Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 12 Dec 2008 03:34:15 -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/2008/Dec/12/t122907811973hw8vx6lbe9cuf.htm/, Retrieved Fri, 17 May 2024 02:39:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32522, Retrieved Fri, 17 May 2024 02:39:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact197
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2008-12-12 10:34:15] [28deb8481dba3cc87d2d53a86e0e0d0b] [Current]
Feedback Forum

Post a new message
Dataseries X:
99,5
98,2
108,9
100,0
105,0
108,4
96,7
100,5
115,6
114,9
110,7
107,7
113,5
106,9
119,6
109,4
106,9
118,7
108,9
113,1
125,1
126,5
122,7
127,5
107,1
112,0
122,1
111,5
113,2
128,2
115,1
117,4
132,0
130,8
128,0
132,7
117,0
110,9
123,5
117,4
122,7
123,5
111,5
113,8
131,2
127,0
126,2
121,2
118,8
117,9
135,2
120,7
126,4
129,6
113,4
120,5
135,5
137,6
130,6
133,1
121,5
120,5
136,9
123,7
128,5
135,0
120,9
121,1
132,2
134,5
133,6
136,1
124,5
124,6
133,5
132,3
125,3
135,5
121,2
117,5
135,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32522&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32522&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32522&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean120.6790123456791.15860537179828104.158857953828
Geometric Mean120.222901828771
Harmonic Mean119.755693811144
Quadratic Mean121.123132940547
Winsorized Mean ( 1 / 27 )120.6888888888891.15240221459243104.728095243702
Winsorized Mean ( 2 / 27 )120.7012345679011.14135707322570105.752386697684
Winsorized Mean ( 3 / 27 )120.7123456790121.13585284040211106.274634693239
Winsorized Mean ( 4 / 27 )120.7172839506171.12699999195320107.113828582556
Winsorized Mean ( 5 / 27 )120.9950617283951.06976243646758113.104608653046
Winsorized Mean ( 6 / 27 )121.1135802469141.04081928953906116.363696814795
Winsorized Mean ( 7 / 27 )121.0962962962961.03791018136524116.673194338464
Winsorized Mean ( 8 / 27 )121.0666666666671.02636689947878117.956518987653
Winsorized Mean ( 9 / 27 )121.0333333333330.999089091295505121.143684169738
Winsorized Mean ( 10 / 27 )121.1074074074070.982953124514664123.207713966222
Winsorized Mean ( 11 / 27 )121.1209876543210.963581789133619125.698709772446
Winsorized Mean ( 12 / 27 )121.0617283950620.95446088444843126.837810084822
Winsorized Mean ( 13 / 27 )121.0777777777780.9320609713538129.903280470928
Winsorized Mean ( 14 / 27 )121.2851851851850.895224144480841135.480243615995
Winsorized Mean ( 15 / 27 )121.2851851851850.884140286741438137.178666105342
Winsorized Mean ( 16 / 27 )121.2456790123460.84323936195578143.785601672024
Winsorized Mean ( 17 / 27 )121.1617283950620.830958779677024145.809553203294
Winsorized Mean ( 18 / 27 )121.2283950617280.80851417329534149.939727794290
Winsorized Mean ( 19 / 27 )121.2518518518520.73870321625194164.141497132047
Winsorized Mean ( 20 / 27 )121.0049382716050.697831520476747173.401365115947
Winsorized Mean ( 21 / 27 )120.9790123456790.680213555902774177.854456583296
Winsorized Mean ( 22 / 27 )120.9518518518520.669252187955838180.726868030550
Winsorized Mean ( 23 / 27 )120.8950617283950.638888650324999189.227123798328
Winsorized Mean ( 24 / 27 )121.0728395061730.575253600397785210.468634046709
Winsorized Mean ( 25 / 27 )120.9802469135800.54729813278642221.049990245065
Winsorized Mean ( 26 / 27 )121.1086419753090.521871033010322232.066227697511
Winsorized Mean ( 27 / 27 )121.5086419753090.453427269444072267.978240753551
Trimmed Mean ( 1 / 27 )120.7683544303801.12772378521847107.090367351775
Trimmed Mean ( 2 / 27 )120.8519480519481.09887877112144109.977507281003
Trimmed Mean ( 3 / 27 )120.9333333333331.07196768361491112.814346161556
Trimmed Mean ( 4 / 27 )121.0150684931511.04274085478207116.054787666723
Trimmed Mean ( 5 / 27 )121.11.01137394843920119.738104967888
Trimmed Mean ( 6 / 27 )121.1246376811590.991984942076913122.103302725101
Trimmed Mean ( 7 / 27 )121.1268656716420.976502731797657124.041502115061
Trimmed Mean ( 8 / 27 )121.1323076923080.958484650604164126.378974995535
Trimmed Mean ( 9 / 27 )121.1428571428570.939293331472368128.972338122493
Trimmed Mean ( 10 / 27 )121.1590163934430.921842942211313131.431300111499
Trimmed Mean ( 11 / 27 )121.1661016949150.903780003311798134.065924506977
Trimmed Mean ( 12 / 27 )121.1719298245610.885393001344236136.856660986244
Trimmed Mean ( 13 / 27 )121.1854545454550.864326359135494140.207981932502
Trimmed Mean ( 14 / 27 )121.1981132075470.84252234885294143.851511324956
Trimmed Mean ( 15 / 27 )121.1882352941180.822495709787123147.342088052330
Trimmed Mean ( 16 / 27 )121.1775510204080.799214459705955151.620819104038
Trimmed Mean ( 17 / 27 )121.1702127659570.777879389746143155.769923156726
Trimmed Mean ( 18 / 27 )121.1711111111110.75276340886059160.968386195232
Trimmed Mean ( 19 / 27 )121.1651162790700.72487738086248167.152568803987
Trimmed Mean ( 20 / 27 )121.1560975609760.703978664973347172.101945114434
Trimmed Mean ( 21 / 27 )121.1717948717950.685062806482164176.876913657040
Trimmed Mean ( 22 / 27 )121.1918918918920.663114165187072182.761729811189
