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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, 21 Nov 2008 07:21:45 -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/Nov/21/t1227277458jo3t6zph9ayhbfd.htm/, Retrieved Sun, 09 Jun 2024 10:12:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25138, Retrieved Sun, 09 Jun 2024 10:12:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact178
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Exercise 1.13] [Exercise 1.13 (Wo...] [2008-10-01 13:28:34] [b98453cac15ba1066b407e146608df68]
F   P   [Exercise 1.13] [vraag 1 result 1 ...] [2008-10-10 13:06:35] [74be16979710d4c4e7c6647856088456]
- RMPD    [Central Tendency] [] [2008-11-21 14:16:19] [fad8a251ac01c156a8ae23a83577546f]
-    D        [Central Tendency] [] [2008-11-21 14:21:45] [fa8b44cd657c07c6ee11bb2476ca3f8d] [Current]
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Dataseries X:
72,5
72,0
98,8
75,2
81,2
88,0
54,6
68,6
101,5
93,4
84,5
91,4
64,5
64,5
117,3
73,5
79,7
102,6
57,9
73,1
102,4
82,3
89,1
84,7
81,4
67,5
113,9
83,8
73,9
103,9
67,9
62,5
125,4
79,1
106,3
96,2
94,3
85,6
117,4
88,5
124,2
119,3
76,8
70,6
122,1
109,5
119,9
102,3
79,6
78,2
103,6
77,8
99,1
105,7
84,1
88,7
108,0
98,1
101,0
82,0




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25138&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25138&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25138&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean89.5252.3126300543670138.7113363985507
Geometric Mean87.7572379038459
Harmonic Mean85.9926807531557
Quadratic Mean91.2703283292732
Winsorized Mean ( 1 / 20 )89.562.2939667861194539.0415417267233
Winsorized Mean ( 2 / 20 )89.64333333333332.2427338627014439.9705621893787
Winsorized Mean ( 3 / 20 )89.63333333333332.1964309347721640.8086281768888
Winsorized Mean ( 4 / 20 )89.59333333333332.1871554504009240.9634044607621
Winsorized Mean ( 5 / 20 )89.6852.1045710608773742.6143843119327
Winsorized Mean ( 6 / 20 )89.7152.0952364927262942.8185554764102
Winsorized Mean ( 7 / 20 )89.41.9952075349057444.8073688756511
Winsorized Mean ( 8 / 20 )89.081.8321174190777648.6213378424407
Winsorized Mean ( 9 / 20 )89.0651.7550086918515750.7490364084946
Winsorized Mean ( 10 / 20 )88.8651.6906152141335752.5637053642292
Winsorized Mean ( 11 / 20 )88.8651.6535970464688253.7404201282091
Winsorized Mean ( 12 / 20 )88.5851.5799946810323156.0666444409305
Winsorized Mean ( 13 / 20 )88.60666666666671.5553876960817256.9675759232772
Winsorized Mean ( 14 / 20 )88.67666666666671.4696849400383560.3371948986243
Winsorized Mean ( 15 / 20 )89.02666666666671.4009215422743363.548645645163
Winsorized Mean ( 16 / 20 )89.26666666666671.3577766527653765.7447353251054
Winsorized Mean ( 17 / 20 )89.15333333333341.3049849376074468.317519048754
Winsorized Mean ( 18 / 20 )89.27333333333331.2430208934766971.8196562920505
Winsorized Mean ( 19 / 20 )88.831.1263718565917978.8638312295768
Winsorized Mean ( 20 / 20 )88.76333333333331.1063273763463980.2324295964468
Trimmed Mean ( 1 / 20 )89.50862068965522.229025765887340.1559381051052
Trimmed Mean ( 2 / 20 )89.45357142857142.1489410927331441.626814123043
Trimmed Mean ( 3 / 20 )89.34814814814812.0840476607497042.872411140543
Trimmed Mean ( 4 / 20 )89.23846153846152.0253784888194444.0601408729671
Trimmed Mean ( 5 / 20 )89.1321.9548650770290445.5949625615394
Trimmed Mean ( 6 / 20 )88.993751.8942250943037646.9816128334583
Trimmed Mean ( 7 / 20 )88.83695652173911.8187705108046248.8445111650936
Trimmed Mean ( 8 / 20 )88.72727272727271.7522542522258650.63607214225
Trimmed Mean ( 9 / 20 )88.66428571428571.7123104909802951.7804955242235
Trimmed Mean ( 10 / 20 )88.59751.6788980188481752.7712219594991
Trimmed Mean ( 11 / 20 )88.55526315789471.6493013192428153.6925922053773
Trimmed Mean ( 12 / 20 )88.50833333333331.6163125532647754.7594171403028
Trimmed Mean ( 13 / 20 )88.49705882352941.5880429176420455.7271203696004
Trimmed Mean ( 14 / 20 )88.481251.5516538880518657.0238315911356
Trimmed Mean ( 15 / 20 )88.45333333333331.5209701481524558.1558641639215
Trimmed Mean ( 16 / 20 )88.37142857142861.4916509899225659.244038430207
Trimmed Mean ( 17 / 20 )88.24230769230771.4549245085033760.6507809694396
Trimmed Mean ( 18 / 20 )88.10833333333331.4109293456291562.4470201901181
Trimmed Mean ( 19 / 20 )87.93181818181821.3570783865877364.7949440878768
Trimmed Mean ( 20 / 20 )87.791.3141917668285766.8015142203
Median86.8
Midrange90
Midmean - Weighted Average at Xnp88.025806451613
Midmean - Weighted Average at X(n+1)p88.4533333333333
Midmean - Empirical Distribution Function88.025806451613
Midmean - Empirical Distribution Function - Averaging88.4533333333333
Midmean - Empirical Distribution Function - Interpolation88.4533333333333
Midmean - Closest Observation88.025806451613
