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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 03 Dec 2007 10:14:03 -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/2007/Dec/03/t1196701366j1z8w3rs4tzdy14.htm/, Retrieved Fri, 03 May 2024 22:56:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2346, Retrieved Fri, 03 May 2024 22:56:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact195
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [q1 - oef 9] [2007-12-03 17:14:03] [6bdd947de0ee04552c8f0fc807f31807] [Current]
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Dataseries X:
10.9846622141056 
432.907328441546 
107.043170430094 
-310.718340613830 
-563.066680162026 
-821.88221024375 
304.409150311039 
222.739102478217 
-153.617567620326 
117.903300209547 
263.985770460607 
137.436428442010 
118.639481312424 
-380.133330845621 
135.687022465525 
1101.94387046273 
282.984862022675 
-277.656619420353 
1213.63229289218 
-205.937519696414 
837.416857980847 
70.1576377968922 
-457.026488841564 
285.390734606293 
633.253313527115 
-24.3105989163414 
-361.404686409927 
-59.5061904717804 
439.442498115066 
576.516427060546 
-682.949120465639 
-727.451380194614 
134.705463012109 
768.15499178165 
-584.071129605762 
967.307222238165 
516.449625765914 
1055.90052753478 
-189.924399550924 
920.784714361121 
-1400.11827739204 
787.658453797334 
-365.585953900272 
446.272932939253 
-211.579722277853 
-488.398843808552 
667.771097626739 
-565.189276526768 
-1909.29498007315 
-213.161114599616 
379.222878002443 
-508.45398793519 
1441.35142606928 
1235.12491915561 
800.229725020592 
935.058799094239 




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2346&T=0

[TABLE]
[ROW][C]Summary of compuational 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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2346&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2346&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean122.98264764386488.54937072175861.38885964565804
Geometric MeanNaN
Harmonic Mean657.929935446472
Quadratic Mean668.116187244826
Winsorized Mean ( 1 / 18 )128.39247256828284.20187131684931.52481732959527
Winsorized Mean ( 2 / 18 )148.27616688559978.2396684526921.89515331312089
Winsorized Mean ( 3 / 18 )147.35165300808275.71000416953071.94626396635946
Winsorized Mean ( 4 / 18 )147.24157563672774.31048637620581.98143738275778
Winsorized Mean ( 5 / 18 )148.15985113344670.87143811452412.0905438788194
Winsorized Mean ( 6 / 18 )146.72771862648969.77575879912162.10284662111531
Winsorized Mean ( 7 / 18 )145.20878258044269.36188091322692.09349545699462
Winsorized Mean ( 8 / 18 )141.10090198709465.57238310462032.15183428306958
Winsorized Mean ( 9 / 18 )138.34754663883463.8541768241812.16661702522243
Winsorized Mean ( 10 / 18 )141.70488302164362.44317768329582.26934131604181
Winsorized Mean ( 11 / 18 )152.97785901776659.1648652759472.58562000106434
Winsorized Mean ( 12 / 18 )134.58431961571754.7063502021172.46012243767833
Winsorized Mean ( 13 / 18 )127.54191397427753.14103420242352.40006458076159
Winsorized Mean ( 14 / 18 )126.02927880665948.62198846807962.59202230878314
Winsorized Mean ( 15 / 18 )118.79577520813544.51775859594232.66850306383042
Winsorized Mean ( 16 / 18 )117.17257863501438.38470966039813.05258473156832
Winsorized Mean ( 17 / 18 )115.57911930392137.98723480159393.04257785299686
Winsorized Mean ( 18 / 18 )115.29209416718137.37847509590133.08445151578222
Trimmed Mean ( 1 / 18 )136.20318189000579.90334308008381.70459929008845
Trimmed Mean ( 2 / 18 )144.61471500570574.4537011543141.94234420537368
Trimmed Mean ( 3 / 18 )142.56430195296571.78155265968481.98608551460094
Trimmed Mean ( 4 / 18 )140.70255432041969.65704320075172.01993291496618
Trimmed Mean ( 5 / 18 )138.71241739806567.49547944280522.05513641125563
Trimmed Mean ( 6 / 18 )136.30761608360465.9173934124262.06785506870345
Trimmed Mean ( 7 / 18 )133.99203774074164.16898363080452.08811220248808
Trimmed Mean ( 8 / 18 )131.74868877280061.9422445617952.12696019824346
Trimmed Mean ( 9 / 18 )130.02591265437860.0943614147392.16369572108453
Trimmed Mean ( 10 / 18 )128.58760554595358.0492153900592.21514803743539
Trimmed Mean ( 11 / 18 )126.42711278525255.59882579311272.27391695744971
Trimmed Mean ( 12 / 18 )122.20313043007953.12199063000222.30042453192748
Trimmed Mean ( 13 / 18 )120.27716766786951.00908690498992.35795570879162
Trimmed Mean ( 14 / 18 )119.15951438996048.36588303066632.4637100973512
Trimmed Mean ( 15 / 18 )118.10262755662145.98461573522532.56830737124442
Trimmed Mean ( 16 / 18 )117.99480458860843.80403874314542.69369692782203
Trimmed Mean ( 17 / 18 )118.12561326304342.68436036744152.76742142194888
