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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 04:51:28 -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/2012/Mar/07/t1331113920mtvcm1re4br77o2.htm/, Retrieved Sun, 28 Apr 2024 23:54:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163572, Retrieved Sun, 28 Apr 2024 23:54:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten gem ...] [2012-03-07 09:51:28] [dd2dd3cf9efab982d1558aa590dba591] [Current]
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Dataseries X:
73,97	
73,97	
73,97	
73,97	
73,97	
73,97	
73,96	
74,44	
75,43	
75,77	
75,82	
75,85	
75,85	
75,85	
77,95	
82,07	
84,82	
85,08	
85,34	
85,65	
85,65	
85,72	
85,73	
85,73	
85,73	
85,73	
85,74	
86,32	
87,59	
87,81	
87,87	
87,94	
87,96	
88,01	
88,01	
88,01	
88,01	
88,01	
88,59	
89,43	
89,63	
89,73	
89,88	
89,89	
89,90	
89,91	
89,86	
90,07	
90,17	
90,17	
90,28	
90,87	
92,05	
92,10	
92,16	
92,22	
92,25	
92,29	
92,29	
92,29	




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163572&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163572&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163572&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean85.1550.81937979508136103.926165266919
Geometric Mean84.9122049596294
Harmonic Mean84.6594561876878
Quadratic Mean85.3872685865209
Winsorized Mean ( 1 / 20 )85.15516666666670.819341215720153103.931262132127
Winsorized Mean ( 2 / 20 )85.15516666666670.819341215720153103.931262132127
Winsorized Mean ( 3 / 20 )85.15316666666670.819046762034529103.966184366744
Winsorized Mean ( 4 / 20 )85.15116666666670.818753568730452104.000971621658
Winsorized Mean ( 5 / 20 )85.14616666666670.818024425051702104.087560296607
Winsorized Mean ( 6 / 20 )85.14016666666670.817155376372028104.190915373608
Winsorized Mean ( 7 / 20 )85.18916666666670.803744425314481105.990367066415
Winsorized Mean ( 8 / 20 )85.16383333333330.752772693675023113.133531607749
Winsorized Mean ( 9 / 20 )85.12633333333330.730667714389533116.504851188691
Winsorized Mean ( 10 / 20 )85.11633333333330.726683549536942117.12984749355
Winsorized Mean ( 11 / 20 )85.12183333333330.725491592216373117.32986880425
Winsorized Mean ( 12 / 20 )85.10183333333330.723147760243375117.682495904699
Winsorized Mean ( 13 / 20 )85.06716666666670.7191509075137118.288339454047
Winsorized Mean ( 14 / 20 )85.55483333333330.614089997437606139.31969856263
Winsorized Mean ( 15 / 20 )86.58233333333330.40650372071227212.992720415019
Winsorized Mean ( 16 / 20 )87.3130.279119711878832312.815599486945
Winsorized Mean ( 17 / 20 )87.3810.267277834243631326.929467410866
Winsorized Mean ( 18 / 20 )87.420.249959996799488349.735962231294
Winsorized Mean ( 19 / 20 )87.48650.231458996258846377.978395370565
Winsorized Mean ( 20 / 20 )87.41983333333330.221087897195329395.407593279965
Trimmed Mean ( 1 / 20 )85.2250.815787997871545104.469543830454
Trimmed Mean ( 2 / 20 )85.29982142857140.810497982687004105.243718369022
Trimmed Mean ( 3 / 20 )85.38018518518520.803055246053401106.319192365388
Trimmed Mean ( 4 / 20 )85.46750.793049124361206107.770751362778
Trimmed Mean ( 5 / 20 )85.56240.779763206338427109.728696230462
Trimmed Mean ( 6 / 20 )85.66645833333330.762381050458243112.366982733689
Trimmed Mean ( 7 / 20 )85.78086956521740.739644635007487115.9757882437
Trimmed Mean ( 8 / 20 )85.89613636363640.713780707281755120.339672237359
Trimmed Mean ( 9 / 20 )86.02690476190480.693818775611364123.990453683098
Trimmed Mean ( 10 / 20 )86.1770.672133056882227128.214196754052
Trimmed Mean ( 11 / 20 )86.34447368421050.642537167022629134.380512312325
Trimmed Mean ( 12 / 20 )86.52972222222220.600574260387389144.078306263755
Trimmed Mean ( 13 / 20 )86.73970588235290.539342949655393160.824770098087
Trimmed Mean ( 14 / 20 )86.98093750.444365341049012195.741948043617
Trimmed Mean ( 15 / 20 )87.18466666666670.346670446486909251.491488675135
Trimmed Mean ( 16 / 20 )87.27071428571430.306177546691885285.033031418
Trimmed Mean ( 17 / 20 )87.26461538461540.298858459305111291.99312473041
Trimmed Mean ( 18 / 20 )87.24750.29036474438645300.475528406028
Trimmed Mean ( 19 / 20 )87.22136363636360.281936942578855309.364792135989
Trimmed Mean ( 20 / 20 )87.17950.273466513874234318.794059151584
Median87.84
Midrange83.125
Midmean - Weighted Average at Xnp86.8867741935484
Midmean - Weighted Average at X(n+1)p87.1846666666667
Midmean - Empirical Distribution Function86.8867741935484
Midmean - Empirical Distribution Function - Averaging87.1846666666667
Midmean - Empirical Distribution Function - Interpolation87.1846666666667
Midmean - Closest Observation86.8867741935484
Midmean - True Basic - Statistics Graphics Toolkit87.1846666666667
Midmean - MS Excel (old versions)86.9809375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 85.155 & 0.81937979508136 & 103.926165266919 \tabularnewline
