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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Wed, 19 Oct 2011 15:36:12 -0400

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/19/t131905307393620v8c2h4tgye.htm/, Retrieved Wed, 15 May 2024 02:54:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132840, Retrieved Wed, 15 May 2024 02:54:23 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDG2011W52a

Estimated Impact

106

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Central Tendency] [Opdracht 5 oefeni...] [2011-10-19 19:36:12] [2a71f74e7f2bee2ce32c293bcda06bce] [Current]

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Dataseries X:

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1,83
1,83
1,87
1,87
1,86
1,87
1,87
1,89
1,89
1,88
1,88
1,87
1,78
1,79
1,8
1,82
1,82
1,83
1,84
1,84
1,83
1,83
1,83
1,84
1,86
1,85
1,85
1,85
1,84
1,85
1,85
1,83
1,82
1,84
1,85
1,88
1,91
1,93
1,91
1,9
1,9
1,89
1,88
1,88
1,92
1,98
2
2
2,02
2,01
2,05
2,07
2,07
2,04
2,05
2,05
2,04
2,03
2,04
2,04
2,1
2,09
2,1
2,09
2,08
2,1
2,11
2,08
2,09
2,1
2,09
2,09

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132840&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132840&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132840&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.93277777777778	0.012352767048907	156.465168502372
Geometric Mean	1.93001610621393
Harmonic Mean	1.9272989965756
Quadratic Mean	1.93557843780326
Winsorized Mean ( 1 / 24 )	1.93277777777778	0.0123019875460443	157.11101726804
Winsorized Mean ( 2 / 24 )	1.93305555555556	0.0122580478640348	157.696851651816
Winsorized Mean ( 3 / 24 )	1.93388888888889	0.0121392474422682	159.308795548165
Winsorized Mean ( 4 / 24 )	1.93388888888889	0.0121392474422682	159.308795548165
Winsorized Mean ( 5 / 24 )	1.93319444444444	0.012008451622229	160.986154190427
Winsorized Mean ( 6 / 24 )	1.93402777777778	0.0119018214473484	162.498470199169
Winsorized Mean ( 7 / 24 )	1.93402777777778	0.0119018214473484	162.498470199169
Winsorized Mean ( 8 / 24 )	1.93402777777778	0.0119018214473484	162.498470199169
Winsorized Mean ( 9 / 24 )	1.93402777777778	0.0119018214473484	162.498470199169
Winsorized Mean ( 10 / 24 )	1.93263888888889	0.011649875669401	165.893520560486
Winsorized Mean ( 11 / 24 )	1.93263888888889	0.011649875669401	165.893520560486
Winsorized Mean ( 12 / 24 )	1.93097222222222	0.0113576784265919	170.014693997781
Winsorized Mean ( 13 / 24 )	1.93277777777778	0.0111386591205584	173.519788769771
Winsorized Mean ( 14 / 24 )	1.92888888888889	0.0104842746010692	183.979241510155
Winsorized Mean ( 15 / 24 )	1.92888888888889	0.0104842746010692	183.979241510155
Winsorized Mean ( 16 / 24 )	1.92888888888889	0.0104842746010692	183.979241510155
Winsorized Mean ( 17 / 24 )	1.92652777777778	0.0101053908865303	190.643568310226
Winsorized Mean ( 18 / 24 )	1.92902777777778	0.00981272153886497	196.584379790819
Winsorized Mean ( 19 / 24 )	1.92902777777778	0.00981272153886497	196.584379790819
Winsorized Mean ( 20 / 24 )	1.92902777777778	0.00981272153886497	196.584379790819
Winsorized Mean ( 21 / 24 )	1.92611111111111	0.00935216819269009	205.953429346642
Winsorized Mean ( 22 / 24 )	1.92305555555556	0.00887806216627276	216.6075793951
Winsorized Mean ( 23 / 24 )	1.91986111111111	0.00839063178217536	228.810077828653
Winsorized Mean ( 24 / 24 )	1.91986111111111	0.00750454493369171	255.826452912805
Trimmed Mean ( 1 / 24 )	1.93242857142857	0.0122541001112134	157.696489655757
Trimmed Mean ( 2 / 24 )	1.93205882352941	0.0121891711024774	158.506169721149
Trimmed Mean ( 3 / 24 )	1.93151515151515	0.0121302996237665	159.230621783718
Trimmed Mean ( 4 / 24 )	1.930625	0.0121005111888608	159.549044653357
Trimmed Mean ( 5 / 24 )	1.92967741935484	0.0120526075433996	160.104559316842
Trimmed Mean ( 6 / 24 )	1.92883333333333	0.0120218531399706	160.443927477395
Trimmed Mean ( 7 / 24 )	1.92775862068966	0.0119967809340543	160.689657607857
Trimmed Mean ( 8 / 24 )	1.92660714285714	0.0119503213718518	161.218019407841
Trimmed Mean ( 9 / 24 )	1.92537037037037	0.011877292968407	162.105151021513
Trimmed Mean ( 10 / 24 )	1.92403846153846	0.0117710038688418	163.455766642933
Trimmed Mean ( 11 / 24 )	1.9228	0.0116795303232377	164.629907777574
Trimmed Mean ( 12 / 24 )	1.92145833333333	0.0115469653965869	166.403749153113
Trimmed Mean ( 13 / 24 )	1.92021739130435	0.0114271019924296	168.040627674145
Trimmed Mean ( 14 / 24 )	1.91863636363636	0.0112936534268726	169.886244168878
Trimmed Mean ( 15 / 24 )	1.91738095238095	0.0112466772680367	170.48421562075
Trimmed Mean ( 16 / 24 )	1.916	0.0111562331663308	171.742556061166
