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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 16 Dec 2007 04:53:46 -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/2007/Dec/16/t1197805749ohksh02e016wbj3.htm/, Retrieved Thu, 02 May 2024 10:06:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4144, Retrieved Thu, 02 May 2024 10:06:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact233
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central tendency ...] [2007-12-16 11:53:46] [908a52009ae83f013a8231794220d3ac] [Current]
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Dataseries X:
103,8
100,8
110,6
104,0
112,6
107,3
98,9
109,8
104,9
102,2
123,9
124,9
112,7
121,9
100,6
104,3
120,4
107,5
102,9
125,6
107,5
108,8
128,4
121,1
119,5
128,7
108,7
105,5
119,8
111,3
110,6
120,1
97,5
107,7
127,3
117,2
119,8
116,2
111,0
112,4
130,6
109,1
118,8
123,9
101,6
112,8
128,0
129,6
125,8
119,5
115,7
113,6
129,7
112,0
116,8
127,0
112,1
113,3
120,5
127,7




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4144&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4144&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4144&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean114.781.1795187182828797.3108762250891
Geometric Mean114.421676876198
Harmonic Mean114.063214390028
Quadratic Mean115.137018373762
Winsorized Mean ( 1 / 20 )114.7883333333331.1706125965596498.0583445545428
Winsorized Mean ( 2 / 20 )114.8416666666671.1574623803642999.2184874557412
Winsorized Mean ( 3 / 20 )114.8066666666671.14589630540880100.189402937039
Winsorized Mean ( 4 / 20 )114.841.13099176516956101.539200847128
Winsorized Mean ( 5 / 20 )114.8566666666671.11449962592899103.056711724715
Winsorized Mean ( 6 / 20 )114.8966666666671.09529287331871104.900405604332
Winsorized Mean ( 7 / 20 )114.9551.06703937256264107.732669436480
Winsorized Mean ( 8 / 20 )114.9416666666671.05453363903522108.997629294998
Winsorized Mean ( 9 / 20 )114.8066666666671.01259823173247113.378300562744
Winsorized Mean ( 10 / 20 )114.8733333333330.989126952448604116.136086524548
Winsorized Mean ( 11 / 20 )114.8550.94718263471351121.259613289616
Winsorized Mean ( 12 / 20 )115.0150.853715127998803134.722925983059
Winsorized Mean ( 13 / 20 )115.0583333333330.847119718413992135.822990342793
Winsorized Mean ( 14 / 20 )114.5916666666670.768031056879506149.201865784243
Winsorized Mean ( 15 / 20 )114.4416666666670.728562905809293157.078634877168
Winsorized Mean ( 16 / 20 )114.5483333333330.663101306550914172.746354443411
Winsorized Mean ( 17 / 20 )114.5483333333330.654573185070956174.996984211805
Winsorized Mean ( 18 / 20 )114.5483333333330.627687404957874182.492642720816
Winsorized Mean ( 19 / 20 )114.6750.581390428635074197.24266921494
Winsorized Mean ( 20 / 20 )114.9416666666670.544387343752282211.139490999941
Trimmed Mean ( 1 / 20 )114.8051724137931.1505237567229999.7851385014333
Trimmed Mean ( 2 / 20 )114.8232142857141.12546091877266102.023279858470
Trimmed Mean ( 3 / 20 )114.8129629629631.10279818894332104.110583526597
Trimmed Mean ( 4 / 20 )114.8153846153851.07967784919140106.342261908376
Trimmed Mean ( 5 / 20 )114.8081.05603354925062108.716243041208
Trimmed Mean ( 6 / 20 )114.7958333333331.03126204413054111.315871641643
Trimmed Mean ( 7 / 20 )114.7739130434781.00510981822479114.190420750431
Trimmed Mean ( 8 / 20 )114.7386363636360.979122530264509117.185166122814
Trimmed Mean ( 9 / 20 )114.7023809523810.94816583189666120.972911165694
Trimmed Mean ( 10 / 20 )114.6850.918726473621683124.830407409404
Trimmed Mean ( 11 / 20 )114.6552631578950.885240902898927129.518713812737
Trimmed Mean ( 12 / 20 )114.6250.851239758813066134.656539257316
Trimmed Mean ( 13 / 20 )114.5676470588240.830144207005549138.009331501675
Trimmed Mean ( 14 / 20 )114.4968750.80071143234193142.993930616325
Trimmed Mean ( 15 / 20 )114.4833333333330.782158571295707146.368444372709
Trimmed Mean ( 16 / 20 )114.4892857142860.765014425387288149.656374984466
Trimmed Mean ( 17 / 20 )114.4807692307690.757323611974721151.164927939142
Trimmed Mean ( 18 / 20 )114.4708333333330.7439241616002153.874331876926
Trimmed Mean ( 19 / 20 )114.4590909090910.728149498555858157.191745838043
Trimmed Mean ( 20 / 20 )114.4250.715794553000554159.857321518220
Median113.05
Midrange114.05
Midmean - Weighted Average at Xnp114.046875
Midmean - Weighted Average at X(n+1)p114.483333333333
Midmean - Empirical Distribution Function114.046875
Midmean - Empirical Distribution Function - Averaging114.483333333333
Midmean - Empirical Distribution Function - Interpolation114.483333333333
Midmean - Closest Observation114.046875
Midmean - True Basic - Statistics Graphics Toolkit114.483333333333
Midmean - MS Excel (old versions)114.284848484848
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 114.78 & 1.17951871828287 & 97.3108762250891 \tabularnewline
