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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 17 Oct 2008 06:13:34 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/17/t1224245675n2xoroube0ij2pf.htm/, Retrieved Wed, 15 May 2024 04:22:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16433, Retrieved Wed, 15 May 2024 04:22:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsZonder extreme waarden
Estimated Impact200

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
-    D    [Central Tendency] [Centrel Tendency ...] [2008-10-17 12:13:34] [54e3d3004a715f41ac868f539d95466f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
72.50
59.40
85.70
88.20
62.80
87.00
79.20
79.20
40.10
69.00
59.40
73.80
57.40
81.10
46.60
41.40
71.20
67.90
72.00
39.70
51.90
73.70
70.90
60.80
61.00
54.50
39.10
66.60
58.50
59.80
80.90
37.30
44.60
48.70
54.00
49.50
61.60
35.00
35.70
51.30
49.00
41.50
72.50
42.10
44.10
45.10
50.30
40.90
47.20
36.90
40.90
38.30
46.30
28.40
78.40
36.80
50.70
42.80

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16433&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16433&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16433&T=0

As an alternative you can also use a QR Code:  
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'George Udny Yule' @ 72.249.76.132






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean56.22758620689662.0685511280920427.1821109197136
Geometric Mean54.0876290136829
Harmonic Mean52.0210686991512
Quadratic Mean58.3561390559489
Winsorized Mean ( 1 / 19 )56.32068965517242.0391283718200727.6199823579042
Winsorized Mean ( 2 / 19 )56.32.0231270232509127.8282081910670
Winsorized Mean ( 3 / 19 )56.11896551724141.9560668601514228.6896969937403
Winsorized Mean ( 4 / 19 )56.11206896551721.9517920745809228.748999289571
Winsorized Mean ( 5 / 19 )561.9139425392516829.2589766158262
Winsorized Mean ( 6 / 19 )56.10344827586211.8965565088208929.5817435520243
Winsorized Mean ( 7 / 19 )56.10344827586211.8603968988898430.1567091997095
Winsorized Mean ( 8 / 19 )55.5517241379311.7210631384564632.2775631507353
Winsorized Mean ( 9 / 19 )55.5982758620691.7082226878355232.5474402476865
Winsorized Mean ( 10 / 19 )55.52931034482761.6485800387320633.6831145835878
Winsorized Mean ( 11 / 19 )55.52931034482761.6485800387320633.6831145835878
Winsorized Mean ( 12 / 19 )55.52931034482761.6139797029931534.4052098312312
Winsorized Mean ( 13 / 19 )55.37241379310341.5787069860339135.0745352259525
Winsorized Mean ( 14 / 19 )55.44482758620691.5438325915927035.9137563801571
Winsorized Mean ( 15 / 19 )55.13448275862071.4314663449406538.5160873348416
Winsorized Mean ( 16 / 19 )55.18965517241381.3267404067137141.5979304565818
Winsorized Mean ( 17 / 19 )54.95517241379311.2418912367850844.2511959067019
Winsorized Mean ( 18 / 19 )53.93103448275861.0322981571026952.2436605274245
Winsorized Mean ( 19 / 19 )53.93103448275860.91545249918335558.911887324431
Trimmed Mean ( 1 / 19 )56.15357142857142.0023638048691628.0436408668707
Trimmed Mean ( 2 / 19 )55.97407407407411.9558744948817028.6184385657422
Trimmed Mean ( 3 / 19 )55.79230769230771.9077555577506729.2449981160529
Trimmed Mean ( 4 / 19 )55.6661.8789980178330229.6253638756882
Trimmed Mean ( 5 / 19 )55.531251.8426900727859730.1359685061102
Trimmed Mean ( 6 / 19 )55.41304347826091.8080646195744830.6477118562842
Trimmed Mean ( 7 / 19 )55.26136363636361.7669960411981231.2741864429381
Trimmed Mean ( 8 / 19 )55.09523809523811.7225698341991331.9843277186224
Trimmed Mean ( 9 / 19 )55.01251.7026457070824132.3100101043730
Trimmed Mean ( 10 / 19 )54.91315789473681.6762213273192132.7600878235810
Trimmed Mean ( 11 / 19 )54.81388888888891.6533859091956233.1525075809773
Trimmed Mean ( 12 / 19 )54.70294117647061.6180878511418333.8071515325132
Trimmed Mean ( 13 / 19 )54.5781251.5750623027551934.651407061504
Trimmed Mean ( 14 / 19 )54.461.5212033953797735.8006037623943
Trimmed Mean ( 15 / 19 )54.31428571428571.4500475661393037.456899333927
Trimmed Mean ( 16 / 19 )54.19230769230771.3817260451715239.2207325624962
Trimmed Mean ( 17 / 19 )54.04166666666671.3123288938386841.1799716674604
Trimmed Mean ( 18 / 19 )53.91.2338655690245443.6838512664001
Trimmed Mean ( 19 / 19 )53.8951.1994620504735944.9326429116455
Median52.95
Midrange58.3
Midmean - Weighted Average at Xnp53.8931034482759
Midmean - Weighted Average at X(n+1)p54.46
Midmean - Empirical Distribution Function54.46
Midmean - Empirical Distribution Function - Averaging54.46
Midmean - Empirical Distribution Function - Interpolation54.3142857142857
Midmean - Closest Observation54.46
Midmean - True Basic - Statistics Graphics Toolkit54.46
Midmean - MS Excel (old versions)54.46
Number of observations58

