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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 05 Mar 2012 18:46:16 -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/05/t1330991331poflt9a9mrgfnyp.htm/, Retrieved Thu, 02 May 2024 22:04:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163506, Retrieved Thu, 02 May 2024 22:04:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robuustheid bepal...] [2012-03-05 23:46:16] [7b0d021f0a275c50b786c74a5009310f] [Current]
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Dataseries X:
369,82
373,1
374,55
375,01
374,81
375,31
375,31
375,39
375,59
376,26
377,18
377,26
377,26
381,87
387,09
387,14
388,78
389,16
389,16
389,42
389,49
388,97
388,97
389,09
389,09
391,76
390,96
391,76
392,8
393,06
393,06
393,26
393,87
394,47
394,57
394,57
394,57
399,57
406,13
407,03
409,46
409,9
409,9
410,14
410,54
410,69
410,79
410,97
410,97
413,8
423,31
423,85
426,6
426,26
426,26
426,32
427,14
427,55
428,29
428,8




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=163506&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=163506&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163506&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 Mean397.3012.26755084159298175.21150693181
Geometric Mean396.922883799593
Harmonic Mean396.548615649849
Quadratic Mean397.68259959839
Winsorized Mean ( 1 / 20 )397.3471666666672.2549638664682176.209992796472
Winsorized Mean ( 2 / 20 )397.3708333333332.24070294271581177.3420410881
Winsorized Mean ( 3 / 20 )397.3633333333332.23381285433074177.88568660215
Winsorized Mean ( 4 / 20 )397.3406666666672.22345555953687178.704118893849
Winsorized Mean ( 5 / 20 )397.3423333333332.21402916917519179.46571746449
Winsorized Mean ( 6 / 20 )397.3363333333332.21269900591385179.570891599526
Winsorized Mean ( 7 / 20 )397.3456666666672.21112624837488179.702840106351
Winsorized Mean ( 8 / 20 )397.0512.13682541739066185.813495463214
Winsorized Mean ( 9 / 20 )397.07052.10266555909156188.841491355169
Winsorized Mean ( 10 / 20 )395.6388333333331.76814846328858223.758831086777
Winsorized Mean ( 11 / 20 )395.1346666666671.67879689343774235.367761407715
Winsorized Mean ( 12 / 20 )395.1346666666671.67879689343774235.367761407715
Winsorized Mean ( 13 / 20 )396.09451.50158538487796263.784200345152
Winsorized Mean ( 14 / 20 )397.2891666666671.31887955982133301.232332936063
Winsorized Mean ( 15 / 20 )397.2641666666671.31079441327749303.071299848886
Winsorized Mean ( 16 / 20 )397.5948333333331.23738270554472321.319209935381
Winsorized Mean ( 17 / 20 )397.5806666666671.21924527147537326.087519851986
Winsorized Mean ( 18 / 20 )397.5806666666671.21924527147537326.087519851986
Winsorized Mean ( 19 / 20 )397.4793333333331.19089186696137333.766099475955
Winsorized Mean ( 20 / 20 )396.6693333333331.05427863432526376.247151766671
Trimmed Mean ( 1 / 20 )397.2317241379312.23093893105379178.055848418181
Trimmed Mean ( 2 / 20 )397.1080357142862.19994401374516180.508246224981
Trimmed Mean ( 3 / 20 )396.9620370370372.16942350622928182.980425858391
Trimmed Mean ( 4 / 20 )396.8076923076922.13311277403257186.022838144437
Trimmed Mean ( 5 / 20 )396.64782.09011784239598189.772936221293
Trimmed Mean ( 6 / 20 )396.4741666666672.03753166083684194.585524380922
Trimmed Mean ( 7 / 20 )396.2867391304351.96946862679192201.215055543153
Trimmed Mean ( 8 / 20 )396.0804545454551.88071713174947210.600758539916
Trimmed Mean ( 9 / 20 )395.9071428571431.78715241045027221.529591176499
Trimmed Mean ( 10 / 20 )395.713251.67207242771527236.660352411112
Trimmed Mean ( 11 / 20 )395.7251.62021189761467244.242744163649
Trimmed Mean ( 12 / 20 )395.8144444444441.57288973994963251.647928262995
Trimmed Mean ( 13 / 20 )395.9144117647061.50546225845018262.985278802198
Trimmed Mean ( 14 / 20 )395.88843751.4633869043178270.528891800187
Trimmed Mean ( 15 / 20 )395.6883333333331.44900648351622273.075612728206
Trimmed Mean ( 16 / 20 )395.4632142857141.4233522036565277.839324146051
Trimmed Mean ( 17 / 20 )395.1557692307691.39729036386384282.801470224177
Trimmed Mean ( 18 / 20 )394.7991666666671.35291230644754291.814306651793
Trimmed Mean ( 19 / 20 )394.3777272727271.26938934970064310.683028312577
Trimmed Mean ( 20 / 20 )393.8881.12882300136959348.93690111036
Median393.06
Midrange399.31
Midmean - Weighted Average at Xnp395.410967741935
Midmean - Weighted Average at X(n+1)p395.688333333333
Midmean - Empirical Distribution Function395.410967741935
Midmean - Empirical Distribution Function - Averaging395.688333333333
Midmean - Empirical Distribution Function - Interpolation395.688333333333
Midmean - Closest Observation395.410967741935
Midmean - True Basic - Statistics Graphics Toolkit395.688333333333
Midmean - MS Excel (old versions)395.8884375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 397.301 & 2.26755084159298 & 175.21150693181 \tabularnewline