Geometric Mean & 114.421676876198 &  &  \tabularnewline
Harmonic Mean & 114.063214390028 &  &  \tabularnewline
Quadratic Mean & 115.137018373762 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 114.788333333333 & 1.17061259655964 & 98.0583445545428 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 114.841666666667 & 1.15746238036429 & 99.2184874557412 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 114.806666666667 & 1.14589630540880 & 100.189402937039 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 114.84 & 1.13099176516956 & 101.539200847128 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 114.856666666667 & 1.11449962592899 & 103.056711724715 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 114.896666666667 & 1.09529287331871 & 104.900405604332 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 114.955 & 1.06703937256264 & 107.732669436480 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 114.941666666667 & 1.05453363903522 & 108.997629294998 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 114.806666666667 & 1.01259823173247 & 113.378300562744 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 114.873333333333 & 0.989126952448604 & 116.136086524548 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 114.855 & 0.94718263471351 & 121.259613289616 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 115.015 & 0.853715127998803 & 134.722925983059 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 115.058333333333 & 0.847119718413992 & 135.822990342793 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 114.591666666667 & 0.768031056879506 & 149.201865784243 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 114.441666666667 & 0.728562905809293 & 157.078634877168 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 114.548333333333 & 0.663101306550914 & 172.746354443411 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 114.548333333333 & 0.654573185070956 & 174.996984211805 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 114.548333333333 & 0.627687404957874 & 182.492642720816 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 114.675 & 0.581390428635074 & 197.24266921494 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 114.941666666667 & 0.544387343752282 & 211.139490999941 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 114.805172413793 & 1.15052375672299 & 99.7851385014333 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 114.823214285714 & 1.12546091877266 & 102.023279858470 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 114.812962962963 & 1.10279818894332 & 104.110583526597 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 114.815384615385 & 1.07967784919140 & 106.342261908376 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 114.808 & 1.05603354925062 & 108.716243041208 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 114.795833333333 & 1.03126204413054 & 111.315871641643 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 114.773913043478 & 1.00510981822479 & 114.190420750431 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 114.738636363636 & 0.979122530264509 & 117.185166122814 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 114.702380952381 & 0.94816583189666 & 120.972911165694 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 114.685 & 0.918726473621683 & 124.830407409404 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 114.655263157895 & 0.885240902898927 & 129.518713812737 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 114.625 & 0.851239758813066 & 134.656539257316 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 114.567647058824 & 0.830144207005549 & 138.009331501675 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 114.496875 & 0.80071143234193 & 142.993930616325 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 114.483333333333 & 0.782158571295707 & 146.368444372709 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 114.489285714286 & 0.765014425387288 & 149.656374984466 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 114.480769230769 & 0.757323611974721 & 151.164927939142 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 114.470833333333 & 0.7439241616002 & 153.874331876926 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 114.459090909091 & 0.728149498555858 & 157.191745838043 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 114.425 & 0.715794553000554 & 159.857321518220 \tabularnewline
Median & 113.05 &  &  \tabularnewline
Midrange & 114.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 114.046875 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 114.483333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 114.046875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 114.483333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 114.483333333333 &  &  \tabularnewline
