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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sun, 26 Oct 2008 05:54:18 -0600

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/2008/Oct/26/t1225022163wanmdu2315rk0iu.htm/, Retrieved Sun, 19 May 2024 00:07:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18859, Retrieved Sun, 19 May 2024 00:07:02 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

gem Q9 GI / NIC

Estimated Impact

188

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

F     [Harrell-Davis Quantiles] [Q5 Distributions] [2007-10-22 09:17:45] [b731da8b544846036771bbf9bf2f34ce]
F RMPD  [Central Tendency] [Gemiddelde vervaa...] [2008-10-24 14:08:17] [495cd80c1a9baafb03c09cd9ab8d8fb5]
F    D      [Central Tendency] [gemiddelde Q9 van...] [2008-10-26 11:54:18] [d8c5724db236abb5950452133b88474d] [Current]

Feedback Forum

2008-11-03 10:13:58 [Joris Deboel] [reply] 
De werkwijze en conclusies zijn correct.

Post a new message

Dataseries X:

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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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18859&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18859&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18859&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	'Gwilym Jenkins' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	0.900479607777778	0.0222106384298357	40.5427160782626
Geometric Mean	0.882054964037387
Harmonic Mean	0.864782595021076
Quadratic Mean	0.919722082286461
Winsorized Mean ( 1 / 24 )	0.900546061805556	0.0221994033367176	40.5662282065059
Winsorized Mean ( 2 / 24 )	0.89983381125	0.0220086438490936	40.8854728814678
Winsorized Mean ( 3 / 24 )	0.900957084166667	0.0217700766403039	41.3851131097391
Winsorized Mean ( 4 / 24 )	0.896675134166667	0.0207284833094616	43.2581159354469
Winsorized Mean ( 5 / 24 )	0.896914849444445	0.0204340160578352	43.8932242641815
Winsorized Mean ( 6 / 24 )	0.896128896111111	0.0197920745414456	45.2771585027417
Winsorized Mean ( 7 / 24 )	0.896551601805556	0.0197322696685639	45.4358072773494
Winsorized Mean ( 8 / 24 )	0.892570911805556	0.0186090134125712	47.964440242844
Winsorized Mean ( 9 / 24 )	0.888685329305556	0.0176456321707983	50.362906848769
Winsorized Mean ( 10 / 24 )	0.888685329305555	0.0176456321707983	50.362906848769
Winsorized Mean ( 11 / 24 )	0.888196663472222	0.0173449834443257	51.2076973911894
Winsorized Mean ( 12 / 24 )	0.889094651805556	0.0172226307309629	51.6236262446908
Winsorized Mean ( 13 / 24 )	0.88903805125	0.0170377456234987	52.1804979893483
Winsorized Mean ( 14 / 24 )	0.885230747361111	0.0161805145282118	54.7096784726872
Winsorized Mean ( 15 / 24 )	0.879125741111111	0.0151933579750168	57.8625042967265
Winsorized Mean ( 16 / 24 )	0.870401774444444	0.0133825291154840	65.0401554843143
Winsorized Mean ( 17 / 24 )	0.872968200694444	0.0130346510188289	66.972886303854
Winsorized Mean ( 18 / 24 )	0.872968200694444	0.0130346510188289	66.972886303854
Winsorized Mean ( 19 / 24 )	0.876848919027778	0.0125320156374827	69.9687061038416
Winsorized Mean ( 20 / 24 )	0.876848919027778	0.0125320156374827	69.9687061038416
Winsorized Mean ( 21 / 24 )	0.877420816111111	0.0124601767228791	70.4180073545837
Winsorized Mean ( 22 / 24 )	0.878204291111111	0.0123624973247778	71.0377740063044
Winsorized Mean ( 23 / 24 )	0.878204291111111	0.0123624973247778	71.0377740063044
Winsorized Mean ( 24 / 24 )	0.879858551111111	0.0121585518652705	72.3654067409398
Trimmed Mean ( 1 / 24 )	0.898137421142857	0.0216396202052605	41.5043061118293
Trimmed Mean ( 2 / 24 )	0.895587095735294	0.0209696679908977	42.7086921988484
Trimmed Mean ( 3 / 24 )	0.893270705454545	0.0202893662343817	44.0265454886825
Trimmed Mean ( 4 / 24 )	0.8903883134375	0.0195760431253164	45.4835692656407
Trimmed Mean ( 5 / 24 )	0.888563107419355	0.0191116837480304	46.4931881007569
Trimmed Mean ( 6 / 24 )	0.886558689333333	0.0186366710967749	47.5706570518783
Trimmed Mean ( 7 / 24 )	0.884578646551724	0.0182356786519553	48.5081286764655
Trimmed Mean ( 8 / 24 )	0.882379532321429	0.0177495189031381	49.7128703677386
Trimmed Mean ( 9 / 24 )	0.880680969074074	0.0174276889036289	50.5334341199246
Trimmed Mean ( 10 / 24 )	0.879449529038462	0.0172418994835339	51.0065338148119
Trimmed Mean ( 11 / 24 )	0.8781195738	0.0169917166026487	51.6792737505473
Trimmed Mean ( 12 / 24 )	0.876745425208333	0.0167254879998393	52.4197216378235
Trimmed Mean ( 13 / 24 )	0.875134656521739	0.0163933422051657	53.3835410479002
Trimmed Mean ( 14 / 24 )	0.873384578863636	0.0159897714422212	54.621454848157
Trimmed Mean ( 15 / 24 )	0.871934027619048	0.0156522437529979	55.7066476460952
Trimmed Mean ( 16 / 24 )	0.871071022	0.0154225727527754	56.4802666820454
Trimmed Mean ( 17 / 24 )	0.871150275	0.0154823749337395	56.267225069041
Trimmed Mean ( 18 / 24 )	0.870936401388889	0.0155773146806514	55.9105609178378
Trimmed Mean ( 19 / 24 )	0.87069736617647	0.0156401568140331	55.6706289156408