Trimmed Mean ( 23 / 27 )121.2171428571430.635219616813456190.827140171177
Trimmed Mean ( 24 / 27 )121.2515151515150.604310921317419200.644255919093
Trimmed Mean ( 25 / 27 )121.2709677419350.579436017015491209.29138710874
Trimmed Mean ( 26 / 27 )121.3034482758620.551296786462661220.03293190623
Trimmed Mean ( 27 / 27 )121.3259259259260.51787403985572234.276902467881
Median121.2
Midrange117.15
Midmean - Weighted Average at Xnp120.9725
Midmean - Weighted Average at X(n+1)p121.156097560976
Midmean - Empirical Distribution Function121.156097560976
Midmean - Empirical Distribution Function - Averaging121.156097560976
Midmean - Empirical Distribution Function - Interpolation121.156097560976
Midmean - Closest Observation120.964285714286
Midmean - True Basic - Statistics Graphics Toolkit121.156097560976
Midmean - MS Excel (old versions)121.156097560976
Number of observations81

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 120.679012345679 & 1.15860537179828 & 104.158857953828 \tabularnewline
Geometric Mean & 120.222901828771 &  &  \tabularnewline
Harmonic Mean & 119.755693811144 &  &  \tabularnewline
Quadratic Mean & 121.123132940547 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 120.688888888889 & 1.15240221459243 & 104.728095243702 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 120.701234567901 & 1.14135707322570 & 105.752386697684 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 120.712345679012 & 1.13585284040211 & 106.274634693239 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 120.717283950617 & 1.12699999195320 & 107.113828582556 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 120.995061728395 & 1.06976243646758 & 113.104608653046 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 121.113580246914 & 1.04081928953906 & 116.363696814795 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 121.096296296296 & 1.03791018136524 & 116.673194338464 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 121.066666666667 & 1.02636689947878 & 117.956518987653 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 121.033333333333 & 0.999089091295505 & 121.143684169738 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 121.107407407407 & 0.982953124514664 & 123.207713966222 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 121.120987654321 & 0.963581789133619 & 125.698709772446 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 121.061728395062 & 0.95446088444843 & 126.837810084822 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 121.077777777778 & 0.9320609713538 & 129.903280470928 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 121.285185185185 & 0.895224144480841 & 135.480243615995 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 121.285185185185 & 0.884140286741438 & 137.178666105342 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 121.245679012346 & 0.84323936195578 & 143.785601672024 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 121.161728395062 & 0.830958779677024 & 145.809553203294 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 121.228395061728 & 0.80851417329534 & 149.939727794290 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 121.251851851852 & 0.73870321625194 & 164.141497132047 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 121.004938271605 & 0.697831520476747 & 173.401365115947 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 120.979012345679 & 0.680213555902774 & 177.854456583296 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 120.951851851852 & 0.669252187955838 & 180.726868030550 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 120.895061728395 & 0.638888650324999 & 189.227123798328 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 121.072839506173 & 0.575253600397785 & 210.468634046709 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 120.980246913580 & 0.54729813278642 & 221.049990245065 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 121.108641975309 & 0.521871033010322 & 232.066227697511 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 121.508641975309 & 0.453427269444072 & 267.978240753551 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 120.768354430380 & 1.12772378521847 & 107.090367351775 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 120.851948051948 & 1.09887877112144 & 109.977507281003 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 120.933333333333 & 1.07196768361491 & 112.814346161556 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 121.015068493151 & 1.04274085478207 & 116.054787666723 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 121.1 & 1.01137394843920 & 119.738104967888 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 121.124637681159 & 0.991984942076913 & 122.103302725101 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 121.126865671642 & 0.976502731797657 & 124.041502115061 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 121.132307692308 & 0.958484650604164 & 126.378974995535 