Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Nov 2007 12:56:11 -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/20/t1195588134bmzu8jgt56fld44.htm/, Retrieved Sun, 05 May 2024 11:58:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5811, Retrieved Sun, 05 May 2024 11:58:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsDuurzame consumptiegoederen
Estimated Impact243
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency] [2007-11-20 19:56:11] [6dd0685065b0babfa744248f2bd1b94f] [Current]
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Dataseries X:
59,7
58,2
75,3
69
66,1
77,5
69,3
70,2
70,2
78,2
85,4
82,4
61,2
52,2
85,3
79,9
72,2
85,7
75,5
69,2
77,6
85,3
77
89,9
60
54,3
84
69,9
75,1
81,7
69,9
68,3
77,3
77,4
85,3
91
60,6
57,6
93,8
78,7
80,3
89,8
77,5
71,7
83,2
86,2
100,7
100,8
57,1
62,5
79,7
80,3
92,4
91,8
85,8
84,2
93,1
101,2
100,6
106,7
64
67,5
101
95,5
97
103,8
95,2
86,7
93,5
102,5
112,3
105,5
75,4
70,4
108
100
93,3
111,1
101,1
98,1




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5811&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5811&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5811&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean82.061251.65322421246449.6370966389938
Geometric Mean80.7138839345492
Harmonic Mean79.3396980933476
Quadratic Mean83.3664658300926
Winsorized Mean ( 1 / 26 )82.07251.6440032713863849.9223459152784
Winsorized Mean ( 2 / 26 )82.0651.6131021101348550.8740268110736
Winsorized Mean ( 3 / 26 )82.0351.5997340562208851.2803985643681
Winsorized Mean ( 4 / 26 )82.0051.5824831272722251.8204577266835
Winsorized Mean ( 5 / 26 )81.99251.5455159465819953.0518628302293
Winsorized Mean ( 6 / 26 )81.91751.5243724326066653.738507892013
Winsorized Mean ( 7 / 26 )81.856251.4958379427958154.7226725958067
Winsorized Mean ( 8 / 26 )81.906251.4835035333244355.2113615910665
Winsorized Mean ( 9 / 26 )82.041251.4563106821713356.3349915676496
Winsorized Mean ( 10 / 26 )82.203751.4210459730201257.8473543859344
Winsorized Mean ( 11 / 26 )82.478751.3735218680434960.0490985392805
Winsorized Mean ( 12 / 26 )82.673751.3400840042509961.692960842562
Winsorized Mean ( 13 / 26 )82.706251.3052514959054063.3642254074797
Winsorized Mean ( 14 / 26 )82.496251.2336749717481266.8703279949846
Winsorized Mean ( 15 / 26 )82.32751.1959398282458968.8391656967821
Winsorized Mean ( 16 / 26 )82.04751.1475703213333271.4967078485194
Winsorized Mean ( 17 / 26 )82.111251.1203652684066573.2897139133707
Winsorized Mean ( 18 / 26 )81.796251.0747864723907676.1046515760958
Winsorized Mean ( 19 / 26 )81.796251.0547968245027277.5469247725152
Winsorized Mean ( 20 / 26 )81.746251.0477959745447478.0173354221165
Winsorized Mean ( 21 / 26 )81.746251.0331697321405679.1218010526066
Winsorized Mean ( 22 / 26 )81.911250.9574243430300885.5537574287752
Winsorized Mean ( 23 / 26 )81.88250.91427804920922389.5597352149292
Winsorized Mean ( 24 / 26 )82.51250.769239257195137107.26506639932
Winsorized Mean ( 25 / 26 )82.231250.714199546961315115.137639543272
Winsorized Mean ( 26 / 26 )82.231250.705797855715722116.508217379908
Trimmed Mean ( 1 / 26 )82.05641025641031.6047834648874451.1323876721063
Trimmed Mean ( 2 / 26 )82.03947368421051.5589842385206152.6236710141865
Trimmed Mean ( 3 / 26 )82.02567567567571.5246658410070953.7991168094219
Trimmed Mean ( 4 / 26 )82.02222222222221.4901925365071455.0413588934447
Trimmed Mean ( 5 / 26 )82.02714285714291.4555795718453156.3535958073064
Trimmed Mean ( 6 / 26 )82.0352941176471.4257151136143057.5397520404206
Trimmed Mean ( 7 / 26 )82.05909090909091.3956659141531058.7956545165647
Trimmed Mean ( 8 / 26 )82.09531251.3665385931705360.0753706556717
Trimmed Mean ( 9 / 26 )82.12580645161291.3341325868523261.5574548294153
Trimmed Mean ( 10 / 26 )82.13833333333331.3008256649321463.1432293716455
Trimmed Mean ( 11 / 26 )82.12931034482761.2676986799941364.7861448788508
Trimmed Mean ( 12 / 26 )82.08392857142861.2367499741696166.3706733663302
Trimmed Mean ( 13 / 26 )82.01111111111111.2049271855504268.0631262159198
Trimmed Mean ( 14 / 26 )81.92884615384621.1720807468183769.9003429381835
Trimmed Mean ( 15 / 26 )81.8641.1454212664129471.4706478747069
Trimmed Mean ( 16 / 26 )81.81251.1189796556944973.1134829696466
Trimmed Mean ( 17 / 26 )81.78695652173911.0947463858051174.7085878357026
Trimmed Mean ( 18 / 26 )81.75227272727271.0683733690875676.520320603922
Trimmed Mean ( 19 / 26 )81.7476190476191.0431861656728978.3634040956523
Trimmed Mean ( 20 / 26 )81.74251.0135232246589580.6518272213311
Trimmed Mean ( 21 / 26 )81.74210526315790.9746694488651983.8664896681952