Geometric Mean & 396.922883799593 &  &  \tabularnewline
Harmonic Mean & 396.548615649849 &  &  \tabularnewline
Quadratic Mean & 397.68259959839 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 397.347166666667 & 2.2549638664682 & 176.209992796472 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 397.370833333333 & 2.24070294271581 & 177.3420410881 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 397.363333333333 & 2.23381285433074 & 177.88568660215 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 397.340666666667 & 2.22345555953687 & 178.704118893849 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 397.342333333333 & 2.21402916917519 & 179.46571746449 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 397.336333333333 & 2.21269900591385 & 179.570891599526 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 397.345666666667 & 2.21112624837488 & 179.702840106351 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 397.051 & 2.13682541739066 & 185.813495463214 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 397.0705 & 2.10266555909156 & 188.841491355169 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 395.638833333333 & 1.76814846328858 & 223.758831086777 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 395.134666666667 & 1.67879689343774 & 235.367761407715 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 395.134666666667 & 1.67879689343774 & 235.367761407715 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 396.0945 & 1.50158538487796 & 263.784200345152 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 397.289166666667 & 1.31887955982133 & 301.232332936063 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 397.264166666667 & 1.31079441327749 & 303.071299848886 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 397.594833333333 & 1.23738270554472 & 321.319209935381 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 397.580666666667 & 1.21924527147537 & 326.087519851986 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 397.580666666667 & 1.21924527147537 & 326.087519851986 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 397.479333333333 & 1.19089186696137 & 333.766099475955 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 396.669333333333 & 1.05427863432526 & 376.247151766671 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 397.231724137931 & 2.23093893105379 & 178.055848418181 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 397.108035714286 & 2.19994401374516 & 180.508246224981 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 396.962037037037 & 2.16942350622928 & 182.980425858391 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 396.807692307692 & 2.13311277403257 & 186.022838144437 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 396.6478 & 2.09011784239598 & 189.772936221293 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 396.474166666667 & 2.03753166083684 & 194.585524380922 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 396.286739130435 & 1.96946862679192 & 201.215055543153 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 396.080454545455 & 1.88071713174947 & 210.600758539916 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 395.907142857143 & 1.78715241045027 & 221.529591176499 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 395.71325 & 1.67207242771527 & 236.660352411112 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 395.725 & 1.62021189761467 & 244.242744163649 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 395.814444444444 & 1.57288973994963 & 251.647928262995 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 395.914411764706 & 1.50546225845018 & 262.985278802198 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 395.8884375 & 1.4633869043178 & 270.528891800187 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 395.688333333333 & 1.44900648351622 & 273.075612728206 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 395.463214285714 & 1.4233522036565 & 277.839324146051 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 395.155769230769 & 1.39729036386384 & 282.801470224177 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 394.799166666667 & 1.35291230644754 & 291.814306651793 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 394.377727272727 & 1.26938934970064 & 310.683028312577 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 393.888 & 1.12882300136959 & 348.93690111036 \tabularnewline
Median & 393.06 &  &  \tabularnewline
Midrange & 399.31 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 395.410967741935 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 395.688333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 395.410967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 395.688333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 395.688333333333 &  &  \tabularnewline
