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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 14 Oct 2012 09:00:00 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/14/t1350219624wsv90yh1awrkqja.htm/, Retrieved Sun, 28 Apr 2024 14:25:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=176141, Retrieved Sun, 28 Apr 2024 14:25:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-14 13:00:00] [de59db95ac8fc769a5d40184c39d6048] [Current]
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Dataseries X:
227,81
227,81
227,01
227,26
227,1
227,59
227,59
227,7
227,75
226,33
225,95
226,33
226,33
226,22
224,84
221,88
222,37
221,8
221,8
221,8
221,9
220,2
219,95
220,05
220,05
220,05
220,62
221,53
221,61
221,5
221,5
221,87
222,27
220,86
221,49
221,67
221,67
221,72
221,67
220,29
220,75
219,59
219,59
219,59
219,82
221,59
220,9
221,01
221,01
219,69
221
219,82
218,04
217,97
217,97
217,53
217
217,18
217,68
217,71
217,71
218,5
218,8
218,94
220
219,89
219,89
220,08
220,16
221
222,16
221,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=176141&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=176141&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=176141&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean221.6640277777780.357662799844893619.757011000043
Geometric Mean221.643683123543
Harmonic Mean221.623480631081
Quadratic Mean221.684513940043
Winsorized Mean ( 1 / 24 )221.6665277777780.357212087886848620.545987368697
Winsorized Mean ( 2 / 24 )221.6745833333330.355150342732313624.171109136211
Winsorized Mean ( 3 / 24 )221.678750.353638196580339626.851828065013
Winsorized Mean ( 4 / 24 )221.6743055555560.351917051819129629.904985875726
Winsorized Mean ( 5 / 24 )221.6743055555560.351917051819129629.904985875726
Winsorized Mean ( 6 / 24 )221.6684722222220.34212597432123647.914770756611
Winsorized Mean ( 7 / 24 )221.6529166666670.338573045674687654.667935024098
Winsorized Mean ( 8 / 24 )221.6506944444440.335127876370636661.391397352183
Winsorized Mean ( 9 / 24 )221.6231944444440.307906177049081719.775083983186
Winsorized Mean ( 10 / 24 )221.6648611111110.302145820349897733.635371339621
Winsorized Mean ( 11 / 24 )221.686250.299335494982366740.594596083767
Winsorized Mean ( 12 / 24 )221.776250.282363393474045785.428476656928
Winsorized Mean ( 13 / 24 )221.72750.271622288924115816.308193551619
Winsorized Mean ( 14 / 24 )221.5116666666670.225443659270953982.558868069293
Winsorized Mean ( 15 / 24 )221.0179166666670.1262905116365481750.07539206694
Winsorized Mean ( 16 / 24 )221.0245833333330.1187681190361041860.97569892594
Winsorized Mean ( 17 / 24 )220.9986111111110.1150019230899211921.69491755638
Winsorized Mean ( 18 / 24 )220.9511111111110.1036409844619072131.88935109278
Winsorized Mean ( 19 / 24 )220.9458333333330.1029634737033382145.86615414637
Winsorized Mean ( 20 / 24 )220.9597222222220.1002219704340172204.70343244443
Winsorized Mean ( 21 / 24 )220.9538888888890.09558271077553842311.65120863506
Winsorized Mean ( 22 / 24 )220.9691666666670.09345057818644182364.55644207802
Winsorized Mean ( 23 / 24 )220.9691666666670.09345057818644182364.55644207802
Winsorized Mean ( 24 / 24 )220.94250.09016064388517972450.54261459548
Trimmed Mean ( 1 / 24 )221.6428571428570.350800099556937631.82096419811
Trimmed Mean ( 2 / 24 )221.6177941176470.343121858166632645.886552671971
Trimmed Mean ( 3 / 24 )221.5868181818180.335197270594539661.063909586108
Trimmed Mean ( 4 / 24 )221.552343750.326303152194882678.977025688307
Trimmed Mean ( 5 / 24 )221.5169354838710.316147284815023700.676381305885
Trimmed Mean ( 6 / 24 )221.4791666666670.303718507392256729.225125489714
Trimmed Mean ( 7 / 24 )221.440.291400128839572759.91730299444
Trimmed Mean ( 8 / 24 )221.4008928571430.277139642796663798.878466548303
Trimmed Mean ( 9 / 24 )221.3592592592590.260162000255205850.85161953751
Trimmed Mean ( 10 / 24 )221.3186538461540.246195030668072898.956624939124
Trimmed Mean ( 11 / 24 )221.26880.22960616503136963.688409541523
Trimmed Mean ( 12 / 24 )221.2118750.2083867994336291061.54456808794
Trimmed Mean ( 13 / 24 )221.1382608695650.1839001263151471202.49107654556
Trimmed Mean ( 14 / 24 )221.0640909090910.1528687335660731446.10402501662
Trimmed Mean ( 15 / 24 )221.0092857142860.1267325427101581743.90319161939
Trimmed Mean ( 16 / 24 )221.008250.1242030427700281779.41091515137
Trimmed Mean ( 17 / 24 )221.0063157894740.1223904980161521805.74733636844
Trimmed Mean ( 18 / 24 )221.0072222222220.1205895643640431832.72261897416