Trimmed Mean ( 20 / 24 )	0.8699688928125	0.0157630874641827	55.1902598262725
Trimmed Mean ( 21 / 24 )	0.869143289666667	0.0158469072247386	54.8462408052624
Trimmed Mean ( 22 / 24 )	0.868129715	0.0158875257260598	54.6422224560768
Trimmed Mean ( 23 / 24 )	0.866861586538462	0.0158653953783103	54.6385114186031
Trimmed Mean ( 24 / 24 )	0.865382103333333	0.0157138044211552	55.0714569266424
Median	0.844129555
Midrange	0.98245614
Midmean - Weighted Average at Xnp	0.874454114102564
Midmean - Weighted Average at X(n+1)p	0.874454114102564
Midmean - Empirical Distribution Function	0.874454114102564
Midmean - Empirical Distribution Function - Averaging	0.874454114102564
Midmean - Empirical Distribution Function - Interpolation	0.874454114102564
Midmean - Closest Observation	0.874454114102564
Midmean - True Basic - Statistics Graphics Toolkit	0.874454114102564
Midmean - MS Excel (old versions)	0.874454114102564
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.900479607777778 & 0.0222106384298357 & 40.5427160782626 \tabularnewline
Geometric Mean & 0.882054964037387 &  &  \tabularnewline
Harmonic Mean & 0.864782595021076 &  &  \tabularnewline
Quadratic Mean & 0.919722082286461 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 0.900546061805556 & 0.0221994033367176 & 40.5662282065059 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 0.89983381125 & 0.0220086438490936 & 40.8854728814678 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 0.900957084166667 & 0.0217700766403039 & 41.3851131097391 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 0.896675134166667 & 0.0207284833094616 & 43.2581159354469 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 0.896914849444445 & 0.0204340160578352 & 43.8932242641815 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 0.896128896111111 & 0.0197920745414456 & 45.2771585027417 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 0.896551601805556 & 0.0197322696685639 & 45.4358072773494 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 0.892570911805556 & 0.0186090134125712 & 47.964440242844 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 0.888685329305556 & 0.0176456321707983 & 50.362906848769 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 0.888685329305555 & 0.0176456321707983 & 50.362906848769 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 0.888196663472222 & 0.0173449834443257 & 51.2076973911894 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 0.889094651805556 & 0.0172226307309629 & 51.6236262446908 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 0.88903805125 & 0.0170377456234987 & 52.1804979893483 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 0.885230747361111 & 0.0161805145282118 & 54.7096784726872 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 0.879125741111111 & 0.0151933579750168 & 57.8625042967265 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 0.870401774444444 & 0.0133825291154840 & 65.0401554843143 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 0.872968200694444 & 0.0130346510188289 & 66.972886303854 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 0.872968200694444 & 0.0130346510188289 & 66.972886303854 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 0.876848919027778 & 0.0125320156374827 & 69.9687061038416 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 0.876848919027778 & 0.0125320156374827 & 69.9687061038416 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 0.877420816111111 & 0.0124601767228791 & 70.4180073545837 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 0.878204291111111 & 0.0123624973247778 & 71.0377740063044 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 0.878204291111111 & 0.0123624973247778 & 71.0377740063044 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 0.879858551111111 & 0.0121585518652705 & 72.3654067409398 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 0.898137421142857 & 0.0216396202052605 & 41.5043061118293 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 0.895587095735294 & 0.0209696679908977 & 42.7086921988484 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 0.893270705454545 & 0.0202893662343817 & 44.0265454886825 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 0.8903883134375 & 0.0195760431253164 & 45.4835692656407 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 0.888563107419355 & 0.0191116837480304 & 46.4931881007569 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 0.886558689333333 & 0.0186366710967749 & 47.5706570518783 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 0.884578646551724 & 0.0182356786519553 & 48.5081286764655 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 0.882379532321429 & 0.0177495189031381 & 49.7128703677386 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 0.880680969074074 & 0.0174276889036289 & 50.5334341199246 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 0.879449529038462 & 0.0172418994835339 & 51.0065338148119 