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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 12 Nov 2007 03:01:05 -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/Nov/12/t1194861445h9wjueeyqz5ew5d.htm/, Retrieved Sun, 28 Apr 2024 19:51:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5148, Retrieved Sun, 28 Apr 2024 19:51:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact227
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-11-12 10:01:05] [addc65c5fbfb06e42e5fd21f3a753dae] [Current]
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Dataseries X:
97,3
101
113,2
101
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
103,6
94,1
98,7
119,5
112,7
104,4
124,7
89,1
97
121,6
118,8
114
111,5
97,2
102,5
113,4
109,8
104,9
126,1
80
96,8
117,2
112,3
117,3
111,1
102,2
104,3
122,9
107,6
121,3
131,5
89
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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5148&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5148&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5148&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic 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=5148&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=5148&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5148&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')