Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 14:43:39 -0600
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/Oct/20/t1224535524jf5qhzshjk31lkr.htm/, Retrieved Sun, 19 May 2024 13:37:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18116, Retrieved Sun, 19 May 2024 13:37:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
F RM D  [Pearson Correlation] [Pearson Correlation] [2008-10-20 11:08:13] [8af599f2ccf50a86f2698320831f9f94]
F RM D      [Central Tendency] [Verbruik voedings...] [2008-10-20 20:43:39] [6d5cd2fe15d123a10639b4bf141c23b5] [Current]
Feedback Forum
2008-10-27 22:58:36 [Jeroen Michel] [reply
Ook hier dezelfde bemerkingen als bij onderstaande links=

1) http://www.freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224536035zt8uh6b4kh05ata.htm

2) http://www.freestatistics.org/blog/index.php?v=date/2008/Oct/20/t12245362452n609207ckrenzl.htm


Post a new message
Dataseries X:
118,01
118,25
117,56
117,5
118,59
118,49
119,34
120,03
119,24
119,17
117,39
116,43
115,85
116,22
115,81
116,04
116,07
116,66
116,96
117,07
116,6
115,59
115,18
115,02
113,82
114,62
114,6
116,17
114,95
114,86
114,93
114,4
114,26
113,65
113,14
112,61
111,41
112,09
112,04
112,33
111,51
111,99
111,89
112,92
112,23
112,13
111,52
112,51
110,24
110,97
111,08
110,69
110,76
110,66
111,22
110,82
109,31
107,38
106,31
106,22
105,45




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=18116&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=18116&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18116&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 Mean113.9468852459020.435256820173218261.792302761745
Geometric Mean113.896564814686
Harmonic Mean113.845794614567
Quadratic Mean113.996752441520
Winsorized Mean ( 1 / 20 )113.9481967213110.428802660625355265.73575022863
Winsorized Mean ( 2 / 20 )113.9478688524590.427237863564391266.708263873914
Winsorized Mean ( 3 / 20 )113.9970491803280.411618114718072276.94857224252
Winsorized Mean ( 4 / 20 )114.0855737704920.373182043256771305.71024472363
Winsorized Mean ( 5 / 20 )114.1536065573770.356395205881392320.300623222657
Winsorized Mean ( 6 / 20 )114.1713114754100.344375452389086331.531503431364
Winsorized Mean ( 7 / 20 )114.1472131147540.338451401871565337.263230359053
Winsorized Mean ( 8 / 20 )114.0973770491800.326043587353913349.945165231329
Winsorized Mean ( 9 / 20 )114.0973770491800.322979207373467353.265394317621
Winsorized Mean ( 10 / 20 )114.1039344262300.315717785604349361.411170447084
Winsorized Mean ( 11 / 20 )114.0660655737710.302663249422994376.874515790171
Winsorized Mean ( 12 / 20 )114.0719672131150.294618936959033387.184776343744
Winsorized Mean ( 13 / 20 )114.0485245901640.277911594630042410.376993237674
Winsorized Mean ( 14 / 20 )114.0577049180330.272154768874088419.091333177415
Winsorized Mean ( 15 / 20 )114.0183606557380.265348639650488429.692651923599
Winsorized Mean ( 16 / 20 )114.0603278688520.242201872086585470.930826777742
Winsorized Mean ( 17 / 20 )114.0742622950820.236002739057041483.359908240346
Winsorized Mean ( 18 / 20 )114.0595081967210.229496648811742496.998578355214
Winsorized Mean ( 19 / 20 )114.0657377049180.225856410090655505.036530329753
Winsorized Mean ( 20 / 20 )114.0165573770490.214973360307394530.375285635463
Trimmed Mean ( 1 / 20 )113.9877966101690.413139472475006275.906332375601
Trimmed Mean ( 2 / 20 )114.0301754385960.393793602926736289.568379453364
Trimmed Mean ( 3 / 20 )114.0758181818180.370701554468633307.729538240905
Trimmed Mean ( 4 / 20 )114.1060377358490.349840969429451326.165451467683
Trimmed Mean ( 5 / 20 )114.1121568627450.339661574792078335.958393093473
Trimmed Mean ( 6 / 20 )114.1018367346940.332500533664012343.162867972996
Trimmed Mean ( 7 / 20 )114.0868085106380.326847570804062349.052031287792
Trimmed Mean ( 8 / 20 )114.0751111111110.321006249698785355.367259105245
Trimmed Mean ( 9 / 20 )114.0711627906980.316485092660344360.431392934897
Trimmed Mean ( 10 / 20 )114.0668292682930.310944948273216366.839306770362
Trimmed Mean ( 11 / 20 )114.0610256410260.305075330816139373.878233077348
Trimmed Mean ( 12 / 20 )114.0602702702700.300138478171413380.025483454103
Trimmed Mean ( 13 / 20 )114.0585714285710.294936296456687386.722735719038
Trimmed Mean ( 14 / 20 )114.060.291503092659929391.282298102627
Trimmed Mean ( 15 / 20 )114.0603225806450.287328250287213396.968702056378
Trimmed Mean ( 16 / 20 )114.0662068965520.282295487589817404.066702838315
Trimmed Mean ( 17 / 20 )114.0670370370370.280755398816006406.286174791571
Trimmed Mean ( 18 / 20 )114.0660.27868022295575409.307839609816
Trimmed Mean ( 19 / 20 )114.0669565217390.275755831434625413.6520193546
Trimmed Mean ( 20 / 20 )114.0671428571430.270253974779935422.073876804315
Median114.4
Midrange112.74
Midmean - Weighted Average at Xnp113.981333333333
Midmean - Weighted Average at X(n+1)p114.060322580645
Midmean - Empirical Distribution Function114.060322580645
Midmean - Empirical Distribution Function - Averaging114.060322580645