Trimmed Mean ( 22 / 26 )81.74166666666670.92497425961611588.3718285313056
Trimmed Mean ( 23 / 26 )81.72352941176470.87731419282534693.1519518093948
Trimmed Mean ( 24 / 26 )81.706250.82264984785595199.3208109293993
Trimmed Mean ( 25 / 26 )81.61666666666670.788627256815012103.492069239767
Trimmed Mean ( 26 / 26 )81.54642857142860.75630475476898107.822181544181
Median81
Midrange82.25
Midmean - Weighted Average at Xnp81.4609756097561
Midmean - Weighted Average at X(n+1)p81.4609756097561
Midmean - Empirical Distribution Function81.4609756097561
Midmean - Empirical Distribution Function - Averaging81.4609756097561
Midmean - Empirical Distribution Function - Interpolation81.4609756097561
Midmean - Closest Observation81.4609756097561
Midmean - True Basic - Statistics Graphics Toolkit81.4609756097561
Midmean - MS Excel (old versions)81.747619047619
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 82.06125 & 1.653224212464 & 49.6370966389938 \tabularnewline
Geometric Mean & 80.7138839345492 &  &  \tabularnewline
Harmonic Mean & 79.3396980933476 &  &  \tabularnewline
Quadratic Mean & 83.3664658300926 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 82.0725 & 1.64400327138638 & 49.9223459152784 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 82.065 & 1.61310211013485 & 50.8740268110736 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 82.035 & 1.59973405622088 & 51.2803985643681 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 82.005 & 1.58248312727222 & 51.8204577266835 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 81.9925 & 1.54551594658199 & 53.0518628302293 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 81.9175 & 1.52437243260666 & 53.738507892013 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 81.85625 & 1.49583794279581 & 54.7226725958067 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 81.90625 & 1.48350353332443 & 55.2113615910665 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 82.04125 & 1.45631068217133 & 56.3349915676496 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 82.20375 & 1.42104597302012 & 57.8473543859344 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 82.47875 & 1.37352186804349 & 60.0490985392805 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 82.67375 & 1.34008400425099 & 61.692960842562 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 82.70625 & 1.30525149590540 & 63.3642254074797 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 82.49625 & 1.23367497174812 & 66.8703279949846 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 82.3275 & 1.19593982824589 & 68.8391656967821 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 82.0475 & 1.14757032133332 & 71.4967078485194 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 82.11125 & 1.12036526840665 & 73.2897139133707 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 81.79625 & 1.07478647239076 & 76.1046515760958 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 81.79625 & 1.05479682450272 & 77.5469247725152 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 81.74625 & 1.04779597454474 & 78.0173354221165 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 81.74625 & 1.03316973214056 & 79.1218010526066 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 81.91125 & 0.95742434303008 & 85.5537574287752 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 81.8825 & 0.914278049209223 & 89.5597352149292 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 82.5125 & 0.769239257195137 & 107.26506639932 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 82.23125 & 0.714199546961315 & 115.137639543272 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 82.23125 & 0.705797855715722 & 116.508217379908 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 82.0564102564103 & 1.60478346488744 & 51.1323876721063 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 82.0394736842105 & 1.55898423852061 & 52.6236710141865 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 82.0256756756757 & 1.52466584100709 & 53.7991168094219 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 82.0222222222222 & 1.49019253650714 & 55.0413588934447 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 82.0271428571429 & 1.45557957184531 & 56.3535958073064 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 82.035294117647 & 1.42571511361430 & 57.5397520404206 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 82.0590909090909 & 1.39566591415310 & 58.7956545165647 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 82.0953125 & 1.36653859317053 & 60.0753706556717 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 