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*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 08 Oct 2012 03:43:49 -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/2012/Oct/08/t1349682253ovmwd4wdnnh6hh7.htm/, Retrieved Thu, 02 May 2024 01:16:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=173231, Retrieved Thu, 02 May 2024 01:16:10 +0000

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Estimated Impact

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

-     [Harrell-Davis Quantiles] [] [2012-10-03 11:59:02] [c0a2ac1e2bf1d66cb9c7a1df64587793]
- RMP     [Central Tendency] [] [2012-10-08 07:43:49] [4580e6b2a2a2b9b99b0ce0e7252c310b] [Current]

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1,33
1,32
1,32
1,4
1,43
1,43
1,45
1,45
1,33
1,27
1,27
1,29
1,25
1,26
1,32
1,36
1,4
1,41
1,42
1,39
1,38
1,41
1,47
1,44
1,47
1,45
1,47
1,49
1,54
1,61
1,63
1,55
1,53
1,41
1,26
1,19
1,17
1,21
1,24
1,26
1,32
1,39
1,35
1,41
1,37
1,32
1,38
1,38
1,41
1,4
1,45
1,49
1,51
1,48
1,47
1,46
1,46
1,45
1,47
1,53
1,55
1,55
1,6
1,65
1,68
1,63
1,62
1,63
1,66
1,63
1,6
1,6

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173231&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173231&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173231&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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.43305555555556	0.0146164297667764	98.044158417737
Geometric Mean	1.42774237432932
Harmonic Mean	1.42241034330242
Quadratic Mean	1.43833816144419
Winsorized Mean ( 1 / 24 )	1.43305555555556	0.0144846782263591	98.9359606862161
Winsorized Mean ( 2 / 24 )	1.43333333333333	0.0142975861692119	100.250022372296
Winsorized Mean ( 3 / 24 )	1.43375	0.0138647579886743	103.409666520771
Winsorized Mean ( 4 / 24 )	1.43430555555556	0.0137576645146851	104.255017559453
Winsorized Mean ( 5 / 24 )	1.435	0.013629343287006	105.287538055345
Winsorized Mean ( 6 / 24 )	1.435	0.013629343287006	105.287538055345
Winsorized Mean ( 7 / 24 )	1.43402777777778	0.0134366008593488	106.725487553649
Winsorized Mean ( 8 / 24 )	1.43402777777778	0.0130225813902249	110.118549833307
Winsorized Mean ( 9 / 24 )	1.43277777777778	0.012788489760444	112.036511317348
Winsorized Mean ( 10 / 24 )	1.43555555555556	0.0123078166583475	116.637710440862
Winsorized Mean ( 11 / 24 )	1.44013888888889	0.0115901127787271	124.255813242143
Winsorized Mean ( 12 / 24 )	1.43180555555556	0.0100843981296496	141.982251905132
Winsorized Mean ( 13 / 24 )	1.43180555555556	0.0100843981296496	141.982251905132
Winsorized Mean ( 14 / 24 )	1.43180555555556	0.0100843981296496	141.982251905132
Winsorized Mean ( 15 / 24 )	1.42972222222222	0.00974633718410905	146.693285407088
Winsorized Mean ( 16 / 24 )	1.42972222222222	0.00904685296665329	158.035311007284
Winsorized Mean ( 17 / 24 )	1.42972222222222	0.00904685296665329	158.035311007284
Winsorized Mean ( 18 / 24 )	1.42972222222222	0.00751621154067573	190.218465045182
Winsorized Mean ( 19 / 24 )	1.42708333333333	0.00635552542618464	224.542148388515
Winsorized Mean ( 20 / 24 )	1.42986111111111	0.0059519892374277	240.232475912383
Winsorized Mean ( 21 / 24 )	1.42986111111111	0.00513698522452705	278.346354644762
Winsorized Mean ( 22 / 24 )	1.42680555555556	0.00472989687497752	301.656799983052
Winsorized Mean ( 23 / 24 )	1.42680555555556	0.00472989687497752	301.656799983052
Winsorized Mean ( 24 / 24 )	1.43013888888889	0.00427668395462109	334.403688480085
Trimmed Mean ( 1 / 24 )	1.43328571428571	0.014112416788109	101.562031210231
Trimmed Mean ( 2 / 24 )	1.43352941176471	0.0136698252474236	104.868159308393
Trimmed Mean ( 3 / 24 )	1.43363636363636	0.0132619939358005	108.101117416913
Trimmed Mean ( 4 / 24 )	1.43359375	0.0129719767930583	110.514671192378
Trimmed Mean ( 5 / 24 )	1.43338709677419	0.0126602755860907	113.219265017343
Trimmed Mean ( 6 / 24 )	1.433	0.0123217230433516	116.298669833615
Trimmed Mean ( 7 / 24 )	1.43258620689655	0.0119069805328646	120.314818936879
Trimmed Mean ( 8 / 24 )	1.43232142857143	0.0114500356473913	125.093185093949
Trimmed Mean ( 9 / 24 )	1.43203703703704	0.0109932309699153	130.265346098524
Trimmed Mean ( 10 / 24 )	1.43192307692308	0.0104824728436775	136.601649083855
Trimmed Mean ( 11 / 24 )	1.4314	0.00995914101697121	143.727254947066
Trimmed Mean ( 12 / 24 )	1.43020833333333	0.00946479845902576	151.108165643978
Trimmed Mean ( 13 / 24 )	1.43	0.0092103701268948	155.259775698299
Trimmed Mean ( 14 / 24 )	1.42977272727273	0.00887717835794083	161.061619990294
Trimmed Mean ( 15 / 24 )	1.42952380952381	0.00843746127243579	169.425821744972