Trimmed Mean ( 17 / 24 )	1.91447368421053	0.0110068992227993	173.933970454181
Trimmed Mean ( 18 / 24 )	1.91305555555556	0.010873146216343	175.943146306642
Trimmed Mean ( 19 / 24 )	1.91117647058824	0.0107122857972611	178.409772364072
Trimmed Mean ( 20 / 24 )	1.9090625	0.0104472501301662	182.733492183519
Trimmed Mean ( 21 / 24 )	1.90666666666667	0.010026784054094	190.157348196621
Trimmed Mean ( 22 / 24 )	1.90428571428571	0.00954560996951468	199.493350384871
Trimmed Mean ( 23 / 24 )	1.90192307692308	0.00897893656148365	211.82052728623
Trimmed Mean ( 24 / 24 )	1.89958333333333	0.00828564252069061	229.262043177673
Median	1.885
Midrange	1.945
Midmean - Weighted Average at Xnp	1.90738095238095
Midmean - Weighted Average at X(n+1)p	1.91648648648649
Midmean - Empirical Distribution Function	1.90738095238095
Midmean - Empirical Distribution Function - Averaging	1.91648648648649
Midmean - Empirical Distribution Function - Interpolation	1.91648648648649
Midmean - Closest Observation	1.90738095238095
Midmean - True Basic - Statistics Graphics Toolkit	1.91648648648649
Midmean - MS Excel (old versions)	1.90738095238095
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.93277777777778 & 0.012352767048907 & 156.465168502372 \tabularnewline
Geometric Mean & 1.93001610621393 &  &  \tabularnewline
Harmonic Mean & 1.9272989965756 &  &  \tabularnewline
Quadratic Mean & 1.93557843780326 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.93277777777778 & 0.0123019875460443 & 157.11101726804 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.93305555555556 & 0.0122580478640348 & 157.696851651816 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.93388888888889 & 0.0121392474422682 & 159.308795548165 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.93388888888889 & 0.0121392474422682 & 159.308795548165 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.93319444444444 & 0.012008451622229 & 160.986154190427 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.93402777777778 & 0.0119018214473484 & 162.498470199169 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.93402777777778 & 0.0119018214473484 & 162.498470199169 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.93402777777778 & 0.0119018214473484 & 162.498470199169 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.93402777777778 & 0.0119018214473484 & 162.498470199169 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.93263888888889 & 0.011649875669401 & 165.893520560486 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.93263888888889 & 0.011649875669401 & 165.893520560486 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.93097222222222 & 0.0113576784265919 & 170.014693997781 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.93277777777778 & 0.0111386591205584 & 173.519788769771 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.92888888888889 & 0.0104842746010692 & 183.979241510155 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.92888888888889 & 0.0104842746010692 & 183.979241510155 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.92888888888889 & 0.0104842746010692 & 183.979241510155 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.92652777777778 & 0.0101053908865303 & 190.643568310226 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.92902777777778 & 0.00981272153886497 & 196.584379790819 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.92902777777778 & 0.00981272153886497 & 196.584379790819 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.92902777777778 & 0.00981272153886497 & 196.584379790819 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.92611111111111 & 0.00935216819269009 & 205.953429346642 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.92305555555556 & 0.00887806216627276 & 216.6075793951 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.91986111111111 & 0.00839063178217536 & 228.810077828653 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.91986111111111 & 0.00750454493369171 & 255.826452912805 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.93242857142857 & 0.0122541001112134 & 157.696489655757 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.93205882352941 & 0.0121891711024774 & 158.506169721149 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.93151515151515 & 0.0121302996237665 & 159.230621783718 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.930625 & 0.0121005111888608 & 159.549044653357 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.92967741935484 & 0.0120526075433996 & 160.104559316842 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.92883333333333 & 