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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 computationFri, 05 Dec 2008 03:37:30 -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/2008/Dec/05/t1228473564yi1l8o01lliio3j.htm/, Retrieved Thu, 16 May 2024 16:56:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29146, Retrieved Thu, 16 May 2024 16:56:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact172
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [1.1 central tende...] [2008-12-05 10:37:30] [cf57b030c45fee9c58a27190db97b24d] [Current]
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Dataseries X:
58.972
59.249
63.955
53.785
52.760
44.795
37.348
32.370
32.717
40.974
33.591
21.124
58.608
46.865
51.378
46.235
47.206
45.382
41.227
33.795
31.295
42.625
33.625
21.538
56.421
53.152
53.536
52.408
41.454
38.271
35.306
26.414
31.917
38.030
27.534
18.387
50.556
43.901
48.572
43.899
37.532
40.357
35.489
29.027
34.485
42.598
30.306
26.451
47.460
50.104
61.465
53.726
39.477
43.895
31.481
29.896
33.842
39.120
33.702
25.094




Summary of computational 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 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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29146&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29146&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29146&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' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean40.94473333333331.4009488132425829.2264306492142
Geometric Mean39.4578772276266
Harmonic Mean37.8926491012231
Quadratic Mean42.3351861316329
Winsorized Mean ( 1 / 20 )40.948851.3781410876714529.7131043884545
Winsorized Mean ( 2 / 20 )40.88878333333331.3569957298334630.1318437740047
Winsorized Mean ( 3 / 20 )41.05273333333331.3139686574241531.2433124651628
Winsorized Mean ( 4 / 20 )41.11646666666671.2908203714448831.8529731759989
Winsorized Mean ( 5 / 20 )40.93731.2501327500809132.7463623342005
Winsorized Mean ( 6 / 20 )40.7821.1767116121119534.6575996873227
Winsorized Mean ( 7 / 20 )40.94931.1433867759330335.8140402372455
Winsorized Mean ( 8 / 20 )41.03983333333331.1185631211632036.6897786605513
Winsorized Mean ( 9 / 20 )41.04373333333331.0974306834645337.3998412398682
Winsorized Mean ( 10 / 20 )41.14323333333331.0585695751366138.8668201880107
Winsorized Mean ( 11 / 20 )41.11281.0412732465104039.4832001473010
Winsorized Mean ( 12 / 20 )40.9940.99040674660909641.3910750712807
Winsorized Mean ( 13 / 20 )40.914050.94400246110261643.3410416665773
Winsorized Mean ( 14 / 20 )40.889550.91350590355691444.7611228792157
Winsorized Mean ( 15 / 20 )40.725050.81673264731444849.8633795696924
Winsorized Mean ( 16 / 20 )40.43758333333330.76822896124003852.6374106855604
Winsorized Mean ( 17 / 20 )40.38743333333330.75385784426488553.5743358520288
Winsorized Mean ( 18 / 20 )40.31303333333330.73408094312181554.9163327437635
Winsorized Mean ( 19 / 20 )40.12841666666670.70202686473442857.1607992264612
Winsorized Mean ( 20 / 20 )40.05841666666670.62823031523346863.7639026569099
Trimmed Mean ( 1 / 20 )40.93693103448281.3369748278021930.6190738847176
Trimmed Mean ( 2 / 20 )40.92416071428571.2862304740296731.8171288432261
Trimmed Mean ( 3 / 20 )40.94381481481481.2376396267146233.0821783102584
Trimmed Mean ( 4 / 20 )40.90192307692311.1982186432065434.1356089798986
Trimmed Mean ( 5 / 20 )40.837561.1577490881667835.2732387504303
Trimmed Mean ( 6 / 20 )40.8126251.1208239424420136.4130560158084
Trimmed Mean ( 7 / 20 )40.81928260869571.0966539449784337.2216621256020
Trimmed Mean ( 8 / 20 )40.79395454545451.0743540593176237.9706803280150
Trimmed Mean ( 9 / 20 )40.75004761904761.0511344537680438.7676833091803
Trimmed Mean ( 10 / 20 )40.70111.0252039320582539.7004915093201
Trimmed Mean ( 11 / 20 )40.63128947368420.99984005115405440.6377894412071
Trimmed Mean ( 12 / 20 )40.55833333333330.96893819237086641.8585350981907
Trimmed Mean ( 13 / 20 )40.49426470588240.93984038667326143.0863211243978
Trimmed Mean ( 14 / 20 )40.433718750.91123312767509244.3725294021762
Trimmed Mean ( 15 / 20 )40.36860.8778983165793645.9832297632055
Trimmed Mean ( 16 / 20 )40.31767857142860.8585159368924646.9620619011047
Trimmed Mean ( 17 / 20 )40.30038461538460.84252096997764547.8330938355801
Trimmed Mean ( 18 / 20 )40.28758333333330.81889694038592649.1973792384018
Trimmed Mean ( 19 / 20 )40.28372727272730.78507522782291751.3119327232342
Trimmed Mean ( 20 / 20 )40.308250.73953220233433654.5050639752628
Median40.6655
Midrange41.171
Midmean - Weighted Average at Xnp40.1217741935484
Midmean - Weighted Average at X(n+1)p40.3686
Midmean - Empirical Distribution Function40.1217741935484
Midmean - Empirical Distribution Function - Averaging40.3686
Midmean - Empirical Distribution Function - Interpolation40.3686
Midmean - Closest Observation40.1217741935484