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 121.142857142857 & 0.939293331472368 & 128.972338122493 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 121.159016393443 & 0.921842942211313 & 131.431300111499 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 121.166101694915 & 0.903780003311798 & 134.065924506977 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 121.171929824561 & 0.885393001344236 & 136.856660986244 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 121.185454545455 & 0.864326359135494 & 140.207981932502 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 121.198113207547 & 0.84252234885294 & 143.851511324956 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 121.188235294118 & 0.822495709787123 & 147.342088052330 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 121.177551020408 & 0.799214459705955 & 151.620819104038 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 121.170212765957 & 0.777879389746143 & 155.769923156726 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 121.171111111111 & 0.75276340886059 & 160.968386195232 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 121.165116279070 & 0.72487738086248 & 167.152568803987 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 121.156097560976 & 0.703978664973347 & 172.101945114434 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 121.171794871795 & 0.685062806482164 & 176.876913657040 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 121.191891891892 & 0.663114165187072 & 182.761729811189 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 121.217142857143 & 0.635219616813456 & 190.827140171177 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 121.251515151515 & 0.604310921317419 & 200.644255919093 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 121.270967741935 & 0.579436017015491 & 209.29138710874 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 121.303448275862 & 0.551296786462661 & 220.03293190623 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 121.325925925926 & 0.51787403985572 & 234.276902467881 \tabularnewline
Median & 121.2 &  &  \tabularnewline
Midrange & 117.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 120.9725 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 121.156097560976 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 121.156097560976 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 121.156097560976 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 121.156097560976 &  &  \tabularnewline
Midmean - Closest Observation & 120.964285714286 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 121.156097560976 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 121.156097560976 &  &  \tabularnewline
Number of observations & 81 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32522&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]120.679012345679[/C][C]1.15860537179828[/C][C]104.158857953828[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]120.222901828771[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]119.755693811144[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]121.123132940547[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]120.688888888889[/C][C]1.15240221459243[/C][C]104.728095243702[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]120.701234567901[/C][C]1.14135707322570[/C][C]105.752386697684[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]120.712345679012[/C][C]1.13585284040211[/C][C]106.274634693239[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]120.717283950617[/C][C]1.12699999195320[/C][C]107.113828582556[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]120.995061728395[/C][C]1.06976243646758[/C][C]113.104608653046[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]121.113580246914[/C][C]1.04081928953906[/C][C]116.363696814795[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]121.096296296296[/C][C]1.03791018136524[/C][C]116.673194338464[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]121.066666666667[/C][C]1.02636689947878[/C][C]117.956518987653[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]121.033333333333[/C][C]0.999089091295505[/C][C]121.143684169738[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]121.107407407407[/C][C]0.982953124514664[/C][C]123.207713966222[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]121.120987654321[/C][C]0.963581789133619[/C][C]125.698709772446[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]121.061728395062[/C][C]0.95446088444843[/C][C]126.837810084822[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]121.077777777778[/C][C]0.9320609713538[/C][C]129.903280470928[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]121.285185185185[/C][C]0.895224144480841[/C][C]135.480243615995[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]121.285185185185[/C][C]0.884140286741438[/C][C]137.178666105342[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]121.245679012346[/C][C]0.84323936195578[/C][C]143.785601672024[