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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sun, 18 Dec 2011 16:08:35 -0500

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/Dec/18/t1324242575x3j5vzhego8nmsp.htm/, Retrieved Sun, 05 May 2024 17:50:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157180, Retrieved Sun, 05 May 2024 17:50:29 +0000

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

-     [Univariate Explorative Data Analysis] [] [2010-11-24 18:11:23] [84ec9e690346b814992f2f0baa963a63]
- RMPD    [Central Tendency] [] [2011-12-18 21:08:35] [1e640daebbc6b5a89eef23229b5a56d5] [Current]

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5,50
5,40
5,90
5,80
5,10
4,10
4,40
3,60
3,50
3,10
2,90
2,20
1,40
1,20
1,30
1,30
1,30
1,80
1,80
1,80
1,70
2,10
2,00
1,70
1,90
2,30
2,40
2,50
2,80
2,60
2,20
2,80
2,80
2,80
2,30
2,20
3,00
2,90
2,70
2,70
2,30
2,40
2,80
2,30
2,00
1,90
2,30
2,70
1,80
2,00
2,10
2,00
2,40
1,70
1,00
1,20
1,40
1,70
1,80
1,40
1,70
1,60
1,40
1,50
0,90
1,50
1,70
1,60
1,20

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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157180&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157180&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157180&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.37826086956522	0.136152050759088	17.4676830521884
Geometric Mean	2.17085317799528
Harmonic Mean	2.00431681219248
Quadratic Mean	2.62995563967658
Winsorized Mean ( 1 / 23 )	2.37826086956522	0.135382845186337	17.566929298109
Winsorized Mean ( 2 / 23 )	2.37536231884058	0.131429380275416	18.0732977197557
Winsorized Mean ( 3 / 23 )	2.37101449275362	0.129923930942391	18.2492515085996
Winsorized Mean ( 4 / 23 )	2.3536231884058	0.124109439889444	18.9640948384135
Winsorized Mean ( 5 / 23 )	2.31014492753623	0.107540609263754	21.4816053521733
Winsorized Mean ( 6 / 23 )	2.28405797101449	0.100332422506348	22.764904045549
Winsorized Mean ( 7 / 23 )	2.23333333333333	0.087707048096927	25.463556028761
Winsorized Mean ( 8 / 23 )	2.23333333333333	0.0833205446282423	26.8041134788301
Winsorized Mean ( 9 / 23 )	2.18115942028985	0.0725634438082852	30.058653583925
Winsorized Mean ( 10 / 23 )	2.16666666666667	0.0699429394358377	30.9776323978243
Winsorized Mean ( 11 / 23 )	2.15072463768116	0.0672382737570294	31.9866129438862
Winsorized Mean ( 12 / 23 )	2.16811594202899	0.0644834135980319	33.6228468850036
Winsorized Mean ( 13 / 23 )	2.14927536231884	0.0614413126787711	34.9809479747891
Winsorized Mean ( 14 / 23 )	2.1695652173913	0.0584068230719312	37.1457494738135
Winsorized Mean ( 15 / 23 )	2.1695652173913	0.0584068230719312	37.1457494738135
Winsorized Mean ( 16 / 23 )	2.19275362318841	0.0552186555180363	39.7103769118786
Winsorized Mean ( 17 / 23 )	2.19275362318841	0.0552186555180363	39.7103769118785
Winsorized Mean ( 18 / 23 )	2.16666666666667	0.0511032031145859	42.3978642162307
Winsorized Mean ( 19 / 23 )	2.16666666666667	0.0511032031145859	42.3978642162307
Winsorized Mean ( 20 / 23 )	2.16666666666667	0.0511032031145859	42.3978642162307
Winsorized Mean ( 21 / 23 )	2.13623188405797	0.0465324009847046	45.9084818073359
Winsorized Mean ( 22 / 23 )	2.13623188405797	0.0376171664625551	56.7887505876982
Winsorized Mean ( 23 / 23 )	2.10289855072464	0.0330317353986643	63.6629751765834
Trimmed Mean ( 1 / 23 )	2.34776119402985	0.127891402388366	18.3574591425656
Trimmed Mean ( 2 / 23 )	2.31538461538462	0.118610358568564	19.520930914699
Trimmed Mean ( 3 / 23 )	2.28253968253968	0.109776565950328	20.7925950568766
Trimmed Mean ( 4 / 23 )	2.24918032786885	0.0993317274639972	22.6431210378785
Trimmed Mean ( 5 / 23 )	2.21864406779661	0.0885454436704978	25.0565582578456
Trimmed Mean ( 6 / 23 )	2.19649122807018	0.0814946879382932	26.9525693470148
Trimmed Mean ( 7 / 23 )	2.17818181818182	0.0751066989211642	29.0011656679007
Trimmed Mean ( 8 / 23 )	2.16792452830189	0.0711594616062638	30.4657241548193
Trimmed Mean ( 9 / 23 )	2.15686274509804	0.0674030837696111	31.9994668562994
Trimmed Mean ( 10 / 23 )	2.1530612244898	0.0656017437455115	32.8201828421231
Trimmed Mean ( 11 / 23 )	2.1530612244898	0.063934542470133	33.6760245918018
Trimmed Mean ( 12 / 23 )	2.15111111111111	0.0624113287940629	34.4666770068152
Trimmed Mean ( 13 / 23 )	2.14883720930233	0.0610331947717381	35.2076803014966
Trimmed Mean ( 14 / 23 )	2.14878048780488	0.0598903419897782	35.878581026831
Trimmed Mean ( 15 / 23 )	2.14615384615385	0.05898902592949	36.382256060969