Midmean - Closest Observation & 395.410967741935 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 395.688333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 395.8884375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163506&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]397.301[/C][C]2.26755084159298[/C][C]175.21150693181[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]396.922883799593[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]396.548615649849[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]397.68259959839[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]397.347166666667[/C][C]2.2549638664682[/C][C]176.209992796472[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]397.370833333333[/C][C]2.24070294271581[/C][C]177.3420410881[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]397.363333333333[/C][C]2.23381285433074[/C][C]177.88568660215[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]397.340666666667[/C][C]2.22345555953687[/C][C]178.704118893849[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]397.342333333333[/C][C]2.21402916917519[/C][C]179.46571746449[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]397.336333333333[/C][C]2.21269900591385[/C][C]179.570891599526[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]397.345666666667[/C][C]2.21112624837488[/C][C]179.702840106351[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]397.051[/C][C]2.13682541739066[/C][C]185.813495463214[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]397.0705[/C][C]2.10266555909156[/C][C]188.841491355169[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]395.638833333333[/C][C]1.76814846328858[/C][C]223.758831086777[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]395.134666666667[/C][C]1.67879689343774[/C][C]235.367761407715[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]395.134666666667[/C][C]1.67879689343774[/C][C]235.367761407715[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]396.0945[/C][C]1.50158538487796[/C][C]263.784200345152[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]397.289166666667[/C][C]1.31887955982133[/C][C]301.232332936063[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]397.264166666667[/C][C]1.31079441327749[/C][C]303.071299848886[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]397.594833333333[/C][C]1.23738270554472[/C][C]321.319209935381[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]397.580666666667[/C][C]1.21924527147537[/C][C]326.087519851986[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]397.580666666667[/C][C]1.21924527147537[/C][C]326.087519851986[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]397.479333333333[/C][C]1.19089186696137[/C][C]333.766099475955[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]396.669333333333[/C][C]1.05427863432526[/C][C]376.247151766671[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]397.231724137931[/C][C]2.23093893105379[/C][C]178.055848418181[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]397.108035714286[/C][C]2.19994401374516[/C][C]180.508246224981[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]396.962037037037[/C][C]2.16942350622928[/C][C]182.980425858391[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]396.807692307692[/C][C]2.13311277403257[/C][C]186.022838144437[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]396.6478[/C][C]2.09011784239598[/C][C]189.772936221293[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]396.474166666667[/C][C]2.03753166083684[/C][C]194.585524380922[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]396.286739130435[/C][C]1.96946862679192[/C][C]201.215055543153[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]396.080454545455[/C][C]1.88071713174947[/C][C]210.600758539916[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]395.907142857143[/C][C]1.78715241045027[/C][C]221.529591176499[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]395.71325[/C][C]1.67207242771527[/C][C]236.660352411112[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]395.725[/C][C]1.62021189761467[/C][C]244.242744163649[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]395.814444444444[/C][C]1.57288973994963[/C][C]251.647928262995[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]395.914411764706[/C][C]1.50546225845018[/C][C]262.985278802198[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]395.8884375[/C][C]1.4633869043178[/C][C]270.528891800187[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]395.688333333333[/C][C]1.44900648351622[/C][C]273.075612728206[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]395.463214285714[/C][C]1.4233522036565[/C][C]277.839324146051[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]395.155769230769[/C][C]1.39729036386384[/C][C]282.801470224177[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]394.799166666667[/C][C]1.35291230644754[/C][C]291.814306651793[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]394.377727272727[/C][C]1.26938934970064[/C][C]310.683028312577[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]393.888[/C][C]1.12882300136959[/C][C]348.93690111036[/C][/ROW]