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 0.8781195738 & 0.0169917166026487 & 51.6792737505473 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 0.876745425208333 & 0.0167254879998393 & 52.4197216378235 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 0.875134656521739 & 0.0163933422051657 & 53.3835410479002 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 0.873384578863636 & 0.0159897714422212 & 54.621454848157 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 0.871934027619048 & 0.0156522437529979 & 55.7066476460952 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 0.871071022 & 0.0154225727527754 & 56.4802666820454 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 0.871150275 & 0.0154823749337395 & 56.267225069041 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 0.870936401388889 & 0.0155773146806514 & 55.9105609178378 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 0.87069736617647 & 0.0156401568140331 & 55.6706289156408 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 0.8699688928125 & 0.0157630874641827 & 55.1902598262725 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 0.869143289666667 & 0.0158469072247386 & 54.8462408052624 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 0.868129715 & 0.0158875257260598 & 54.6422224560768 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 0.866861586538462 & 0.0158653953783103 & 54.6385114186031 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 0.865382103333333 & 0.0157138044211552 & 55.0714569266424 \tabularnewline
Median & 0.844129555 &  &  \tabularnewline
Midrange & 0.98245614 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.874454114102564 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.874454114102564 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.874454114102564 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.874454114102564 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.874454114102564 &  &  \tabularnewline
Midmean - Closest Observation & 0.874454114102564 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.874454114102564 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.874454114102564 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18859&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]0.900479607777778[/C][C]0.0222106384298357[/C][C]40.5427160782626[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.882054964037387[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.864782595021076[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.919722082286461[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]0.900546061805556[/C][C]0.0221994033367176[/C][C]40.5662282065059[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]0.89983381125[/C][C]0.0220086438490936[/C][C]40.8854728814678[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]0.900957084166667[/C][C]0.0217700766403039[/C][C]41.3851131097391[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]0.896675134166667[/C][C]0.0207284833094616[/C][C]43.2581159354469[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]0.896914849444445[/C][C]0.0204340160578352[/C][C]43.8932242641815[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]0.896128896111111[/C][C]0.0197920745414456[/C][C]45.2771585027417[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]0.896551601805556[/C][C]0.0197322696685639[/C][C]45.4358072773494[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]0.892570911805556[/C][C]0.0186090134125712[/C][C]47.964440242844[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]0.888685329305556[/C][C]0.0176456321707983[/C][C]50.362906848769[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]0.888685329305555[/C][C]0.0176456321707983[/C][C]50.362906848769[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]0.888196663472222[/C][C]0.0173449834443257[/C][C]51.2076973911894[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]0.889094651805556[/C][C]0.0172226307309629[/C][C]51.6236262446908[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]0.88903805125[/C][C]0.0170377456234987[/C][C]52.1804979893483[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]0.885230747361111[/C][C]0.0161805145282118[/C][C]54.7096784726872[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]0.879125741111111[/C][C]0.0151933579750168[/C][C]57.8625042967265[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]0.870401774444444[/C][C]0.0133825291154840[/C][C]65.0401554843143[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]0.872968200694444[/C][C]0.0130346510188289[/C][C]66.972886303854[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]0.872968200694444[/C][C]0.0130346510188289[/C][C]66.972886303854[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]0.876848919027778[/C][C]0.0125320156374827[/C][C]69.9687061038416[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]0.876848919027778[/C][C]0.0125320156374827[/C][C]69.9687061038416[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