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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 computationTue, 16 Dec 2008 10:15:20 -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/16/t1229447924kbxzccwpwmm3un6.htm/, Retrieved Wed, 15 May 2024 23:00:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34045, Retrieved Wed, 15 May 2024 23:00:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact162
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central tendency:...] [2008-12-16 17:15:20] [e515c0250d6233b5d2604259ab52cebe] [Current]
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Dataseries X:
101,3
91,5
152,6
86,6
86,6
98,5
86,7
89,1
111
92,6
85,1
116,1
98,3
97,7
177,9
94,2
83,8
109,5
102,3
102,5
116,4
85,3
88,2
104,7
99,4
113,8
166,6
89,2
93,2
115
97,2
112,5
121,8
100,2
93,8
113,6
110,7
127,6
185,9
105,9
108
125,2
106,2
123,3
145,2
114,3
108,4
120,9
126,3
141,3
208,2
131,6
119,8
122,5
137,6
141
154,1
127
106,1
129,9




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34045&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34045&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34045&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean115.033.3449069979386234.3895959053241
Geometric Mean112.542087239989
Harmonic Mean110.366314079267
Quadratic Mean117.864399487999
Winsorized Mean ( 1 / 20 )114.683.1828457934107936.0306491245707
Winsorized Mean ( 2 / 20 )114.423.0846492534726137.0933583036026
Winsorized Mean ( 3 / 20 )113.922.8879926757031939.4460834192601
Winsorized Mean ( 4 / 20 )113.0866666666672.6489902848425542.6904799590038
Winsorized Mean ( 5 / 20 )112.972.6151182579043843.1988112424897
Winsorized Mean ( 6 / 20 )112.382.4087104175691646.6556706776783
Winsorized Mean ( 7 / 20 )112.032.2889334599723148.9441925504272
Winsorized Mean ( 8 / 20 )112.0033333333332.2780207072697049.1669513696274
Winsorized Mean ( 9 / 20 )111.8383333333332.1127646648858552.9345909613535
Winsorized Mean ( 10 / 20 )111.0216666666671.8862423286551958.8586445018549
Winsorized Mean ( 11 / 20 )110.821.8114135941412061.1787392776746
Winsorized Mean ( 12 / 20 )110.481.7114961901913664.5517066489334
Winsorized Mean ( 13 / 20 )110.4366666666671.6753058016941965.9203033589362
Winsorized Mean ( 14 / 20 )110.9733333333331.5369826384462372.2020734375497
Winsorized Mean ( 15 / 20 )110.8233333333331.4720337725389675.2858632734936
Winsorized Mean ( 16 / 20 )110.4766666666671.3655370141815380.9034581408865
Winsorized Mean ( 17 / 20 )110.3066666666671.3211916096097583.4902869987562
Winsorized Mean ( 18 / 20 )110.3666666666671.2478923851424188.4424554398345
Winsorized Mean ( 19 / 20 )110.3351.1663473937630594.5987452709269
Winsorized Mean ( 20 / 20 )110.3351.05676412871029104.408350929414
Trimmed Mean ( 1 / 20 )113.9620689655173.0065886789665937.9041103170414
Trimmed Mean ( 2 / 20 )113.1928571428572.7823432817126140.6825634661385
Trimmed Mean ( 3 / 20 )112.5111111111112.5666172048198643.8363425990545
Trimmed Mean ( 4 / 20 )111.9692307692312.3973048253827646.7062968312148
Trimmed Mean ( 5 / 20 )111.6342.2872327277783548.8074513118885
Trimmed Mean ( 6 / 20 )111.32.1585780550765751.5617212628671
Trimmed Mean ( 7 / 20 )111.0652173913042.0649343309704453.7863193640197
Trimmed Mean ( 8 / 20 )110.8772727272731.9814436822487655.9578219257977
Trimmed Mean ( 9 / 20 )110.6761904761901.8742766611680959.0500819698702
Trimmed Mean ( 10 / 20 )110.48251.7822338600899961.991022880926
Trimmed Mean ( 11 / 20 )110.3973684210531.7261089652499263.9573576428696
Trimmed Mean ( 12 / 20 )110.3333333333331.6697257640056166.0787152667799
Trimmed Mean ( 13 / 20 )110.3117647058821.6191135792883968.130961358724
Trimmed Mean ( 14 / 20 )110.293751.5564831733596170.8608688405766
Trimmed Mean ( 15 / 20 )110.1966666666671.5068158048453773.1321415081488
Trimmed Mean ( 16 / 20 )110.1071428571431.4519821206231275.8322993742444
Trimmed Mean ( 17 / 20 )110.0538461538461.4034597993117078.4161015568956
Trimmed Mean ( 18 / 20 )110.0166666666671.3404745356314482.0729254769785
Trimmed Mean ( 19 / 20 )109.9636363636361.2658098968652386.872157214097
Trimmed Mean ( 20 / 20 )109.9051.1756851306007993.4816620023403
Median110.1
Midrange146
Midmean - Weighted Average at Xnp109.777419354839
Midmean - Weighted Average at X(n+1)p110.196666666667
Midmean - Empirical Distribution Function109.777419354839
Midmean - Empirical Distribution Function - Averaging110.196666666667
Midmean - Empirical Distribution Function - Interpolation110.196666666667
Midmean - Closest Observation109.777419354839
Midmean - True Basic - Statistics Graphics Toolkit110.196666666667
Midmean - MS Excel (old versions)110.29375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 115.03 & 3.34490699793862 & 34.3895959053241 \tabularnewline
