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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 05 Dec 2008 04:38:27 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/05/t122847721913aprgzcbvrpxat.htm/, Retrieved Thu, 16 May 2024 19:12:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29187, Retrieved Thu, 16 May 2024 19:12:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact197
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Run sequence plot...] [2008-12-02 21:55:47] [ed2ba3b6182103c15c0ab511ae4e6284]
- RMP   [Central Tendency] [central tendency ...] [2008-12-05 10:05:35] [ed2ba3b6182103c15c0ab511ae4e6284]
-   PD      [Central Tendency] [Central tendency ...] [2008-12-05 11:38:27] [577b699a0819d2125728ba9ae2c57238] [Current]
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Dataseries X:
60,93
60,93
60,93
60,93
61,8
62,74
62,86
62,86
62,92
62,92
62,92
62,92
62,95
64,17
65,33
65,68
65,97
66,58
66,78
66,83
66,85
66,86
66,86
66,86
66,96
67,66
68,44
68,56
68,65
68,68
68,69
68,71
68,71
68,82
69,75
70,43
70,91
71,47
71,87
72,31
72,56
73,23
73,57
73,72
73,68
73,76
73,76
73,78
73,97
73,97
73,97
73,97
73,97
73,97
73,96
74,44
75,43
75,77
75,82
75,85
75,85




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29187&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29187&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29187&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean68.96721311475410.60382479143476114.21725986255
Geometric Mean68.806884939098
Harmonic Mean68.6450975095622
Quadratic Mean69.1256301782558
Winsorized Mean ( 1 / 20 )68.96721311475410.60382479143476114.21725986255
Winsorized Mean ( 2 / 20 )68.96622950819670.603638293422505114.250918571074
Winsorized Mean ( 3 / 20 )68.96377049180330.603174397020017114.334711208763
Winsorized Mean ( 4 / 20 )68.9985245901640.586870734320087117.570225528628
Winsorized Mean ( 5 / 20 )68.99442622950820.557744017737409123.702673691413
Winsorized Mean ( 6 / 20 )68.960.54826278051928125.779101646633
Winsorized Mean ( 7 / 20 )68.960.54826278051928125.779101646633
Winsorized Mean ( 8 / 20 )68.9678688524590.546807930972605126.128142892489
Winsorized Mean ( 9 / 20 )68.9678688524590.546807930972605126.128142892489
Winsorized Mean ( 10 / 20 )68.9678688524590.546807930972605126.128142892489
Winsorized Mean ( 11 / 20 )68.9678688524590.546807930972605126.128142892489
Winsorized Mean ( 12 / 20 )68.97180327868850.545421104079936126.456058929066
Winsorized Mean ( 13 / 20 )69.19344262295080.493457074566438140.221806899305
Winsorized Mean ( 14 / 20 )69.45508196721310.449695684774067154.449073715502
Winsorized Mean ( 15 / 20 )69.54114754098360.436772883571069159.215807932976
Winsorized Mean ( 16 / 20 )69.60672131147540.424037819307209164.152153751754
Winsorized Mean ( 17 / 20 )69.76557377049180.398731425871607174.968836775250
Winsorized Mean ( 18 / 20 )69.7921311475410.385654302767897180.970705231687
Winsorized Mean ( 19 / 20 )69.70180327868850.366478628500165190.193364245951
Winsorized Mean ( 20 / 20 )69.48868852459020.330971617772627209.953617751985
Trimmed Mean ( 1 / 20 )68.9867796610170.59769181196099115.421992204771
Trimmed Mean ( 2 / 20 )69.00771929824560.589809929535726116.999928015057
Trimmed Mean ( 3 / 20 )69.03072727272730.579891308435486119.040803454993
Trimmed Mean ( 4 / 20 )69.05641509433960.567523015034268121.680378178442
Trimmed Mean ( 5 / 20 )69.07372549019610.558136111081237123.757850672633
Trimmed Mean ( 6 / 20 )69.09346938775510.555367099207981124.410447587353
Trimmed Mean ( 7 / 20 )69.12234042553190.553668132377972124.844354195817
Trimmed Mean ( 8 / 20 )69.15377777777780.550480257619818125.624446690944
Trimmed Mean ( 9 / 20 )69.18674418604650.545744507673342126.774971095923
Trimmed Mean ( 10 / 20 )69.22292682926830.53856655316054128.531796902423
Trimmed Mean ( 11 / 20 )69.26282051282050.52813218971531131.146750494714
Trimmed Mean ( 12 / 20 )69.3070270270270.513265156474293135.031622842098
Trimmed Mean ( 13 / 20 )69.35571428571430.492599567329787140.795321160487
Trimmed Mean ( 14 / 20 )69.37878787878790.478985622762929144.845240820780
Trimmed Mean ( 15 / 20 )69.3680645161290.471424156514202147.145757292222
Trimmed Mean ( 16 / 20 )69.34379310344830.462611832782965149.896280616715
Trimmed Mean ( 17 / 20 )69.30666666666670.451658860751925153.449146444917
Trimmed Mean ( 18 / 20 )69.24080.440711137443413157.111527522697
Trimmed Mean ( 19 / 20 )69.15956521739130.425442098939152162.559289242513
Trimmed Mean ( 20 / 20 )69.07666666666670.406632121873916169.875085982719
Median68.69
Midrange68.39
Midmean - Weighted Average at Xnp69.2216666666666
Midmean - Weighted Average at X(n+1)p69.5053125
Midmean - Empirical Distribution Function69.5053125
Midmean - Empirical Distribution Function - Averaging69.5053125
Midmean - Empirical Distribution Function - Interpolation69.5053125
Midmean - Closest Observation69.3787878787879
Midmean - True Basic - Statistics Graphics Toolkit69.5053125