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]121.161728395062[/C][C]0.830958779677024[/C][C]145.809553203294[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]121.228395061728[/C][C]0.80851417329534[/C][C]149.939727794290[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]121.251851851852[/C][C]0.73870321625194[/C][C]164.141497132047[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]121.004938271605[/C][C]0.697831520476747[/C][C]173.401365115947[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]120.979012345679[/C][C]0.680213555902774[/C][C]177.854456583296[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]120.951851851852[/C][C]0.669252187955838[/C][C]180.726868030550[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]120.895061728395[/C][C]0.638888650324999[/C][C]189.227123798328[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]121.072839506173[/C][C]0.575253600397785[/C][C]210.468634046709[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]120.980246913580[/C][C]0.54729813278642[/C][C]221.049990245065[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]121.108641975309[/C][C]0.521871033010322[/C][C]232.066227697511[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]121.508641975309[/C][C]0.453427269444072[/C][C]267.978240753551[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]120.768354430380[/C][C]1.12772378521847[/C][C]107.090367351775[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]120.851948051948[/C][C]1.09887877112144[/C][C]109.977507281003[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]120.933333333333[/C][C]1.07196768361491[/C][C]112.814346161556[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]121.015068493151[/C][C]1.04274085478207[/C][C]116.054787666723[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]121.1[/C][C]1.01137394843920[/C][C]119.738104967888[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]121.124637681159[/C][C]0.991984942076913[/C][C]122.103302725101[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]121.126865671642[/C][C]0.976502731797657[/C][C]124.041502115061[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]121.132307692308[/C][C]0.958484650604164[/C][C]126.378974995535[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]121.142857142857[/C][C]0.939293331472368[/C][C]128.972338122493[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]121.159016393443[/C][C]0.921842942211313[/C][C]131.431300111499[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]121.166101694915[/C][C]0.903780003311798[/C][C]134.065924506977[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]121.171929824561[/C][C]0.885393001344236[/C][C]136.856660986244[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]121.185454545455[/C][C]0.864326359135494[/C][C]140.207981932502[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]121.198113207547[/C][C]0.84252234885294[/C][C]143.851511324956[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]121.188235294118[/C][C]0.822495709787123[/C][C]147.342088052330[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]121.177551020408[/C][C]0.799214459705955[/C][C]151.620819104038[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]121.170212765957[/C][C]0.777879389746143[/C][C]155.769923156726[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]121.171111111111[/C][C]0.75276340886059[/C][C]160.968386195232[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]121.165116279070[/C][C]0.72487738086248[/C][C]167.152568803987[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]121.156097560976[/C][C]0.703978664973347[/C][C]172.101945114434[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]121.171794871795[/C][C]0.685062806482164[/C][C]176.876913657040[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]121.191891891892[/C][C]0.663114165187072[/C][C]182.761729811189[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]121.217142857143[/C][C]0.635219616813456[/C][C]190.827140171177[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]121.251515151515[/C][C]0.604310921317419[/C][C]200.644255919093[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]121.270967741935[/C][C]0.579436017015491[/C][C]209.29138710874[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]121.303448275862[/C][C]0.551296786462661[/C][C]220.03293190623[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]121.325925925926[/C][C]0.51787403985572[/C][C]234.276902467881[/C][/ROW]
[ROW][C]Median[/C][C]121.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]117.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]120.9725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]121.156097560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]121.156097560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]121.156097560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]121.156097560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]120.964285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]121.156097560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]121.156097560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]81[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32522&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32522&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 Mean120.6790123456791.15860537179828104.158857953828