0.0120218531399706 & 160.443927477395 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.92775862068966 & 0.0119967809340543 & 160.689657607857 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.92660714285714 & 0.0119503213718518 & 161.218019407841 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.92537037037037 & 0.011877292968407 & 162.105151021513 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.92403846153846 & 0.0117710038688418 & 163.455766642933 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.9228 & 0.0116795303232377 & 164.629907777574 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.92145833333333 & 0.0115469653965869 & 166.403749153113 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.92021739130435 & 0.0114271019924296 & 168.040627674145 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.91863636363636 & 0.0112936534268726 & 169.886244168878 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.91738095238095 & 0.0112466772680367 & 170.48421562075 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.916 & 0.0111562331663308 & 171.742556061166 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.91447368421053 & 0.0110068992227993 & 173.933970454181 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.91305555555556 & 0.010873146216343 & 175.943146306642 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.91117647058824 & 0.0107122857972611 & 178.409772364072 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.9090625 & 0.0104472501301662 & 182.733492183519 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.90666666666667 & 0.010026784054094 & 190.157348196621 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.90428571428571 & 0.00954560996951468 & 199.493350384871 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.90192307692308 & 0.00897893656148365 & 211.82052728623 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.89958333333333 & 0.00828564252069061 & 229.262043177673 \tabularnewline
Median & 1.885 &  &  \tabularnewline
Midrange & 1.945 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.90738095238095 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.91648648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.90738095238095 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.91648648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.91648648648649 &  &  \tabularnewline
Midmean - Closest Observation & 1.90738095238095 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.91648648648649 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.90738095238095 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132840&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]1.93277777777778[/C][C]0.012352767048907[/C][C]156.465168502372[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.93001610621393[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.9272989965756[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.93557843780326[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.93277777777778[/C][C]0.0123019875460443[/C][C]157.11101726804[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.93305555555556[/C][C]0.0122580478640348[/C][C]157.696851651816[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.93388888888889[/C][C]0.0121392474422682[/C][C]159.308795548165[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.93388888888889[/C][C]0.0121392474422682[/C][C]159.308795548165[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.93319444444444[/C][C]0.012008451622229[/C][C]160.986154190427[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.93402777777778[/C][C]0.0119018214473484[/C][C]162.498470199169[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.93402777777778[/C][C]0.0119018214473484[/C][C]162.498470199169[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.93402777777778[/C][C]0.0119018214473484[/C][C]162.498470199169[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.93402777777778[/C][C]0.0119018214473484[/C][C]162.498470199169[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.93263888888889[/C][C]0.011649875669401[/C][C]165.893520560486[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.93263888888889[/C][C]0.011649875669401[/C][C]165.893520560486[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.93097222222222[/C][C]0.0113576784265919[/C][C]170.014693997781[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.93277777777778[/C][C]0.0111386591205584[/C][C]173.519788769771[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.92888888888889[/C][C]0.0104842746010692[/C][C]183.979241510155[