Geometric Mean & 84.9122049596294 &  &  \tabularnewline
Harmonic Mean & 84.6594561876878 &  &  \tabularnewline
Quadratic Mean & 85.3872685865209 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 85.1551666666667 & 0.819341215720153 & 103.931262132127 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 85.1551666666667 & 0.819341215720153 & 103.931262132127 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 85.1531666666667 & 0.819046762034529 & 103.966184366744 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 85.1511666666667 & 0.818753568730452 & 104.000971621658 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 85.1461666666667 & 0.818024425051702 & 104.087560296607 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 85.1401666666667 & 0.817155376372028 & 104.190915373608 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 85.1891666666667 & 0.803744425314481 & 105.990367066415 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 85.1638333333333 & 0.752772693675023 & 113.133531607749 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 85.1263333333333 & 0.730667714389533 & 116.504851188691 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 85.1163333333333 & 0.726683549536942 & 117.12984749355 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 85.1218333333333 & 0.725491592216373 & 117.32986880425 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 85.1018333333333 & 0.723147760243375 & 117.682495904699 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 85.0671666666667 & 0.7191509075137 & 118.288339454047 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 85.5548333333333 & 0.614089997437606 & 139.31969856263 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 86.5823333333333 & 0.40650372071227 & 212.992720415019 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 87.313 & 0.279119711878832 & 312.815599486945 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 87.381 & 0.267277834243631 & 326.929467410866 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 87.42 & 0.249959996799488 & 349.735962231294 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 87.4865 & 0.231458996258846 & 377.978395370565 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 87.4198333333333 & 0.221087897195329 & 395.407593279965 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 85.225 & 0.815787997871545 & 104.469543830454 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 85.2998214285714 & 0.810497982687004 & 105.243718369022 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 85.3801851851852 & 0.803055246053401 & 106.319192365388 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 85.4675 & 0.793049124361206 & 107.770751362778 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 85.5624 & 0.779763206338427 & 109.728696230462 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 85.6664583333333 & 0.762381050458243 & 112.366982733689 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 85.7808695652174 & 0.739644635007487 & 115.9757882437 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 85.8961363636364 & 0.713780707281755 & 120.339672237359 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 86.0269047619048 & 0.693818775611364 & 123.990453683098 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 86.177 & 0.672133056882227 & 128.214196754052 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 86.3444736842105 & 0.642537167022629 & 134.380512312325 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 86.5297222222222 & 0.600574260387389 & 144.078306263755 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 86.7397058823529 & 0.539342949655393 & 160.824770098087 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 86.9809375 & 0.444365341049012 & 195.741948043617 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 87.1846666666667 & 0.346670446486909 & 251.491488675135 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 87.2707142857143 & 0.306177546691885 & 285.033031418 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 87.2646153846154 & 0.298858459305111 & 291.99312473041 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 87.2475 & 0.29036474438645 & 300.475528406028 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 87.2213636363636 & 0.281936942578855 & 309.364792135989 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 87.1795 & 0.273466513874234 & 318.794059151584 \tabularnewline
Median & 87.84 &  &  \tabularnewline
Midrange & 83.125 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 86.8867741935484 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 87.1846666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 86.8867741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 87.1846666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 87.1846666666667 &  &  \tabularnewline