Midmean - True Basic - Statistics Graphics Toolkit40.3686
Midmean - MS Excel (old versions)40.43371875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 40.9447333333333 & 1.40094881324258 & 29.2264306492142 \tabularnewline
Geometric Mean & 39.4578772276266 &  &  \tabularnewline
Harmonic Mean & 37.8926491012231 &  &  \tabularnewline
Quadratic Mean & 42.3351861316329 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 40.94885 & 1.37814108767145 & 29.7131043884545 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 40.8887833333333 & 1.35699572983346 & 30.1318437740047 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 41.0527333333333 & 1.31396865742415 & 31.2433124651628 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 41.1164666666667 & 1.29082037144488 & 31.8529731759989 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 40.9373 & 1.25013275008091 & 32.7463623342005 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 40.782 & 1.17671161211195 & 34.6575996873227 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 40.9493 & 1.14338677593303 & 35.8140402372455 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 41.0398333333333 & 1.11856312116320 & 36.6897786605513 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 41.0437333333333 & 1.09743068346453 & 37.3998412398682 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 41.1432333333333 & 1.05856957513661 & 38.8668201880107 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 41.1128 & 1.04127324651040 & 39.4832001473010 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 40.994 & 0.990406746609096 & 41.3910750712807 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 40.91405 & 0.944002461102616 & 43.3410416665773 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 40.88955 & 0.913505903556914 & 44.7611228792157 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 40.72505 & 0.816732647314448 & 49.8633795696924 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 40.4375833333333 & 0.768228961240038 & 52.6374106855604 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 40.3874333333333 & 0.753857844264885 & 53.5743358520288 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 40.3130333333333 & 0.734080943121815 & 54.9163327437635 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 40.1284166666667 & 0.702026864734428 & 57.1607992264612 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 40.0584166666667 & 0.628230315233468 & 63.7639026569099 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 40.9369310344828 & 1.33697482780219 & 30.6190738847176 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 40.9241607142857 & 1.28623047402967 & 31.8171288432261 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 40.9438148148148 & 1.23763962671462 & 33.0821783102584 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 40.9019230769231 & 1.19821864320654 & 34.1356089798986 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 40.83756 & 1.15774908816678 & 35.2732387504303 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 40.812625 & 1.12082394244201 & 36.4130560158084 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 40.8192826086957 & 1.09665394497843 & 37.2216621256020 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 40.7939545454545 & 1.07435405931762 & 37.9706803280150 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 40.7500476190476 & 1.05113445376804 & 38.7676833091803 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 40.7011 & 1.02520393205825 & 39.7004915093201 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 40.6312894736842 & 0.999840051154054 & 40.6377894412071 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 40.5583333333333 & 0.968938192370866 & 41.8585350981907 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 40.4942647058824 & 0.939840386673261 & 43.0863211243978 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 40.43371875 & 0.911233127675092 & 44.3725294021762 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 40.3686 & 0.87789831657936 & 45.9832297632055 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 40.3176785714286 & 0.85851593689246 & 46.9620619011047 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 40.3003846153846 & 0.842520969977645 & 47.8330938355801 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 40.2875833333333 & 0.818896940385926 & 49.1973792384018 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 40.2837272727273 & 0.785075227822917 & 51.3119327232342 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 40.30825 & 0.739532202334336 & 54.5050639752628 \tabularnewline
Median & 40.6655 &  &  \tabularnewline