Midmean - True Basic - Statistics Graphics Toolkit88.4533333333333
Midmean - MS Excel (old versions)88.48125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 89.525 & 2.31263005436701 & 38.7113363985507 \tabularnewline
Geometric Mean & 87.7572379038459 &  &  \tabularnewline
Harmonic Mean & 85.9926807531557 &  &  \tabularnewline
Quadratic Mean & 91.2703283292732 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 89.56 & 2.29396678611945 & 39.0415417267233 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 89.6433333333333 & 2.24273386270144 & 39.9705621893787 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 89.6333333333333 & 2.19643093477216 & 40.8086281768888 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 89.5933333333333 & 2.18715545040092 & 40.9634044607621 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 89.685 & 2.10457106087737 & 42.6143843119327 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 89.715 & 2.09523649272629 & 42.8185554764102 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 89.4 & 1.99520753490574 & 44.8073688756511 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 89.08 & 1.83211741907776 & 48.6213378424407 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 89.065 & 1.75500869185157 & 50.7490364084946 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 88.865 & 1.69061521413357 & 52.5637053642292 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 88.865 & 1.65359704646882 & 53.7404201282091 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 88.585 & 1.57999468103231 & 56.0666444409305 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 88.6066666666667 & 1.55538769608172 & 56.9675759232772 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 88.6766666666667 & 1.46968494003835 & 60.3371948986243 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 89.0266666666667 & 1.40092154227433 & 63.548645645163 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 89.2666666666667 & 1.35777665276537 & 65.7447353251054 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 89.1533333333334 & 1.30498493760744 & 68.317519048754 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 89.2733333333333 & 1.24302089347669 & 71.8196562920505 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 88.83 & 1.12637185659179 & 78.8638312295768 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 88.7633333333333 & 1.10632737634639 & 80.2324295964468 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 89.5086206896552 & 2.2290257658873 & 40.1559381051052 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 89.4535714285714 & 2.14894109273314 & 41.626814123043 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 89.3481481481481 & 2.08404766074970 & 42.872411140543 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 89.2384615384615 & 2.02537848881944 & 44.0601408729671 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 89.132 & 1.95486507702904 & 45.5949625615394 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 88.99375 & 1.89422509430376 & 46.9816128334583 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 88.8369565217391 & 1.81877051080462 & 48.8445111650936 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 88.7272727272727 & 1.75225425222586 & 50.63607214225 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 88.6642857142857 & 1.71231049098029 & 51.7804955242235 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 88.5975 & 1.67889801884817 & 52.7712219594991 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 88.5552631578947 & 1.64930131924281 & 53.6925922053773 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 88.5083333333333 & 1.61631255326477 & 54.7594171403028 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 88.4970588235294 & 1.58804291764204 & 55.7271203696004 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 88.48125 & 1.55165388805186 & 57.0238315911356 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 88.4533333333333 & 1.52097014815245 & 58.1558641639215 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 88.3714285714286 & 1.49165098992256 & 59.244038430207 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 88.2423076923077 & 1.45492450850337 & 60.6507809694396 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 88.1083333333333 & 1.41092934562915 & 62.4470201901181 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 87.9318181818182 & 1.35707838658773 & 64.7949440878768 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 87.79 & 1.31419176682857 & 66.8015142203 \tabularnewline
Median & 86.8 &  &  \tabularnewline
