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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 computationWed, 30 Dec 2009 10:38:16 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/30/t1262194741eqnb1eufyem8cdj.htm/, Retrieved Mon, 29 Apr 2024 05:56:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71337, Retrieved Mon, 29 Apr 2024 05:56:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [arima backward se...] [2008-12-17 10:56:10] [11edab5c4db3615abbf782b1c6e7cacf]
- RMPD  [Central Tendency] [central tendency ...] [2008-12-23 10:31:31] [74be16979710d4c4e7c6647856088456]
- RMPD    [ARIMA Forecasting] [paper arima forec...] [2009-12-30 15:31:43] [db72903d7941c8279d5ce0e4e873d517]
- RMPD        [Central Tendency] [paper robustnessc...] [2009-12-30 17:38:16] [90d336e5f53609c0c5a6217e988a780d] [Current]
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Dataseries X:
4.73340311691683 
-131.627803300321 
98.171435767387 
51.2018527275281 
589.771817500419 
383.947803419080 
-146.085428835697 
-261.407407211733 
226.504028975978 
649.805080858438 
-233.615418468216 
161.172888695564 
264.618555619178 
375.758030724546 
-159.037440097016 
309.946708427587 
-704.224708912839 
260.661713393615 
-606.265665321482 
383.71498765789 
135.657607017376 
-122.074556052411 
349.727017653986 
266.989691028707 
-419.171317869569 
328.533766080892 
417.125477506274 
408.464454323018 
-121.90623714687 
-272.48450632376 
59.6987914932272 
808.976152082131 
303.777905081449 
494.425825689603 
-69.5533824749021 
166.534648047124 
-458.996604651524 
28.5701232943685 
-299.759681487742 
-839.557785242867 
1179.10237804785 
210.377414453306 
-198.458660744812 
-22.1927126909486 
-471.176610797859 
118.767607948217 
-0.958960805112838 
-1119.60848652358 
-571.694119236914 
-482.685409414204 




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=71337&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=71337&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71337&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 Mean26.483885260425560.75273916724260.435929072885416
Geometric MeanNaN
Harmonic Mean-62.3887670177612
Quadratic Mean426.093025850359
Winsorized Mean ( 1 / 16 )24.682374766725456.28932715415480.438491202766199
Winsorized Mean ( 2 / 16 )23.728854970978853.00313160981650.447687792216867
Winsorized Mean ( 3 / 16 )26.004401784979150.58367121841970.514086881371112
Winsorized Mean ( 4 / 16 )21.142446126879248.25063910748770.438179607938048
Winsorized Mean ( 5 / 16 )22.313282290817344.62908028293590.499971815447626
Winsorized Mean ( 6 / 16 )22.655015342788044.12533800575950.513424176826271
Winsorized Mean ( 7 / 16 )20.927885076723643.13589044358940.485161772749119
Winsorized Mean ( 8 / 16 )27.26268044004641.70962490254740.653630439107135
Winsorized Mean ( 9 / 16 )47.32452274077337.03502565721831.27783150952264
Winsorized Mean ( 10 / 16 )47.573355159457335.07595700483041.35629528662343
Winsorized Mean ( 11 / 16 )45.347801618022633.81496490538461.34105718414635
Winsorized Mean ( 12 / 16 )47.556985079673531.83947712701351.49364843178674
Winsorized Mean ( 13 / 16 )55.093853217762629.9545120465571.83925056539504
Winsorized Mean ( 14 / 16 )55.831095064377826.36450203244812.11766165716552
Winsorized Mean ( 15 / 16 )59.005357819914725.60731692968222.30423819808782
Winsorized Mean ( 16 / 16 )62.365608479054924.64988903654092.53005635792536
Trimmed Mean ( 1 / 16 )26.347924406187653.26500855283490.494657282933738
Trimmed Mean ( 2 / 16 )28.158304449081449.33463138944420.570761423690422
Trimmed Mean ( 3 / 16 )30.675037107094246.63676398294160.657743687326037
Trimmed Mean ( 4 / 16 )32.528463822219244.41286792467690.7324107931374
Trimmed Mean ( 5 / 16 )36.086594352012942.49969359865610.84910245925053
Trimmed Mean ( 6 / 16 )39.711150157590741.34040700669080.960589240235676
Trimmed Mean ( 7 / 16 )43.659329512869139.89419191947831.09437808894564
Trimmed Mean ( 8 / 16 )48.434843049874538.18654406916551.26837461285176
Trimmed Mean ( 9 / 16 )52.570031059606636.26318642173091.44968041275335
Trimmed Mean ( 10 / 16 )53.541421489020235.16600243131641.52253363439855
Trimmed Mean ( 11 / 16 )54.607147619299334.15326697919961.59888503938896
Trimmed Mean ( 12 / 16 )56.225914402739332.97700331970851.70500375239178
Trimmed Mean ( 13 / 16 )57.730936854660531.80634292039461.81507622549220
Trimmed Mean ( 14 / 16 )58.191965462509730.58768843270641.90246365267298