Trimmed Mean ( 16 / 23 )	2.14324324324324	0.0576752506943035	37.1605362342175
Trimmed Mean ( 17 / 23 )	2.13714285714286	0.0565218354899667	37.8109245500745
Trimmed Mean ( 18 / 23 )	2.13030303030303	0.0547869234295895	38.8834213886974
Trimmed Mean ( 19 / 23 )	2.1258064516129	0.0534744923486506	39.7536537187257
Trimmed Mean ( 20 / 23 )	2.12068965517241	0.051427722092528	41.2363131961571
Trimmed Mean ( 21 / 23 )	2.11481481481481	0.0482466666854754	43.8333870524464
Trimmed Mean ( 22 / 23 )	2.11481481481481	0.0452106182218293	46.776949707662
Trimmed Mean ( 23 / 23 )	2.10869565217391	0.0439695562476027	47.9580835498853
Median	2.1
Midrange	3.4
Midmean - Weighted Average at Xnp	2.10571428571429
Midmean - Weighted Average at X(n+1)p	2.1925
Midmean - Empirical Distribution Function	2.1925
Midmean - Empirical Distribution Function - Averaging	2.1925
Midmean - Empirical Distribution Function - Interpolation	2.1925
Midmean - Closest Observation	2.1925
Midmean - True Basic - Statistics Graphics Toolkit	2.1925
Midmean - MS Excel (old versions)	2.1925
Number of observations	69

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.37826086956522 & 0.136152050759088 & 17.4676830521884 \tabularnewline
Geometric Mean & 2.17085317799528 &  &  \tabularnewline
Harmonic Mean & 2.00431681219248 &  &  \tabularnewline
Quadratic Mean & 2.62995563967658 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 2.37826086956522 & 0.135382845186337 & 17.566929298109 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 2.37536231884058 & 0.131429380275416 & 18.0732977197557 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 2.37101449275362 & 0.129923930942391 & 18.2492515085996 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 2.3536231884058 & 0.124109439889444 & 18.9640948384135 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 2.31014492753623 & 0.107540609263754 & 21.4816053521733 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 2.28405797101449 & 0.100332422506348 & 22.764904045549 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 2.23333333333333 & 0.087707048096927 & 25.463556028761 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 2.23333333333333 & 0.0833205446282423 & 26.8041134788301 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 2.18115942028985 & 0.0725634438082852 & 30.058653583925 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 2.16666666666667 & 0.0699429394358377 & 30.9776323978243 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 2.15072463768116 & 0.0672382737570294 & 31.9866129438862 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 2.16811594202899 & 0.0644834135980319 & 33.6228468850036 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 2.14927536231884 & 0.0614413126787711 & 34.9809479747891 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 2.1695652173913 & 0.0584068230719312 & 37.1457494738135 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 2.1695652173913 & 0.0584068230719312 & 37.1457494738135 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 2.19275362318841 & 0.0552186555180363 & 39.7103769118786 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 2.19275362318841 & 0.0552186555180363 & 39.7103769118785 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 2.16666666666667 & 0.0511032031145859 & 42.3978642162307 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 2.16666666666667 & 0.0511032031145859 & 42.3978642162307 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 2.16666666666667 & 0.0511032031145859 & 42.3978642162307 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 2.13623188405797 & 0.0465324009847046 & 45.9084818073359 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 2.13623188405797 & 0.0376171664625551 & 56.7887505876982 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 2.10289855072464 & 0.0330317353986643 & 63.6629751765834 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 2.34776119402985 & 0.127891402388366 & 18.3574591425656 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 2.31538461538462 & 0.118610358568564 & 19.520930914699 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 2.28253968253968 & 0.109776565950328 & 20.7925950568766 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 2.24918032786885 & 0.0993317274639972 & 22.6431210378785 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 2.21864406779661 & 0.0885454436704978 & 25.0565582578456 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 