Geometric Mean & 112.542087239989 &  &  \tabularnewline
Harmonic Mean & 110.366314079267 &  &  \tabularnewline
Quadratic Mean & 117.864399487999 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 114.68 & 3.18284579341079 & 36.0306491245707 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 114.42 & 3.08464925347261 & 37.0933583036026 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 113.92 & 2.88799267570319 & 39.4460834192601 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 113.086666666667 & 2.64899028484255 & 42.6904799590038 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 112.97 & 2.61511825790438 & 43.1988112424897 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 112.38 & 2.40871041756916 & 46.6556706776783 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 112.03 & 2.28893345997231 & 48.9441925504272 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 112.003333333333 & 2.27802070726970 & 49.1669513696274 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 111.838333333333 & 2.11276466488585 & 52.9345909613535 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 111.021666666667 & 1.88624232865519 & 58.8586445018549 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 110.82 & 1.81141359414120 & 61.1787392776746 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 110.48 & 1.71149619019136 & 64.5517066489334 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 110.436666666667 & 1.67530580169419 & 65.9203033589362 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 110.973333333333 & 1.53698263844623 & 72.2020734375497 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 110.823333333333 & 1.47203377253896 & 75.2858632734936 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 110.476666666667 & 1.36553701418153 & 80.9034581408865 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 110.306666666667 & 1.32119160960975 & 83.4902869987562 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 110.366666666667 & 1.24789238514241 & 88.4424554398345 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 110.335 & 1.16634739376305 & 94.5987452709269 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 110.335 & 1.05676412871029 & 104.408350929414 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 113.962068965517 & 3.00658867896659 & 37.9041103170414 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 113.192857142857 & 2.78234328171261 & 40.6825634661385 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 112.511111111111 & 2.56661720481986 & 43.8363425990545 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 111.969230769231 & 2.39730482538276 & 46.7062968312148 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 111.634 & 2.28723272777835 & 48.8074513118885 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 111.3 & 2.15857805507657 & 51.5617212628671 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 111.065217391304 & 2.06493433097044 & 53.7863193640197 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 110.877272727273 & 1.98144368224876 & 55.9578219257977 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 110.676190476190 & 1.87427666116809 & 59.0500819698702 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 110.4825 & 1.78223386008999 & 61.991022880926 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 110.397368421053 & 1.72610896524992 & 63.9573576428696 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 110.333333333333 & 1.66972576400561 & 66.0787152667799 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 110.311764705882 & 1.61911357928839 & 68.130961358724 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 110.29375 & 1.55648317335961 & 70.8608688405766 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 110.196666666667 & 1.50681580484537 & 73.1321415081488 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 110.107142857143 & 1.45198212062312 & 75.8322993742444 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 110.053846153846 & 1.40345979931170 & 78.4161015568956 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 110.016666666667 & 1.34047453563144 & 82.0729254769785 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 109.963636363636 & 1.26580989686523 & 86.872157214097 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 109.905 & 1.17568513060079 & 93.4816620023403 \tabularnewline
Median & 110.1 &  &  \tabularnewline
Midrange & 146 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 109.777419354839 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 110.196666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 109.777419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 110.196666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 110.196666666667 &  &  \tabularnewline
