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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 20 Oct 2007 07:43:42 -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/Oct/20/m3wbhl0d3fypucr1192891205.htm/, Retrieved Fri, 03 May 2024 03:33:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1148, Retrieved Fri, 03 May 2024 03:33:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS2CTOM
Estimated Impact233
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS2 - Central ten...] [2007-10-20 14:43:42] [e51d7ab0e549b3dc96ac85a81d9bd259] [Current]
-    D    [Central Tendency] [Robuustheid Produ...] [2008-12-26 14:38:16] [c29178f7f550574a75dc881e636e0923]
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Dataseries X:
97,3
101,0
113,2
101,0
105,7
113,9
86,4
96,5
103,3
114,9
105,8
94,2
98,4
99,4
108,8
112,6
104,4
112,2
81,1
97,1
112,6
113,8
107,8
103,2
103,3
101,2
107,7
110,4
101,9
115,9
89,9
88,6
117,2
123,9
100,0
103,6
94,1
98,7
119,5
112,7
104,4
124,7
89,1
97,0
121,6
118,8
114,0
111,5
97,2
102,5
113,4
109,8
104,9
126,1
80,0
96,8
117,2
112,3
117,3
111,1
102,2
104,3
122,9
107,6
121,3
131,5
89,0
104,4
128,9
135,9
133,3
121,3
120,5
120,4
137,9
126,1
133,2
146,6
103,4
117,2




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1148&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]2 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=1148&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1148&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean109.3851.4762744976477374.0952987904973
Geometric Mean108.601231238788
Harmonic Mean107.818091357526
Quadratic Mean110.169186935368
Winsorized Mean ( 1 / 26 )109.291.4417877439949975.8017263325963
Winsorized Mean ( 2 / 26 )109.37251.3993013344821678.1622208918108
Winsorized Mean ( 3 / 26 )109.35751.3601793615437780.399323127416
Winsorized Mean ( 4 / 26 )109.37251.3552312790148680.7039371755828
Winsorized Mean ( 5 / 26 )109.27251.3309782437902782.0993885586145
Winsorized Mean ( 6 / 26 )109.13751.2798145323998285.2760280783442
Winsorized Mean ( 7 / 26 )109.261.1680742563529293.5385737728203
Winsorized Mean ( 8 / 26 )109.271.1664351186739793.6785923628749
Winsorized Mean ( 9 / 26 )109.371251.0976978120369299.6369390561578
Winsorized Mean ( 10 / 26 )109.308751.07471838193765101.709202928978
Winsorized Mean ( 11 / 26 )109.198751.04746150914146104.250847450713
Winsorized Mean ( 12 / 26 )109.018751.01376615432976107.538360335255
Winsorized Mean ( 13 / 26 )108.986251.00373470912262108.580732547614
Winsorized Mean ( 14 / 26 )109.003751.00113929364740108.879704044851
Winsorized Mean ( 15 / 26 )109.060.948063649521647115.034470581197
Winsorized Mean ( 16 / 26 )109.10.936521641399774116.494905378730
Winsorized Mean ( 17 / 26 )109.05750.886944290274554122.958680940650
Winsorized Mean ( 18 / 26 )109.0350.845245638778111128.998003654442
Winsorized Mean ( 19 / 26 )108.916250.762651611301988142.812587537919
Winsorized Mean ( 20 / 26 )108.891250.759180507858743143.432620928488
Winsorized Mean ( 21 / 26 )108.943750.752306251078238144.813033048519
Winsorized Mean ( 22 / 26 )109.136250.727641942631962149.986200087975
Winsorized Mean ( 23 / 26 )108.848750.665427895431945163.577076866223
Winsorized Mean ( 24 / 26 )108.638750.614550607009667176.777548929003
Winsorized Mean ( 25 / 26 )108.576250.551531939439158196.863032284965
Winsorized Mean ( 26 / 26 )108.576250.543492118391026199.775206163860
Trimmed Mean ( 1 / 26 )109.2846153846151.3852189086874678.8933898456283
Trimmed Mean ( 2 / 26 )109.2789473684211.3186440613997582.872209845939
Trimmed Mean ( 3 / 26 )109.2283783783781.2675258169634786.1744801696033
Trimmed Mean ( 4 / 26 )109.1805555555561.2252105930075389.1116647037381
Trimmed Mean ( 5 / 26 )109.1257142857141.1768500007574392.7269526409316
Trimmed Mean ( 6 / 26 )109.0911764705881.1270980539599096.7894284683675
Trimmed Mean ( 7 / 26 )109.0818181818181.08249670206469100.768730263808
Trimmed Mean ( 8 / 26 )109.051.05795362517261103.076351746711
Trimmed Mean ( 9 / 26 )109.0145161290321.02861966617011105.981364846863
Trimmed Mean ( 10 / 26 )108.9616666666671.00826553444381108.068423390841
Trimmed Mean ( 11 / 26 )108.9137931034480.9880668773514110.229171324315
Trimmed Mean ( 12 / 26 )108.8767857142860.968654814582817112.399984055390
Trimmed Mean ( 13 / 26 )108.8592592592590.95117536808004114.447096626349
Trimmed Mean ( 14 / 26 )108.8442307692310.930995564456267116.911653422108
Trimmed Mean ( 15 / 26 )108.8260.905808061842120.142450243485
Trimmed Mean ( 16 / 26 )108.80.88455522341028122.999669348553
Trimmed Mean ( 17 / 26 )108.7673913043480.859322586522933126.573411440809
Trimmed Mean ( 18 / 26 )108.7363636363640.837033236873532129.906864920339
