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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 20 Apr 2008 06:49:19 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/20/t1208695881oqwsl7nk9b14uak.htm/, Retrieved Sun, 12 May 2024 22:57:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10336, Retrieved Sun, 12 May 2024 22:57:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact228
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [hfd 5 oef 2 vraag...] [2008-04-20 12:49:19] [b46ff5180a79ecd706507099e9497e04] [Current]
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Dataseries X:
10,99
11
10,9
10,99
11,04
11,03
10,99
11
10,87
10,88
10,91
10,92
10,83
10,9
10,82
10,79
10,77
10,72
10,71
10,63
10,61
10,57
10,65
10,57
10,57
10,57
10,52
10,43
10,35
10,2
10,2
10,17
10,14
10,05
10,12
10,12
10,03
10,03
9,96
9,94
9,9
9,84
9,82
9,78
9,77
9,75
9,72
9,65
9,63
9,62
9,63
9,62
9,65
9,61
9,57
9,61
9,58
9,55
9,5
9,47
9,43
9,38
9,35
9,34
9,35
9,33
9,31
9,29
9,27
9,29
9,27
9,26




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=10336&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=10336&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10336&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 Mean10.11986111111110.0709921563961764142.549002943882
Geometric Mean10.1022338145366
Harmonic Mean10.0846883845457
Quadratic Mean10.1375253801573
Winsorized Mean ( 1 / 24 )10.11986111111110.0709433674641264142.647036260696
Winsorized Mean ( 2 / 24 )10.11902777777780.0707950489530764142.934116543726
Winsorized Mean ( 3 / 24 )10.11986111111110.0706557406557991143.227726681265
Winsorized Mean ( 4 / 24 )10.11930555555560.070558726577787143.416782676762
Winsorized Mean ( 5 / 24 )10.12069444444440.0703310210300342143.900860476951
Winsorized Mean ( 6 / 24 )10.12236111111110.0700629867121354144.475158512731
Winsorized Mean ( 7 / 24 )10.11652777777780.0687543311261207147.140225380425
Winsorized Mean ( 8 / 24 )10.11652777777780.0683960435147754147.911008559908
Winsorized Mean ( 9 / 24 )10.11527777777780.068192621705112148.333903651918
Winsorized Mean ( 10 / 24 )10.11944444444440.0675420488309702149.824363038930
Winsorized Mean ( 11 / 24 )10.12402777777780.0658906298839465153.648975516083
Winsorized Mean ( 12 / 24 )10.12902777777780.0646481871017942156.679223840086
Winsorized Mean ( 13 / 24 )10.12722222222220.0627247827058943161.454879321098
Winsorized Mean ( 14 / 24 )10.1350.0610769928944841165.938097468372
Winsorized Mean ( 15 / 24 )10.13291666666670.0595389949610359170.189582025997
Winsorized Mean ( 16 / 24 )10.13069444444440.0585566905567157173.006608606616
Winsorized Mean ( 17 / 24 )10.12597222222220.0558336520634944181.359661207669
Winsorized Mean ( 18 / 24 )10.12347222222220.0554601464581313182.535980676949
Winsorized Mean ( 19 / 24 )10.11027777777780.0527954731063671191.498952143275
Winsorized Mean ( 20 / 24 )10.10472222222220.0520002754530377194.320551846845
Winsorized Mean ( 21 / 24 )10.10180555555560.0507919774776599198.885848852778
Winsorized Mean ( 22 / 24 )10.08958333333330.049088099675318205.540312215559
Winsorized Mean ( 23 / 24 )10.09597222222220.0482509658056956209.238759341694
Winsorized Mean ( 24 / 24 )10.09597222222220.0482509658056956209.238759341694
Trimmed Mean ( 1 / 24 )10.1190.0707514092068978143.021886255425
Trimmed Mean ( 2 / 24 )10.11808823529410.0704728969730023143.574177732048
Trimmed Mean ( 3 / 24 )10.11757575757580.0701812706558188144.163473573941
Trimmed Mean ( 4 / 24 )10.116718750.0698396884139167144.856298470886
Trimmed Mean ( 5 / 24 )10.11596774193550.069409178348373145.743948893361
Trimmed Mean ( 6 / 24 )10.11483333333330.0689032284905566146.797669063063
Trimmed Mean ( 7 / 24 )10.11327586206900.0683056491208229148.059142870893
Trimmed Mean ( 8 / 24 )10.11267857142860.0678422018752898149.061768219406
Trimmed Mean ( 9 / 24 )10.11203703703700.0672887016233158150.27837947661
Trimmed Mean ( 10 / 24 )10.11153846153850.0665823663551834151.865111065571
Trimmed Mean ( 11 / 24 )10.11040.0657763433685605153.708757316426
Trimmed Mean ( 12 / 24 )10.10854166666670.0650443040387409155.410098025585
Trimmed Mean ( 13 / 24 )10.10586956521740.0642936921399083157.182909067132
Trimmed Mean ( 14 / 24 )10.10318181818180.0636493870696468158.731800624045
Trimmed Mean ( 15 / 24 )10.09928571428570.063045429905396160.190607462593
Trimmed Mean ( 16 / 24 )10.095250.0624633097434211161.618877409282
Trimmed Mean ( 17 / 24 )10.09105263157890.0617729857976003163.357048413401
Trimmed Mean ( 18 / 24 )10.08694444444440.06131860517321164.500552743353