Trimmed Mean ( 15 / 16 )58.613549462176229.97637790812531.95532461065913
Trimmed Mean ( 16 / 16 )58.540992358891228.98736479910782.01953481334368
Median55.4503221103776
Midrange29.7469457621349
Midmean - Weighted Average at Xnp46.0770826417454
Midmean - Weighted Average at X(n+1)p56.2259144027393
Midmean - Empirical Distribution Function56.2259144027393
Midmean - Empirical Distribution Function - Averaging56.2259144027393
Midmean - Empirical Distribution Function - Interpolation57.7309368546605
Midmean - Closest Observation56.2259144027393
Midmean - True Basic - Statistics Graphics Toolkit56.2259144027393
Midmean - MS Excel (old versions)56.2259144027393
Number of observations50

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 26.4838852604255 & 60.7527391672426 & 0.435929072885416 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -62.3887670177612 &  &  \tabularnewline
Quadratic Mean & 426.093025850359 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 24.6823747667254 & 56.2893271541548 & 0.438491202766199 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 23.7288549709788 & 53.0031316098165 & 0.447687792216867 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 26.0044017849791 & 50.5836712184197 & 0.514086881371112 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 21.1424461268792 & 48.2506391074877 & 0.438179607938048 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 22.3132822908173 & 44.6290802829359 & 0.499971815447626 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 22.6550153427880 & 44.1253380057595 & 0.513424176826271 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 20.9278850767236 & 43.1358904435894 & 0.485161772749119 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 27.262680440046 & 41.7096249025474 & 0.653630439107135 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 47.324522740773 & 37.0350256572183 & 1.27783150952264 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 47.5733551594573 & 35.0759570048304 & 1.35629528662343 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 45.3478016180226 & 33.8149649053846 & 1.34105718414635 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 47.5569850796735 & 31.8394771270135 & 1.49364843178674 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 55.0938532177626 & 29.954512046557 & 1.83925056539504 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 55.8310950643778 & 26.3645020324481 & 2.11766165716552 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 59.0053578199147 & 25.6073169296822 & 2.30423819808782 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 62.3656084790549 & 24.6498890365409 & 2.53005635792536 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 26.3479244061876 & 53.2650085528349 & 0.494657282933738 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 28.1583044490814 & 49.3346313894442 & 0.570761423690422 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 30.6750371070942 & 46.6367639829416 & 0.657743687326037 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 32.5284638222192 & 44.4128679246769 & 0.7324107931374 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 36.0865943520129 & 42.4996935986561 & 0.84910245925053 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 39.7111501575907 & 41.3404070066908 & 0.960589240235676 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 43.6593295128691 & 39.8941919194783 & 1.09437808894564 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 48.4348430498745 & 38.1865440691655 & 1.26837461285176 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 52.5700310596066 & 36.2631864217309 & 1.44968041275335 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 53.5414214890202 & 35.1660024313164 & 1.52253363439855 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 54.6071476192993 & 34.1532669791996 & 1.59888503938896 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 56.2259144027393 & 32.9770033197085 & 1.70500375239178 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 57.7309368546605 & 31.8063429203946 & 1.81507622549220 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 58.1919654625097 & 30.5876884327064 & 1.90246365267298 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 58.6135494621762 & 29.9763779081253 & 1.95532461065913 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 58.5409923588912 & 28.9873647991078 & 2.01953481334368 \tabularnewline