Trimmed Mean ( 16 / 24 )	1.4295	0.00794169458116546	179.999367312639
Trimmed Mean ( 17 / 24 )	1.42947368421053	0.00746682914435499	191.443202539491
Trimmed Mean ( 18 / 24 )	1.42944444444444	0.00680737746911795	209.984601401817
Trimmed Mean ( 19 / 24 )	1.42941176470588	0.00637426276147548	224.247386434225
Trimmed Mean ( 20 / 24 )	1.4296875	0.00611523044101972	233.791271447425
Trimmed Mean ( 21 / 24 )	1.42966666666667	0.00586208023438178	243.883844898865
Trimmed Mean ( 22 / 24 )	1.42964285714286	0.00573862211899695	249.126502407296
Trimmed Mean ( 23 / 24 )	1.43	0.00565685424949239	252.790674274191
Trimmed Mean ( 24 / 24 )	1.43041666666667	0.00549964315926289	260.092632420607
Median	1.43
Midrange	1.425
Midmean - Weighted Average at Xnp	1.42421052631579
Midmean - Weighted Average at X(n+1)p	1.42944444444444
Midmean - Empirical Distribution Function	1.42421052631579
Midmean - Empirical Distribution Function - Averaging	1.42944444444444
Midmean - Empirical Distribution Function - Interpolation	1.42944444444444
Midmean - Closest Observation	1.42421052631579
Midmean - True Basic - Statistics Graphics Toolkit	1.42944444444444
Midmean - MS Excel (old versions)	1.4295
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.43305555555556 & 0.0146164297667764 & 98.044158417737 \tabularnewline
Geometric Mean & 1.42774237432932 &  &  \tabularnewline
Harmonic Mean & 1.42241034330242 &  &  \tabularnewline
Quadratic Mean & 1.43833816144419 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.43305555555556 & 0.0144846782263591 & 98.9359606862161 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.43333333333333 & 0.0142975861692119 & 100.250022372296 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.43375 & 0.0138647579886743 & 103.409666520771 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.43430555555556 & 0.0137576645146851 & 104.255017559453 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.435 & 0.013629343287006 & 105.287538055345 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.435 & 0.013629343287006 & 105.287538055345 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.43402777777778 & 0.0134366008593488 & 106.725487553649 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.43402777777778 & 0.0130225813902249 & 110.118549833307 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.43277777777778 & 0.012788489760444 & 112.036511317348 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.43555555555556 & 0.0123078166583475 & 116.637710440862 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.44013888888889 & 0.0115901127787271 & 124.255813242143 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.43180555555556 & 0.0100843981296496 & 141.982251905132 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.43180555555556 & 0.0100843981296496 & 141.982251905132 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.43180555555556 & 0.0100843981296496 & 141.982251905132 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.42972222222222 & 0.00974633718410905 & 146.693285407088 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.42972222222222 & 0.00904685296665329 & 158.035311007284 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.42972222222222 & 0.00904685296665329 & 158.035311007284 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.42972222222222 & 0.00751621154067573 & 190.218465045182 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.42708333333333 & 0.00635552542618464 & 224.542148388515 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.42986111111111 & 0.0059519892374277 & 240.232475912383 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.42986111111111 & 0.00513698522452705 & 278.346354644762 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.42680555555556 & 0.00472989687497752 & 301.656799983052 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.42680555555556 & 0.00472989687497752 & 301.656799983052 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.43013888888889 & 0.00427668395462109 & 334.403688480085 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.43328571428571 & 0.014112416788109 & 101.562031210231 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.43352941176471 & 0.0136698252474236 & 104.868159308393 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.43363636363636 & 0.0132619939358005 & 108.101117416913 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.43359375 & 0.0129719767930583 & 110.514671192378 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.43338709677419 & 0.0126602755860907 & 113.219265017343 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.433 & 0.0123217230433516 & 116.298669833615 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.43258620689655 & 0.0119069805328646 & 120.314818936879 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.43232142857143 & 0.0114500356473913 & 125.093185093949 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.43203703703704 & 0.0109932309699153 & 130.265346098524 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.43192307692308 & 0.0104824728436775 & 136.601649083855 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.4314 & 0.00995914101697121 & 143.727254947066 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.43020833333333 & 0.00946479845902576 & 151.108165643978 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.43 & 0.0092103701268948 & 155.259775698299 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.42977272727273 & 0.00887717835794083 & 161.061619990294 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.42952380952381 & 0.00843746127243579 & 169.425821744972 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.4295 & 0.00794169458116546 & 179.999367312639 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.42947368421053 & 0.00746682914435499 & 191.443202539491 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.42944444444444 & 0.00680737746911795 & 209.984601401817 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.42941176470588 & 0.00637426276147548 & 224.247386434225 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.4296875 & 0.00611523044101972 & 233.791271447425 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.42966666666667 & 0.00586208023438178 & 243.883844898865 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.42964285714286 & 0.00573862211899695 & 249.126502407296 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.43 & 0.00565685424949239 & 252.790674274191 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.43041666666667 & 0.00549964315926289 & 260.092632420607 \tabularnewline
Median & 1.43 &  &  \tabularnewline
Midrange & 1.425 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.42421052631579 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.42944444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.42421052631579 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.42944444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.42944444444444 &  &  \tabularnewline
Midmean - Closest Observation & 1.42421052631579 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.42944444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.4295 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173231&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]1.43305555555556[/C][C]0.0146164297667764[/C][C]98.044158417737[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.42774237432932[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.42241034330242[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.43833816144419[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.43305555555556[/C][C]0.0144846782263591[/C][C]98.9359606862161[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.43333333333333[/C][C]0.0142975861692119[/C][C]100.250022372296[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.43375[/C][C]0.0138647579886743[/C][C]103.409666520771[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.43430555555556[/C][C]0.0137576645146851[/C][C]104.255017559453[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.435[/C][C]0.013629343287006[/C][C]105.287538055345[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.435[/C][C]0.013629343287006[/C][C]105.287538055345[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.43402777777778[/C][C]0.0134366008593488[/C][C]106.725487553649[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.43402777777778[/C][C]0.0130225813902249[/C][C]110.118549833307[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.43277777777778[/C][C]0.012788489760444[/C][C]112.036511317348[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.43555555555556[/C][C]0.0123078166583475[/C][C]116.637710440862[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.44013888888889[/C][C]0.0115901127787271[/C][C]124.255813242143[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.43180555555556[/C][C]0.0100843981296496[/C][C]141.982251905132[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.43180555555556[/C][C]0.0100843981296496[/C][C]141.982251905132[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