Trimmed Mean ( 19 / 24 )221.0138235294120.1204418593369821835.02500497805
Trimmed Mean ( 20 / 24 )221.0218750.1198986782427351843.40543398269
Trimmed Mean ( 21 / 24 )221.0293333333330.1193410387289481852.08152775798
Trimmed Mean ( 22 / 24 )221.0385714285710.1191623256904021854.93670208196
Trimmed Mean ( 23 / 24 )221.0473076923080.1188140857905681860.44698506493
Trimmed Mean ( 24 / 24 )221.05750.1174321419842731882.42755573346
Median221.01
Midrange222.405
Midmean - Weighted Average at Xnp220.944736842105
Midmean - Weighted Average at X(n+1)p221.007222222222
Midmean - Empirical Distribution Function220.944736842105
Midmean - Empirical Distribution Function - Averaging221.007222222222
Midmean - Empirical Distribution Function - Interpolation221.007222222222
Midmean - Closest Observation220.944736842105
Midmean - True Basic - Statistics Graphics Toolkit221.007222222222
Midmean - MS Excel (old versions)220.975897435897
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 221.664027777778 & 0.357662799844893 & 619.757011000043 \tabularnewline
Geometric Mean & 221.643683123543 &  &  \tabularnewline
Harmonic Mean & 221.623480631081 &  &  \tabularnewline
Quadratic Mean & 221.684513940043 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 221.666527777778 & 0.357212087886848 & 620.545987368697 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 221.674583333333 & 0.355150342732313 & 624.171109136211 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 221.67875 & 0.353638196580339 & 626.851828065013 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 221.674305555556 & 0.351917051819129 & 629.904985875726 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 221.674305555556 & 0.351917051819129 & 629.904985875726 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 221.668472222222 & 0.34212597432123 & 647.914770756611 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 221.652916666667 & 0.338573045674687 & 654.667935024098 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 221.650694444444 & 0.335127876370636 & 661.391397352183 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 221.623194444444 & 0.307906177049081 & 719.775083983186 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 221.664861111111 & 0.302145820349897 & 733.635371339621 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 221.68625 & 0.299335494982366 & 740.594596083767 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 221.77625 & 0.282363393474045 & 785.428476656928 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 221.7275 & 0.271622288924115 & 816.308193551619 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 221.511666666667 & 0.225443659270953 & 982.558868069293 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 221.017916666667 & 0.126290511636548 & 1750.07539206694 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 221.024583333333 & 0.118768119036104 & 1860.97569892594 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 220.998611111111 & 0.115001923089921 & 1921.69491755638 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 220.951111111111 & 0.103640984461907 & 2131.88935109278 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 220.945833333333 & 0.102963473703338 & 2145.86615414637 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 220.959722222222 & 0.100221970434017 & 2204.70343244443 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 220.953888888889 & 0.0955827107755384 & 2311.65120863506 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 220.969166666667 & 0.0934505781864418 & 2364.55644207802 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 220.969166666667 & 0.0934505781864418 & 2364.55644207802 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 220.9425 & 0.0901606438851797 & 2450.54261459548 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 221.642857142857 & 0.350800099556937 & 631.82096419811 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 221.617794117647 & 0.343121858166632 & 645.886552671971 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 221.586818181818 & 0.335197270594539 & 661.063909586108 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 221.55234375 & 0.326303152194882 & 678.977025688307 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 221.516935483871 & 0.316147284815023 & 700.676381305885 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 221.479166666667 & 0.303718507392256 & 729.225125489714 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 221.44 & 