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 56.2275862068966 & 2.06855112809204 & 27.1821109197136 \tabularnewline
Geometric Mean & 54.0876290136829 &  &  \tabularnewline
Harmonic Mean & 52.0210686991512 &  &  \tabularnewline
Quadratic Mean & 58.3561390559489 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 56.3206896551724 & 2.03912837182007 & 27.6199823579042 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 56.3 & 2.02312702325091 & 27.8282081910670 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 56.1189655172414 & 1.95606686015142 & 28.6896969937403 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 56.1120689655172 & 1.95179207458092 & 28.748999289571 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 56 & 1.91394253925168 & 29.2589766158262 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 56.1034482758621 & 1.89655650882089 & 29.5817435520243 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 56.1034482758621 & 1.86039689888984 & 30.1567091997095 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 55.551724137931 & 1.72106313845646 & 32.2775631507353 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 55.598275862069 & 1.70822268783552 & 32.5474402476865 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 55.5293103448276 & 1.64858003873206 & 33.6831145835878 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 55.5293103448276 & 1.64858003873206 & 33.6831145835878 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 55.5293103448276 & 1.61397970299315 & 34.4052098312312 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 55.3724137931034 & 1.57870698603391 & 35.0745352259525 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 55.4448275862069 & 1.54383259159270 & 35.9137563801571 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 55.1344827586207 & 1.43146634494065 & 38.5160873348416 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 55.1896551724138 & 1.32674040671371 & 41.5979304565818 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 54.9551724137931 & 1.24189123678508 & 44.2511959067019 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 53.9310344827586 & 1.03229815710269 & 52.2436605274245 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 53.9310344827586 & 0.915452499183355 & 58.911887324431 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 56.1535714285714 & 2.00236380486916 & 28.0436408668707 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 55.9740740740741 & 1.95587449488170 & 28.6184385657422 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 55.7923076923077 & 1.90775555775067 & 29.2449981160529 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 55.666 & 1.87899801783302 & 29.6253638756882 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 55.53125 & 1.84269007278597 & 30.1359685061102 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 55.4130434782609 & 1.80806461957448 & 30.6477118562842 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 55.2613636363636 & 1.76699604119812 & 31.2741864429381 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 55.0952380952381 & 1.72256983419913 & 31.9843277186224 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 55.0125 & 1.70264570708241 & 32.3100101043730 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 54.9131578947368 & 1.67622132731921 & 32.7600878235810 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 54.8138888888889 & 1.65338590919562 & 33.1525075809773 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 54.7029411764706 & 1.61808785114183 & 33.8071515325132 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 54.578125 & 1.57506230275519 & 34.651407061504 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 54.46 & 1.52120339537977 & 35.8006037623943 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 54.3142857142857 & 1.45004756613930 & 37.456899333927 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 54.1923076923077 & 1.38172604517152 & 39.2207325624962 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 54.0416666666667 & 1.31232889383868 & 41.1799716674604 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 53.9 & 1.23386556902454 & 43.6838512664001 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 53.895 & 1.19946205047359 & 44.9326429116455 \tabularnewline
Median & 52.95 &  &  \tabularnewline
Midrange & 58.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 53.8931034482759 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 54.46 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 54.46 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 54.46 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 54.3142857142857 &  &  \tabularnewline