Midmean - Closest Observation & 114.046875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 114.483333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 114.284848484848 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4144&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]114.78[/C][C]1.17951871828287[/C][C]97.3108762250891[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]114.421676876198[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]114.063214390028[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]115.137018373762[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]114.788333333333[/C][C]1.17061259655964[/C][C]98.0583445545428[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]114.841666666667[/C][C]1.15746238036429[/C][C]99.2184874557412[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]114.806666666667[/C][C]1.14589630540880[/C][C]100.189402937039[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]114.84[/C][C]1.13099176516956[/C][C]101.539200847128[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]114.856666666667[/C][C]1.11449962592899[/C][C]103.056711724715[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]114.896666666667[/C][C]1.09529287331871[/C][C]104.900405604332[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]114.955[/C][C]1.06703937256264[/C][C]107.732669436480[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]114.941666666667[/C][C]1.05453363903522[/C][C]108.997629294998[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]114.806666666667[/C][C]1.01259823173247[/C][C]113.378300562744[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]114.873333333333[/C][C]0.989126952448604[/C][C]116.136086524548[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]114.855[/C][C]0.94718263471351[/C][C]121.259613289616[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]115.015[/C][C]0.853715127998803[/C][C]134.722925983059[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]115.058333333333[/C][C]0.847119718413992[/C][C]135.822990342793[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]114.591666666667[/C][C]0.768031056879506[/C][C]149.201865784243[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]114.441666666667[/C][C]0.728562905809293[/C][C]157.078634877168[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]114.548333333333[/C][C]0.663101306550914[/C][C]172.746354443411[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]114.548333333333[/C][C]0.654573185070956[/C][C]174.996984211805[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]114.548333333333[/C][C]0.627687404957874[/C][C]182.492642720816[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]114.675[/C][C]0.581390428635074[/C][C]197.24266921494[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]114.941666666667[/C][C]0.544387343752282[/C][C]211.139490999941[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]114.805172413793[/C][C]1.15052375672299[/C][C]99.7851385014333[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]114.823214285714[/C][C]1.12546091877266[/C][C]102.023279858470[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]114.812962962963[/C][C]1.10279818894332[/C][C]104.110583526597[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]114.815384615385[/C][C]1.07967784919140[/C][C]106.342261908376[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]114.808[/C][C]1.05603354925062[/C][C]108.716243041208[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]114.795833333333[/C][C]1.03126204413054[/C][C]111.315871641643[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]114.773913043478[/C][C]1.00510981822479[/C][C]114.190420750431[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]114.738636363636[/C][C]0.979122530264509[/C][C]117.185166122814[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]114.702380952381[/C][C]0.94816583189666[/C][C]120.972911165694[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]114.685[/C][C]0.918726473621683[/C][C]124.830407409404[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]114.655263157895[/C][C]0.885240902898927[/C][C]129.518713812737[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]114.625[/C][C]0.851239758813066[/C][C]134.656539257316[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]114.567647058824[/C][C]0.830144207005549[/C][C]138.009331501675[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]114.496875[/C][C]0.80071143234193[/C][C]142.993930616325[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]114.483333333333[/C][C]0.782158571295707[/C][C]146.368444372709[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]114.489285714286[/C][C]0.765014425387288[/C][C]149.656374984466[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]114.480769230769[/C][C]0.757323611974721[/C][C]151.164927939142[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]114.470833333333[/C][C]0.7439241616002[/C][C]153.874331876926[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]114.459090909091[/C][C]0.728149498555858[/C][C]157.191745838043[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]114.425[/C][C]0.715794553000554[/C][C]159.857321518220[/C][/ROW]