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.92888888888889[/C][C]0.0104842746010692[/C][C]183.979241510155[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.92888888888889[/C][C]0.0104842746010692[/C][C]183.979241510155[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.92652777777778[/C][C]0.0101053908865303[/C][C]190.643568310226[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.92902777777778[/C][C]0.00981272153886497[/C][C]196.584379790819[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.92902777777778[/C][C]0.00981272153886497[/C][C]196.584379790819[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.92902777777778[/C][C]0.00981272153886497[/C][C]196.584379790819[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.92611111111111[/C][C]0.00935216819269009[/C][C]205.953429346642[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.92305555555556[/C][C]0.00887806216627276[/C][C]216.6075793951[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.91986111111111[/C][C]0.00839063178217536[/C][C]228.810077828653[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.91986111111111[/C][C]0.00750454493369171[/C][C]255.826452912805[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.93242857142857[/C][C]0.0122541001112134[/C][C]157.696489655757[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.93205882352941[/C][C]0.0121891711024774[/C][C]158.506169721149[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.93151515151515[/C][C]0.0121302996237665[/C][C]159.230621783718[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.930625[/C][C]0.0121005111888608[/C][C]159.549044653357[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.92967741935484[/C][C]0.0120526075433996[/C][C]160.104559316842[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.92883333333333[/C][C]0.0120218531399706[/C][C]160.443927477395[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.92775862068966[/C][C]0.0119967809340543[/C][C]160.689657607857[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.92660714285714[/C][C]0.0119503213718518[/C][C]161.218019407841[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.92537037037037[/C][C]0.011877292968407[/C][C]162.105151021513[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.92403846153846[/C][C]0.0117710038688418[/C][C]163.455766642933[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.9228[/C][C]0.0116795303232377[/C][C]164.629907777574[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.92145833333333[/C][C]0.0115469653965869[/C][C]166.403749153113[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.92021739130435[/C][C]0.0114271019924296[/C][C]168.040627674145[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.91863636363636[/C][C]0.0112936534268726[/C][C]169.886244168878[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.91738095238095[/C][C]0.0112466772680367[/C][C]170.48421562075[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.916[/C][C]0.0111562331663308[/C][C]171.742556061166[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.91447368421053[/C][C]0.0110068992227993[/C][C]173.933970454181[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.91305555555556[/C][C]0.010873146216343[/C][C]175.943146306642[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.91117647058824[/C][C]0.0107122857972611[/C][C]178.409772364072[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.9090625[/C][C]0.0104472501301662[/C][C]182.733492183519[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.90666666666667[/C][C]0.010026784054094[/C][C]190.157348196621[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.90428571428571[/C][C]0.00954560996951468[/C][C]199.493350384871[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.90192307692308[/C][C]0.00897893656148365[/C][C]211.82052728623[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.89958333333333[/C][C]0.00828564252069061[/C][C]229.262043177673[/C][/ROW]
[ROW][C]Median[/C][C]1.885[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.945[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.90738095238095[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.91648648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.90738095238095[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.91648648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.91648648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.90738095238095[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.91648648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.90738095238095[/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=132840&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132840&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.93277777777778	0.012352767048907	156.465168502372
