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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 08 Mar 2016 19:56:22 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/08/t145746701348vkje1b2llbow8.htm/, Retrieved Sun, 28 Apr 2024 23:24:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293751, Retrieved Sun, 28 Apr 2024 23:24:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-08 19:56:22] [1e8cb0485fd9b8c1cf436607044e417d] [Current]
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Dataseries X:
92,86
94,06
95,51
96,05
96,71
97,91
97,74
97,64
98,55
98,46
99,19
99,18
99,95
100,66
101,12
101,14
100,73
99,92
100,06
100,64
100,89
100,87
100,72
100,72
100,98
100,15
100,13
100,39
99,87
99,93
99,96
99,61
99,57
99,71
99,78
99,92
100,3
100,83
100,84
97,87
97,99
98,03
97,58
97,45
97,47
98,31
98,29
98,13
98,44
98,05
98,32
97,55
97,74
98,01
97,93
99,23
101,03
100,81
100,57
100,1












Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=293751&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=293751&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293751&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'Sir Maurice George Kendall' @ kendall.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean99.03583333333330.224954520408802440.248247305095
Geometric Mean99.0205401916419
Harmonic Mean99.0050217246777
Quadratic Mean99.0509058598995
Winsorized Mean ( 1 / 20 )99.05550.216319420783039457.913115897944
Winsorized Mean ( 2 / 20 )99.10083333333340.19888947213983498.270885166109
Winsorized Mean ( 3 / 20 )99.12533333333330.190646456990652519.943223168284
Winsorized Mean ( 4 / 20 )99.16333333333330.178490321101539555.567006218347
Winsorized Mean ( 5 / 20 )99.22333333333330.165365656581552600.02382226445
Winsorized Mean ( 6 / 20 )99.22233333333330.164500161706628603.174685689903
Winsorized Mean ( 7 / 20 )99.23050.162645749500282610.102018066128
Winsorized Mean ( 8 / 20 )99.23183333333330.16150571375152614.41685887351
Winsorized Mean ( 9 / 20 )99.22883333333330.157998264251831628.037490178842
Winsorized Mean ( 10 / 20 )99.24383333333330.154937766195324640.539977891641
Winsorized Mean ( 11 / 20 )99.24383333333330.154937766195324640.539977891641
Winsorized Mean ( 12 / 20 )99.25783333333330.148815301227638666.986744740058
Winsorized Mean ( 13 / 20 )99.26216666666670.146762826399624676.344065467802
Winsorized Mean ( 14 / 20 )99.25050.143461529519162691.826584678533
Winsorized Mean ( 15 / 20 )99.22050.134291702273205738.843117783588
Winsorized Mean ( 16 / 20 )99.20183333333330.129972507233394763.25244041953
Winsorized Mean ( 17 / 20 )99.1650.123161622718826805.161525245492
Winsorized Mean ( 18 / 20 )99.1650.121415265377409816.742439196208
Winsorized Mean ( 19 / 20 )99.18083333333330.116225305175287853.349734670539
Winsorized Mean ( 20 / 20 )99.22083333333330.106393707511848932.581781890474
Trimmed Mean ( 1 / 20 )99.10603448275860.203036379262444488.119591389356
Trimmed Mean ( 2 / 20 )99.16017857142860.186041381214285533.000657833295
Trimmed Mean ( 3 / 20 )99.19314814814820.177059968062495560.223461201219
Trimmed Mean ( 4 / 20 )99.21923076923080.169971128360546583.741672637277
Trimmed Mean ( 5 / 20 )99.2360.166003442305101597.794832577101
Trimmed Mean ( 6 / 20 )99.23916666666670.165315578648037600.301359849156
Trimmed Mean ( 7 / 20 )99.24282608695650.164421886669005603.586469523616
Trimmed Mean ( 8 / 20 )99.24522727272730.163498514141461607.009964548418
Trimmed Mean ( 9 / 20 )99.24761904761910.162291162875496611.540500968363
Trimmed Mean ( 10 / 20 )99.250750.16126995503638615.432366044939
Trimmed Mean ( 11 / 20 )99.25184210526320.160305919873207619.140217552575
Trimmed Mean ( 12 / 20 )99.25305555555560.158590427584203625.845185409173
Trimmed Mean ( 13 / 20 )99.25235294117650.157401503493064630.568010715033
Trimmed Mean ( 14 / 20 )99.25093750.155770301953762637.162130747241
Trimmed Mean ( 15 / 20 )99.2510.153822819406338645.229364427514
Trimmed Mean ( 16 / 20 )99.25535714285710.153001264080659648.722464740759
Trimmed Mean ( 17 / 20 )99.26307692307690.152182854822004652.261892702544
Trimmed Mean ( 18 / 20 )99.27750.151929915669569653.442737478494
Trimmed Mean ( 19 / 20 )99.29454545454550.150768202109777658.590764266378
Trimmed Mean ( 20 / 20 )99.31250.1494760586357664.404058458903
Median99.59
Midrange97
Midmean - Weighted Average at Xnp99.2083870967742
Midmean - Weighted Average at X(n+1)p99.251
Midmean - Empirical Distribution Function99.2083870967742
Midmean - Empirical Distribution Function - Averaging99.251
Midmean - Empirical Distribution Function - Interpolation99.251
Midmean - Closest Observation99.2083870967742
Midmean - True Basic - Statistics Graphics Toolkit99.251
Midmean - MS Excel (old versions)99.2509375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 99.0358333333333 & 0.224954520408802 & 440.248247305095 \tabularnewline