.43180555555556[/C][C]0.0100843981296496[/C][C]141.982251905132[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.42972222222222[/C][C]0.00974633718410905[/C][C]146.693285407088[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.42972222222222[/C][C]0.00904685296665329[/C][C]158.035311007284[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.42972222222222[/C][C]0.00904685296665329[/C][C]158.035311007284[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.42972222222222[/C][C]0.00751621154067573[/C][C]190.218465045182[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.42708333333333[/C][C]0.00635552542618464[/C][C]224.542148388515[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.42986111111111[/C][C]0.0059519892374277[/C][C]240.232475912383[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.42986111111111[/C][C]0.00513698522452705[/C][C]278.346354644762[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.42680555555556[/C][C]0.00472989687497752[/C][C]301.656799983052[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.42680555555556[/C][C]0.00472989687497752[/C][C]301.656799983052[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.43013888888889[/C][C]0.00427668395462109[/C][C]334.403688480085[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.43328571428571[/C][C]0.014112416788109[/C][C]101.562031210231[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.43352941176471[/C][C]0.0136698252474236[/C][C]104.868159308393[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.43363636363636[/C][C]0.0132619939358005[/C][C]108.101117416913[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.43359375[/C][C]0.0129719767930583[/C][C]110.514671192378[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.43338709677419[/C][C]0.0126602755860907[/C][C]113.219265017343[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.433[/C][C]0.0123217230433516[/C][C]116.298669833615[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.43258620689655[/C][C]0.0119069805328646[/C][C]120.314818936879[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.43232142857143[/C][C]0.0114500356473913[/C][C]125.093185093949[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.43203703703704[/C][C]0.0109932309699153[/C][C]130.265346098524[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.43192307692308[/C][C]0.0104824728436775[/C][C]136.601649083855[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.4314[/C][C]0.00995914101697121[/C][C]143.727254947066[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.43020833333333[/C][C]0.00946479845902576[/C][C]151.108165643978[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.43[/C][C]0.0092103701268948[/C][C]155.259775698299[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.42977272727273[/C][C]0.00887717835794083[/C][C]161.061619990294[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.42952380952381[/C][C]0.00843746127243579[/C][C]169.425821744972[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.4295[/C][C]0.00794169458116546[/C][C]179.999367312639[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.42947368421053[/C][C]0.00746682914435499[/C][C]191.443202539491[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.42944444444444[/C][C]0.00680737746911795[/C][C]209.984601401817[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.42941176470588[/C][C]0.00637426276147548[/C][C]224.247386434225[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.4296875[/C][C]0.00611523044101972[/C][C]233.791271447425[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.42966666666667[/C][C]0.00586208023438178[/C][C]243.883844898865[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.42964285714286[/C][C]0.00573862211899695[/C][C]249.126502407296[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.43[/C][C]0.00565685424949239[/C][C]252.790674274191[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.43041666666667[/C][C]0.00549964315926289[/C][C]260.092632420607[/C][/ROW]
[ROW][C]Median[/C][C]1.43[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.42421052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.42944444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.42421052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.42944444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.42944444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.42421052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.42944444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.4295[/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=173231&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173231&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	1.43305555555556	0.0146164297667764	98.044158417737