[ROW][C]Median[/C][C]113.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]114.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]114.046875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]114.483333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]114.046875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]114.483333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]114.483333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]114.046875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]114.483333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]114.284848484848[/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=4144&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4144&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 Mean114.781.1795187182828797.3108762250891
Geometric Mean114.421676876198
Harmonic Mean114.063214390028
Quadratic Mean115.137018373762
Winsorized Mean ( 1 / 20 )114.7883333333331.1706125965596498.0583445545428
Winsorized Mean ( 2 / 20 )114.8416666666671.1574623803642999.2184874557412
Winsorized Mean ( 3 / 20 )114.8066666666671.14589630540880100.189402937039
Winsorized Mean ( 4 / 20 )114.841.13099176516956101.539200847128
Winsorized Mean ( 5 / 20 )114.8566666666671.11449962592899103.056711724715
Winsorized Mean ( 6 / 20 )114.8966666666671.09529287331871104.900405604332
Winsorized Mean ( 7 / 20 )114.9551.06703937256264107.732669436480
Winsorized Mean ( 8 / 20 )114.9416666666671.05453363903522108.997629294998
Winsorized Mean ( 9 / 20 )114.8066666666671.01259823173247113.378300562744
Winsorized Mean ( 10 / 20 )114.8733333333330.989126952448604116.136086524548
Winsorized Mean ( 11 / 20 )114.8550.94718263471351121.259613289616
Winsorized Mean ( 12 / 20 )115.0150.853715127998803134.722925983059
Winsorized Mean ( 13 / 20 )115.0583333333330.847119718413992135.822990342793
Winsorized Mean ( 14 / 20 )114.5916666666670.768031056879506149.201865784243
Winsorized Mean ( 15 / 20 )114.4416666666670.728562905809293157.078634877168
Winsorized Mean ( 16 / 20 )114.5483333333330.663101306550914172.746354443411
Winsorized Mean ( 17 / 20 )114.5483333333330.654573185070956174.996984211805
Winsorized Mean ( 18 / 20 )114.5483333333330.627687404957874182.492642720816
Winsorized Mean ( 19 / 20 )114.6750.581390428635074197.24266921494
Winsorized Mean ( 20 / 20 )114.9416666666670.544387343752282211.139490999941
Trimmed Mean ( 1 / 20 )114.8051724137931.1505237567229999.7851385014333
Trimmed Mean ( 2 / 20 )114.8232142857141.12546091877266102.023279858470
Trimmed Mean ( 3 / 20 )114.8129629629631.10279818894332104.110583526597
Trimmed Mean ( 4 / 20 )114.8153846153851.07967784919140106.342261908376
Trimmed Mean ( 5 / 20 )114.8081.05603354925062108.716243041208
Trimmed Mean ( 6 / 20 )114.7958333333331.03126204413054111.315871641643
Trimmed Mean ( 7 / 20 )114.7739130434781.00510981822479114.190420750431
Trimmed Mean ( 8 / 20 )114.7386363636360.979122530264509117.185166122814
Trimmed Mean ( 9 / 20 )114.7023809523810.94816583189666120.972911165694
Trimmed Mean ( 10 / 20 )114.6850.918726473621683124.830407409404
Trimmed Mean ( 11 / 20 )114.6552631578950.885240902898927129.518713812737
Trimmed Mean ( 12 / 20 )114.6250.851239758813066134.656539257316
Trimmed Mean ( 13 / 20 )114.5676470588240.830144207005549138.009331501675
Trimmed Mean ( 14 / 20 )114.4968750.80071143234193142.993930616325
Trimmed Mean ( 15 / 20 )114.4833333333330.782158571295707146.368444372709
Trimmed Mean ( 16 / 20 )114.4892857142860.765014425387288149.656374984466
Trimmed Mean ( 17 / 20 )114.4807692307690.757323611974721151.164927939142
Trimmed Mean ( 18 / 20 )114.4708333333330.7439241616002153.874331876926
Trimmed Mean ( 19 / 20 )114.4590909090910.728149498555858157.191745838043
Trimmed Mean ( 20 / 20 )114.4250.715794553000554159.857321518220
Median113.05
Midrange114.05
Midmean - Weighted Average at Xnp114.046875
Midmean - Weighted Average at X(n+1)p114.483333333333
Midmean - Empirical Distribution Function114.046875
Midmean - Empirical Distribution Function - Averaging114.483333333333
Midmean - Empirical Distribution Function - Interpolation114.483333333333
Midmean - Closest Observation114.046875
Midmean - True Basic - Statistics Graphics Toolkit114.483333333333
Midmean - MS Excel (old versions)114.284848484848
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')