2.19649122807018 & 0.0814946879382932 & 26.9525693470148 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 2.17818181818182 & 0.0751066989211642 & 29.0011656679007 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 2.16792452830189 & 0.0711594616062638 & 30.4657241548193 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 2.15686274509804 & 0.0674030837696111 & 31.9994668562994 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 2.1530612244898 & 0.0656017437455115 & 32.8201828421231 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 2.1530612244898 & 0.063934542470133 & 33.6760245918018 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 2.15111111111111 & 0.0624113287940629 & 34.4666770068152 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 2.14883720930233 & 0.0610331947717381 & 35.2076803014966 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 2.14878048780488 & 0.0598903419897782 & 35.878581026831 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 2.14615384615385 & 0.05898902592949 & 36.382256060969 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 2.14324324324324 & 0.0576752506943035 & 37.1605362342175 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 2.13714285714286 & 0.0565218354899667 & 37.8109245500745 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 2.13030303030303 & 0.0547869234295895 & 38.8834213886974 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 2.1258064516129 & 0.0534744923486506 & 39.7536537187257 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 2.12068965517241 & 0.051427722092528 & 41.2363131961571 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 2.11481481481481 & 0.0482466666854754 & 43.8333870524464 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 2.11481481481481 & 0.0452106182218293 & 46.776949707662 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 2.10869565217391 & 0.0439695562476027 & 47.9580835498853 \tabularnewline
Median & 2.1 &  &  \tabularnewline
Midrange & 3.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.10571428571429 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.1925 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.1925 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.1925 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.1925 &  &  \tabularnewline
Midmean - Closest Observation & 2.1925 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.1925 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.1925 &  &  \tabularnewline
Number of observations & 69 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157180&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]2.37826086956522[/C][C]0.136152050759088[/C][C]17.4676830521884[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.17085317799528[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.00431681219248[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.62995563967658[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]2.37826086956522[/C][C]0.135382845186337[/C][C]17.566929298109[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]2.37536231884058[/C][C]0.131429380275416[/C][C]18.0732977197557[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]2.37101449275362[/C][C]0.129923930942391[/C][C]18.2492515085996[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]2.3536231884058[/C][C]0.124109439889444[/C][C]18.9640948384135[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]2.31014492753623[/C][C]0.107540609263754[/C][C]21.4816053521733[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]2.28405797101449[/C][C]0.100332422506348[/C][C]22.764904045549[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]2.23333333333333[/C][C]0.087707048096927[/C][C]25.463556028761[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]2.23333333333333[/C][C]0.0833205446282423[/C][C]26.8041134788301[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]2.18115942028985[/C][C]0.0725634438082852[/C][C]30.058653583925[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]2.16666666666667[/C][C]0.0699429394358377[/C][C]30.9776323978243[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]2.15072463768116[/C][C]0.0672382737570294[/C][C]31.9866129438862[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]2.16811594202899[/C][C]0.0644834135980319[/C][C]33.6228468850036[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]2.14927536231884[/C][C]0.0614413126787711[/C][C]34.9809