Midmean - MS Excel (old versions)69.5053125
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 68.9672131147541 & 0.60382479143476 & 114.21725986255 \tabularnewline
Geometric Mean & 68.806884939098 &  &  \tabularnewline
Harmonic Mean & 68.6450975095622 &  &  \tabularnewline
Quadratic Mean & 69.1256301782558 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 68.9672131147541 & 0.60382479143476 & 114.21725986255 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 68.9662295081967 & 0.603638293422505 & 114.250918571074 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 68.9637704918033 & 0.603174397020017 & 114.334711208763 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 68.998524590164 & 0.586870734320087 & 117.570225528628 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 68.9944262295082 & 0.557744017737409 & 123.702673691413 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 68.96 & 0.54826278051928 & 125.779101646633 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 68.96 & 0.54826278051928 & 125.779101646633 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 68.967868852459 & 0.546807930972605 & 126.128142892489 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 68.967868852459 & 0.546807930972605 & 126.128142892489 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 68.967868852459 & 0.546807930972605 & 126.128142892489 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 68.967868852459 & 0.546807930972605 & 126.128142892489 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 68.9718032786885 & 0.545421104079936 & 126.456058929066 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 69.1934426229508 & 0.493457074566438 & 140.221806899305 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 69.4550819672131 & 0.449695684774067 & 154.449073715502 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 69.5411475409836 & 0.436772883571069 & 159.215807932976 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 69.6067213114754 & 0.424037819307209 & 164.152153751754 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 69.7655737704918 & 0.398731425871607 & 174.968836775250 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 69.792131147541 & 0.385654302767897 & 180.970705231687 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 69.7018032786885 & 0.366478628500165 & 190.193364245951 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 69.4886885245902 & 0.330971617772627 & 209.953617751985 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 68.986779661017 & 0.59769181196099 & 115.421992204771 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 69.0077192982456 & 0.589809929535726 & 116.999928015057 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 69.0307272727273 & 0.579891308435486 & 119.040803454993 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 69.0564150943396 & 0.567523015034268 & 121.680378178442 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 69.0737254901961 & 0.558136111081237 & 123.757850672633 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 69.0934693877551 & 0.555367099207981 & 124.410447587353 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 69.1223404255319 & 0.553668132377972 & 124.844354195817 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 69.1537777777778 & 0.550480257619818 & 125.624446690944 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 69.1867441860465 & 0.545744507673342 & 126.774971095923 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 69.2229268292683 & 0.53856655316054 & 128.531796902423 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 69.2628205128205 & 0.52813218971531 & 131.146750494714 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 69.307027027027 & 0.513265156474293 & 135.031622842098 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 69.3557142857143 & 0.492599567329787 & 140.795321160487 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 69.3787878787879 & 0.478985622762929 & 144.845240820780 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 69.368064516129 & 0.471424156514202 & 147.145757292222 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 69.3437931034483 & 0.462611832782965 & 149.896280616715 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 69.3066666666667 & 0.451658860751925 & 153.449146444917 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 69.2408 & 0.440711137443413 & 157.111527522697 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 69.1595652173913 & 0.425442098939152 & 162.559289242513 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 69.0766666666667 & 0.406632121873916 & 169.875085982719 \tabularnewline
Median & 68.69 &  &  \tabularnewline