Geometric Mean120.222901828771
Harmonic Mean119.755693811144
Quadratic Mean121.123132940547
Winsorized Mean ( 1 / 27 )120.6888888888891.15240221459243104.728095243702
Winsorized Mean ( 2 / 27 )120.7012345679011.14135707322570105.752386697684
Winsorized Mean ( 3 / 27 )120.7123456790121.13585284040211106.274634693239
Winsorized Mean ( 4 / 27 )120.7172839506171.12699999195320107.113828582556
Winsorized Mean ( 5 / 27 )120.9950617283951.06976243646758113.104608653046
Winsorized Mean ( 6 / 27 )121.1135802469141.04081928953906116.363696814795
Winsorized Mean ( 7 / 27 )121.0962962962961.03791018136524116.673194338464
Winsorized Mean ( 8 / 27 )121.0666666666671.02636689947878117.956518987653
Winsorized Mean ( 9 / 27 )121.0333333333330.999089091295505121.143684169738
Winsorized Mean ( 10 / 27 )121.1074074074070.982953124514664123.207713966222
Winsorized Mean ( 11 / 27 )121.1209876543210.963581789133619125.698709772446
Winsorized Mean ( 12 / 27 )121.0617283950620.95446088444843126.837810084822
Winsorized Mean ( 13 / 27 )121.0777777777780.9320609713538129.903280470928
Winsorized Mean ( 14 / 27 )121.2851851851850.895224144480841135.480243615995
Winsorized Mean ( 15 / 27 )121.2851851851850.884140286741438137.178666105342
Winsorized Mean ( 16 / 27 )121.2456790123460.84323936195578143.785601672024
Winsorized Mean ( 17 / 27 )121.1617283950620.830958779677024145.809553203294
Winsorized Mean ( 18 / 27 )121.2283950617280.80851417329534149.939727794290
Winsorized Mean ( 19 / 27 )121.2518518518520.73870321625194164.141497132047
Winsorized Mean ( 20 / 27 )121.0049382716050.697831520476747173.401365115947
Winsorized Mean ( 21 / 27 )120.9790123456790.680213555902774177.854456583296
Winsorized Mean ( 22 / 27 )120.9518518518520.669252187955838180.726868030550
Winsorized Mean ( 23 / 27 )120.8950617283950.638888650324999189.227123798328
Winsorized Mean ( 24 / 27 )121.0728395061730.575253600397785210.468634046709
Winsorized Mean ( 25 / 27 )120.9802469135800.54729813278642221.049990245065
Winsorized Mean ( 26 / 27 )121.1086419753090.521871033010322232.066227697511
Winsorized Mean ( 27 / 27 )121.5086419753090.453427269444072267.978240753551
Trimmed Mean ( 1 / 27 )120.7683544303801.12772378521847107.090367351775
Trimmed Mean ( 2 / 27 )120.8519480519481.09887877112144109.977507281003
Trimmed Mean ( 3 / 27 )120.9333333333331.07196768361491112.814346161556
Trimmed Mean ( 4 / 27 )121.0150684931511.04274085478207116.054787666723
Trimmed Mean ( 5 / 27 )121.11.01137394843920119.738104967888
Trimmed Mean ( 6 / 27 )121.1246376811590.991984942076913122.103302725101
Trimmed Mean ( 7 / 27 )121.1268656716420.976502731797657124.041502115061
Trimmed Mean ( 8 / 27 )121.1323076923080.958484650604164126.378974995535
Trimmed Mean ( 9 / 27 )121.1428571428570.939293331472368128.972338122493
Trimmed Mean ( 10 / 27 )121.1590163934430.921842942211313131.431300111499
Trimmed Mean ( 11 / 27 )121.1661016949150.903780003311798134.065924506977
Trimmed Mean ( 12 / 27 )121.1719298245610.885393001344236136.856660986244
Trimmed Mean ( 13 / 27 )121.1854545454550.864326359135494140.207981932502
Trimmed Mean ( 14 / 27 )121.1981132075470.84252234885294143.851511324956
Trimmed Mean ( 15 / 27 )121.1882352941180.822495709787123147.342088052330
Trimmed Mean ( 16 / 27 )121.1775510204080.799214459705955151.620819104038
Trimmed Mean ( 17 / 27 )121.1702127659570.777879389746143155.769923156726
Trimmed Mean ( 18 / 27 )121.1711111111110.75276340886059160.968386195232
Trimmed Mean ( 19 / 27 )121.1651162790700.72487738086248167.152568803987
Trimmed Mean ( 20 / 27 )121.1560975609760.703978664973347172.101945114434
Trimmed Mean ( 21 / 27 )121.1717948717950.685062806482164176.876913657040
Trimmed Mean ( 22 / 27 )121.1918918918920.663114165187072182.761729811189
Trimmed Mean ( 23 / 27 )121.2171428571430.635219616813456190.827140171177
Trimmed Mean ( 24 / 27 )121.2515151515150.604310921317419200.644255919093
Trimmed Mean ( 25 / 27 )121.2709677419350.579436017015491209.29138710874
Trimmed Mean ( 26 / 27 )121.3034482758620.551296786462661220.03293190623
Trimmed Mean ( 27 / 27 )121.3259259259260.51787403985572234.276902467881
Median121.2
Midrange117.15
Midmean - Weighted Average at Xnp120.9725
Midmean - Weighted Average at X(n+1)p121.156097560976
Midmean - Empirical Distribution Function121.156097560976
Midmean - Empirical Distribution Function - Averaging121.156097560976
Midmean - Empirical Distribution Function - Interpolation121.156097560976
Midmean - Closest Observation120.964285714286
Midmean - True Basic - Statistics Graphics Toolkit121.156097560976
Midmean - MS Excel (old versions)121.156097560976
Number of observations81



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')