479747891[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]2.1695652173913[/C][C]0.0584068230719312[/C][C]37.1457494738135[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]2.1695652173913[/C][C]0.0584068230719312[/C][C]37.1457494738135[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]2.19275362318841[/C][C]0.0552186555180363[/C][C]39.7103769118786[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]2.19275362318841[/C][C]0.0552186555180363[/C][C]39.7103769118785[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]2.16666666666667[/C][C]0.0511032031145859[/C][C]42.3978642162307[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]2.16666666666667[/C][C]0.0511032031145859[/C][C]42.3978642162307[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]2.16666666666667[/C][C]0.0511032031145859[/C][C]42.3978642162307[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]2.13623188405797[/C][C]0.0465324009847046[/C][C]45.9084818073359[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]2.13623188405797[/C][C]0.0376171664625551[/C][C]56.7887505876982[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]2.10289855072464[/C][C]0.0330317353986643[/C][C]63.6629751765834[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]2.34776119402985[/C][C]0.127891402388366[/C][C]18.3574591425656[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]2.31538461538462[/C][C]0.118610358568564[/C][C]19.520930914699[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]2.28253968253968[/C][C]0.109776565950328[/C][C]20.7925950568766[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]2.24918032786885[/C][C]0.0993317274639972[/C][C]22.6431210378785[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]2.21864406779661[/C][C]0.0885454436704978[/C][C]25.0565582578456[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]2.19649122807018[/C][C]0.0814946879382932[/C][C]26.9525693470148[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]2.17818181818182[/C][C]0.0751066989211642[/C][C]29.0011656679007[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]2.16792452830189[/C][C]0.0711594616062638[/C][C]30.4657241548193[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]2.15686274509804[/C][C]0.0674030837696111[/C][C]31.9994668562994[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]2.1530612244898[/C][C]0.0656017437455115[/C][C]32.8201828421231[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]2.1530612244898[/C][C]0.063934542470133[/C][C]33.6760245918018[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]2.15111111111111[/C][C]0.0624113287940629[/C][C]34.4666770068152[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]2.14883720930233[/C][C]0.0610331947717381[/C][C]35.2076803014966[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]2.14878048780488[/C][C]0.0598903419897782[/C][C]35.878581026831[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]2.14615384615385[/C][C]0.05898902592949[/C][C]36.382256060969[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]2.14324324324324[/C][C]0.0576752506943035[/C][C]37.1605362342175[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]2.13714285714286[/C][C]0.0565218354899667[/C][C]37.8109245500745[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]2.13030303030303[/C][C]0.0547869234295895[/C][C]38.8834213886974[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]2.1258064516129[/C][C]0.0534744923486506[/C][C]39.7536537187257[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]2.12068965517241[/C][C]0.051427722092528[/C][C]41.2363131961571[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]2.11481481481481[/C][C]0.0482466666854754[/C][C]43.8333870524464[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]2.11481481481481[/C][C]0.0452106182218293[/C][C]46.776949707662[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]2.10869565217391[/C][C]0.0439695562476027[/C][C]47.9580835498853[/C][/ROW]
[ROW][C]Median[/C][C]2.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.10571428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.1925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.1925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.1925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.1925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.1925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.1925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.1925[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]69[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157180&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157180&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	2.37826086956522	0.136152050759088	17.4676830521884