Trimmed Mean ( 19 / 26 )108.7047619047620.816474904938502133.139134157405
Trimmed Mean ( 20 / 26 )108.68250.80649516745496134.759021982695
Trimmed Mean ( 21 / 26 )108.6605263157890.792519610157906137.107681529974
Trimmed Mean ( 22 / 26 )108.6305555555560.773815730540838140.382976551318
Trimmed Mean ( 23 / 26 )108.5764705882350.752678625124219144.253426315004
Trimmed Mean ( 24 / 26 )108.5468750.73870506215323146.942102553893
Trimmed Mean ( 25 / 26 )108.5366666666670.73060333016873148.557585470628
Trimmed Mean ( 26 / 26 )108.5321428571430.732883223542443148.089271756754
Median108.3
Midrange113.3
Midmean - Weighted Average at Xnp108.495121951220
Midmean - Weighted Average at X(n+1)p108.495121951220
Midmean - Empirical Distribution Function108.495121951220
Midmean - Empirical Distribution Function - Averaging108.495121951220
Midmean - Empirical Distribution Function - Interpolation108.495121951220
Midmean - Closest Observation108.495121951220
Midmean - True Basic - Statistics Graphics Toolkit108.495121951220
Midmean - MS Excel (old versions)108.704761904762
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 109.385 & 1.47627449764773 & 74.0952987904973 \tabularnewline
Geometric Mean & 108.601231238788 &  &  \tabularnewline
Harmonic Mean & 107.818091357526 &  &  \tabularnewline
Quadratic Mean & 110.169186935368 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 109.29 & 1.44178774399499 & 75.8017263325963 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 109.3725 & 1.39930133448216 & 78.1622208918108 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 109.3575 & 1.36017936154377 & 80.399323127416 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 109.3725 & 1.35523127901486 & 80.7039371755828 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 109.2725 & 1.33097824379027 & 82.0993885586145 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 109.1375 & 1.27981453239982 & 85.2760280783442 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 109.26 & 1.16807425635292 & 93.5385737728203 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 109.27 & 1.16643511867397 & 93.6785923628749 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 109.37125 & 1.09769781203692 & 99.6369390561578 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 109.30875 & 1.07471838193765 & 101.709202928978 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 109.19875 & 1.04746150914146 & 104.250847450713 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 109.01875 & 1.01376615432976 & 107.538360335255 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 108.98625 & 1.00373470912262 & 108.580732547614 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 109.00375 & 1.00113929364740 & 108.879704044851 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 109.06 & 0.948063649521647 & 115.034470581197 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 109.1 & 0.936521641399774 & 116.494905378730 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 109.0575 & 0.886944290274554 & 122.958680940650 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 109.035 & 0.845245638778111 & 128.998003654442 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 108.91625 & 0.762651611301988 & 142.812587537919 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 108.89125 & 0.759180507858743 & 143.432620928488 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 108.94375 & 0.752306251078238 & 144.813033048519 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 109.13625 & 0.727641942631962 & 149.986200087975 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 108.84875 & 0.665427895431945 & 163.577076866223 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 108.63875 & 0.614550607009667 & 176.777548929003 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 108.57625 & 0.551531939439158 & 196.863032284965 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 108.57625 & 0.543492118391026 & 199.775206163860 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 109.284615384615 & 1.38521890868746 & 78.8933898456283 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 109.278947368421 & 1.31864406139975 & 82.872209845939 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 109.228378378378 & 1.26752581696347 & 86.1744801696033 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 109.180555555556 & 1.22521059300753 & 89.1116647037381 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 109.125714285714 & 1.17685000075743 & 92.7269526409316 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 109.091176470588 & 1.12709805395990 & 96.7894284683675 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 109.081818181818 & 1.08249670206469 & 100.768730263808 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 109.05 & 1.05795362517261 & 103.076351746711 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 109.014516129032 & 1.02861966617011 & 105.981364846863 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 108.961666666667 & 1.00826553444381 & 108.068423390841 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 108.913793103448 & 0.9880668773514 & 110.229171324315 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 108.876785714286 & 0.968654814582817 & 112.399984055390 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 108.859259259259 & 0.95117536808004 & 114.447096626349 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 108.844230769231 & 0.930995564456267 & 116.911653422108 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 108.826 & 0.905808061842 & 120.142450243485 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 108.8 & 0.88455522341028 & 122.999669348553 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 108.767391304348 & 0.859322586522933 & 126.573411440809 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 108.736363636364 & 0.837033236873532 & 129.906864920339 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 108.704761904762 & 0.816474904938502 & 133.139134157405 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 108.6825 & 0.80649516745496 & 134.759021982695 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 108.660526315789 & 0.792519610157906 & 137.107681529974 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 108.630555555556 & 0.773815730540838 & 140.382976551318 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 108.576470588235 & 0.752678625124219 & 144.253426315004 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 108.546875 & 0.73870506215323 & 146.942102553893 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 108.536666666667 & 0.73060333016873 & 148.557585470628 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 108.532142857143 & 0.732883223542443 & 148.089271756754 \tabularnewline
Median & 108.3 &  &  \tabularnewline
Midrange & 113.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.495121951220 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.495121951220 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.495121951220 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.495121951220 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.495121951220 &  &  \tabularnewline
Midmean - Closest Observation & 108.495121951220 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.495121951220 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.704761904762 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1148&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]109.385[/C][C]1.47627449764773[/C][C]74.0952987904973[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]108.601231238788[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]107.818091357526[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]110.169186935368[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]109.29[/C][C]1.44178774399499[/C][C]75.8017263325963[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]109.3725[/C][C]1.39930133448216[/C][C]78.1622208918108[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]109.3575[/C][C]1.36017936154377[/C][C]80.399323127416[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]109.3725[/C][C]1.35523127901486[/C][C]80.7039371755828[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]109.2725[/C][C]1.33097824379027[/C][C]82.0993885586145[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]109.1375[/C][C]1.27981453239982[/C][C]85.2760280783442[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]109.26[/C][C]1.16807425635292[/C][C]93.5385737728203[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]109.27[/C][C]1.16643511867397[/C][C]93.6785923628749[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]109.37125[/C][C]1.09769781203692[/C][C]99.6369390561578[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]109.30875[/C][C]1.07471838193765[/C][C]101.709202928978[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]109.19875[/C][C]1.04746150914146[/C][C]104.250847450713[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]109.01875[/C][C]1.01376615432976[/C][C]107.538360335255[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]108.98625[/C][C]1.00373470912262[/C][C]108.580732547614[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]109.00375[/C][C]1.00113929364740[/C][C]108.879704044851[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]109.06[/C][C]0.948063649521647[/C][C]115.