Trimmed Mean ( 19 / 24 )10.08264705882350.0606064256306508166.362674483882
Trimmed Mean ( 20 / 24 )10.0793750.0601157108376515167.666236655179
Trimmed Mean ( 21 / 24 )10.07633333333330.0594079667503438169.612492810571
Trimmed Mean ( 22 / 24 )10.07321428571430.0584885770320587172.225326668367
Trimmed Mean ( 23 / 24 )10.07115384615380.0574170355933791175.403584355636
Trimmed Mean ( 24 / 24 )10.06791666666670.0557621084747151180.551219135336
Median10.04
Midrange10.15
Midmean - Weighted Average at Xnp10.0740540540541
Midmean - Weighted Average at X(n+1)p10.0740540540541
Midmean - Empirical Distribution Function10.0740540540541
Midmean - Empirical Distribution Function - Averaging10.0740540540541
Midmean - Empirical Distribution Function - Interpolation10.0740540540541
Midmean - Closest Observation10.0740540540541
Midmean - True Basic - Statistics Graphics Toolkit10.0740540540541
Midmean - MS Excel (old versions)10.0910526315789
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 10.1198611111111 & 0.0709921563961764 & 142.549002943882 \tabularnewline
Geometric Mean & 10.1022338145366 &  &  \tabularnewline
Harmonic Mean & 10.0846883845457 &  &  \tabularnewline
Quadratic Mean & 10.1375253801573 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 10.1198611111111 & 0.0709433674641264 & 142.647036260696 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 10.1190277777778 & 0.0707950489530764 & 142.934116543726 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 10.1198611111111 & 0.0706557406557991 & 143.227726681265 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 10.1193055555556 & 0.070558726577787 & 143.416782676762 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 10.1206944444444 & 0.0703310210300342 & 143.900860476951 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 10.1223611111111 & 0.0700629867121354 & 144.475158512731 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 10.1165277777778 & 0.0687543311261207 & 147.140225380425 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 10.1165277777778 & 0.0683960435147754 & 147.911008559908 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 10.1152777777778 & 0.068192621705112 & 148.333903651918 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 10.1194444444444 & 0.0675420488309702 & 149.824363038930 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 10.1240277777778 & 0.0658906298839465 & 153.648975516083 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 10.1290277777778 & 0.0646481871017942 & 156.679223840086 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 10.1272222222222 & 0.0627247827058943 & 161.454879321098 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 10.135 & 0.0610769928944841 & 165.938097468372 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 10.1329166666667 & 0.0595389949610359 & 170.189582025997 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 10.1306944444444 & 0.0585566905567157 & 173.006608606616 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 10.1259722222222 & 0.0558336520634944 & 181.359661207669 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 10.1234722222222 & 0.0554601464581313 & 182.535980676949 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 10.1102777777778 & 0.0527954731063671 & 191.498952143275 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 10.1047222222222 & 0.0520002754530377 & 194.320551846845 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 10.1018055555556 & 0.0507919774776599 & 198.885848852778 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 10.0895833333333 & 0.049088099675318 & 205.540312215559 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 10.0959722222222 & 0.0482509658056956 & 209.238759341694 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 10.0959722222222 & 0.0482509658056956 & 209.238759341694 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 10.119 & 0.0707514092068978 & 143.021886255425 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 10.1180882352941 & 0.0704728969730023 & 143.574177732048 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 10.1175757575758 & 0.0701812706558188 & 144.163473573941 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 10.11671875 & 0.0698396884139167 & 144.856298470886 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 10.1159677419355 & 0.069409178348373 & 145.743948893361 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 10.1148333333333 & 0.0689032284905566 & 146.797669063063 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 10.1132758620690 & 0.0683056491208229 & 148.059142870893 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 10.1126785714286 & 0.0678422018752898 & 149.061768219406 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 10.1120370370370 & 0.0672887016233158 & 150.27837947661 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 10.1115384615385 & 0.0665823663551834 & 151.865111065571 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 10.1104 & 0.0657763433685605 & 153.708757316426 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 10.1085416666667 & 0.0650443040387409 & 155.410098025585 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 10.1058695652174 & 0.0642936921399083 & 157.182909067132 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 10.1031818181818 & 0.0636493870696468 & 158.731800624045 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 10.0992857142857 & 0.063045429905396 & 160.190607462593 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 10.09525 & 0.0624633097434211 & 161.618877409282 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 10.0910526315789 & 0.0617729857976003 & 163.357048413401 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 10.0869444444444 & 0.06131860517321 & 164.500552743353 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 10.0826470588235 & 0.0606064256306508 & 166.362674483882 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 10.079375 & 0.0601157108376515 & 167.666236655179 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 10.0763333333333 & 0.0594079667503438 & 169.612492810571 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 10.0732142857143 & 0.0584885770320587 & 172.225326668367 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 10.0711538461538 & 0.0574170355933791 & 175.403584355636 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 10.0679166666667 & 0.0557621084747151 & 180.551219135336 \tabularnewline
Median & 10.04 &  &  \tabularnewline
Midrange & 10.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 10.0740540540541 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 10.0740540540541 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 10.0740540540541 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 10.0740540540541 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 10.0740540540541 &  &  \tabularnewline
Midmean - Closest Observation & 10.0740540540541 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 10.0740540540541 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 10.0910526315789 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10336&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]10.1198611111111[/C][C]0.0709921563961764[/C][C]142.549002943882[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]10.1022338145366[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]10.0846883845457[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10.1375253801573[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]10.1198611111111[/C][C]0.0709433674641264[/C][C]142.647036260696[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]10.1190277777778[/C][C]0.0707950489530764[/C][C]142.934116543726[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]10.1198611111111[/C][C]0.0706557406557991[/C][C]143.227726681265[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]10.1193055555556[/C][C]0.070558726577787[/C][C]143.416782676762[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]10.1206944444444[/C][C]0.0703310210300342[/C][C]143.900860476951[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]10.1223611111111[/C][C]0.0700629867121354[/C][C]144.475158512731[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]10.1165277777778[/C][C]0.0687543311261207[/C][C]147.140225380425[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]10.1165277777778[/C][C]0.0683960435147754[/C][C]147.911008559908[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]10.1152777777778[/C][C]0.068192621705112[/C][C]148.333903651918[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]10.1194444444444[/C][C]0.0675420488309702[/C][C]149.824363038930[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]10.1240277777778[/C][C]0.0658906298839465[/C][C]153.648975516083[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]10.1290277777778[/C][C]0.0646481871017942[/C][C]156.679223840086[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]10.1272222222222[/C][C]0.0627247827058943[/C][C]161.454879321098[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]10.135[/C][C]0.0610769928