764706 & 1.53869738767361 & 75.7000126846342 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 116.3875 & 1.48470529007850 & 78.3909781811621 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 116.283333333333 & 1.42621662791169 & 81.5327286595997 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 116.167857142857 & 1.35797715236085 & 85.5447802939089 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 116.130769230769 & 1.29704716990044 & 89.5347308299382 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 116.154166666667 & 1.22706464824238 & 94.6601850465204 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 116.209090909091 & 1.14693095258436 & 101.321784582794 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 116.16 & 1.07799521530039 & 107.755580313621 \tabularnewline
Median & 117.25 &  &  \tabularnewline
Midrange & 118.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 115.874193548387 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 116.283333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 115.874193548387 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 116.283333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 116.283333333333 &  &  \tabularnewline
Midmean - Closest Observation & 115.874193548387 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 116.283333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 116.3875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103789&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]117.061666666667[/C][C]2.44888086011617[/C][C]47.8021077191618[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]115.536166516681[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]113.999953921588[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]118.563307280682[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]117.036666666667[/C][C]2.41649225943819[/C][C]48.4324608156935[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]117.046666666667[/C][C]2.40004527578135[/C][C]48.7685244306741[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]117.066666666667[/C][C]2.35681325909155[/C][C]49.6715920173457[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]117.173333333333[/C][C]2.32851382813894[/C][C]50.3210811623068[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]117.24[/C][C]2.30774573891498[/C][C]50.8028237353056[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]116.55[/C][C]2.08926162179220[/C][C]55.7852586695301[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]116.468333333333[/C][C]2.05536983306147[/C][C]56.6653900723326[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]116.681666666667[/C][C]1.94258912158282[/C][C]60.0650262941834[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]116.696666666667[/C][C]1.89532575001812[/C][C]61.5707704417308[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]117.513333333333[/C][C]1.68479485694288[/C][C]69.7493423897113[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]117.33[/C][C]1.65130371367664[/C][C]71.0529498772602[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]117.03[/C][C]1.59156374086712[/C][C]73.5314565134787[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]117.116666666667[/C][C]1.57082540947214[/C][C]74.5574052726984[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]117.116666666667[/C][C]1.50225850060385[/C][C]77.9603953777529[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]117.091666666667[/C][C]1.44167842325633[/C][C]81.2189908497005[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]116.425[/C][C]1.32336803879408[/C][C]87.9762821732435[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]115.971666666667[/C][C]1.25236068987804[/C][C]92.602448802478[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]115.791666666667[/C][C]1.16968364950728[/C][C]98.9940029643425[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]116.52[/C][C]1.03031397770552[/C][C]113.091739529233[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]115.586666666667[/C][C]0.883279925898518[/C][C]130.860742192330[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]117.005172413793[/C][C]2.35602151967514[/C][C]49.6621832341863[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]116.971428571429[/C][C]2.28137676916687[/C][C]51.2722975671157[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]116.929629629630[/C][C]2.19981676009272[/C][C]53.1542589141384[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]116.876923076923[/C][C]2.11931542097426[/C][C]55.1484323287726[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]116.788[/C][C]2.02929089857034[/C][C]57.551137731056[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]116.675[/C][C]1.92193963233880[/C][C]60.7069015263599[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]116.702173913043[/C][C]1.85808973936167[/C][C]62.8076090410658[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]116.747727272727[/C][C]1.78534227131785[/C][C]65.3923503343424[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]116.759523809524[/C][C]1.72341279981251[/C][C]67.7490174276447[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]116.77[/C][C]1.65442375125539[/C][C]70.5804664079527[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]116.652631578947[/C][C]1.61962860731542[/C][C]72.024309185488[