Trimmed Mean ( 18 / 18 )118.54503579748740.71044633006132.91190705295587
Median126.672472162267
Midrange-233.971777001935
Midmean - Weighted Average at Xnp102.588335052032
Midmean - Weighted Average at X(n+1)p119.159514389960
Midmean - Empirical Distribution Function102.588335052032
Midmean - Empirical Distribution Function - Averaging119.159514389960
Midmean - Empirical Distribution Function - Interpolation119.159514389960
Midmean - Closest Observation102.588335052032
Midmean - True Basic - Statistics Graphics Toolkit119.159514389960
Midmean - MS Excel (old versions)120.277167667869
Number of observations56

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 122.982647643864 & 88.5493707217586 & 1.38885964565804 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 657.929935446472 &  &  \tabularnewline
Quadratic Mean & 668.116187244826 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & 128.392472568282 & 84.2018713168493 & 1.52481732959527 \tabularnewline
Winsorized Mean ( 2 / 18 ) & 148.276166885599 & 78.239668452692 & 1.89515331312089 \tabularnewline
Winsorized Mean ( 3 / 18 ) & 147.351653008082 & 75.7100041695307 & 1.94626396635946 \tabularnewline
Winsorized Mean ( 4 / 18 ) & 147.241575636727 & 74.3104863762058 & 1.98143738275778 \tabularnewline
Winsorized Mean ( 5 / 18 ) & 148.159851133446 & 70.8714381145241 & 2.0905438788194 \tabularnewline
Winsorized Mean ( 6 / 18 ) & 146.727718626489 & 69.7757587991216 & 2.10284662111531 \tabularnewline
Winsorized Mean ( 7 / 18 ) & 145.208782580442 & 69.3618809132269 & 2.09349545699462 \tabularnewline
Winsorized Mean ( 8 / 18 ) & 141.100901987094 & 65.5723831046203 & 2.15183428306958 \tabularnewline
Winsorized Mean ( 9 / 18 ) & 138.347546638834 & 63.854176824181 & 2.16661702522243 \tabularnewline
Winsorized Mean ( 10 / 18 ) & 141.704883021643 & 62.4431776832958 & 2.26934131604181 \tabularnewline
Winsorized Mean ( 11 / 18 ) & 152.977859017766 & 59.164865275947 & 2.58562000106434 \tabularnewline
Winsorized Mean ( 12 / 18 ) & 134.584319615717 & 54.706350202117 & 2.46012243767833 \tabularnewline
Winsorized Mean ( 13 / 18 ) & 127.541913974277 & 53.1410342024235 & 2.40006458076159 \tabularnewline
Winsorized Mean ( 14 / 18 ) & 126.029278806659 & 48.6219884680796 & 2.59202230878314 \tabularnewline
Winsorized Mean ( 15 / 18 ) & 118.795775208135 & 44.5177585959423 & 2.66850306383042 \tabularnewline
Winsorized Mean ( 16 / 18 ) & 117.172578635014 & 38.3847096603981 & 3.05258473156832 \tabularnewline
Winsorized Mean ( 17 / 18 ) & 115.579119303921 & 37.9872348015939 & 3.04257785299686 \tabularnewline
Winsorized Mean ( 18 / 18 ) & 115.292094167181 & 37.3784750959013 & 3.08445151578222 \tabularnewline
Trimmed Mean ( 1 / 18 ) & 136.203181890005 & 79.9033430800838 & 1.70459929008845 \tabularnewline
Trimmed Mean ( 2 / 18 ) & 144.614715005705 & 74.453701154314 & 1.94234420537368 \tabularnewline
Trimmed Mean ( 3 / 18 ) & 142.564301952965 & 71.7815526596848 & 1.98608551460094 \tabularnewline
Trimmed Mean ( 4 / 18 ) & 140.702554320419 & 69.6570432007517 & 2.01993291496618 \tabularnewline
Trimmed Mean ( 5 / 18 ) & 138.712417398065 & 67.4954794428052 & 2.05513641125563 \tabularnewline
Trimmed Mean ( 6 / 18 ) & 136.307616083604 & 65.917393412426 & 2.06785506870345 \tabularnewline
Trimmed Mean ( 7 / 18 ) & 133.992037740741 & 64.1689836308045 & 2.08811220248808 \tabularnewline
Trimmed Mean ( 8 / 18 ) & 131.748688772800 & 61.942244561795 & 2.12696019824346 \tabularnewline
Trimmed Mean ( 9 / 18 ) & 130.025912654378 & 60.094361414739 & 2.16369572108453 \tabularnewline
Trimmed Mean ( 10 / 18 ) & 128.587605545953 & 58.049215390059 & 2.21514803743539 \tabularnewline
Trimmed Mean ( 11 / 18 ) & 126.427112785252 & 55.5988257931127 & 2.27391695744971 \tabularnewline
Trimmed Mean ( 12 / 18 ) & 122.203130430079 & 53.1219906300022 & 2.30042453192748 \tabularnewline
Trimmed Mean ( 13 / 18 ) & 120.277167667869 & 51.0090869049899 & 2.35795570879162 \tabularnewline
Trimmed Mean ( 14 / 18 ) & 119.159514389960 & 48.3658830306663 & 2.4637100973512 \tabularnewline
Trimmed Mean ( 15 / 18 ) & 118.102627556621 & 45.9846157352253 & 2.56830737124442 \tabularnewline
Trimmed Mean ( 16 / 18 ) & 117.994804588608 & 43.8040387431454 & 2.69369692782203 \tabularnewline
Trimmed Mean ( 17 / 18 ) & 118.125613263043 & 42.6843603674415 & 2.76742142194888 \tabularnewline
Trimmed Mean ( 18 / 18 ) & 118.545035797487 & 40.7104463300613 & 2.91190705295587 \tabularnewline
Median & 126.672472162267 &  &  \tabularnewline