0.291400128839572 & 759.91730299444 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 221.400892857143 & 0.277139642796663 & 798.878466548303 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 221.359259259259 & 0.260162000255205 & 850.85161953751 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 221.318653846154 & 0.246195030668072 & 898.956624939124 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 221.2688 & 0.22960616503136 & 963.688409541523 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 221.211875 & 0.208386799433629 & 1061.54456808794 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 221.138260869565 & 0.183900126315147 & 1202.49107654556 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 221.064090909091 & 0.152868733566073 & 1446.10402501662 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 221.009285714286 & 0.126732542710158 & 1743.90319161939 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 221.00825 & 0.124203042770028 & 1779.41091515137 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 221.006315789474 & 0.122390498016152 & 1805.74733636844 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 221.007222222222 & 0.120589564364043 & 1832.72261897416 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 221.013823529412 & 0.120441859336982 & 1835.02500497805 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 221.021875 & 0.119898678242735 & 1843.40543398269 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 221.029333333333 & 0.119341038728948 & 1852.08152775798 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 221.038571428571 & 0.119162325690402 & 1854.93670208196 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 221.047307692308 & 0.118814085790568 & 1860.44698506493 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 221.0575 & 0.117432141984273 & 1882.42755573346 \tabularnewline
Median & 221.01 &  &  \tabularnewline
Midrange & 222.405 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 220.944736842105 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 221.007222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 220.944736842105 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 221.007222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 221.007222222222 &  &  \tabularnewline
Midmean - Closest Observation & 220.944736842105 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 221.007222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 220.975897435897 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=176141&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]221.664027777778[/C][C]0.357662799844893[/C][C]619.757011000043[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]221.643683123543[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]221.623480631081[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]221.684513940043[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]221.666527777778[/C][C]0.357212087886848[/C][C]620.545987368697[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]221.674583333333[/C][C]0.355150342732313[/C][C]624.171109136211[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]221.67875[/C][C]0.353638196580339[/C][C]626.851828065013[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]221.674305555556[/C][C]0.351917051819129[/C][C]629.904985875726[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]221.674305555556[/C][C]0.351917051819129[/C][C]629.904985875726[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]221.668472222222[/C][C]0.34212597432123[/C][C]647.914770756611[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]221.652916666667[/C][C]0.338573045674687[/C][C]654.667935024098[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]221.650694444444[/C][C]0.335127876370636[/C][C]661.391397352183[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]221.623194444444[/C][C]0.307906177049081[/C][C]719.775083983186[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]221.664861111111[/C][C]0.302145820349897[/C][C]733.635371339621[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]221.68625[/C][C]0.299335494982366[/C][C]740.594596083767[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]221.77625[/C][C]0.282363393474045[/C][C]785.428476656928[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]221.7275[/C][C]0.271622288924115[/C][C]816.308193551619[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]221.511666666667[/C][C]0.225443659270953[/C][C]982.558868069293