944841[/C][C]165.938097468372[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]10.1329166666667[/C][C]0.0595389949610359[/C][C]170.189582025997[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]10.1306944444444[/C][C]0.0585566905567157[/C][C]173.006608606616[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]10.1259722222222[/C][C]0.0558336520634944[/C][C]181.359661207669[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]10.1234722222222[/C][C]0.0554601464581313[/C][C]182.535980676949[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]10.1102777777778[/C][C]0.0527954731063671[/C][C]191.498952143275[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]10.1047222222222[/C][C]0.0520002754530377[/C][C]194.320551846845[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]10.1018055555556[/C][C]0.0507919774776599[/C][C]198.885848852778[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]10.0895833333333[/C][C]0.049088099675318[/C][C]205.540312215559[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]10.0959722222222[/C][C]0.0482509658056956[/C][C]209.238759341694[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]10.0959722222222[/C][C]0.0482509658056956[/C][C]209.238759341694[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]10.119[/C][C]0.0707514092068978[/C][C]143.021886255425[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]10.1180882352941[/C][C]0.0704728969730023[/C][C]143.574177732048[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]10.1175757575758[/C][C]0.0701812706558188[/C][C]144.163473573941[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]10.11671875[/C][C]0.0698396884139167[/C][C]144.856298470886[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]10.1159677419355[/C][C]0.069409178348373[/C][C]145.743948893361[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]10.1148333333333[/C][C]0.0689032284905566[/C][C]146.797669063063[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]10.1132758620690[/C][C]0.0683056491208229[/C][C]148.059142870893[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]10.1126785714286[/C][C]0.0678422018752898[/C][C]149.061768219406[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]10.1120370370370[/C][C]0.0672887016233158[/C][C]150.27837947661[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]10.1115384615385[/C][C]0.0665823663551834[/C][C]151.865111065571[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]10.1104[/C][C]0.0657763433685605[/C][C]153.708757316426[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]10.1085416666667[/C][C]0.0650443040387409[/C][C]155.410098025585[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]10.1058695652174[/C][C]0.0642936921399083[/C][C]157.182909067132[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]10.1031818181818[/C][C]0.0636493870696468[/C][C]158.731800624045[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]10.0992857142857[/C][C]0.063045429905396[/C][C]160.190607462593[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]10.09525[/C][C]0.0624633097434211[/C][C]161.618877409282[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]10.0910526315789[/C][C]0.0617729857976003[/C][C]163.357048413401[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]10.0869444444444[/C][C]0.06131860517321[/C][C]164.500552743353[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]10.0826470588235[/C][C]0.0606064256306508[/C][C]166.362674483882[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]10.079375[/C][C]0.0601157108376515[/C][C]167.666236655179[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]10.0763333333333[/C][C]0.0594079667503438[/C][C]169.612492810571[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]10.0732142857143[/C][C]0.0584885770320587[/C][C]172.225326668367[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]10.0711538461538[/C][C]0.0574170355933791[/C][C]175.403584355636[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]10.0679166666667[/C][C]0.0557621084747151[/C][C]180.551219135336[/C][/ROW]
[ROW][C]Median[/C][C]10.04[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]10.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]10.0740540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]10.0740540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]10.0740540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]10.0740540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]10.0740540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]10.0740540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]10.0740540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]10.0910526315789[/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=10336&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10336&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 Mean10.11986111111110.0709921563961764142.549002943882