Midmean - Closest Observation & 86.8867741935484 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 87.1846666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 86.9809375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163572&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]85.155[/C][C]0.81937979508136[/C][C]103.926165266919[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]84.9122049596294[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]84.6594561876878[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]85.3872685865209[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]85.1551666666667[/C][C]0.819341215720153[/C][C]103.931262132127[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]85.1551666666667[/C][C]0.819341215720153[/C][C]103.931262132127[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]85.1531666666667[/C][C]0.819046762034529[/C][C]103.966184366744[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]85.1511666666667[/C][C]0.818753568730452[/C][C]104.000971621658[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]85.1461666666667[/C][C]0.818024425051702[/C][C]104.087560296607[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]85.1401666666667[/C][C]0.817155376372028[/C][C]104.190915373608[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]85.1891666666667[/C][C]0.803744425314481[/C][C]105.990367066415[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]85.1638333333333[/C][C]0.752772693675023[/C][C]113.133531607749[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]85.1263333333333[/C][C]0.730667714389533[/C][C]116.504851188691[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]85.1163333333333[/C][C]0.726683549536942[/C][C]117.12984749355[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]85.1218333333333[/C][C]0.725491592216373[/C][C]117.32986880425[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]85.1018333333333[/C][C]0.723147760243375[/C][C]117.682495904699[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]85.0671666666667[/C][C]0.7191509075137[/C][C]118.288339454047[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]85.5548333333333[/C][C]0.614089997437606[/C][C]139.31969856263[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]86.5823333333333[/C][C]0.40650372071227[/C][C]212.992720415019[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]87.313[/C][C]0.279119711878832[/C][C]312.815599486945[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]87.381[/C][C]0.267277834243631[/C][C]326.929467410866[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]87.42[/C][C]0.249959996799488[/C][C]349.735962231294[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]87.4865[/C][C]0.231458996258846[/C][C]377.978395370565[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]87.4198333333333[/C][C]0.221087897195329[/C][C]395.407593279965[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]85.225[/C][C]0.815787997871545[/C][C]104.469543830454[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]85.2998214285714[/C][C]0.810497982687004[/C][C]105.243718369022[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]85.3801851851852[/C][C]0.803055246053401[/C][C]106.319192365388[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]85.4675[/C][C]0.793049124361206[/C][C]107.770751362778[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]85.5624[/C][C]0.779763206338427[/C][C]109.728696230462[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]85.6664583333333[/C][C]0.762381050458243[/C][C]112.366982733689[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]85.7808695652174[/C][C]0.739644635007487[/C][C]115.9757882437[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]85.8961363636364[/C][C]0.713780707281755[/C][C]120.339672237359[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]86.0269047619048[/C][C]0.693818775611364[/C][C]123.990453683098[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]86.177[/C][C]0.672133056882227[/C][C]128.214196754052[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]86.3444736842105[/C][C]0.642537167022629[/C][C]134.380512312325[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]86.5297222222222[/C][C]0.600574260387389[/C][C]144.078306263755[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]86.7397058823529[/C][C]0.539342949655393[/C][C]160.824770098087[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]86.9809375[/C][C]0.444365341049012[/C][C]195.741948043617[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]87.1846666666667[/C][C]0.346670446486909[/C][C]251.491488675135[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]87.2707142857143[/C][C]0.306177546691885[/C][C]285.033031418[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]87.2646153846154[/C][C]0.298858459305111[/C][C]291.99312473041[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]87.2475[/C][C]0.29036474438645[/C][C]300.475528406028[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]87.2213636363636[/C][C]0.281936942578855[/C][C]309.364792135989[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]87.1795[/C][C]0.273466513874234[/C][C]318.794059151584[/C][/ROW]