82.1258064516129 & 1.33413258685232 & 61.5574548294153 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 82.1383333333333 & 1.30082566493214 & 63.1432293716455 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 82.1293103448276 & 1.26769867999413 & 64.7861448788508 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 82.0839285714286 & 1.23674997416961 & 66.3706733663302 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 82.0111111111111 & 1.20492718555042 & 68.0631262159198 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 81.9288461538462 & 1.17208074681837 & 69.9003429381835 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 81.864 & 1.14542126641294 & 71.4706478747069 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 81.8125 & 1.11897965569449 & 73.1134829696466 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 81.7869565217391 & 1.09474638580511 & 74.7085878357026 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 81.7522727272727 & 1.06837336908756 & 76.520320603922 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 81.747619047619 & 1.04318616567289 & 78.3634040956523 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 81.7425 & 1.01352322465895 & 80.6518272213311 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 81.7421052631579 & 0.97466944886519 & 83.8664896681952 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 81.7416666666667 & 0.924974259616115 & 88.3718285313056 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 81.7235294117647 & 0.877314192825346 & 93.1519518093948 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 81.70625 & 0.822649847855951 & 99.3208109293993 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 81.6166666666667 & 0.788627256815012 & 103.492069239767 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 81.5464285714286 & 0.75630475476898 & 107.822181544181 \tabularnewline
Median & 81 &  &  \tabularnewline
Midrange & 82.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 81.4609756097561 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 81.4609756097561 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 81.4609756097561 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 81.4609756097561 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 81.4609756097561 &  &  \tabularnewline
Midmean - Closest Observation & 81.4609756097561 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 81.4609756097561 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 81.747619047619 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5811&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]82.06125[/C][C]1.653224212464[/C][C]49.6370966389938[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]80.7138839345492[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]79.3396980933476[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]83.3664658300926[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]82.0725[/C][C]1.64400327138638[/C][C]49.9223459152784[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]82.065[/C][C]1.61310211013485[/C][C]50.8740268110736[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]82.035[/C][C]1.59973405622088[/C][C]51.2803985643681[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]82.005[/C][C]1.58248312727222[/C][C]51.8204577266835[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]81.9925[/C][C]1.54551594658199[/C][C]53.0518628302293[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]81.9175[/C][C]1.52437243260666[/C][C]53.738507892013[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]81.85625[/C][C]1.49583794279581[/C][C]54.7226725958067[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]81.90625[/C][C]1.48350353332443[/C][C]55.2113615910665[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]82.04125[/C][C]1.45631068217133[/C][C]56.3349915676496[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]82.20375[/C][C]1.42104597302012[/C][C]57.8473543859344[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]82.47875[/C][C]1.37352186804349[/C][C]60.0490985392805[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]82.67375[/C][C]1.34008400425099[/C][C]61.692960842562[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]82.70625[/C][C]1.30525149590540[/C][C]63.3642254074797[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]82.49625[/C][C]1.23367497174812[/C][C]66.8703279949846[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]82.3275[/C][C]1.19593982824589[/C][C]68.8391656967821[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]82.0475[/C][C