Geometric Mean10.1022338145366
Harmonic Mean10.0846883845457
Quadratic Mean10.1375253801573
Winsorized Mean ( 1 / 24 )10.11986111111110.0709433674641264142.647036260696
Winsorized Mean ( 2 / 24 )10.11902777777780.0707950489530764142.934116543726
Winsorized Mean ( 3 / 24 )10.11986111111110.0706557406557991143.227726681265
Winsorized Mean ( 4 / 24 )10.11930555555560.070558726577787143.416782676762
Winsorized Mean ( 5 / 24 )10.12069444444440.0703310210300342143.900860476951
Winsorized Mean ( 6 / 24 )10.12236111111110.0700629867121354144.475158512731
Winsorized Mean ( 7 / 24 )10.11652777777780.0687543311261207147.140225380425
Winsorized Mean ( 8 / 24 )10.11652777777780.0683960435147754147.911008559908
Winsorized Mean ( 9 / 24 )10.11527777777780.068192621705112148.333903651918
Winsorized Mean ( 10 / 24 )10.11944444444440.0675420488309702149.824363038930
Winsorized Mean ( 11 / 24 )10.12402777777780.0658906298839465153.648975516083
Winsorized Mean ( 12 / 24 )10.12902777777780.0646481871017942156.679223840086
Winsorized Mean ( 13 / 24 )10.12722222222220.0627247827058943161.454879321098
Winsorized Mean ( 14 / 24 )10.1350.0610769928944841165.938097468372
Winsorized Mean ( 15 / 24 )10.13291666666670.0595389949610359170.189582025997
Winsorized Mean ( 16 / 24 )10.13069444444440.0585566905567157173.006608606616
Winsorized Mean ( 17 / 24 )10.12597222222220.0558336520634944181.359661207669
Winsorized Mean ( 18 / 24 )10.12347222222220.0554601464581313182.535980676949
Winsorized Mean ( 19 / 24 )10.11027777777780.0527954731063671191.498952143275
Winsorized Mean ( 20 / 24 )10.10472222222220.0520002754530377194.320551846845
Winsorized Mean ( 21 / 24 )10.10180555555560.0507919774776599198.885848852778
Winsorized Mean ( 22 / 24 )10.08958333333330.049088099675318205.540312215559
Winsorized Mean ( 23 / 24 )10.09597222222220.0482509658056956209.238759341694
Winsorized Mean ( 24 / 24 )10.09597222222220.0482509658056956209.238759341694
Trimmed Mean ( 1 / 24 )10.1190.0707514092068978143.021886255425
Trimmed Mean ( 2 / 24 )10.11808823529410.0704728969730023143.574177732048
Trimmed Mean ( 3 / 24 )10.11757575757580.0701812706558188144.163473573941
Trimmed Mean ( 4 / 24 )10.116718750.0698396884139167144.856298470886
Trimmed Mean ( 5 / 24 )10.11596774193550.069409178348373145.743948893361
Trimmed Mean ( 6 / 24 )10.11483333333330.0689032284905566146.797669063063
Trimmed Mean ( 7 / 24 )10.11327586206900.0683056491208229148.059142870893
Trimmed Mean ( 8 / 24 )10.11267857142860.0678422018752898149.061768219406
Trimmed Mean ( 9 / 24 )10.11203703703700.0672887016233158150.27837947661
Trimmed Mean ( 10 / 24 )10.11153846153850.0665823663551834151.865111065571
Trimmed Mean ( 11 / 24 )10.11040.0657763433685605153.708757316426
Trimmed Mean ( 12 / 24 )10.10854166666670.0650443040387409155.410098025585
Trimmed Mean ( 13 / 24 )10.10586956521740.0642936921399083157.182909067132
Trimmed Mean ( 14 / 24 )10.10318181818180.0636493870696468158.731800624045
Trimmed Mean ( 15 / 24 )10.09928571428570.063045429905396160.190607462593
Trimmed Mean ( 16 / 24 )10.095250.0624633097434211161.618877409282
Trimmed Mean ( 17 / 24 )10.09105263157890.0617729857976003163.357048413401
Trimmed Mean ( 18 / 24 )10.08694444444440.06131860517321164.500552743353
Trimmed Mean ( 19 / 24 )10.08264705882350.0606064256306508166.362674483882
Trimmed Mean ( 20 / 24 )10.0793750.0601157108376515167.666236655179
Trimmed Mean ( 21 / 24 )10.07633333333330.0594079667503438169.612492810571
Trimmed Mean ( 22 / 24 )10.07321428571430.0584885770320587172.225326668367
Trimmed Mean ( 23 / 24 )10.07115384615380.0574170355933791175.403584355636
Trimmed Mean ( 24 / 24 )10.06791666666670.0557621084747151180.551219135336
Median10.04
Midrange10.15
Midmean - Weighted Average at Xnp10.0740540540541
Midmean - Weighted Average at X(n+1)p10.0740540540541
Midmean - Empirical Distribution Function10.0740540540541
Midmean - Empirical Distribution Function - Averaging10.0740540540541
Midmean - Empirical Distribution Function - Interpolation10.0740540540541
Midmean - Closest Observation10.0740540540541
Midmean - True Basic - Statistics Graphics Toolkit10.0740540540541
Midmean - MS Excel (old versions)10.0910526315789
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')