[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]221.017916666667[/C][C]0.126290511636548[/C][C]1750.07539206694[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]221.024583333333[/C][C]0.118768119036104[/C][C]1860.97569892594[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]220.998611111111[/C][C]0.115001923089921[/C][C]1921.69491755638[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]220.951111111111[/C][C]0.103640984461907[/C][C]2131.88935109278[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]220.945833333333[/C][C]0.102963473703338[/C][C]2145.86615414637[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]220.959722222222[/C][C]0.100221970434017[/C][C]2204.70343244443[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]220.953888888889[/C][C]0.0955827107755384[/C][C]2311.65120863506[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]220.969166666667[/C][C]0.0934505781864418[/C][C]2364.55644207802[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]220.969166666667[/C][C]0.0934505781864418[/C][C]2364.55644207802[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]220.9425[/C][C]0.0901606438851797[/C][C]2450.54261459548[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]221.642857142857[/C][C]0.350800099556937[/C][C]631.82096419811[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]221.617794117647[/C][C]0.343121858166632[/C][C]645.886552671971[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]221.586818181818[/C][C]0.335197270594539[/C][C]661.063909586108[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]221.55234375[/C][C]0.326303152194882[/C][C]678.977025688307[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]221.516935483871[/C][C]0.316147284815023[/C][C]700.676381305885[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]221.479166666667[/C][C]0.303718507392256[/C][C]729.225125489714[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]221.44[/C][C]0.291400128839572[/C][C]759.91730299444[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]221.400892857143[/C][C]0.277139642796663[/C][C]798.878466548303[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]221.359259259259[/C][C]0.260162000255205[/C][C]850.85161953751[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]221.318653846154[/C][C]0.246195030668072[/C][C]898.956624939124[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]221.2688[/C][C]0.22960616503136[/C][C]963.688409541523[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]221.211875[/C][C]0.208386799433629[/C][C]1061.54456808794[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]221.138260869565[/C][C]0.183900126315147[/C][C]1202.49107654556[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]221.064090909091[/C][C]0.152868733566073[/C][C]1446.10402501662[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]221.009285714286[/C][C]0.126732542710158[/C][C]1743.90319161939[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]221.00825[/C][C]0.124203042770028[/C][C]1779.41091515137[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]221.006315789474[/C][C]0.122390498016152[/C][C]1805.74733636844[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]221.007222222222[/C][C]0.120589564364043[/C][C]1832.72261897416[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]221.013823529412[/C][C]0.120441859336982[/C][C]1835.02500497805[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]221.021875[/C][C]0.119898678242735[/C][C]1843.40543398269[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]221.029333333333[/C][C]0.119341038728948[/C][C]1852.08152775798[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]221.038571428571[/C][C]0.119162325690402[/C][C]1854.93670208196[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]221.047307692308[/C][C]0.118814085790568[/C][C]1860.44698506493[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]221.0575[/C][C]0.117432141984273[/C][C]1882.42755573346[/C][/ROW]
[ROW][C]Median[/C][C]221.01[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]222.405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]220.944736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]221.007222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]220.944736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]221.007222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]221.007222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]220.944736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]221.007222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]220.975897435897[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=176141&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=176141&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 Mean221.6640277777780.357662799844893619.757011000043