Midrange & 90 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 88.025806451613 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 88.4533333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 88.025806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 88.4533333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 88.4533333333333 &  &  \tabularnewline
Midmean - Closest Observation & 88.025806451613 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 88.4533333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 88.48125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25138&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]89.525[/C][C]2.31263005436701[/C][C]38.7113363985507[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]87.7572379038459[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]85.9926807531557[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]91.2703283292732[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]89.56[/C][C]2.29396678611945[/C][C]39.0415417267233[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]89.6433333333333[/C][C]2.24273386270144[/C][C]39.9705621893787[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]89.6333333333333[/C][C]2.19643093477216[/C][C]40.8086281768888[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]89.5933333333333[/C][C]2.18715545040092[/C][C]40.9634044607621[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]89.685[/C][C]2.10457106087737[/C][C]42.6143843119327[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]89.715[/C][C]2.09523649272629[/C][C]42.8185554764102[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]89.4[/C][C]1.99520753490574[/C][C]44.8073688756511[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]89.08[/C][C]1.83211741907776[/C][C]48.6213378424407[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]89.065[/C][C]1.75500869185157[/C][C]50.7490364084946[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]88.865[/C][C]1.69061521413357[/C][C]52.5637053642292[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]88.865[/C][C]1.65359704646882[/C][C]53.7404201282091[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]88.585[/C][C]1.57999468103231[/C][C]56.0666444409305[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]88.6066666666667[/C][C]1.55538769608172[/C][C]56.9675759232772[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]88.6766666666667[/C][C]1.46968494003835[/C][C]60.3371948986243[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]89.0266666666667[/C][C]1.40092154227433[/C][C]63.548645645163[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]89.2666666666667[/C][C]1.35777665276537[/C][C]65.7447353251054[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]89.1533333333334[/C][C]1.30498493760744[/C][C]68.317519048754[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]89.2733333333333[/C][C]1.24302089347669[/C][C]71.8196562920505[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]88.83[/C][C]1.12637185659179[/C][C]78.8638312295768[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]88.7633333333333[/C][C]1.10632737634639[/C][C]80.2324295964468[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]89.5086206896552[/C][C]2.2290257658873[/C][C]40.1559381051052[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]89.4535714285714[/C][C]2.14894109273314[/C][C]41.626814123043[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]89.3481481481481[/C][C]2.08404766074970[/C][C]42.872411140543[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]89.2384615384615[/C][C]2.02537848881944[/C][C]44.0601408729671[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]89.132[/C][C]1.95486507702904[/C][C]45.5949625615394[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]88.99375[/C][C]1.89422509430376[/C][C]46.9816128334583[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]88.8369565217391[/C][C]1.81877051080462[/C][C]48.8445111650936[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]88.7272727272727[/C][C]1.75225425222586[/C][C]50.63607214225[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]88.6642857142857[/C][C]1.71231049098029[/C][C]51.7804955242235[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]88.5975[/C][C]1.67889801884817[/C][C]52.7712219594991[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]88.5552631578947[/C][C]1.64930131924281[/C][C]53.6925922053773[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]88.5083333333333[/C][C]1.61631255326477[/C][C]54.7594171403028[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]88.4970588235294[/C][C]1.58804291764204[/C][C]55.7271203696004[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]88.48125[/C][C]1.55165388805186[/C][C]57.0238315911356[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]88.4533333333333[/C][C]1.52097014815245[/C][C]58.1558641639215[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]88.3714285714286[/C][C]1.49165098992256[/C][C]59.244038430207[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]88.2423076923077[/C][C]1.45492450850337[/C][C]60.6507809694396[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]88.1083333333333[/C][C]1.41092934562915[/C][C]62.4470201901181[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]87.9318181818182[/C][C]1.35707838658773[/C][C]64.7949440878768[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]87.79[/C][C]1.31419176682857[/C][C]66.8015142203[/C][/ROW]