Midmean - Closest Observation & 54.46 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 54.46 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 54.46 &  &  \tabularnewline
Number of observations & 58 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16433&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]56.2275862068966[/C][C]2.06855112809204[/C][C]27.1821109197136[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]54.0876290136829[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]52.0210686991512[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]58.3561390559489[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]56.3206896551724[/C][C]2.03912837182007[/C][C]27.6199823579042[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]56.3[/C][C]2.02312702325091[/C][C]27.8282081910670[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]56.1189655172414[/C][C]1.95606686015142[/C][C]28.6896969937403[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]56.1120689655172[/C][C]1.95179207458092[/C][C]28.748999289571[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]56[/C][C]1.91394253925168[/C][C]29.2589766158262[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]56.1034482758621[/C][C]1.89655650882089[/C][C]29.5817435520243[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]56.1034482758621[/C][C]1.86039689888984[/C][C]30.1567091997095[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]55.551724137931[/C][C]1.72106313845646[/C][C]32.2775631507353[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]55.598275862069[/C][C]1.70822268783552[/C][C]32.5474402476865[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]55.5293103448276[/C][C]1.64858003873206[/C][C]33.6831145835878[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]55.5293103448276[/C][C]1.64858003873206[/C][C]33.6831145835878[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]55.5293103448276[/C][C]1.61397970299315[/C][C]34.4052098312312[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]55.3724137931034[/C][C]1.57870698603391[/C][C]35.0745352259525[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]55.4448275862069[/C][C]1.54383259159270[/C][C]35.9137563801571[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]55.1344827586207[/C][C]1.43146634494065[/C][C]38.5160873348416[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]55.1896551724138[/C][C]1.32674040671371[/C][C]41.5979304565818[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]54.9551724137931[/C][C]1.24189123678508[/C][C]44.2511959067019[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]53.9310344827586[/C][C]1.03229815710269[/C][C]52.2436605274245[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]53.9310344827586[/C][C]0.915452499183355[/C][C]58.911887324431[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]56.1535714285714[/C][C]2.00236380486916[/C][C]28.0436408668707[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]55.9740740740741[/C][C]1.95587449488170[/C][C]28.6184385657422[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]55.7923076923077[/C][C]1.90775555775067[/C][C]29.2449981160529[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]55.666[/C][C]1.87899801783302[/C][C]29.6253638756882[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]55.53125[/C][C]1.84269007278597[/C][C]30.1359685061102[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]55.4130434782609[/C][C]1.80806461957448[/C][C]30.6477118562842[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]55.2613636363636[/C][C]1.76699604119812[/C][C]31.2741864429381[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]55.0952380952381[/C][C]1.72256983419913[/C][C]31.9843277186224[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]55.0125[/C][C]1.70264570708241[/C][C]32.3100101043730[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]54.9131578947368[/C][C]1.67622132731921[/C][C]32.7600878235810[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]54.8138888888889[/C][C]1.65338590919562[/C][C]33.1525075809773[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]54.7029411764706[/C][C]1.61808785114183[/C][C]33.8071515325132[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]54.578125[/C][C]1.57506230275519[/C][C]34.651407061504[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]54.46[/C][C]1.52120339537977[/C][C]35.8006037623943[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]54.3142857142857[/C][C]1.45004756613930[/C][C]37.456899333927[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]54.1923076923077[/C][C]1.38172604517152[/C][C]39.2207325624962[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]54.0416666666667[/C][C]1.31232889383868[/C][C]41.1799716674604[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]53.9[/C][C]1.23386556902454[/C][C]43.6838512664001[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]53.895[/C][C]1.19946205047359[/C][C]44.9326429116455[/C][/ROW]