]1.14757032133332[/C][C]71.4967078485194[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]82.11125[/C][C]1.12036526840665[/C][C]73.2897139133707[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]81.79625[/C][C]1.07478647239076[/C][C]76.1046515760958[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]81.79625[/C][C]1.05479682450272[/C][C]77.5469247725152[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]81.74625[/C][C]1.04779597454474[/C][C]78.0173354221165[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]81.74625[/C][C]1.03316973214056[/C][C]79.1218010526066[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]81.91125[/C][C]0.95742434303008[/C][C]85.5537574287752[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]81.8825[/C][C]0.914278049209223[/C][C]89.5597352149292[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]82.5125[/C][C]0.769239257195137[/C][C]107.26506639932[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]82.23125[/C][C]0.714199546961315[/C][C]115.137639543272[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]82.23125[/C][C]0.705797855715722[/C][C]116.508217379908[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]82.0564102564103[/C][C]1.60478346488744[/C][C]51.1323876721063[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]82.0394736842105[/C][C]1.55898423852061[/C][C]52.6236710141865[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]82.0256756756757[/C][C]1.52466584100709[/C][C]53.7991168094219[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]82.0222222222222[/C][C]1.49019253650714[/C][C]55.0413588934447[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]82.0271428571429[/C][C]1.45557957184531[/C][C]56.3535958073064[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]82.035294117647[/C][C]1.42571511361430[/C][C]57.5397520404206[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]82.0590909090909[/C][C]1.39566591415310[/C][C]58.7956545165647[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]82.0953125[/C][C]1.36653859317053[/C][C]60.0753706556717[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]82.1258064516129[/C][C]1.33413258685232[/C][C]61.5574548294153[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]82.1383333333333[/C][C]1.30082566493214[/C][C]63.1432293716455[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]82.1293103448276[/C][C]1.26769867999413[/C][C]64.7861448788508[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]82.0839285714286[/C][C]1.23674997416961[/C][C]66.3706733663302[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]82.0111111111111[/C][C]1.20492718555042[/C][C]68.0631262159198[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]81.9288461538462[/C][C]1.17208074681837[/C][C]69.9003429381835[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]81.864[/C][C]1.14542126641294[/C][C]71.4706478747069[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]81.8125[/C][C]1.11897965569449[/C][C]73.1134829696466[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]81.7869565217391[/C][C]1.09474638580511[/C][C]74.7085878357026[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]81.7522727272727[/C][C]1.06837336908756[/C][C]76.520320603922[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]81.747619047619[/C][C]1.04318616567289[/C][C]78.3634040956523[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]81.7425[/C][C]1.01352322465895[/C][C]80.6518272213311[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]81.7421052631579[/C][C]0.97466944886519[/C][C]83.8664896681952[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]81.7416666666667[/C][C]0.924974259616115[/C][C]88.3718285313056[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]81.7235294117647[/C][C]0.877314192825346[/C][C]93.1519518093948[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]81.70625[/C][C]0.822649847855951[/C][C]99.3208109293993[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]81.6166666666667[/C][C]0.788627256815012[/C][C]103.492069239767[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]81.5464285714286[/C][C]0.75630475476898[/C][C]107.822181544181[/C][/ROW]
[ROW][C]Median[/C][C]81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]82.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]81.4609756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]81.4609756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]81.4609756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]81.4609756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]81.4609756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]81.4609756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]81.4609756097561[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]81.747619047619[/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=5811&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5811&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 Mean82.061251.65322421246449.6370966389938