Geometric Mean	2.17085317799528
Harmonic Mean	2.00431681219248
Quadratic Mean	2.62995563967658
Winsorized Mean ( 1 / 23 )	2.37826086956522	0.135382845186337	17.566929298109
Winsorized Mean ( 2 / 23 )	2.37536231884058	0.131429380275416	18.0732977197557
Winsorized Mean ( 3 / 23 )	2.37101449275362	0.129923930942391	18.2492515085996
Winsorized Mean ( 4 / 23 )	2.3536231884058	0.124109439889444	18.9640948384135
Winsorized Mean ( 5 / 23 )	2.31014492753623	0.107540609263754	21.4816053521733
Winsorized Mean ( 6 / 23 )	2.28405797101449	0.100332422506348	22.764904045549
Winsorized Mean ( 7 / 23 )	2.23333333333333	0.087707048096927	25.463556028761
Winsorized Mean ( 8 / 23 )	2.23333333333333	0.0833205446282423	26.8041134788301
Winsorized Mean ( 9 / 23 )	2.18115942028985	0.0725634438082852	30.058653583925
Winsorized Mean ( 10 / 23 )	2.16666666666667	0.0699429394358377	30.9776323978243
Winsorized Mean ( 11 / 23 )	2.15072463768116	0.0672382737570294	31.9866129438862
Winsorized Mean ( 12 / 23 )	2.16811594202899	0.0644834135980319	33.6228468850036
Winsorized Mean ( 13 / 23 )	2.14927536231884	0.0614413126787711	34.9809479747891
Winsorized Mean ( 14 / 23 )	2.1695652173913	0.0584068230719312	37.1457494738135
Winsorized Mean ( 15 / 23 )	2.1695652173913	0.0584068230719312	37.1457494738135
Winsorized Mean ( 16 / 23 )	2.19275362318841	0.0552186555180363	39.7103769118786
Winsorized Mean ( 17 / 23 )	2.19275362318841	0.0552186555180363	39.7103769118785
Winsorized Mean ( 18 / 23 )	2.16666666666667	0.0511032031145859	42.3978642162307
Winsorized Mean ( 19 / 23 )	2.16666666666667	0.0511032031145859	42.3978642162307
Winsorized Mean ( 20 / 23 )	2.16666666666667	0.0511032031145859	42.3978642162307
Winsorized Mean ( 21 / 23 )	2.13623188405797	0.0465324009847046	45.9084818073359
Winsorized Mean ( 22 / 23 )	2.13623188405797	0.0376171664625551	56.7887505876982
Winsorized Mean ( 23 / 23 )	2.10289855072464	0.0330317353986643	63.6629751765834
Trimmed Mean ( 1 / 23 )	2.34776119402985	0.127891402388366	18.3574591425656
Trimmed Mean ( 2 / 23 )	2.31538461538462	0.118610358568564	19.520930914699
Trimmed Mean ( 3 / 23 )	2.28253968253968	0.109776565950328	20.7925950568766
Trimmed Mean ( 4 / 23 )	2.24918032786885	0.0993317274639972	22.6431210378785
Trimmed Mean ( 5 / 23 )	2.21864406779661	0.0885454436704978	25.0565582578456
Trimmed Mean ( 6 / 23 )	2.19649122807018	0.0814946879382932	26.9525693470148
Trimmed Mean ( 7 / 23 )	2.17818181818182	0.0751066989211642	29.0011656679007
Trimmed Mean ( 8 / 23 )	2.16792452830189	0.0711594616062638	30.4657241548193
Trimmed Mean ( 9 / 23 )	2.15686274509804	0.0674030837696111	31.9994668562994
Trimmed Mean ( 10 / 23 )	2.1530612244898	0.0656017437455115	32.8201828421231
Trimmed Mean ( 11 / 23 )	2.1530612244898	0.063934542470133	33.6760245918018
Trimmed Mean ( 12 / 23 )	2.15111111111111	0.0624113287940629	34.4666770068152
Trimmed Mean ( 13 / 23 )	2.14883720930233	0.0610331947717381	35.2076803014966
Trimmed Mean ( 14 / 23 )	2.14878048780488	0.0598903419897782	35.878581026831
Trimmed Mean ( 15 / 23 )	2.14615384615385	0.05898902592949	36.382256060969
Trimmed Mean ( 16 / 23 )	2.14324324324324	0.0576752506943035	37.1605362342175
Trimmed Mean ( 17 / 23 )	2.13714285714286	0.0565218354899667	37.8109245500745
Trimmed Mean ( 18 / 23 )	2.13030303030303	0.0547869234295895	38.8834213886974
Trimmed Mean ( 19 / 23 )	2.1258064516129	0.0534744923486506	39.7536537187257
Trimmed Mean ( 20 / 23 )	2.12068965517241	0.051427722092528	41.2363131961571
Trimmed Mean ( 21 / 23 )	2.11481481481481	0.0482466666854754	43.8333870524464
Trimmed Mean ( 22 / 23 )	2.11481481481481	0.0452106182218293	46.776949707662
Trimmed Mean ( 23 / 23 )	2.10869565217391	0.0439695562476027	47.9580835498853
Median	2.1
Midrange	3.4
Midmean - Weighted Average at Xnp	2.10571428571429
Midmean - Weighted Average at X(n+1)p	2.1925
Midmean - Empirical Distribution Function	2.1925
Midmean - Empirical Distribution Function - Averaging	2.1925
Midmean - Empirical Distribution Function - Interpolation	2.1925
Midmean - Closest Observation	2.1925
Midmean - True Basic - Statistics Graphics Toolkit	2.1925
Midmean - MS Excel (old versions)	2.1925
Number of observations	69

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