Midrange & 41.171 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 40.1217741935484 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 40.3686 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 40.1217741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 40.3686 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 40.3686 &  &  \tabularnewline
Midmean - Closest Observation & 40.1217741935484 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 40.3686 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 40.43371875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29146&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]40.9447333333333[/C][C]1.40094881324258[/C][C]29.2264306492142[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]39.4578772276266[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]37.8926491012231[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]42.3351861316329[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]40.94885[/C][C]1.37814108767145[/C][C]29.7131043884545[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]40.8887833333333[/C][C]1.35699572983346[/C][C]30.1318437740047[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]41.0527333333333[/C][C]1.31396865742415[/C][C]31.2433124651628[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]41.1164666666667[/C][C]1.29082037144488[/C][C]31.8529731759989[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]40.9373[/C][C]1.25013275008091[/C][C]32.7463623342005[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]40.782[/C][C]1.17671161211195[/C][C]34.6575996873227[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]40.9493[/C][C]1.14338677593303[/C][C]35.8140402372455[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]41.0398333333333[/C][C]1.11856312116320[/C][C]36.6897786605513[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]41.0437333333333[/C][C]1.09743068346453[/C][C]37.3998412398682[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]41.1432333333333[/C][C]1.05856957513661[/C][C]38.8668201880107[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]41.1128[/C][C]1.04127324651040[/C][C]39.4832001473010[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]40.994[/C][C]0.990406746609096[/C][C]41.3910750712807[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]40.91405[/C][C]0.944002461102616[/C][C]43.3410416665773[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]40.88955[/C][C]0.913505903556914[/C][C]44.7611228792157[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]40.72505[/C][C]0.816732647314448[/C][C]49.8633795696924[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]40.4375833333333[/C][C]0.768228961240038[/C][C]52.6374106855604[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]40.3874333333333[/C][C]0.753857844264885[/C][C]53.5743358520288[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]40.3130333333333[/C][C]0.734080943121815[/C][C]54.9163327437635[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]40.1284166666667[/C][C]0.702026864734428[/C][C]57.1607992264612[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]40.0584166666667[/C][C]0.628230315233468[/C][C]63.7639026569099[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]40.9369310344828[/C][C]1.33697482780219[/C][C]30.6190738847176[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]40.9241607142857[/C][C]1.28623047402967[/C][C]31.8171288432261[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]40.9438148148148[/C][C]1.23763962671462[/C][C]33.0821783102584[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]40.9019230769231[/C][C]1.19821864320654[/C][C]34.1356089798986[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]40.83756[/C][C]1.15774908816678[/C][C]35.2732387504303[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]40.812625[/C][C]1.12082394244201[/C][C]36.4130560158084[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]40.8192826086957[/C][C]1.09665394497843[/C][C]37.2216621256020[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]40.7939545454545[/C][C]1.07435405931762[/C][C]37.9706803280150[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]40.7500476190476[/C][C]1.05113445376804[/C][C]38.7676833091803[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]40.7011[/C][C]1.02520393205825[/C][C]39.7004915093201[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]40.6312894736842[/C][C]0.999840051154054[/C][C]40.6377894412071[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]40.5583333333333[/C][C]0.968938192370866[/C][C]41.8585350981907[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]40.4942647058824[/C][C]0.939840386673261[/C][C]43.0863211243978[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]40.43371875[/C][C]0.911233127675092[/C][C]44.3725294021762[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]40.3686[/C][C]0.87789831657936[/C][C]45.9832297632055[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]40.3176785714286[/C][C]0.85851593689246[/C][C]46.9620619011047[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]40.3003846153846[/C][C]0.842520969977645[/C][C]47.8330938355801[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]40.2875833333333[/C][C]0.818896940385926[/C][C]49.1973792384018[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]40.2837272727273[/C][C]0.785075227822917[/C][C]51.3119327232342[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]40.30825[/C][C]0.739532202334336[/C][C]54.5050639752628[/C][/ROW]