Geometric Mean80.7138839345492
Harmonic Mean79.3396980933476
Quadratic Mean83.3664658300926
Winsorized Mean ( 1 / 26 )82.07251.6440032713863849.9223459152784
Winsorized Mean ( 2 / 26 )82.0651.6131021101348550.8740268110736
Winsorized Mean ( 3 / 26 )82.0351.5997340562208851.2803985643681
Winsorized Mean ( 4 / 26 )82.0051.5824831272722251.8204577266835
Winsorized Mean ( 5 / 26 )81.99251.5455159465819953.0518628302293
Winsorized Mean ( 6 / 26 )81.91751.5243724326066653.738507892013
Winsorized Mean ( 7 / 26 )81.856251.4958379427958154.7226725958067
Winsorized Mean ( 8 / 26 )81.906251.4835035333244355.2113615910665
Winsorized Mean ( 9 / 26 )82.041251.4563106821713356.3349915676496
Winsorized Mean ( 10 / 26 )82.203751.4210459730201257.8473543859344
Winsorized Mean ( 11 / 26 )82.478751.3735218680434960.0490985392805
Winsorized Mean ( 12 / 26 )82.673751.3400840042509961.692960842562
Winsorized Mean ( 13 / 26 )82.706251.3052514959054063.3642254074797
Winsorized Mean ( 14 / 26 )82.496251.2336749717481266.8703279949846
Winsorized Mean ( 15 / 26 )82.32751.1959398282458968.8391656967821
Winsorized Mean ( 16 / 26 )82.04751.1475703213333271.4967078485194
Winsorized Mean ( 17 / 26 )82.111251.1203652684066573.2897139133707
Winsorized Mean ( 18 / 26 )81.796251.0747864723907676.1046515760958
Winsorized Mean ( 19 / 26 )81.796251.0547968245027277.5469247725152
Winsorized Mean ( 20 / 26 )81.746251.0477959745447478.0173354221165
Winsorized Mean ( 21 / 26 )81.746251.0331697321405679.1218010526066
Winsorized Mean ( 22 / 26 )81.911250.9574243430300885.5537574287752
Winsorized Mean ( 23 / 26 )81.88250.91427804920922389.5597352149292
Winsorized Mean ( 24 / 26 )82.51250.769239257195137107.26506639932
Winsorized Mean ( 25 / 26 )82.231250.714199546961315115.137639543272
Winsorized Mean ( 26 / 26 )82.231250.705797855715722116.508217379908
Trimmed Mean ( 1 / 26 )82.05641025641031.6047834648874451.1323876721063
Trimmed Mean ( 2 / 26 )82.03947368421051.5589842385206152.6236710141865
Trimmed Mean ( 3 / 26 )82.02567567567571.5246658410070953.7991168094219
Trimmed Mean ( 4 / 26 )82.02222222222221.4901925365071455.0413588934447
Trimmed Mean ( 5 / 26 )82.02714285714291.4555795718453156.3535958073064
Trimmed Mean ( 6 / 26 )82.0352941176471.4257151136143057.5397520404206
Trimmed Mean ( 7 / 26 )82.05909090909091.3956659141531058.7956545165647
Trimmed Mean ( 8 / 26 )82.09531251.3665385931705360.0753706556717
Trimmed Mean ( 9 / 26 )82.12580645161291.3341325868523261.5574548294153
Trimmed Mean ( 10 / 26 )82.13833333333331.3008256649321463.1432293716455
Trimmed Mean ( 11 / 26 )82.12931034482761.2676986799941364.7861448788508
Trimmed Mean ( 12 / 26 )82.08392857142861.2367499741696166.3706733663302
Trimmed Mean ( 13 / 26 )82.01111111111111.2049271855504268.0631262159198
Trimmed Mean ( 14 / 26 )81.92884615384621.1720807468183769.9003429381835
Trimmed Mean ( 15 / 26 )81.8641.1454212664129471.4706478747069
Trimmed Mean ( 16 / 26 )81.81251.1189796556944973.1134829696466
Trimmed Mean ( 17 / 26 )81.78695652173911.0947463858051174.7085878357026
Trimmed Mean ( 18 / 26 )81.75227272727271.0683733690875676.520320603922
Trimmed Mean ( 19 / 26 )81.7476190476191.0431861656728978.3634040956523
Trimmed Mean ( 20 / 26 )81.74251.0135232246589580.6518272213311
Trimmed Mean ( 21 / 26 )81.74210526315790.9746694488651983.8664896681952
Trimmed Mean ( 22 / 26 )81.74166666666670.92497425961611588.3718285313056
Trimmed Mean ( 23 / 26 )81.72352941176470.87731419282534693.1519518093948
Trimmed Mean ( 24 / 26 )81.706250.82264984785595199.3208109293993
Trimmed Mean ( 25 / 26 )81.61666666666670.788627256815012103.492069239767
Trimmed Mean ( 26 / 26 )81.54642857142860.75630475476898107.822181544181
Median81
Midrange82.25
Midmean - Weighted Average at Xnp81.4609756097561
Midmean - Weighted Average at X(n+1)p81.4609756097561
Midmean - Empirical Distribution Function81.4609756097561
Midmean - Empirical Distribution Function - Averaging81.4609756097561
Midmean - Empirical Distribution Function - Interpolation81.4609756097561
Midmean - Closest Observation81.4609756097561
Midmean - True Basic - Statistics Graphics Toolkit81.4609756097561
Midmean - MS Excel (old versions)81.747619047619
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')