Midmean - Closest Observation & 109.777419354839 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 110.196666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 110.29375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34045&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]115.03[/C][C]3.34490699793862[/C][C]34.3895959053241[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]112.542087239989[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]110.366314079267[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]117.864399487999[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]114.68[/C][C]3.18284579341079[/C][C]36.0306491245707[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]114.42[/C][C]3.08464925347261[/C][C]37.0933583036026[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]113.92[/C][C]2.88799267570319[/C][C]39.4460834192601[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]113.086666666667[/C][C]2.64899028484255[/C][C]42.6904799590038[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]112.97[/C][C]2.61511825790438[/C][C]43.1988112424897[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]112.38[/C][C]2.40871041756916[/C][C]46.6556706776783[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]112.03[/C][C]2.28893345997231[/C][C]48.9441925504272[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]112.003333333333[/C][C]2.27802070726970[/C][C]49.1669513696274[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]111.838333333333[/C][C]2.11276466488585[/C][C]52.9345909613535[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]111.021666666667[/C][C]1.88624232865519[/C][C]58.8586445018549[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]110.82[/C][C]1.81141359414120[/C][C]61.1787392776746[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]110.48[/C][C]1.71149619019136[/C][C]64.5517066489334[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]110.436666666667[/C][C]1.67530580169419[/C][C]65.9203033589362[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]110.973333333333[/C][C]1.53698263844623[/C][C]72.2020734375497[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]110.823333333333[/C][C]1.47203377253896[/C][C]75.2858632734936[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]110.476666666667[/C][C]1.36553701418153[/C][C]80.9034581408865[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]110.306666666667[/C][C]1.32119160960975[/C][C]83.4902869987562[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]110.366666666667[/C][C]1.24789238514241[/C][C]88.4424554398345[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]110.335[/C][C]1.16634739376305[/C][C]94.5987452709269[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]110.335[/C][C]1.05676412871029[/C][C]104.408350929414[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]113.962068965517[/C][C]3.00658867896659[/C][C]37.9041103170414[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]113.192857142857[/C][C]2.78234328171261[/C][C]40.6825634661385[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]112.511111111111[/C][C]2.56661720481986[/C][C]43.8363425990545[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]111.969230769231[/C][C]2.39730482538276[/C][C]46.7062968312148[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]111.634[/C][C]2.28723272777835[/C][C]48.8074513118885[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]111.3[/C][C]2.15857805507657[/C][C]51.5617212628671[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]111.065217391304[/C][C]2.06493433097044[/C][C]53.7863193640197[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]110.877272727273[/C][C]1.98144368224876[/C][C]55.9578219257977[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]110.676190476190[/C][C]1.87427666116809[/C][C]59.0500819698702[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]110.4825[/C][C]1.78223386008999[/C][C]61.991022880926[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]110.397368421053[/C][C]1.72610896524992[/C][C]63.9573576428696[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]110.333333333333[/C][C]1.66972576400561[/C][C]66.0787152667799[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]110.311764705882[/C][C]1.61911357928839[/C][C]68.130961358724[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]110.29375[/C][C]1.55648317335961[/C][C]70.8608688405766[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]110.196666666667[/C][C]1.50681580484537[/C][C]73.1321415081488[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]110.107142857143[/C][C]1.45198212062312[/C][C]75.8322993742444[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]110.053846153846[/C][C]1.40345979931170[/C][C]78.4161015568956[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]110.016666666667[/C][C]1.34047453563144[/C][C]82.0729254769785[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]109.963636363636[/C][C]1.26580989686523[/C][C]86.872157214097[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]109.905[/C][C]1.17568513060079[/C][C]93.4816620023403[/C][/ROW]