[ROW][C]Median[/C][C]393.06[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]399.31[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]395.410967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]395.688333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]395.410967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]395.688333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]395.688333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]395.410967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]395.688333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]395.8884375[/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=163506&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163506&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 Mean397.3012.26755084159298175.21150693181
Geometric Mean396.922883799593
Harmonic Mean396.548615649849
Quadratic Mean397.68259959839
Winsorized Mean ( 1 / 20 )397.3471666666672.2549638664682176.209992796472
Winsorized Mean ( 2 / 20 )397.3708333333332.24070294271581177.3420410881
Winsorized Mean ( 3 / 20 )397.3633333333332.23381285433074177.88568660215
Winsorized Mean ( 4 / 20 )397.3406666666672.22345555953687178.704118893849
Winsorized Mean ( 5 / 20 )397.3423333333332.21402916917519179.46571746449
Winsorized Mean ( 6 / 20 )397.3363333333332.21269900591385179.570891599526
Winsorized Mean ( 7 / 20 )397.3456666666672.21112624837488179.702840106351
Winsorized Mean ( 8 / 20 )397.0512.13682541739066185.813495463214
Winsorized Mean ( 9 / 20 )397.07052.10266555909156188.841491355169
Winsorized Mean ( 10 / 20 )395.6388333333331.76814846328858223.758831086777
Winsorized Mean ( 11 / 20 )395.1346666666671.67879689343774235.367761407715
Winsorized Mean ( 12 / 20 )395.1346666666671.67879689343774235.367761407715
Winsorized Mean ( 13 / 20 )396.09451.50158538487796263.784200345152
Winsorized Mean ( 14 / 20 )397.2891666666671.31887955982133301.232332936063
Winsorized Mean ( 15 / 20 )397.2641666666671.31079441327749303.071299848886
Winsorized Mean ( 16 / 20 )397.5948333333331.23738270554472321.319209935381
Winsorized Mean ( 17 / 20 )397.5806666666671.21924527147537326.087519851986
Winsorized Mean ( 18 / 20 )397.5806666666671.21924527147537326.087519851986
Winsorized Mean ( 19 / 20 )397.4793333333331.19089186696137333.766099475955
Winsorized Mean ( 20 / 20 )396.6693333333331.05427863432526376.247151766671
Trimmed Mean ( 1 / 20 )397.2317241379312.23093893105379178.055848418181
Trimmed Mean ( 2 / 20 )397.1080357142862.19994401374516180.508246224981
Trimmed Mean ( 3 / 20 )396.9620370370372.16942350622928182.980425858391
Trimmed Mean ( 4 / 20 )396.8076923076922.13311277403257186.022838144437
Trimmed Mean ( 5 / 20 )396.64782.09011784239598189.772936221293
Trimmed Mean ( 6 / 20 )396.4741666666672.03753166083684194.585524380922
Trimmed Mean ( 7 / 20 )396.2867391304351.96946862679192201.215055543153
Trimmed Mean ( 8 / 20 )396.0804545454551.88071713174947210.600758539916
Trimmed Mean ( 9 / 20 )395.9071428571431.78715241045027221.529591176499
Trimmed Mean ( 10 / 20 )395.713251.67207242771527236.660352411112
Trimmed Mean ( 11 / 20 )395.7251.62021189761467244.242744163649
Trimmed Mean ( 12 / 20 )395.8144444444441.57288973994963251.647928262995
Trimmed Mean ( 13 / 20 )395.9144117647061.50546225845018262.985278802198
Trimmed Mean ( 14 / 20 )395.88843751.4633869043178270.528891800187
Trimmed Mean ( 15 / 20 )395.6883333333331.44900648351622273.075612728206
Trimmed Mean ( 16 / 20 )395.4632142857141.4233522036565277.839324146051
Trimmed Mean ( 17 / 20 )395.1557692307691.39729036386384282.801470224177
Trimmed Mean ( 18 / 20 )394.7991666666671.35291230644754291.814306651793
Trimmed Mean ( 19 / 20 )394.3777272727271.26938934970064310.683028312577
Trimmed Mean ( 20 / 20 )393.8881.12882300136959348.93690111036
Median393.06
Midrange399.31
Midmean - Weighted Average at Xnp395.410967741935
Midmean - Weighted Average at X(n+1)p395.688333333333
Midmean - Empirical Distribution Function395.410967741935
Midmean - Empirical Distribution Function - Averaging395.688333333333
Midmean - Empirical Distribution Function - Interpolation395.688333333333
Midmean - Closest Observation395.410967741935
Midmean - True Basic - Statistics Graphics Toolkit395.688333333333
Midmean - MS Excel (old versions)395.8884375
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')