[ROW][C]Median[/C][C]87.84[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]83.125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]86.8867741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]87.1846666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]86.8867741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]87.1846666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]87.1846666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]86.8867741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]87.1846666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]86.9809375[/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=163572&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163572&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 Mean85.1550.81937979508136103.926165266919
Geometric Mean84.9122049596294
Harmonic Mean84.6594561876878
Quadratic Mean85.3872685865209
Winsorized Mean ( 1 / 20 )85.15516666666670.819341215720153103.931262132127
Winsorized Mean ( 2 / 20 )85.15516666666670.819341215720153103.931262132127
Winsorized Mean ( 3 / 20 )85.15316666666670.819046762034529103.966184366744
Winsorized Mean ( 4 / 20 )85.15116666666670.818753568730452104.000971621658
Winsorized Mean ( 5 / 20 )85.14616666666670.818024425051702104.087560296607
Winsorized Mean ( 6 / 20 )85.14016666666670.817155376372028104.190915373608
Winsorized Mean ( 7 / 20 )85.18916666666670.803744425314481105.990367066415
Winsorized Mean ( 8 / 20 )85.16383333333330.752772693675023113.133531607749
Winsorized Mean ( 9 / 20 )85.12633333333330.730667714389533116.504851188691
Winsorized Mean ( 10 / 20 )85.11633333333330.726683549536942117.12984749355
Winsorized Mean ( 11 / 20 )85.12183333333330.725491592216373117.32986880425
Winsorized Mean ( 12 / 20 )85.10183333333330.723147760243375117.682495904699
Winsorized Mean ( 13 / 20 )85.06716666666670.7191509075137118.288339454047
Winsorized Mean ( 14 / 20 )85.55483333333330.614089997437606139.31969856263
Winsorized Mean ( 15 / 20 )86.58233333333330.40650372071227212.992720415019
Winsorized Mean ( 16 / 20 )87.3130.279119711878832312.815599486945
Winsorized Mean ( 17 / 20 )87.3810.267277834243631326.929467410866
Winsorized Mean ( 18 / 20 )87.420.249959996799488349.735962231294
Winsorized Mean ( 19 / 20 )87.48650.231458996258846377.978395370565
Winsorized Mean ( 20 / 20 )87.41983333333330.221087897195329395.407593279965
Trimmed Mean ( 1 / 20 )85.2250.815787997871545104.469543830454
Trimmed Mean ( 2 / 20 )85.29982142857140.810497982687004105.243718369022
Trimmed Mean ( 3 / 20 )85.38018518518520.803055246053401106.319192365388
Trimmed Mean ( 4 / 20 )85.46750.793049124361206107.770751362778
Trimmed Mean ( 5 / 20 )85.56240.779763206338427109.728696230462
Trimmed Mean ( 6 / 20 )85.66645833333330.762381050458243112.366982733689
Trimmed Mean ( 7 / 20 )85.78086956521740.739644635007487115.9757882437
Trimmed Mean ( 8 / 20 )85.89613636363640.713780707281755120.339672237359
Trimmed Mean ( 9 / 20 )86.02690476190480.693818775611364123.990453683098
Trimmed Mean ( 10 / 20 )86.1770.672133056882227128.214196754052
Trimmed Mean ( 11 / 20 )86.34447368421050.642537167022629134.380512312325
Trimmed Mean ( 12 / 20 )86.52972222222220.600574260387389144.078306263755
Trimmed Mean ( 13 / 20 )86.73970588235290.539342949655393160.824770098087
Trimmed Mean ( 14 / 20 )86.98093750.444365341049012195.741948043617
Trimmed Mean ( 15 / 20 )87.18466666666670.346670446486909251.491488675135
Trimmed Mean ( 16 / 20 )87.27071428571430.306177546691885285.033031418
Trimmed Mean ( 17 / 20 )87.26461538461540.298858459305111291.99312473041
Trimmed Mean ( 18 / 20 )87.24750.29036474438645300.475528406028
Trimmed Mean ( 19 / 20 )87.22136363636360.281936942578855309.364792135989
Trimmed Mean ( 20 / 20 )87.17950.273466513874234318.794059151584
Median87.84
Midrange83.125
Midmean - Weighted Average at Xnp86.8867741935484
Midmean - Weighted Average at X(n+1)p87.1846666666667
Midmean - Empirical Distribution Function86.8867741935484
Midmean - Empirical Distribution Function - Averaging87.1846666666667
Midmean - Empirical Distribution Function - Interpolation87.1846666666667
Midmean - Closest Observation86.8867741935484
Midmean - True Basic - Statistics Graphics Toolkit87.1846666666667
Midmean - MS Excel (old versions)86.9809375
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')