Midrange & -233.971777001935 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 102.588335052032 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 119.159514389960 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 102.588335052032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 119.159514389960 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 119.159514389960 &  &  \tabularnewline
Midmean - Closest Observation & 102.588335052032 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 119.159514389960 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 120.277167667869 &  &  \tabularnewline
Number of observations & 56 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2346&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]122.982647643864[/C][C]88.5493707217586[/C][C]1.38885964565804[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]657.929935446472[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]668.116187244826[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]128.392472568282[/C][C]84.2018713168493[/C][C]1.52481732959527[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]148.276166885599[/C][C]78.239668452692[/C][C]1.89515331312089[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]147.351653008082[/C][C]75.7100041695307[/C][C]1.94626396635946[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]147.241575636727[/C][C]74.3104863762058[/C][C]1.98143738275778[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]148.159851133446[/C][C]70.8714381145241[/C][C]2.0905438788194[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]146.727718626489[/C][C]69.7757587991216[/C][C]2.10284662111531[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]145.208782580442[/C][C]69.3618809132269[/C][C]2.09349545699462[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]141.100901987094[/C][C]65.5723831046203[/C][C]2.15183428306958[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]138.347546638834[/C][C]63.854176824181[/C][C]2.16661702522243[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]141.704883021643[/C][C]62.4431776832958[/C][C]2.26934131604181[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]152.977859017766[/C][C]59.164865275947[/C][C]2.58562000106434[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]134.584319615717[/C][C]54.706350202117[/C][C]2.46012243767833[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]127.541913974277[/C][C]53.1410342024235[/C][C]2.40006458076159[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]126.029278806659[/C][C]48.6219884680796[/C][C]2.59202230878314[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]118.795775208135[/C][C]44.5177585959423[/C][C]2.66850306383042[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]117.172578635014[/C][C]38.3847096603981[/C][C]3.05258473156832[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]115.579119303921[/C][C]37.9872348015939[/C][C]3.04257785299686[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]115.292094167181[/C][C]37.3784750959013[/C][C]3.08445151578222[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]136.203181890005[/C][C]79.9033430800838[/C][C]1.70459929008845[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]144.614715005705[/C][C]74.453701154314[/C][C]1.94234420537368[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]142.564301952965[/C][C]71.7815526596848[/C][C]1.98608551460094[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]140.702554320419[/C][C]69.6570432007517[/C][C]2.01993291496618[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]138.712417398065[/C][C]67.4954794428052[/C][C]2.05513641125563[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]136.307616083604[/C][C]65.917393412426[/C][C]2.06785506870345[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]133.992037740741[/C][C]64.1689836308045[/C][C]2.08811220248808[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]131.748688772800[/C][C]61.942244561795[/C][C]2.12696019824346[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]130.025912654378[/C][C]60.094361414739[/C][C]2.16369572108453[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]128.587605545953[/C][C]58.049215390059[/C][C]2.21514803743539[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]126.427112785252[/C][C]55.5988257931127[/C][C]2.27391695744971[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]122.203130430079[/C][C]53.1219906300022[/C][C]2.30042453192748[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]120.277167667869[/C][C]51.0090869049899[/C][C]2.35795570879162[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]119.159514389960[/C][C]48.3658830306663[/C][C]2.4637100973512[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]118.102627556621[/C][C]45.9846157352253[/C][C]2.56830737124442[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]117.994804588608[/C][C]43.8040387431454[/C][C]2.69369692782203[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]118.125613263043[/C][C]42.6843603674415[/C][C]2.76742142194888[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]118.545035797487[/C][C]40.7104463300613[/C][C]2.91190705295587[/C][/ROW]