Geometric Mean & 99.0205401916419 &  &  \tabularnewline
Harmonic Mean & 99.0050217246777 &  &  \tabularnewline
Quadratic Mean & 99.0509058598995 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 99.0555 & 0.216319420783039 & 457.913115897944 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 99.1008333333334 & 0.19888947213983 & 498.270885166109 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 99.1253333333333 & 0.190646456990652 & 519.943223168284 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 99.1633333333333 & 0.178490321101539 & 555.567006218347 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 99.2233333333333 & 0.165365656581552 & 600.02382226445 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 99.2223333333333 & 0.164500161706628 & 603.174685689903 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 99.2305 & 0.162645749500282 & 610.102018066128 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 99.2318333333333 & 0.16150571375152 & 614.41685887351 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 99.2288333333333 & 0.157998264251831 & 628.037490178842 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 99.2438333333333 & 0.154937766195324 & 640.539977891641 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 99.2438333333333 & 0.154937766195324 & 640.539977891641 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 99.2578333333333 & 0.148815301227638 & 666.986744740058 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 99.2621666666667 & 0.146762826399624 & 676.344065467802 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 99.2505 & 0.143461529519162 & 691.826584678533 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 99.2205 & 0.134291702273205 & 738.843117783588 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 99.2018333333333 & 0.129972507233394 & 763.25244041953 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 99.165 & 0.123161622718826 & 805.161525245492 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 99.165 & 0.121415265377409 & 816.742439196208 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 99.1808333333333 & 0.116225305175287 & 853.349734670539 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 99.2208333333333 & 0.106393707511848 & 932.581781890474 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 99.1060344827586 & 0.203036379262444 & 488.119591389356 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 99.1601785714286 & 0.186041381214285 & 533.000657833295 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 99.1931481481482 & 0.177059968062495 & 560.223461201219 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 99.2192307692308 & 0.169971128360546 & 583.741672637277 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 99.236 & 0.166003442305101 & 597.794832577101 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 99.2391666666667 & 0.165315578648037 & 600.301359849156 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 99.2428260869565 & 0.164421886669005 & 603.586469523616 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 99.2452272727273 & 0.163498514141461 & 607.009964548418 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 99.2476190476191 & 0.162291162875496 & 611.540500968363 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 99.25075 & 0.16126995503638 & 615.432366044939 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 99.2518421052632 & 0.160305919873207 & 619.140217552575 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 99.2530555555556 & 0.158590427584203 & 625.845185409173 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 99.2523529411765 & 0.157401503493064 & 630.568010715033 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 99.2509375 & 0.155770301953762 & 637.162130747241 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 99.251 & 0.153822819406338 & 645.229364427514 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 99.2553571428571 & 0.153001264080659 & 648.722464740759 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 99.2630769230769 & 0.152182854822004 & 652.261892702544 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 99.2775 & 0.151929915669569 & 653.442737478494 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 99.2945454545455 & 0.150768202109777 & 658.590764266378 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 99.3125 & 0.1494760586357 & 664.404058458903 \tabularnewline
Median & 99.59 &  &  \tabularnewline
Midrange & 97 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.2083870967742 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.251 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.2083870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.251 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.251 &  &  \tabularnewline