Midmean - Empirical Distribution Function - Interpolation114.060322580645
Midmean - Closest Observation113.980625
Midmean - True Basic - Statistics Graphics Toolkit114.060322580645
Midmean - MS Excel (old versions)114.060322580645
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 113.946885245902 & 0.435256820173218 & 261.792302761745 \tabularnewline
Geometric Mean & 113.896564814686 &  &  \tabularnewline
Harmonic Mean & 113.845794614567 &  &  \tabularnewline
Quadratic Mean & 113.996752441520 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 113.948196721311 & 0.428802660625355 & 265.73575022863 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 113.947868852459 & 0.427237863564391 & 266.708263873914 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 113.997049180328 & 0.411618114718072 & 276.94857224252 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 114.085573770492 & 0.373182043256771 & 305.71024472363 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 114.153606557377 & 0.356395205881392 & 320.300623222657 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 114.171311475410 & 0.344375452389086 & 331.531503431364 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 114.147213114754 & 0.338451401871565 & 337.263230359053 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 114.097377049180 & 0.326043587353913 & 349.945165231329 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 114.097377049180 & 0.322979207373467 & 353.265394317621 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 114.103934426230 & 0.315717785604349 & 361.411170447084 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 114.066065573771 & 0.302663249422994 & 376.874515790171 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 114.071967213115 & 0.294618936959033 & 387.184776343744 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 114.048524590164 & 0.277911594630042 & 410.376993237674 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 114.057704918033 & 0.272154768874088 & 419.091333177415 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 114.018360655738 & 0.265348639650488 & 429.692651923599 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 114.060327868852 & 0.242201872086585 & 470.930826777742 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 114.074262295082 & 0.236002739057041 & 483.359908240346 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 114.059508196721 & 0.229496648811742 & 496.998578355214 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 114.065737704918 & 0.225856410090655 & 505.036530329753 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 114.016557377049 & 0.214973360307394 & 530.375285635463 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 113.987796610169 & 0.413139472475006 & 275.906332375601 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 114.030175438596 & 0.393793602926736 & 289.568379453364 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 114.075818181818 & 0.370701554468633 & 307.729538240905 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 114.106037735849 & 0.349840969429451 & 326.165451467683 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 114.112156862745 & 0.339661574792078 & 335.958393093473 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 114.101836734694 & 0.332500533664012 & 343.162867972996 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 114.086808510638 & 0.326847570804062 & 349.052031287792 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 114.075111111111 & 0.321006249698785 & 355.367259105245 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 114.071162790698 & 0.316485092660344 & 360.431392934897 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 114.066829268293 & 0.310944948273216 & 366.839306770362 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 114.061025641026 & 0.305075330816139 & 373.878233077348 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 114.060270270270 & 0.300138478171413 & 380.025483454103 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 114.058571428571 & 0.294936296456687 & 386.722735719038 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 114.06 & 0.291503092659929 & 391.282298102627 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 114.060322580645 & 0.287328250287213 & 396.968702056378 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 114.066206896552 & 0.282295487589817 & 404.066702838315 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 114.067037037037 & 0.280755398816006 & 406.286174791571 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 114.066 & 0.27868022295575 & 409.307839609816 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 114.066956521739 & 0.275755831434625 & 413.6520193546 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 114.067142857143 & 0.270253974779935 & 422.073876804315 \tabularnewline
Median & 114.4 &  &  \tabularnewline