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]116.55[/C][C]1.57940364473933[/C][C]73.7936754725142[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]116.479411764706[/C][C]1.53869738767361[/C][C]75.7000126846342[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]116.3875[/C][C]1.48470529007850[/C][C]78.3909781811621[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]116.283333333333[/C][C]1.42621662791169[/C][C]81.5327286595997[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]116.167857142857[/C][C]1.35797715236085[/C][C]85.5447802939089[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]116.130769230769[/C][C]1.29704716990044[/C][C]89.5347308299382[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]116.154166666667[/C][C]1.22706464824238[/C][C]94.6601850465204[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]116.209090909091[/C][C]1.14693095258436[/C][C]101.321784582794[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]116.16[/C][C]1.07799521530039[/C][C]107.755580313621[/C][/ROW]
[ROW][C]Median[/C][C]117.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]118.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]115.874193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]116.283333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]115.874193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]116.283333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]116.283333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]115.874193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]116.283333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]116.3875[/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=103789&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103789&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 Mean117.0616666666672.4488808601161747.8021077191618
Geometric Mean115.536166516681
Harmonic Mean113.999953921588
Quadratic Mean118.563307280682
Winsorized Mean ( 1 / 20 )117.0366666666672.4164922594381948.4324608156935
Winsorized Mean ( 2 / 20 )117.0466666666672.4000452757813548.7685244306741
Winsorized Mean ( 3 / 20 )117.0666666666672.3568132590915549.6715920173457
Winsorized Mean ( 4 / 20 )117.1733333333332.3285138281389450.3210811623068
Winsorized Mean ( 5 / 20 )117.242.3077457389149850.8028237353056
Winsorized Mean ( 6 / 20 )116.552.0892616217922055.7852586695301
Winsorized Mean ( 7 / 20 )116.4683333333332.0553698330614756.6653900723326
Winsorized Mean ( 8 / 20 )116.6816666666671.9425891215828260.0650262941834
Winsorized Mean ( 9 / 20 )116.6966666666671.8953257500181261.5707704417308
Winsorized Mean ( 10 / 20 )117.5133333333331.6847948569428869.7493423897113
Winsorized Mean ( 11 / 20 )117.331.6513037136766471.0529498772602
Winsorized Mean ( 12 / 20 )117.031.5915637408671273.5314565134787
Winsorized Mean ( 13 / 20 )117.1166666666671.5708254094721474.5574052726984
Winsorized Mean ( 14 / 20 )117.1166666666671.5022585006038577.9603953777529
Winsorized Mean ( 15 / 20 )117.0916666666671.4416784232563381.2189908497005
Winsorized Mean ( 16 / 20 )116.4251.3233680387940887.9762821732435
Winsorized Mean ( 17 / 20 )115.9716666666671.2523606898780492.602448802478
Winsorized Mean ( 18 / 20 )115.7916666666671.1696836495072898.9940029643425
Winsorized Mean ( 19 / 20 )116.521.03031397770552113.091739529233
Winsorized Mean ( 20 / 20 )115.5866666666670.883279925898518130.860742192330
Trimmed Mean ( 1 / 20 )117.0051724137932.3560215196751449.6621832341863
Trimmed Mean ( 2 / 20 )116.9714285714292.2813767691668751.2722975671157
Trimmed Mean ( 3 / 20 )116.9296296296302.1998167600927253.1542589141384
Trimmed Mean ( 4 / 20 )116.8769230769232.1193154209742655.1484323287726
Trimmed Mean ( 5 / 20 )116.7882.0292908985703457.551137731056
Trimmed Mean ( 6 / 20 )116.6751.9219396323388060.7069015263599
Trimmed Mean ( 7 / 20 )116.7021739130431.8580897393616762.8076090410658
Trimmed Mean ( 8 / 20 )116.7477272727271.7853422713178565.3923503343424
Trimmed Mean ( 9 / 20 )116.7595238095241.7234127998125167.7490174276447
Trimmed Mean ( 10 / 20 )116.771.6544237512553970.5804664079527
Trimmed Mean ( 11 / 20 )116.6526315789471.6196286073154272.024309185488
Trimmed Mean ( 12 / 20 )116.551.5794036447393373.7936754725142
Trimmed Mean ( 13 / 20 )116.4794117647061.5386973876736175.7000126846342
Trimmed Mean ( 14 / 20 )116.38751.4847052900785078.3909781811621
Trimmed Mean ( 15 / 20 )116.2833333333331.4262166279116981.5327286595997
Trimmed Mean ( 16 / 20 )116.1678571428571.3579771523608585.5447802939089
Trimmed Mean ( 17 / 20 )116.1307692307691.2970471699004489.5347308299382
Trimmed Mean ( 18 / 20 )116.1541666666671.2270646482423894.6601850465204
Trimmed Mean ( 19 / 20 )116.2090909090911.14693095258436101.321784582794
Trimmed Mean ( 20 / 20 )116.161.07799521530039107.755580313621
Median117.25
Midrange118.7
Midmean - Weighted Average at Xnp115.874193548387
Midmean - Weighted Average at X(n+1)p116.283333333333
Midmean - Empirical Distribution Function115.874193548387
Midmean - Empirical Distribution Function - Averaging116.283333333333
Midmean - Empirical Distribution Function - Interpolation116.283333333333
Midmean - Closest Observation115.874193548387
Midmean - True Basic - Statistics Graphics Toolkit116.283333333333
Midmean - MS Excel (old versions)116.3875
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')