[ROW][C]Median[/C][C]110.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]146[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]109.777419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]110.196666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]109.777419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]110.196666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]110.196666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]109.777419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]110.196666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]110.29375[/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=34045&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34045&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 Mean115.033.3449069979386234.3895959053241
Geometric Mean112.542087239989
Harmonic Mean110.366314079267
Quadratic Mean117.864399487999
Winsorized Mean ( 1 / 20 )114.683.1828457934107936.0306491245707
Winsorized Mean ( 2 / 20 )114.423.0846492534726137.0933583036026
Winsorized Mean ( 3 / 20 )113.922.8879926757031939.4460834192601
Winsorized Mean ( 4 / 20 )113.0866666666672.6489902848425542.6904799590038
Winsorized Mean ( 5 / 20 )112.972.6151182579043843.1988112424897
Winsorized Mean ( 6 / 20 )112.382.4087104175691646.6556706776783
Winsorized Mean ( 7 / 20 )112.032.2889334599723148.9441925504272
Winsorized Mean ( 8 / 20 )112.0033333333332.2780207072697049.1669513696274
Winsorized Mean ( 9 / 20 )111.8383333333332.1127646648858552.9345909613535
Winsorized Mean ( 10 / 20 )111.0216666666671.8862423286551958.8586445018549
Winsorized Mean ( 11 / 20 )110.821.8114135941412061.1787392776746
Winsorized Mean ( 12 / 20 )110.481.7114961901913664.5517066489334
Winsorized Mean ( 13 / 20 )110.4366666666671.6753058016941965.9203033589362
Winsorized Mean ( 14 / 20 )110.9733333333331.5369826384462372.2020734375497
Winsorized Mean ( 15 / 20 )110.8233333333331.4720337725389675.2858632734936
Winsorized Mean ( 16 / 20 )110.4766666666671.3655370141815380.9034581408865
Winsorized Mean ( 17 / 20 )110.3066666666671.3211916096097583.4902869987562
Winsorized Mean ( 18 / 20 )110.3666666666671.2478923851424188.4424554398345
Winsorized Mean ( 19 / 20 )110.3351.1663473937630594.5987452709269
Winsorized Mean ( 20 / 20 )110.3351.05676412871029104.408350929414
Trimmed Mean ( 1 / 20 )113.9620689655173.0065886789665937.9041103170414
Trimmed Mean ( 2 / 20 )113.1928571428572.7823432817126140.6825634661385
Trimmed Mean ( 3 / 20 )112.5111111111112.5666172048198643.8363425990545
Trimmed Mean ( 4 / 20 )111.9692307692312.3973048253827646.7062968312148
Trimmed Mean ( 5 / 20 )111.6342.2872327277783548.8074513118885
Trimmed Mean ( 6 / 20 )111.32.1585780550765751.5617212628671
Trimmed Mean ( 7 / 20 )111.0652173913042.0649343309704453.7863193640197
Trimmed Mean ( 8 / 20 )110.8772727272731.9814436822487655.9578219257977
Trimmed Mean ( 9 / 20 )110.6761904761901.8742766611680959.0500819698702
Trimmed Mean ( 10 / 20 )110.48251.7822338600899961.991022880926
Trimmed Mean ( 11 / 20 )110.3973684210531.7261089652499263.9573576428696
Trimmed Mean ( 12 / 20 )110.3333333333331.6697257640056166.0787152667799
Trimmed Mean ( 13 / 20 )110.3117647058821.6191135792883968.130961358724
Trimmed Mean ( 14 / 20 )110.293751.5564831733596170.8608688405766
Trimmed Mean ( 15 / 20 )110.1966666666671.5068158048453773.1321415081488
Trimmed Mean ( 16 / 20 )110.1071428571431.4519821206231275.8322993742444
Trimmed Mean ( 17 / 20 )110.0538461538461.4034597993117078.4161015568956
Trimmed Mean ( 18 / 20 )110.0166666666671.3404745356314482.0729254769785
Trimmed Mean ( 19 / 20 )109.9636363636361.2658098968652386.872157214097
Trimmed Mean ( 20 / 20 )109.9051.1756851306007993.4816620023403
Median110.1
Midrange146
Midmean - Weighted Average at Xnp109.777419354839
Midmean - Weighted Average at X(n+1)p110.196666666667
Midmean - Empirical Distribution Function109.777419354839
Midmean - Empirical Distribution Function - Averaging110.196666666667
Midmean - Empirical Distribution Function - Interpolation110.196666666667
Midmean - Closest Observation109.777419354839
Midmean - True Basic - Statistics Graphics Toolkit110.196666666667
Midmean - MS Excel (old versions)110.29375
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')