Midmean - Closest Observation & 99.2083870967742 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.251 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.2509375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293751&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]99.0358333333333[/C][C]0.224954520408802[/C][C]440.248247305095[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]99.0205401916419[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.0050217246777[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]99.0509058598995[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]99.0555[/C][C]0.216319420783039[/C][C]457.913115897944[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]99.1008333333334[/C][C]0.19888947213983[/C][C]498.270885166109[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]99.1253333333333[/C][C]0.190646456990652[/C][C]519.943223168284[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]99.1633333333333[/C][C]0.178490321101539[/C][C]555.567006218347[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]99.2233333333333[/C][C]0.165365656581552[/C][C]600.02382226445[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]99.2223333333333[/C][C]0.164500161706628[/C][C]603.174685689903[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]99.2305[/C][C]0.162645749500282[/C][C]610.102018066128[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]99.2318333333333[/C][C]0.16150571375152[/C][C]614.41685887351[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]99.2288333333333[/C][C]0.157998264251831[/C][C]628.037490178842[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]99.2438333333333[/C][C]0.154937766195324[/C][C]640.539977891641[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]99.2438333333333[/C][C]0.154937766195324[/C][C]640.539977891641[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]99.2578333333333[/C][C]0.148815301227638[/C][C]666.986744740058[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]99.2621666666667[/C][C]0.146762826399624[/C][C]676.344065467802[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]99.2505[/C][C]0.143461529519162[/C][C]691.826584678533[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]99.2205[/C][C]0.134291702273205[/C][C]738.843117783588[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]99.2018333333333[/C][C]0.129972507233394[/C][C]763.25244041953[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]99.165[/C][C]0.123161622718826[/C][C]805.161525245492[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]99.165[/C][C]0.121415265377409[/C][C]816.742439196208[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]99.1808333333333[/C][C]0.116225305175287[/C][C]853.349734670539[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]99.2208333333333[/C][C]0.106393707511848[/C][C]932.581781890474[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]99.1060344827586[/C][C]0.203036379262444[/C][C]488.119591389356[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]99.1601785714286[/C][C]0.186041381214285[/C][C]533.000657833295[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]99.1931481481482[/C][C]0.177059968062495[/C][C]560.223461201219[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]99.2192307692308[/C][C]0.169971128360546[/C][C]583.741672637277[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]99.236[/C][C]0.166003442305101[/C][C]597.794832577101[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]99.2391666666667[/C][C]0.165315578648037[/C][C]600.301359849156[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]99.2428260869565[/C][C]0.164421886669005[/C][C]603.586469523616[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]99.2452272727273[/C][C]0.163498514141461[/C][C]607.009964548418[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]99.2476190476191[/C][C]0.162291162875496[/C][C]611.540500968363[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]99.25075[/C][C]0.16126995503638[/C][C]615.432366044939[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]99.2518421052632[/C][C]0.160305919873207[/C][C]619.140217552575[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]99.2530555555556[/C][C]0.158590427584203[/C][C]625.845185409173[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]99.2523529411765[/C][C]0.157401503493064[/C][C]630.568010715033[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]99.2509375[/C][C]0.155770301953762[/C][C]637.162130747241[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]99.251[/C][C]0.153822819406338[/C][C]645.229364427514[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]99.2553571428571[/C][C]0.153001264080659[/C][C]648.722464740759[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]99.2630769230769[/C][C]0.152182854822004[/C][C]652.261892702544[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]99.2775[/C][C]0.151929915669569[/C][C]653.442737478494[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]99.2945454545455[/C][C]0.150768202109777[/C][C]658.590764266378[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]99.3125[/C][C]0.1494760586357[/C][C]664.404058458903[/C][/ROW]