Midrange & 112.74 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 113.981333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 114.060322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 114.060322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 114.060322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 114.060322580645 &  &  \tabularnewline
Midmean - Closest Observation & 113.980625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 114.060322580645 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 114.060322580645 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18116&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]113.946885245902[/C][C]0.435256820173218[/C][C]261.792302761745[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]113.896564814686[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]113.845794614567[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]113.996752441520[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]113.948196721311[/C][C]0.428802660625355[/C][C]265.73575022863[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]113.947868852459[/C][C]0.427237863564391[/C][C]266.708263873914[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]113.997049180328[/C][C]0.411618114718072[/C][C]276.94857224252[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]114.085573770492[/C][C]0.373182043256771[/C][C]305.71024472363[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]114.153606557377[/C][C]0.356395205881392[/C][C]320.300623222657[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]114.171311475410[/C][C]0.344375452389086[/C][C]331.531503431364[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]114.147213114754[/C][C]0.338451401871565[/C][C]337.263230359053[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]114.097377049180[/C][C]0.326043587353913[/C][C]349.945165231329[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]114.097377049180[/C][C]0.322979207373467[/C][C]353.265394317621[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]114.103934426230[/C][C]0.315717785604349[/C][C]361.411170447084[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]114.066065573771[/C][C]0.302663249422994[/C][C]376.874515790171[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]114.071967213115[/C][C]0.294618936959033[/C][C]387.184776343744[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]114.048524590164[/C][C]0.277911594630042[/C][C]410.376993237674[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]114.057704918033[/C][C]0.272154768874088[/C][C]419.091333177415[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]114.018360655738[/C][C]0.265348639650488[/C][C]429.692651923599[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]114.060327868852[/C][C]0.242201872086585[/C][C]470.930826777742[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]114.074262295082[/C][C]0.236002739057041[/C][C]483.359908240346[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]114.059508196721[/C][C]0.229496648811742[/C][C]496.998578355214[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]114.065737704918[/C][C]0.225856410090655[/C][C]505.036530329753[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]114.016557377049[/C][C]0.214973360307394[/C][C]530.375285635463[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]113.987796610169[/C][C]0.413139472475006[/C][C]275.906332375601[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]114.030175438596[/C][C]0.393793602926736[/C][C]289.568379453364[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]114.075818181818[/C][C]0.370701554468633[/C][C]307.729538240905[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]114.106037735849[/C][C]0.349840969429451[/C][C]326.165451467683[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]114.112156862745[/C][C]0.339661574792078[/C][C]335.958393093473[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]114.101836734694[/C][C]0.332500533664012[/C][C]343.162867972996[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]114.086808510638[/C][C]0.326847570804062[/C][C]349.052031287792[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]114.075111111111[/C][C]0.321006249698785[/C][C]355.367259105245[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]114.071162790698[/C][C]0.316485092660344[/C][C]360.431392934897[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]114.066829268293[/C][C]0.310944948273216[/C][C]366.839306770362[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]114.061025641026[/C][C]0.305075330816139[/C][C]373.878233077348[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]114.060270270270[/C][C]0.300138478171413[/C][C]380.025483454103[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]114.058571428571[/C][C]0.294936296456687[/C][C]386.722735719038[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]114.06[/C][C]0.291503092659929[/C][C]391.282298102627[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]114.060322580645[/C][C]0.287328250287213[/C][C]396.968702056378[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]114.066206896552[/C][C]0.282295487589817[/C][C]404.066702838315[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]114.067037037037[/C][C]0.280755398816006[/C][C]406.286174791571[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]114.066[/C][C]0.27868022295575[/C][C]409.307839609816[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]114.066956521739[/C][C]0.275755831434625[/C][C]413.6520193546[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]114.067142857143[/C][C]0.270253974779935[/C][C]422.073876804315[/C][/ROW]