Midrange & 68.39 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 69.2216666666666 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 69.5053125 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 69.5053125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 69.5053125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 69.5053125 &  &  \tabularnewline
Midmean - Closest Observation & 69.3787878787879 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 69.5053125 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 69.5053125 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29187&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]68.9672131147541[/C][C]0.60382479143476[/C][C]114.21725986255[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]68.806884939098[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]68.6450975095622[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]69.1256301782558[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]68.9672131147541[/C][C]0.60382479143476[/C][C]114.21725986255[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]68.9662295081967[/C][C]0.603638293422505[/C][C]114.250918571074[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]68.9637704918033[/C][C]0.603174397020017[/C][C]114.334711208763[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]68.998524590164[/C][C]0.586870734320087[/C][C]117.570225528628[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]68.9944262295082[/C][C]0.557744017737409[/C][C]123.702673691413[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]68.96[/C][C]0.54826278051928[/C][C]125.779101646633[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]68.96[/C][C]0.54826278051928[/C][C]125.779101646633[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]68.967868852459[/C][C]0.546807930972605[/C][C]126.128142892489[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]68.967868852459[/C][C]0.546807930972605[/C][C]126.128142892489[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]68.967868852459[/C][C]0.546807930972605[/C][C]126.128142892489[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]68.967868852459[/C][C]0.546807930972605[/C][C]126.128142892489[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]68.9718032786885[/C][C]0.545421104079936[/C][C]126.456058929066[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]69.1934426229508[/C][C]0.493457074566438[/C][C]140.221806899305[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]69.4550819672131[/C][C]0.449695684774067[/C][C]154.449073715502[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]69.5411475409836[/C][C]0.436772883571069[/C][C]159.215807932976[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]69.6067213114754[/C][C]0.424037819307209[/C][C]164.152153751754[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]69.7655737704918[/C][C]0.398731425871607[/C][C]174.968836775250[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]69.792131147541[/C][C]0.385654302767897[/C][C]180.970705231687[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]69.7018032786885[/C][C]0.366478628500165[/C][C]190.193364245951[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]69.4886885245902[/C][C]0.330971617772627[/C][C]209.953617751985[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]68.986779661017[/C][C]0.59769181196099[/C][C]115.421992204771[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]69.0077192982456[/C][C]0.589809929535726[/C][C]116.999928015057[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]69.0307272727273[/C][C]0.579891308435486[/C][C]119.040803454993[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]69.0564150943396[/C][C]0.567523015034268[/C][C]121.680378178442[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]69.0737254901961[/C][C]0.558136111081237[/C][C]123.757850672633[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]69.0934693877551[/C][C]0.555367099207981[/C][C]124.410447587353[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]69.1223404255319[/C][C]0.553668132377972[/C][C]124.844354195817[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]69.1537777777778[/C][C]0.550480257619818[/C][C]125.624446690944[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]69.1867441860465[/C][C]0.545744507673342[/C][C]126.774971095923[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]69.2229268292683[/C][C]0.53856655316054[/C][C]128.531796902423[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]69.2628205128205[/C][C]0.52813218971531[/C][C]131.146750494714[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]69.307027027027[/C][C]0.513265156474293[/C][C]135.031622842098[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]69.3557142857143[/C][C]0.492599567329787[/C][C]140.795321160487[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]69.3787878787879[/C][C]0.478985622762929[/C][C]144.845240820780[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]69.368064516129[/C][C]0.471424156514202[/C][C]147.145757292222[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]69.3437931034483[/C][C]0.462611832782965[/C][C]149.896280616715[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]69.3066666666667[/C][C]0.451658860751925[/C][C]153.449146444917[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]69.2408[/C][C]0.440711137443413[/C][C]157.111527522697[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]69.1595652173913[/C][C]0.425442098939152[/C][C]162.559289242513[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]69.0766666666667[/C][C]0.406632121873916[/C][C]169.875085982719[/C][/ROW]