Geometric Mean	1.93001610621393
Harmonic Mean	1.9272989965756
Quadratic Mean	1.93557843780326
Winsorized Mean ( 1 / 24 )	1.93277777777778	0.0123019875460443	157.11101726804
Winsorized Mean ( 2 / 24 )	1.93305555555556	0.0122580478640348	157.696851651816
Winsorized Mean ( 3 / 24 )	1.93388888888889	0.0121392474422682	159.308795548165
Winsorized Mean ( 4 / 24 )	1.93388888888889	0.0121392474422682	159.308795548165
Winsorized Mean ( 5 / 24 )	1.93319444444444	0.012008451622229	160.986154190427
Winsorized Mean ( 6 / 24 )	1.93402777777778	0.0119018214473484	162.498470199169
Winsorized Mean ( 7 / 24 )	1.93402777777778	0.0119018214473484	162.498470199169
Winsorized Mean ( 8 / 24 )	1.93402777777778	0.0119018214473484	162.498470199169
Winsorized Mean ( 9 / 24 )	1.93402777777778	0.0119018214473484	162.498470199169
Winsorized Mean ( 10 / 24 )	1.93263888888889	0.011649875669401	165.893520560486
Winsorized Mean ( 11 / 24 )	1.93263888888889	0.011649875669401	165.893520560486
Winsorized Mean ( 12 / 24 )	1.93097222222222	0.0113576784265919	170.014693997781
Winsorized Mean ( 13 / 24 )	1.93277777777778	0.0111386591205584	173.519788769771
Winsorized Mean ( 14 / 24 )	1.92888888888889	0.0104842746010692	183.979241510155
Winsorized Mean ( 15 / 24 )	1.92888888888889	0.0104842746010692	183.979241510155
Winsorized Mean ( 16 / 24 )	1.92888888888889	0.0104842746010692	183.979241510155
Winsorized Mean ( 17 / 24 )	1.92652777777778	0.0101053908865303	190.643568310226
Winsorized Mean ( 18 / 24 )	1.92902777777778	0.00981272153886497	196.584379790819
Winsorized Mean ( 19 / 24 )	1.92902777777778	0.00981272153886497	196.584379790819
Winsorized Mean ( 20 / 24 )	1.92902777777778	0.00981272153886497	196.584379790819
Winsorized Mean ( 21 / 24 )	1.92611111111111	0.00935216819269009	205.953429346642
Winsorized Mean ( 22 / 24 )	1.92305555555556	0.00887806216627276	216.6075793951
Winsorized Mean ( 23 / 24 )	1.91986111111111	0.00839063178217536	228.810077828653
Winsorized Mean ( 24 / 24 )	1.91986111111111	0.00750454493369171	255.826452912805
Trimmed Mean ( 1 / 24 )	1.93242857142857	0.0122541001112134	157.696489655757
Trimmed Mean ( 2 / 24 )	1.93205882352941	0.0121891711024774	158.506169721149
Trimmed Mean ( 3 / 24 )	1.93151515151515	0.0121302996237665	159.230621783718
Trimmed Mean ( 4 / 24 )	1.930625	0.0121005111888608	159.549044653357
Trimmed Mean ( 5 / 24 )	1.92967741935484	0.0120526075433996	160.104559316842
Trimmed Mean ( 6 / 24 )	1.92883333333333	0.0120218531399706	160.443927477395
Trimmed Mean ( 7 / 24 )	1.92775862068966	0.0119967809340543	160.689657607857
Trimmed Mean ( 8 / 24 )	1.92660714285714	0.0119503213718518	161.218019407841
Trimmed Mean ( 9 / 24 )	1.92537037037037	0.011877292968407	162.105151021513
Trimmed Mean ( 10 / 24 )	1.92403846153846	0.0117710038688418	163.455766642933
Trimmed Mean ( 11 / 24 )	1.9228	0.0116795303232377	164.629907777574
Trimmed Mean ( 12 / 24 )	1.92145833333333	0.0115469653965869	166.403749153113
Trimmed Mean ( 13 / 24 )	1.92021739130435	0.0114271019924296	168.040627674145
Trimmed Mean ( 14 / 24 )	1.91863636363636	0.0112936534268726	169.886244168878
Trimmed Mean ( 15 / 24 )	1.91738095238095	0.0112466772680367	170.48421562075
Trimmed Mean ( 16 / 24 )	1.916	0.0111562331663308	171.742556061166
Trimmed Mean ( 17 / 24 )	1.91447368421053	0.0110068992227993	173.933970454181
Trimmed Mean ( 18 / 24 )	1.91305555555556	0.010873146216343	175.943146306642
Trimmed Mean ( 19 / 24 )	1.91117647058824	0.0107122857972611	178.409772364072
Trimmed Mean ( 20 / 24 )	1.9090625	0.0104472501301662	182.733492183519
Trimmed Mean ( 21 / 24 )	1.90666666666667	0.010026784054094	190.157348196621
Trimmed Mean ( 22 / 24 )	1.90428571428571	0.00954560996951468	199.493350384871
Trimmed Mean ( 23 / 24 )	1.90192307692308	0.00897893656148365	211.82052728623
Trimmed Mean ( 24 / 24 )	1.89958333333333	0.00828564252069061	229.262043177673
Median	1.885
Midrange	1.945
Midmean - Weighted Average at Xnp	1.90738095238095
Midmean - Weighted Average at X(n+1)p	1.91648648648649
Midmean - Empirical Distribution Function	1.90738095238095
Midmean - Empirical Distribution Function - Averaging	1.91648648648649
Midmean - Empirical Distribution Function - Interpolation	1.91648648648649
Midmean - Closest Observation	1.90738095238095
Midmean - True Basic - Statistics Graphics Toolkit	1.91648648648649
Midmean - MS Excel (old versions)	1.90738095238095
Number of observations	72

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code