[ROW][C]Median[/C][C]114.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]112.74[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]113.981333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]114.060322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]114.060322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]114.060322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]114.060322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]113.980625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]114.060322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]114.060322580645[/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=18116&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18116&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 Mean113.9468852459020.435256820173218261.792302761745
Geometric Mean113.896564814686
Harmonic Mean113.845794614567
Quadratic Mean113.996752441520
Winsorized Mean ( 1 / 20 )113.9481967213110.428802660625355265.73575022863
Winsorized Mean ( 2 / 20 )113.9478688524590.427237863564391266.708263873914
Winsorized Mean ( 3 / 20 )113.9970491803280.411618114718072276.94857224252
Winsorized Mean ( 4 / 20 )114.0855737704920.373182043256771305.71024472363
Winsorized Mean ( 5 / 20 )114.1536065573770.356395205881392320.300623222657
Winsorized Mean ( 6 / 20 )114.1713114754100.344375452389086331.531503431364
Winsorized Mean ( 7 / 20 )114.1472131147540.338451401871565337.263230359053
Winsorized Mean ( 8 / 20 )114.0973770491800.326043587353913349.945165231329
Winsorized Mean ( 9 / 20 )114.0973770491800.322979207373467353.265394317621
Winsorized Mean ( 10 / 20 )114.1039344262300.315717785604349361.411170447084
Winsorized Mean ( 11 / 20 )114.0660655737710.302663249422994376.874515790171
Winsorized Mean ( 12 / 20 )114.0719672131150.294618936959033387.184776343744
Winsorized Mean ( 13 / 20 )114.0485245901640.277911594630042410.376993237674
Winsorized Mean ( 14 / 20 )114.0577049180330.272154768874088419.091333177415
Winsorized Mean ( 15 / 20 )114.0183606557380.265348639650488429.692651923599
Winsorized Mean ( 16 / 20 )114.0603278688520.242201872086585470.930826777742
Winsorized Mean ( 17 / 20 )114.0742622950820.236002739057041483.359908240346
Winsorized Mean ( 18 / 20 )114.0595081967210.229496648811742496.998578355214
Winsorized Mean ( 19 / 20 )114.0657377049180.225856410090655505.036530329753
Winsorized Mean ( 20 / 20 )114.0165573770490.214973360307394530.375285635463
Trimmed Mean ( 1 / 20 )113.9877966101690.413139472475006275.906332375601
Trimmed Mean ( 2 / 20 )114.0301754385960.393793602926736289.568379453364
Trimmed Mean ( 3 / 20 )114.0758181818180.370701554468633307.729538240905
Trimmed Mean ( 4 / 20 )114.1060377358490.349840969429451326.165451467683
Trimmed Mean ( 5 / 20 )114.1121568627450.339661574792078335.958393093473
Trimmed Mean ( 6 / 20 )114.1018367346940.332500533664012343.162867972996
Trimmed Mean ( 7 / 20 )114.0868085106380.326847570804062349.052031287792
Trimmed Mean ( 8 / 20 )114.0751111111110.321006249698785355.367259105245
Trimmed Mean ( 9 / 20 )114.0711627906980.316485092660344360.431392934897
Trimmed Mean ( 10 / 20 )114.0668292682930.310944948273216366.839306770362
Trimmed Mean ( 11 / 20 )114.0610256410260.305075330816139373.878233077348
Trimmed Mean ( 12 / 20 )114.0602702702700.300138478171413380.025483454103
Trimmed Mean ( 13 / 20 )114.0585714285710.294936296456687386.722735719038
Trimmed Mean ( 14 / 20 )114.060.291503092659929391.282298102627
Trimmed Mean ( 15 / 20 )114.0603225806450.287328250287213396.968702056378
Trimmed Mean ( 16 / 20 )114.0662068965520.282295487589817404.066702838315
Trimmed Mean ( 17 / 20 )114.0670370370370.280755398816006406.286174791571
Trimmed Mean ( 18 / 20 )114.0660.27868022295575409.307839609816
Trimmed Mean ( 19 / 20 )114.0669565217390.275755831434625413.6520193546
Trimmed Mean ( 20 / 20 )114.0671428571430.270253974779935422.073876804315
Median114.4
Midrange112.74
Midmean - Weighted Average at Xnp113.981333333333
Midmean - Weighted Average at X(n+1)p114.060322580645
Midmean - Empirical Distribution Function114.060322580645
Midmean - Empirical Distribution Function - Averaging114.060322580645
Midmean - Empirical Distribution Function - Interpolation114.060322580645
Midmean - Closest Observation113.980625
Midmean - True Basic - Statistics Graphics Toolkit114.060322580645
Midmean - MS Excel (old versions)114.060322580645
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')