Geometric Mean	1.42774237432932
Harmonic Mean	1.42241034330242
Quadratic Mean	1.43833816144419
Winsorized Mean ( 1 / 24 )	1.43305555555556	0.0144846782263591	98.9359606862161
Winsorized Mean ( 2 / 24 )	1.43333333333333	0.0142975861692119	100.250022372296
Winsorized Mean ( 3 / 24 )	1.43375	0.0138647579886743	103.409666520771
Winsorized Mean ( 4 / 24 )	1.43430555555556	0.0137576645146851	104.255017559453
Winsorized Mean ( 5 / 24 )	1.435	0.013629343287006	105.287538055345
Winsorized Mean ( 6 / 24 )	1.435	0.013629343287006	105.287538055345
Winsorized Mean ( 7 / 24 )	1.43402777777778	0.0134366008593488	106.725487553649
Winsorized Mean ( 8 / 24 )	1.43402777777778	0.0130225813902249	110.118549833307
Winsorized Mean ( 9 / 24 )	1.43277777777778	0.012788489760444	112.036511317348
Winsorized Mean ( 10 / 24 )	1.43555555555556	0.0123078166583475	116.637710440862
Winsorized Mean ( 11 / 24 )	1.44013888888889	0.0115901127787271	124.255813242143
Winsorized Mean ( 12 / 24 )	1.43180555555556	0.0100843981296496	141.982251905132
Winsorized Mean ( 13 / 24 )	1.43180555555556	0.0100843981296496	141.982251905132
Winsorized Mean ( 14 / 24 )	1.43180555555556	0.0100843981296496	141.982251905132
Winsorized Mean ( 15 / 24 )	1.42972222222222	0.00974633718410905	146.693285407088
Winsorized Mean ( 16 / 24 )	1.42972222222222	0.00904685296665329	158.035311007284
Winsorized Mean ( 17 / 24 )	1.42972222222222	0.00904685296665329	158.035311007284
Winsorized Mean ( 18 / 24 )	1.42972222222222	0.00751621154067573	190.218465045182
Winsorized Mean ( 19 / 24 )	1.42708333333333	0.00635552542618464	224.542148388515
Winsorized Mean ( 20 / 24 )	1.42986111111111	0.0059519892374277	240.232475912383
Winsorized Mean ( 21 / 24 )	1.42986111111111	0.00513698522452705	278.346354644762
Winsorized Mean ( 22 / 24 )	1.42680555555556	0.00472989687497752	301.656799983052
Winsorized Mean ( 23 / 24 )	1.42680555555556	0.00472989687497752	301.656799983052
Winsorized Mean ( 24 / 24 )	1.43013888888889	0.00427668395462109	334.403688480085
Trimmed Mean ( 1 / 24 )	1.43328571428571	0.014112416788109	101.562031210231
Trimmed Mean ( 2 / 24 )	1.43352941176471	0.0136698252474236	104.868159308393
Trimmed Mean ( 3 / 24 )	1.43363636363636	0.0132619939358005	108.101117416913
Trimmed Mean ( 4 / 24 )	1.43359375	0.0129719767930583	110.514671192378
Trimmed Mean ( 5 / 24 )	1.43338709677419	0.0126602755860907	113.219265017343
Trimmed Mean ( 6 / 24 )	1.433	0.0123217230433516	116.298669833615
Trimmed Mean ( 7 / 24 )	1.43258620689655	0.0119069805328646	120.314818936879
Trimmed Mean ( 8 / 24 )	1.43232142857143	0.0114500356473913	125.093185093949
Trimmed Mean ( 9 / 24 )	1.43203703703704	0.0109932309699153	130.265346098524
Trimmed Mean ( 10 / 24 )	1.43192307692308	0.0104824728436775	136.601649083855
Trimmed Mean ( 11 / 24 )	1.4314	0.00995914101697121	143.727254947066
Trimmed Mean ( 12 / 24 )	1.43020833333333	0.00946479845902576	151.108165643978
Trimmed Mean ( 13 / 24 )	1.43	0.0092103701268948	155.259775698299
Trimmed Mean ( 14 / 24 )	1.42977272727273	0.00887717835794083	161.061619990294
Trimmed Mean ( 15 / 24 )	1.42952380952381	0.00843746127243579	169.425821744972
Trimmed Mean ( 16 / 24 )	1.4295	0.00794169458116546	179.999367312639
Trimmed Mean ( 17 / 24 )	1.42947368421053	0.00746682914435499	191.443202539491
Trimmed Mean ( 18 / 24 )	1.42944444444444	0.00680737746911795	209.984601401817
Trimmed Mean ( 19 / 24 )	1.42941176470588	0.00637426276147548	224.247386434225
Trimmed Mean ( 20 / 24 )	1.4296875	0.00611523044101972	233.791271447425
Trimmed Mean ( 21 / 24 )	1.42966666666667	0.00586208023438178	243.883844898865
Trimmed Mean ( 22 / 24 )	1.42964285714286	0.00573862211899695	249.126502407296
Trimmed Mean ( 23 / 24 )	1.43	0.00565685424949239	252.790674274191
Trimmed Mean ( 24 / 24 )	1.43041666666667	0.00549964315926289	260.092632420607
Median	1.43
Midrange	1.425
Midmean - Weighted Average at Xnp	1.42421052631579
Midmean - Weighted Average at X(n+1)p	1.42944444444444
Midmean - Empirical Distribution Function	1.42421052631579
Midmean - Empirical Distribution Function - Averaging	1.42944444444444
Midmean - Empirical Distribution Function - Interpolation	1.42944444444444
Midmean - Closest Observation	1.42421052631579
Midmean - True Basic - Statistics Graphics Toolkit	1.42944444444444
Midmean - MS Excel (old versions)	1.4295
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