Median & 55.4503221103776 &  &  \tabularnewline
Midrange & 29.7469457621349 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 46.0770826417454 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 56.2259144027393 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 56.2259144027393 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 56.2259144027393 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 57.7309368546605 &  &  \tabularnewline
Midmean - Closest Observation & 56.2259144027393 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 56.2259144027393 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 56.2259144027393 &  &  \tabularnewline
Number of observations & 50 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71337&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]26.4838852604255[/C][C]60.7527391672426[/C][C]0.435929072885416[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-62.3887670177612[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]426.093025850359[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]24.6823747667254[/C][C]56.2893271541548[/C][C]0.438491202766199[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]23.7288549709788[/C][C]53.0031316098165[/C][C]0.447687792216867[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]26.0044017849791[/C][C]50.5836712184197[/C][C]0.514086881371112[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]21.1424461268792[/C][C]48.2506391074877[/C][C]0.438179607938048[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]22.3132822908173[/C][C]44.6290802829359[/C][C]0.499971815447626[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]22.6550153427880[/C][C]44.1253380057595[/C][C]0.513424176826271[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]20.9278850767236[/C][C]43.1358904435894[/C][C]0.485161772749119[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]27.262680440046[/C][C]41.7096249025474[/C][C]0.653630439107135[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]47.324522740773[/C][C]37.0350256572183[/C][C]1.27783150952264[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]47.5733551594573[/C][C]35.0759570048304[/C][C]1.35629528662343[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]45.3478016180226[/C][C]33.8149649053846[/C][C]1.34105718414635[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]47.5569850796735[/C][C]31.8394771270135[/C][C]1.49364843178674[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]55.0938532177626[/C][C]29.954512046557[/C][C]1.83925056539504[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]55.8310950643778[/C][C]26.3645020324481[/C][C]2.11766165716552[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]59.0053578199147[/C][C]25.6073169296822[/C][C]2.30423819808782[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]62.3656084790549[/C][C]24.6498890365409[/C][C]2.53005635792536[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]26.3479244061876[/C][C]53.2650085528349[/C][C]0.494657282933738[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]28.1583044490814[/C][C]49.3346313894442[/C][C]0.570761423690422[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]30.6750371070942[/C][C]46.6367639829416[/C][C]0.657743687326037[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]32.5284638222192[/C][C]44.4128679246769[/C][C]0.7324107931374[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]36.0865943520129[/C][C]42.4996935986561[/C][C]0.84910245925053[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]39.7111501575907[/C][C]41.3404070066908[/C][C]0.960589240235676[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]43.6593295128691[/C][C]39.8941919194783[/C][C]1.09437808894564[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]48.4348430498745[/C][C]38.1865440691655[/C][C]1.26837461285176[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]52.5700310596066[/C][C]36.2631864217309[/C][C]1.44968041275335[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]53.5414214890202[/C][C]35.1660024313164[/C][C]1.52253363439855[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]54.6071476192993[/C][C]34.1532669791996[/C][C]1.59888503938896[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]56.2259144027393[/C][C]32.9770033197085[/C][C]1.70500375239178[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]57.7309368546605[/C][C]31.8063429203946[/C][C]1.81507622549220[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]58.1919654625097[/C][C]30.5876884327064[/C][C]1.90246365267298[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]58.6135494621762[/C][C]29.9763779081253[/C][C]1.95532461065913[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]58.5409923588912[/C][C]28.9873647991078[/C][C]2.01953481334368[/C][/ROW]