[ROW][C]Median[/C][C]68.69[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]68.39[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]69.2216666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]69.5053125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]69.5053125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]69.5053125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]69.5053125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]69.3787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]69.5053125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]69.5053125[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29187&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29187&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 Mean68.96721311475410.60382479143476114.21725986255
Geometric Mean68.806884939098
Harmonic Mean68.6450975095622
Quadratic Mean69.1256301782558
Winsorized Mean ( 1 / 20 )68.96721311475410.60382479143476114.21725986255
Winsorized Mean ( 2 / 20 )68.96622950819670.603638293422505114.250918571074
Winsorized Mean ( 3 / 20 )68.96377049180330.603174397020017114.334711208763
Winsorized Mean ( 4 / 20 )68.9985245901640.586870734320087117.570225528628
Winsorized Mean ( 5 / 20 )68.99442622950820.557744017737409123.702673691413
Winsorized Mean ( 6 / 20 )68.960.54826278051928125.779101646633
Winsorized Mean ( 7 / 20 )68.960.54826278051928125.779101646633
Winsorized Mean ( 8 / 20 )68.9678688524590.546807930972605126.128142892489
Winsorized Mean ( 9 / 20 )68.9678688524590.546807930972605126.128142892489
Winsorized Mean ( 10 / 20 )68.9678688524590.546807930972605126.128142892489
Winsorized Mean ( 11 / 20 )68.9678688524590.546807930972605126.128142892489
Winsorized Mean ( 12 / 20 )68.97180327868850.545421104079936126.456058929066
Winsorized Mean ( 13 / 20 )69.19344262295080.493457074566438140.221806899305
Winsorized Mean ( 14 / 20 )69.45508196721310.449695684774067154.449073715502
Winsorized Mean ( 15 / 20 )69.54114754098360.436772883571069159.215807932976
Winsorized Mean ( 16 / 20 )69.60672131147540.424037819307209164.152153751754
Winsorized Mean ( 17 / 20 )69.76557377049180.398731425871607174.968836775250
Winsorized Mean ( 18 / 20 )69.7921311475410.385654302767897180.970705231687
Winsorized Mean ( 19 / 20 )69.70180327868850.366478628500165190.193364245951
Winsorized Mean ( 20 / 20 )69.48868852459020.330971617772627209.953617751985
Trimmed Mean ( 1 / 20 )68.9867796610170.59769181196099115.421992204771
Trimmed Mean ( 2 / 20 )69.00771929824560.589809929535726116.999928015057
Trimmed Mean ( 3 / 20 )69.03072727272730.579891308435486119.040803454993
Trimmed Mean ( 4 / 20 )69.05641509433960.567523015034268121.680378178442
Trimmed Mean ( 5 / 20 )69.07372549019610.558136111081237123.757850672633
Trimmed Mean ( 6 / 20 )69.09346938775510.555367099207981124.410447587353
Trimmed Mean ( 7 / 20 )69.12234042553190.553668132377972124.844354195817
Trimmed Mean ( 8 / 20 )69.15377777777780.550480257619818125.624446690944
Trimmed Mean ( 9 / 20 )69.18674418604650.545744507673342126.774971095923
Trimmed Mean ( 10 / 20 )69.22292682926830.53856655316054128.531796902423
Trimmed Mean ( 11 / 20 )69.26282051282050.52813218971531131.146750494714
Trimmed Mean ( 12 / 20 )69.3070270270270.513265156474293135.031622842098
Trimmed Mean ( 13 / 20 )69.35571428571430.492599567329787140.795321160487
Trimmed Mean ( 14 / 20 )69.37878787878790.478985622762929144.845240820780
Trimmed Mean ( 15 / 20 )69.3680645161290.471424156514202147.145757292222
Trimmed Mean ( 16 / 20 )69.34379310344830.462611832782965149.896280616715
Trimmed Mean ( 17 / 20 )69.30666666666670.451658860751925153.449146444917
Trimmed Mean ( 18 / 20 )69.24080.440711137443413157.111527522697
Trimmed Mean ( 19 / 20 )69.15956521739130.425442098939152162.559289242513
Trimmed Mean ( 20 / 20 )69.07666666666670.406632121873916169.875085982719
Median68.69
Midrange68.39
Midmean - Weighted Average at Xnp69.2216666666666
Midmean - Weighted Average at X(n+1)p69.5053125
Midmean - Empirical Distribution Function69.5053125
Midmean - Empirical Distribution Function - Averaging69.5053125
Midmean - Empirical Distribution Function - Interpolation69.5053125
Midmean - Closest Observation69.3787878787879
Midmean - True Basic - Statistics Graphics Toolkit69.5053125
Midmean - MS Excel (old versions)69.5053125
Number of observations61



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')