034470581197[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]109.1[/C][C]0.936521641399774[/C][C]116.494905378730[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]109.0575[/C][C]0.886944290274554[/C][C]122.958680940650[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]109.035[/C][C]0.845245638778111[/C][C]128.998003654442[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]108.91625[/C][C]0.762651611301988[/C][C]142.812587537919[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]108.89125[/C][C]0.759180507858743[/C][C]143.432620928488[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]108.94375[/C][C]0.752306251078238[/C][C]144.813033048519[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]109.13625[/C][C]0.727641942631962[/C][C]149.986200087975[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]108.84875[/C][C]0.665427895431945[/C][C]163.577076866223[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]108.63875[/C][C]0.614550607009667[/C][C]176.777548929003[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]108.57625[/C][C]0.551531939439158[/C][C]196.863032284965[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]108.57625[/C][C]0.543492118391026[/C][C]199.775206163860[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]109.284615384615[/C][C]1.38521890868746[/C][C]78.8933898456283[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]109.278947368421[/C][C]1.31864406139975[/C][C]82.872209845939[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]109.228378378378[/C][C]1.26752581696347[/C][C]86.1744801696033[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]109.180555555556[/C][C]1.22521059300753[/C][C]89.1116647037381[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]109.125714285714[/C][C]1.17685000075743[/C][C]92.7269526409316[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]109.091176470588[/C][C]1.12709805395990[/C][C]96.7894284683675[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]109.081818181818[/C][C]1.08249670206469[/C][C]100.768730263808[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]109.05[/C][C]1.05795362517261[/C][C]103.076351746711[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]109.014516129032[/C][C]1.02861966617011[/C][C]105.981364846863[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]108.961666666667[/C][C]1.00826553444381[/C][C]108.068423390841[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]108.913793103448[/C][C]0.9880668773514[/C][C]110.229171324315[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]108.876785714286[/C][C]0.968654814582817[/C][C]112.399984055390[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]108.859259259259[/C][C]0.95117536808004[/C][C]114.447096626349[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]108.844230769231[/C][C]0.930995564456267[/C][C]116.911653422108[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]108.826[/C][C]0.905808061842[/C][C]120.142450243485[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]108.8[/C][C]0.88455522341028[/C][C]122.999669348553[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]108.767391304348[/C][C]0.859322586522933[/C][C]126.573411440809[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]108.736363636364[/C][C]0.837033236873532[/C][C]129.906864920339[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]108.704761904762[/C][C]0.816474904938502[/C][C]133.139134157405[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]108.6825[/C][C]0.80649516745496[/C][C]134.759021982695[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]108.660526315789[/C][C]0.792519610157906[/C][C]137.107681529974[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]108.630555555556[/C][C]0.773815730540838[/C][C]140.382976551318[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]108.576470588235[/C][C]0.752678625124219[/C][C]144.253426315004[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]108.546875[/C][C]0.73870506215323[/C][C]146.942102553893[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]108.536666666667[/C][C]0.73060333016873[/C][C]148.557585470628[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]108.532142857143[/C][C]0.732883223542443[/C][C]148.089271756754[/C][/ROW]
[ROW][C]Median[/C][C]108.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]113.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.495121951220[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.495121951220[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.495121951220[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.495121951220[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.495121951220[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.495121951220[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.495121951220[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.704761904762[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1148&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1148&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 Mean109.3851.4762744976477374.0952987904973