[ROW][C]Median[/C][C]86.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]90[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]88.025806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]88.4533333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]88.025806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]88.4533333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]88.4533333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]88.025806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]88.4533333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]88.48125[/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=25138&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25138&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 Mean89.5252.3126300543670138.7113363985507
Geometric Mean87.7572379038459
Harmonic Mean85.9926807531557
Quadratic Mean91.2703283292732
Winsorized Mean ( 1 / 20 )89.562.2939667861194539.0415417267233
Winsorized Mean ( 2 / 20 )89.64333333333332.2427338627014439.9705621893787
Winsorized Mean ( 3 / 20 )89.63333333333332.1964309347721640.8086281768888
Winsorized Mean ( 4 / 20 )89.59333333333332.1871554504009240.9634044607621
Winsorized Mean ( 5 / 20 )89.6852.1045710608773742.6143843119327
Winsorized Mean ( 6 / 20 )89.7152.0952364927262942.8185554764102
Winsorized Mean ( 7 / 20 )89.41.9952075349057444.8073688756511
Winsorized Mean ( 8 / 20 )89.081.8321174190777648.6213378424407
Winsorized Mean ( 9 / 20 )89.0651.7550086918515750.7490364084946
Winsorized Mean ( 10 / 20 )88.8651.6906152141335752.5637053642292
Winsorized Mean ( 11 / 20 )88.8651.6535970464688253.7404201282091
Winsorized Mean ( 12 / 20 )88.5851.5799946810323156.0666444409305
Winsorized Mean ( 13 / 20 )88.60666666666671.5553876960817256.9675759232772
Winsorized Mean ( 14 / 20 )88.67666666666671.4696849400383560.3371948986243
Winsorized Mean ( 15 / 20 )89.02666666666671.4009215422743363.548645645163
Winsorized Mean ( 16 / 20 )89.26666666666671.3577766527653765.7447353251054
Winsorized Mean ( 17 / 20 )89.15333333333341.3049849376074468.317519048754
Winsorized Mean ( 18 / 20 )89.27333333333331.2430208934766971.8196562920505
Winsorized Mean ( 19 / 20 )88.831.1263718565917978.8638312295768
Winsorized Mean ( 20 / 20 )88.76333333333331.1063273763463980.2324295964468
Trimmed Mean ( 1 / 20 )89.50862068965522.229025765887340.1559381051052
Trimmed Mean ( 2 / 20 )89.45357142857142.1489410927331441.626814123043
Trimmed Mean ( 3 / 20 )89.34814814814812.0840476607497042.872411140543
Trimmed Mean ( 4 / 20 )89.23846153846152.0253784888194444.0601408729671
Trimmed Mean ( 5 / 20 )89.1321.9548650770290445.5949625615394
Trimmed Mean ( 6 / 20 )88.993751.8942250943037646.9816128334583
Trimmed Mean ( 7 / 20 )88.83695652173911.8187705108046248.8445111650936
Trimmed Mean ( 8 / 20 )88.72727272727271.7522542522258650.63607214225
Trimmed Mean ( 9 / 20 )88.66428571428571.7123104909802951.7804955242235
Trimmed Mean ( 10 / 20 )88.59751.6788980188481752.7712219594991
Trimmed Mean ( 11 / 20 )88.55526315789471.6493013192428153.6925922053773
Trimmed Mean ( 12 / 20 )88.50833333333331.6163125532647754.7594171403028
Trimmed Mean ( 13 / 20 )88.49705882352941.5880429176420455.7271203696004
Trimmed Mean ( 14 / 20 )88.481251.5516538880518657.0238315911356
Trimmed Mean ( 15 / 20 )88.45333333333331.5209701481524558.1558641639215
Trimmed Mean ( 16 / 20 )88.37142857142861.4916509899225659.244038430207
Trimmed Mean ( 17 / 20 )88.24230769230771.4549245085033760.6507809694396
Trimmed Mean ( 18 / 20 )88.10833333333331.4109293456291562.4470201901181
Trimmed Mean ( 19 / 20 )87.93181818181821.3570783865877364.7949440878768
Trimmed Mean ( 20 / 20 )87.791.3141917668285766.8015142203
Median86.8
Midrange90
Midmean - Weighted Average at Xnp88.025806451613
Midmean - Weighted Average at X(n+1)p88.4533333333333
Midmean - Empirical Distribution Function88.025806451613
Midmean - Empirical Distribution Function - Averaging88.4533333333333
Midmean - Empirical Distribution Function - Interpolation88.4533333333333
Midmean - Closest Observation88.025806451613
Midmean - True Basic - Statistics Graphics Toolkit88.4533333333333
Midmean - MS Excel (old versions)88.48125
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')