Geometric Mean221.643683123543
Harmonic Mean221.623480631081
Quadratic Mean221.684513940043
Winsorized Mean ( 1 / 24 )221.6665277777780.357212087886848620.545987368697
Winsorized Mean ( 2 / 24 )221.6745833333330.355150342732313624.171109136211
Winsorized Mean ( 3 / 24 )221.678750.353638196580339626.851828065013
Winsorized Mean ( 4 / 24 )221.6743055555560.351917051819129629.904985875726
Winsorized Mean ( 5 / 24 )221.6743055555560.351917051819129629.904985875726
Winsorized Mean ( 6 / 24 )221.6684722222220.34212597432123647.914770756611
Winsorized Mean ( 7 / 24 )221.6529166666670.338573045674687654.667935024098
Winsorized Mean ( 8 / 24 )221.6506944444440.335127876370636661.391397352183
Winsorized Mean ( 9 / 24 )221.6231944444440.307906177049081719.775083983186
Winsorized Mean ( 10 / 24 )221.6648611111110.302145820349897733.635371339621
Winsorized Mean ( 11 / 24 )221.686250.299335494982366740.594596083767
Winsorized Mean ( 12 / 24 )221.776250.282363393474045785.428476656928
Winsorized Mean ( 13 / 24 )221.72750.271622288924115816.308193551619
Winsorized Mean ( 14 / 24 )221.5116666666670.225443659270953982.558868069293
Winsorized Mean ( 15 / 24 )221.0179166666670.1262905116365481750.07539206694
Winsorized Mean ( 16 / 24 )221.0245833333330.1187681190361041860.97569892594
Winsorized Mean ( 17 / 24 )220.9986111111110.1150019230899211921.69491755638
Winsorized Mean ( 18 / 24 )220.9511111111110.1036409844619072131.88935109278
Winsorized Mean ( 19 / 24 )220.9458333333330.1029634737033382145.86615414637
Winsorized Mean ( 20 / 24 )220.9597222222220.1002219704340172204.70343244443
Winsorized Mean ( 21 / 24 )220.9538888888890.09558271077553842311.65120863506
Winsorized Mean ( 22 / 24 )220.9691666666670.09345057818644182364.55644207802
Winsorized Mean ( 23 / 24 )220.9691666666670.09345057818644182364.55644207802
Winsorized Mean ( 24 / 24 )220.94250.09016064388517972450.54261459548
Trimmed Mean ( 1 / 24 )221.6428571428570.350800099556937631.82096419811
Trimmed Mean ( 2 / 24 )221.6177941176470.343121858166632645.886552671971
Trimmed Mean ( 3 / 24 )221.5868181818180.335197270594539661.063909586108
Trimmed Mean ( 4 / 24 )221.552343750.326303152194882678.977025688307
Trimmed Mean ( 5 / 24 )221.5169354838710.316147284815023700.676381305885
Trimmed Mean ( 6 / 24 )221.4791666666670.303718507392256729.225125489714
Trimmed Mean ( 7 / 24 )221.440.291400128839572759.91730299444
Trimmed Mean ( 8 / 24 )221.4008928571430.277139642796663798.878466548303
Trimmed Mean ( 9 / 24 )221.3592592592590.260162000255205850.85161953751
Trimmed Mean ( 10 / 24 )221.3186538461540.246195030668072898.956624939124
Trimmed Mean ( 11 / 24 )221.26880.22960616503136963.688409541523
Trimmed Mean ( 12 / 24 )221.2118750.2083867994336291061.54456808794
Trimmed Mean ( 13 / 24 )221.1382608695650.1839001263151471202.49107654556
Trimmed Mean ( 14 / 24 )221.0640909090910.1528687335660731446.10402501662
Trimmed Mean ( 15 / 24 )221.0092857142860.1267325427101581743.90319161939
Trimmed Mean ( 16 / 24 )221.008250.1242030427700281779.41091515137
Trimmed Mean ( 17 / 24 )221.0063157894740.1223904980161521805.74733636844
Trimmed Mean ( 18 / 24 )221.0072222222220.1205895643640431832.72261897416
Trimmed Mean ( 19 / 24 )221.0138235294120.1204418593369821835.02500497805
Trimmed Mean ( 20 / 24 )221.0218750.1198986782427351843.40543398269
Trimmed Mean ( 21 / 24 )221.0293333333330.1193410387289481852.08152775798
Trimmed Mean ( 22 / 24 )221.0385714285710.1191623256904021854.93670208196
Trimmed Mean ( 23 / 24 )221.0473076923080.1188140857905681860.44698506493
Trimmed Mean ( 24 / 24 )221.05750.1174321419842731882.42755573346
Median221.01
Midrange222.405
Midmean - Weighted Average at Xnp220.944736842105
Midmean - Weighted Average at X(n+1)p221.007222222222
Midmean - Empirical Distribution Function220.944736842105
Midmean - Empirical Distribution Function - Averaging221.007222222222
Midmean - Empirical Distribution Function - Interpolation221.007222222222
Midmean - Closest Observation220.944736842105
Midmean - True Basic - Statistics Graphics Toolkit221.007222222222
Midmean - MS Excel (old versions)220.975897435897
Number of observations72



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')