[ROW][C]Median[/C][C]99.59[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]97[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.2083870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.251[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.2083870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.251[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.251[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.2083870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.251[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.2509375[/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=293751&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293751&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 Mean99.03583333333330.224954520408802440.248247305095
Geometric Mean99.0205401916419
Harmonic Mean99.0050217246777
Quadratic Mean99.0509058598995
Winsorized Mean ( 1 / 20 )99.05550.216319420783039457.913115897944
Winsorized Mean ( 2 / 20 )99.10083333333340.19888947213983498.270885166109
Winsorized Mean ( 3 / 20 )99.12533333333330.190646456990652519.943223168284
Winsorized Mean ( 4 / 20 )99.16333333333330.178490321101539555.567006218347
Winsorized Mean ( 5 / 20 )99.22333333333330.165365656581552600.02382226445
Winsorized Mean ( 6 / 20 )99.22233333333330.164500161706628603.174685689903
Winsorized Mean ( 7 / 20 )99.23050.162645749500282610.102018066128
Winsorized Mean ( 8 / 20 )99.23183333333330.16150571375152614.41685887351
Winsorized Mean ( 9 / 20 )99.22883333333330.157998264251831628.037490178842
Winsorized Mean ( 10 / 20 )99.24383333333330.154937766195324640.539977891641
Winsorized Mean ( 11 / 20 )99.24383333333330.154937766195324640.539977891641
Winsorized Mean ( 12 / 20 )99.25783333333330.148815301227638666.986744740058
Winsorized Mean ( 13 / 20 )99.26216666666670.146762826399624676.344065467802
Winsorized Mean ( 14 / 20 )99.25050.143461529519162691.826584678533
Winsorized Mean ( 15 / 20 )99.22050.134291702273205738.843117783588
Winsorized Mean ( 16 / 20 )99.20183333333330.129972507233394763.25244041953
Winsorized Mean ( 17 / 20 )99.1650.123161622718826805.161525245492
Winsorized Mean ( 18 / 20 )99.1650.121415265377409816.742439196208
Winsorized Mean ( 19 / 20 )99.18083333333330.116225305175287853.349734670539
Winsorized Mean ( 20 / 20 )99.22083333333330.106393707511848932.581781890474
Trimmed Mean ( 1 / 20 )99.10603448275860.203036379262444488.119591389356
Trimmed Mean ( 2 / 20 )99.16017857142860.186041381214285533.000657833295
Trimmed Mean ( 3 / 20 )99.19314814814820.177059968062495560.223461201219
Trimmed Mean ( 4 / 20 )99.21923076923080.169971128360546583.741672637277
Trimmed Mean ( 5 / 20 )99.2360.166003442305101597.794832577101
Trimmed Mean ( 6 / 20 )99.23916666666670.165315578648037600.301359849156
Trimmed Mean ( 7 / 20 )99.24282608695650.164421886669005603.586469523616
Trimmed Mean ( 8 / 20 )99.24522727272730.163498514141461607.009964548418
Trimmed Mean ( 9 / 20 )99.24761904761910.162291162875496611.540500968363
Trimmed Mean ( 10 / 20 )99.250750.16126995503638615.432366044939
Trimmed Mean ( 11 / 20 )99.25184210526320.160305919873207619.140217552575
Trimmed Mean ( 12 / 20 )99.25305555555560.158590427584203625.845185409173
Trimmed Mean ( 13 / 20 )99.25235294117650.157401503493064630.568010715033
Trimmed Mean ( 14 / 20 )99.25093750.155770301953762637.162130747241
Trimmed Mean ( 15 / 20 )99.2510.153822819406338645.229364427514
Trimmed Mean ( 16 / 20 )99.25535714285710.153001264080659648.722464740759
Trimmed Mean ( 17 / 20 )99.26307692307690.152182854822004652.261892702544
Trimmed Mean ( 18 / 20 )99.27750.151929915669569653.442737478494
Trimmed Mean ( 19 / 20 )99.29454545454550.150768202109777658.590764266378
Trimmed Mean ( 20 / 20 )99.31250.1494760586357664.404058458903
Median99.59
Midrange97
Midmean - Weighted Average at Xnp99.2083870967742
Midmean - Weighted Average at X(n+1)p99.251
Midmean - Empirical Distribution Function99.2083870967742
Midmean - Empirical Distribution Function - Averaging99.251
Midmean - Empirical Distribution Function - Interpolation99.251
Midmean - Closest Observation99.2083870967742
Midmean - True Basic - Statistics Graphics Toolkit99.251
Midmean - MS Excel (old versions)99.2509375
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')