[ROW][C]Median[/C][C]55.4503221103776[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]29.7469457621349[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]46.0770826417454[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]56.2259144027393[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]56.2259144027393[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]56.2259144027393[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]57.7309368546605[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]56.2259144027393[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]56.2259144027393[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]56.2259144027393[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]50[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71337&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71337&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 Mean26.483885260425560.75273916724260.435929072885416
Geometric MeanNaN
Harmonic Mean-62.3887670177612
Quadratic Mean426.093025850359
Winsorized Mean ( 1 / 16 )24.682374766725456.28932715415480.438491202766199
Winsorized Mean ( 2 / 16 )23.728854970978853.00313160981650.447687792216867
Winsorized Mean ( 3 / 16 )26.004401784979150.58367121841970.514086881371112
Winsorized Mean ( 4 / 16 )21.142446126879248.25063910748770.438179607938048
Winsorized Mean ( 5 / 16 )22.313282290817344.62908028293590.499971815447626
Winsorized Mean ( 6 / 16 )22.655015342788044.12533800575950.513424176826271
Winsorized Mean ( 7 / 16 )20.927885076723643.13589044358940.485161772749119
Winsorized Mean ( 8 / 16 )27.26268044004641.70962490254740.653630439107135
Winsorized Mean ( 9 / 16 )47.32452274077337.03502565721831.27783150952264
Winsorized Mean ( 10 / 16 )47.573355159457335.07595700483041.35629528662343
Winsorized Mean ( 11 / 16 )45.347801618022633.81496490538461.34105718414635
Winsorized Mean ( 12 / 16 )47.556985079673531.83947712701351.49364843178674
Winsorized Mean ( 13 / 16 )55.093853217762629.9545120465571.83925056539504
Winsorized Mean ( 14 / 16 )55.831095064377826.36450203244812.11766165716552
Winsorized Mean ( 15 / 16 )59.005357819914725.60731692968222.30423819808782
Winsorized Mean ( 16 / 16 )62.365608479054924.64988903654092.53005635792536
Trimmed Mean ( 1 / 16 )26.347924406187653.26500855283490.494657282933738
Trimmed Mean ( 2 / 16 )28.158304449081449.33463138944420.570761423690422
Trimmed Mean ( 3 / 16 )30.675037107094246.63676398294160.657743687326037
Trimmed Mean ( 4 / 16 )32.528463822219244.41286792467690.7324107931374
Trimmed Mean ( 5 / 16 )36.086594352012942.49969359865610.84910245925053
Trimmed Mean ( 6 / 16 )39.711150157590741.34040700669080.960589240235676
Trimmed Mean ( 7 / 16 )43.659329512869139.89419191947831.09437808894564
Trimmed Mean ( 8 / 16 )48.434843049874538.18654406916551.26837461285176
Trimmed Mean ( 9 / 16 )52.570031059606636.26318642173091.44968041275335
Trimmed Mean ( 10 / 16 )53.541421489020235.16600243131641.52253363439855
Trimmed Mean ( 11 / 16 )54.607147619299334.15326697919961.59888503938896
Trimmed Mean ( 12 / 16 )56.225914402739332.97700331970851.70500375239178
Trimmed Mean ( 13 / 16 )57.730936854660531.80634292039461.81507622549220
Trimmed Mean ( 14 / 16 )58.191965462509730.58768843270641.90246365267298
Trimmed Mean ( 15 / 16 )58.613549462176229.97637790812531.95532461065913
Trimmed Mean ( 16 / 16 )58.540992358891228.98736479910782.01953481334368
Median55.4503221103776
Midrange29.7469457621349
Midmean - Weighted Average at Xnp46.0770826417454
Midmean - Weighted Average at X(n+1)p56.2259144027393
Midmean - Empirical Distribution Function56.2259144027393
Midmean - Empirical Distribution Function - Averaging56.2259144027393
Midmean - Empirical Distribution Function - Interpolation57.7309368546605
Midmean - Closest Observation56.2259144027393
Midmean - True Basic - Statistics Graphics Toolkit56.2259144027393
Midmean - MS Excel (old versions)56.2259144027393
Number of observations50



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')