[ROW][C]Median[/C][C]126.672472162267[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-233.971777001935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]102.588335052032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]119.159514389960[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]102.588335052032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]119.159514389960[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]119.159514389960[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]102.588335052032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]119.159514389960[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]120.277167667869[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]56[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2346&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2346&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 Mean122.98264764386488.54937072175861.38885964565804
Geometric MeanNaN
Harmonic Mean657.929935446472
Quadratic Mean668.116187244826
Winsorized Mean ( 1 / 18 )128.39247256828284.20187131684931.52481732959527
Winsorized Mean ( 2 / 18 )148.27616688559978.2396684526921.89515331312089
Winsorized Mean ( 3 / 18 )147.35165300808275.71000416953071.94626396635946
Winsorized Mean ( 4 / 18 )147.24157563672774.31048637620581.98143738275778
Winsorized Mean ( 5 / 18 )148.15985113344670.87143811452412.0905438788194
Winsorized Mean ( 6 / 18 )146.72771862648969.77575879912162.10284662111531
Winsorized Mean ( 7 / 18 )145.20878258044269.36188091322692.09349545699462
Winsorized Mean ( 8 / 18 )141.10090198709465.57238310462032.15183428306958
Winsorized Mean ( 9 / 18 )138.34754663883463.8541768241812.16661702522243
Winsorized Mean ( 10 / 18 )141.70488302164362.44317768329582.26934131604181
Winsorized Mean ( 11 / 18 )152.97785901776659.1648652759472.58562000106434
Winsorized Mean ( 12 / 18 )134.58431961571754.7063502021172.46012243767833
Winsorized Mean ( 13 / 18 )127.54191397427753.14103420242352.40006458076159
Winsorized Mean ( 14 / 18 )126.02927880665948.62198846807962.59202230878314
Winsorized Mean ( 15 / 18 )118.79577520813544.51775859594232.66850306383042
Winsorized Mean ( 16 / 18 )117.17257863501438.38470966039813.05258473156832
Winsorized Mean ( 17 / 18 )115.57911930392137.98723480159393.04257785299686
Winsorized Mean ( 18 / 18 )115.29209416718137.37847509590133.08445151578222
Trimmed Mean ( 1 / 18 )136.20318189000579.90334308008381.70459929008845
Trimmed Mean ( 2 / 18 )144.61471500570574.4537011543141.94234420537368
Trimmed Mean ( 3 / 18 )142.56430195296571.78155265968481.98608551460094
Trimmed Mean ( 4 / 18 )140.70255432041969.65704320075172.01993291496618
Trimmed Mean ( 5 / 18 )138.71241739806567.49547944280522.05513641125563
Trimmed Mean ( 6 / 18 )136.30761608360465.9173934124262.06785506870345
Trimmed Mean ( 7 / 18 )133.99203774074164.16898363080452.08811220248808
Trimmed Mean ( 8 / 18 )131.74868877280061.9422445617952.12696019824346
Trimmed Mean ( 9 / 18 )130.02591265437860.0943614147392.16369572108453
Trimmed Mean ( 10 / 18 )128.58760554595358.0492153900592.21514803743539
Trimmed Mean ( 11 / 18 )126.42711278525255.59882579311272.27391695744971
Trimmed Mean ( 12 / 18 )122.20313043007953.12199063000222.30042453192748
Trimmed Mean ( 13 / 18 )120.27716766786951.00908690498992.35795570879162
Trimmed Mean ( 14 / 18 )119.15951438996048.36588303066632.4637100973512
Trimmed Mean ( 15 / 18 )118.10262755662145.98461573522532.56830737124442
Trimmed Mean ( 16 / 18 )117.99480458860843.80403874314542.69369692782203
Trimmed Mean ( 17 / 18 )118.12561326304342.68436036744152.76742142194888
Trimmed Mean ( 18 / 18 )118.54503579748740.71044633006132.91190705295587
Median126.672472162267
Midrange-233.971777001935
Midmean - Weighted Average at Xnp102.588335052032
Midmean - Weighted Average at X(n+1)p119.159514389960
Midmean - Empirical Distribution Function102.588335052032
Midmean - Empirical Distribution Function - Averaging119.159514389960
Midmean - Empirical Distribution Function - Interpolation119.159514389960
Midmean - Closest Observation102.588335052032
Midmean - True Basic - Statistics Graphics Toolkit119.159514389960
Midmean - MS Excel (old versions)120.277167667869
Number of observations56



Parameters (Session):
par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;
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')