[ROW][C]Median[/C][C]40.6655[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]41.171[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]40.1217741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]40.3686[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]40.1217741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]40.3686[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]40.3686[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]40.1217741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]40.3686[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]40.43371875[/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=29146&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29146&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 Mean40.94473333333331.4009488132425829.2264306492142
Geometric Mean39.4578772276266
Harmonic Mean37.8926491012231
Quadratic Mean42.3351861316329
Winsorized Mean ( 1 / 20 )40.948851.3781410876714529.7131043884545
Winsorized Mean ( 2 / 20 )40.88878333333331.3569957298334630.1318437740047
Winsorized Mean ( 3 / 20 )41.05273333333331.3139686574241531.2433124651628
Winsorized Mean ( 4 / 20 )41.11646666666671.2908203714448831.8529731759989
Winsorized Mean ( 5 / 20 )40.93731.2501327500809132.7463623342005
Winsorized Mean ( 6 / 20 )40.7821.1767116121119534.6575996873227
Winsorized Mean ( 7 / 20 )40.94931.1433867759330335.8140402372455
Winsorized Mean ( 8 / 20 )41.03983333333331.1185631211632036.6897786605513
Winsorized Mean ( 9 / 20 )41.04373333333331.0974306834645337.3998412398682
Winsorized Mean ( 10 / 20 )41.14323333333331.0585695751366138.8668201880107
Winsorized Mean ( 11 / 20 )41.11281.0412732465104039.4832001473010
Winsorized Mean ( 12 / 20 )40.9940.99040674660909641.3910750712807
Winsorized Mean ( 13 / 20 )40.914050.94400246110261643.3410416665773
Winsorized Mean ( 14 / 20 )40.889550.91350590355691444.7611228792157
Winsorized Mean ( 15 / 20 )40.725050.81673264731444849.8633795696924
Winsorized Mean ( 16 / 20 )40.43758333333330.76822896124003852.6374106855604
Winsorized Mean ( 17 / 20 )40.38743333333330.75385784426488553.5743358520288
Winsorized Mean ( 18 / 20 )40.31303333333330.73408094312181554.9163327437635
Winsorized Mean ( 19 / 20 )40.12841666666670.70202686473442857.1607992264612
Winsorized Mean ( 20 / 20 )40.05841666666670.62823031523346863.7639026569099
Trimmed Mean ( 1 / 20 )40.93693103448281.3369748278021930.6190738847176
Trimmed Mean ( 2 / 20 )40.92416071428571.2862304740296731.8171288432261
Trimmed Mean ( 3 / 20 )40.94381481481481.2376396267146233.0821783102584
Trimmed Mean ( 4 / 20 )40.90192307692311.1982186432065434.1356089798986
Trimmed Mean ( 5 / 20 )40.837561.1577490881667835.2732387504303
Trimmed Mean ( 6 / 20 )40.8126251.1208239424420136.4130560158084
Trimmed Mean ( 7 / 20 )40.81928260869571.0966539449784337.2216621256020
Trimmed Mean ( 8 / 20 )40.79395454545451.0743540593176237.9706803280150
Trimmed Mean ( 9 / 20 )40.75004761904761.0511344537680438.7676833091803
Trimmed Mean ( 10 / 20 )40.70111.0252039320582539.7004915093201
Trimmed Mean ( 11 / 20 )40.63128947368420.99984005115405440.6377894412071
Trimmed Mean ( 12 / 20 )40.55833333333330.96893819237086641.8585350981907
Trimmed Mean ( 13 / 20 )40.49426470588240.93984038667326143.0863211243978
Trimmed Mean ( 14 / 20 )40.433718750.91123312767509244.3725294021762
Trimmed Mean ( 15 / 20 )40.36860.8778983165793645.9832297632055
Trimmed Mean ( 16 / 20 )40.31767857142860.8585159368924646.9620619011047
Trimmed Mean ( 17 / 20 )40.30038461538460.84252096997764547.8330938355801
Trimmed Mean ( 18 / 20 )40.28758333333330.81889694038592649.1973792384018
Trimmed Mean ( 19 / 20 )40.28372727272730.78507522782291751.3119327232342
Trimmed Mean ( 20 / 20 )40.308250.73953220233433654.5050639752628
Median40.6655
Midrange41.171
Midmean - Weighted Average at Xnp40.1217741935484
Midmean - Weighted Average at X(n+1)p40.3686
Midmean - Empirical Distribution Function40.1217741935484
Midmean - Empirical Distribution Function - Averaging40.3686
Midmean - Empirical Distribution Function - Interpolation40.3686
Midmean - Closest Observation40.1217741935484
Midmean - True Basic - Statistics Graphics Toolkit40.3686
Midmean - MS Excel (old versions)40.43371875
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')