[ROW][C]Median[/C][C]52.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]58.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]53.8931034482759[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]54.46[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]54.46[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]54.46[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]54.3142857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]54.46[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]54.46[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]54.46[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]58[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16433&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16433&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean56.22758620689662.0685511280920427.1821109197136
Geometric Mean54.0876290136829
Harmonic Mean52.0210686991512
Quadratic Mean58.3561390559489
Winsorized Mean ( 1 / 19 )56.32068965517242.0391283718200727.6199823579042
Winsorized Mean ( 2 / 19 )56.32.0231270232509127.8282081910670
Winsorized Mean ( 3 / 19 )56.11896551724141.9560668601514228.6896969937403
Winsorized Mean ( 4 / 19 )56.11206896551721.9517920745809228.748999289571
Winsorized Mean ( 5 / 19 )561.9139425392516829.2589766158262
Winsorized Mean ( 6 / 19 )56.10344827586211.8965565088208929.5817435520243
Winsorized Mean ( 7 / 19 )56.10344827586211.8603968988898430.1567091997095
Winsorized Mean ( 8 / 19 )55.5517241379311.7210631384564632.2775631507353
Winsorized Mean ( 9 / 19 )55.5982758620691.7082226878355232.5474402476865
Winsorized Mean ( 10 / 19 )55.52931034482761.6485800387320633.6831145835878
Winsorized Mean ( 11 / 19 )55.52931034482761.6485800387320633.6831145835878
Winsorized Mean ( 12 / 19 )55.52931034482761.6139797029931534.4052098312312
Winsorized Mean ( 13 / 19 )55.37241379310341.5787069860339135.0745352259525
Winsorized Mean ( 14 / 19 )55.44482758620691.5438325915927035.9137563801571
Winsorized Mean ( 15 / 19 )55.13448275862071.4314663449406538.5160873348416
Winsorized Mean ( 16 / 19 )55.18965517241381.3267404067137141.5979304565818
Winsorized Mean ( 17 / 19 )54.95517241379311.2418912367850844.2511959067019
Winsorized Mean ( 18 / 19 )53.93103448275861.0322981571026952.2436605274245
Winsorized Mean ( 19 / 19 )53.93103448275860.91545249918335558.911887324431
Trimmed Mean ( 1 / 19 )56.15357142857142.0023638048691628.0436408668707
Trimmed Mean ( 2 / 19 )55.97407407407411.9558744948817028.6184385657422
Trimmed Mean ( 3 / 19 )55.79230769230771.9077555577506729.2449981160529
Trimmed Mean ( 4 / 19 )55.6661.8789980178330229.6253638756882
Trimmed Mean ( 5 / 19 )55.531251.8426900727859730.1359685061102
Trimmed Mean ( 6 / 19 )55.41304347826091.8080646195744830.6477118562842
Trimmed Mean ( 7 / 19 )55.26136363636361.7669960411981231.2741864429381
Trimmed Mean ( 8 / 19 )55.09523809523811.7225698341991331.9843277186224
Trimmed Mean ( 9 / 19 )55.01251.7026457070824132.3100101043730
Trimmed Mean ( 10 / 19 )54.91315789473681.6762213273192132.7600878235810
Trimmed Mean ( 11 / 19 )54.81388888888891.6533859091956233.1525075809773
Trimmed Mean ( 12 / 19 )54.70294117647061.6180878511418333.8071515325132
Trimmed Mean ( 13 / 19 )54.5781251.5750623027551934.651407061504
Trimmed Mean ( 14 / 19 )54.461.5212033953797735.8006037623943
Trimmed Mean ( 15 / 19 )54.31428571428571.4500475661393037.456899333927
Trimmed Mean ( 16 / 19 )54.19230769230771.3817260451715239.2207325624962
Trimmed Mean ( 17 / 19 )54.04166666666671.3123288938386841.1799716674604
Trimmed Mean ( 18 / 19 )53.91.2338655690245443.6838512664001
Trimmed Mean ( 19 / 19 )53.8951.1994620504735944.9326429116455
Median52.95
Midrange58.3
Midmean - Weighted Average at Xnp53.8931034482759
Midmean - Weighted Average at X(n+1)p54.46
Midmean - Empirical Distribution Function54.46
Midmean - Empirical Distribution Function - Averaging54.46
Midmean - Empirical Distribution Function - Interpolation54.3142857142857
Midmean - Closest Observation54.46
Midmean - True Basic - Statistics Graphics Toolkit54.46
Midmean - MS Excel (old versions)54.46
Number of observations58


Figures (Output of Computation)

Input Parameters & R Code

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')