Geometric Mean108.601231238788
Harmonic Mean107.818091357526
Quadratic Mean110.169186935368
Winsorized Mean ( 1 / 26 )109.291.4417877439949975.8017263325963
Winsorized Mean ( 2 / 26 )109.37251.3993013344821678.1622208918108
Winsorized Mean ( 3 / 26 )109.35751.3601793615437780.399323127416
Winsorized Mean ( 4 / 26 )109.37251.3552312790148680.7039371755828
Winsorized Mean ( 5 / 26 )109.27251.3309782437902782.0993885586145
Winsorized Mean ( 6 / 26 )109.13751.2798145323998285.2760280783442
Winsorized Mean ( 7 / 26 )109.261.1680742563529293.5385737728203
Winsorized Mean ( 8 / 26 )109.271.1664351186739793.6785923628749
Winsorized Mean ( 9 / 26 )109.371251.0976978120369299.6369390561578
Winsorized Mean ( 10 / 26 )109.308751.07471838193765101.709202928978
Winsorized Mean ( 11 / 26 )109.198751.04746150914146104.250847450713
Winsorized Mean ( 12 / 26 )109.018751.01376615432976107.538360335255
Winsorized Mean ( 13 / 26 )108.986251.00373470912262108.580732547614
Winsorized Mean ( 14 / 26 )109.003751.00113929364740108.879704044851
Winsorized Mean ( 15 / 26 )109.060.948063649521647115.034470581197
Winsorized Mean ( 16 / 26 )109.10.936521641399774116.494905378730
Winsorized Mean ( 17 / 26 )109.05750.886944290274554122.958680940650
Winsorized Mean ( 18 / 26 )109.0350.845245638778111128.998003654442
Winsorized Mean ( 19 / 26 )108.916250.762651611301988142.812587537919
Winsorized Mean ( 20 / 26 )108.891250.759180507858743143.432620928488
Winsorized Mean ( 21 / 26 )108.943750.752306251078238144.813033048519
Winsorized Mean ( 22 / 26 )109.136250.727641942631962149.986200087975
Winsorized Mean ( 23 / 26 )108.848750.665427895431945163.577076866223
Winsorized Mean ( 24 / 26 )108.638750.614550607009667176.777548929003
Winsorized Mean ( 25 / 26 )108.576250.551531939439158196.863032284965
Winsorized Mean ( 26 / 26 )108.576250.543492118391026199.775206163860
Trimmed Mean ( 1 / 26 )109.2846153846151.3852189086874678.8933898456283
Trimmed Mean ( 2 / 26 )109.2789473684211.3186440613997582.872209845939
Trimmed Mean ( 3 / 26 )109.2283783783781.2675258169634786.1744801696033
Trimmed Mean ( 4 / 26 )109.1805555555561.2252105930075389.1116647037381
Trimmed Mean ( 5 / 26 )109.1257142857141.1768500007574392.7269526409316
Trimmed Mean ( 6 / 26 )109.0911764705881.1270980539599096.7894284683675
Trimmed Mean ( 7 / 26 )109.0818181818181.08249670206469100.768730263808
Trimmed Mean ( 8 / 26 )109.051.05795362517261103.076351746711
Trimmed Mean ( 9 / 26 )109.0145161290321.02861966617011105.981364846863
Trimmed Mean ( 10 / 26 )108.9616666666671.00826553444381108.068423390841
Trimmed Mean ( 11 / 26 )108.9137931034480.9880668773514110.229171324315
Trimmed Mean ( 12 / 26 )108.8767857142860.968654814582817112.399984055390
Trimmed Mean ( 13 / 26 )108.8592592592590.95117536808004114.447096626349
Trimmed Mean ( 14 / 26 )108.8442307692310.930995564456267116.911653422108
Trimmed Mean ( 15 / 26 )108.8260.905808061842120.142450243485
Trimmed Mean ( 16 / 26 )108.80.88455522341028122.999669348553
Trimmed Mean ( 17 / 26 )108.7673913043480.859322586522933126.573411440809
Trimmed Mean ( 18 / 26 )108.7363636363640.837033236873532129.906864920339
Trimmed Mean ( 19 / 26 )108.7047619047620.816474904938502133.139134157405
Trimmed Mean ( 20 / 26 )108.68250.80649516745496134.759021982695
Trimmed Mean ( 21 / 26 )108.6605263157890.792519610157906137.107681529974
Trimmed Mean ( 22 / 26 )108.6305555555560.773815730540838140.382976551318
Trimmed Mean ( 23 / 26 )108.5764705882350.752678625124219144.253426315004
Trimmed Mean ( 24 / 26 )108.5468750.73870506215323146.942102553893
Trimmed Mean ( 25 / 26 )108.5366666666670.73060333016873148.557585470628
Trimmed Mean ( 26 / 26 )108.5321428571430.732883223542443148.089271756754
Median108.3
Midrange113.3
Midmean - Weighted Average at Xnp108.495121951220
Midmean - Weighted Average at X(n+1)p108.495121951220
Midmean - Empirical Distribution Function108.495121951220
Midmean - Empirical Distribution Function - Averaging108.495121951220
Midmean - Empirical Distribution Function - Interpolation108.495121951220
Midmean - Closest Observation108.495121951220
Midmean - True Basic - Statistics Graphics Toolkit108.495121951220
Midmean - MS Excel (old versions)108.704761904762
Number of observations80



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')