]0.877420816111111[/C][C]0.0124601767228791[/C][C]70.4180073545837[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]0.878204291111111[/C][C]0.0123624973247778[/C][C]71.0377740063044[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]0.878204291111111[/C][C]0.0123624973247778[/C][C]71.0377740063044[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]0.879858551111111[/C][C]0.0121585518652705[/C][C]72.3654067409398[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]0.898137421142857[/C][C]0.0216396202052605[/C][C]41.5043061118293[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]0.895587095735294[/C][C]0.0209696679908977[/C][C]42.7086921988484[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]0.893270705454545[/C][C]0.0202893662343817[/C][C]44.0265454886825[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]0.8903883134375[/C][C]0.0195760431253164[/C][C]45.4835692656407[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]0.888563107419355[/C][C]0.0191116837480304[/C][C]46.4931881007569[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]0.886558689333333[/C][C]0.0186366710967749[/C][C]47.5706570518783[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]0.884578646551724[/C][C]0.0182356786519553[/C][C]48.5081286764655[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]0.882379532321429[/C][C]0.0177495189031381[/C][C]49.7128703677386[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]0.880680969074074[/C][C]0.0174276889036289[/C][C]50.5334341199246[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]0.879449529038462[/C][C]0.0172418994835339[/C][C]51.0065338148119[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]0.8781195738[/C][C]0.0169917166026487[/C][C]51.6792737505473[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]0.876745425208333[/C][C]0.0167254879998393[/C][C]52.4197216378235[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]0.875134656521739[/C][C]0.0163933422051657[/C][C]53.3835410479002[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]0.873384578863636[/C][C]0.0159897714422212[/C][C]54.621454848157[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]0.871934027619048[/C][C]0.0156522437529979[/C][C]55.7066476460952[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]0.871071022[/C][C]0.0154225727527754[/C][C]56.4802666820454[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]0.871150275[/C][C]0.0154823749337395[/C][C]56.267225069041[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]0.870936401388889[/C][C]0.0155773146806514[/C][C]55.9105609178378[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]0.87069736617647[/C][C]0.0156401568140331[/C][C]55.6706289156408[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]0.8699688928125[/C][C]0.0157630874641827[/C][C]55.1902598262725[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]0.869143289666667[/C][C]0.0158469072247386[/C][C]54.8462408052624[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]0.868129715[/C][C]0.0158875257260598[/C][C]54.6422224560768[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]0.866861586538462[/C][C]0.0158653953783103[/C][C]54.6385114186031[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]0.865382103333333[/C][C]0.0157138044211552[/C][C]55.0714569266424[/C][/ROW]
[ROW][C]Median[/C][C]0.844129555[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.98245614[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.874454114102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.874454114102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.874454114102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.874454114102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.874454114102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.874454114102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.874454114102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.874454114102564[/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=18859&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18859&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	0.900479607777778	0.0222106384298357	40.5427160782626
Geometric Mean	0.882054964037387
Harmonic Mean	0.864782595021076
Quadratic Mean	0.919722082286461
Winsorized Mean ( 1 / 24 )	0.900546061805556	0.0221994033367176	40.5662282065059
Winsorized Mean ( 2 / 24 )	0.89983381125	0.0220086438490936	40.8854728814678
Winsorized Mean ( 3 / 24 )	0.900957084166667	0.0217700766403039	41.3851131097391
Winsorized Mean ( 4 / 24 )	0.896675134166667	0.0207284833094616	43.2581159354469
Winsorized Mean ( 5 / 24 )	0.896914849444445	0.0204340160578352	43.8932242641815
Winsorized Mean ( 6 / 24 )	0.896128896111111	0.0197920745414456	45.2771585027417
Winsorized Mean ( 7 / 24 )	0.896551601805556	0.0197322696685639	45.4358072773494
Winsorized Mean ( 8 / 24 )	0.892570911805556	0.0186090134125712	47.964440242844
Winsorized Mean ( 9 / 24 )	0.888685329305556	0.0176456321707983	50.362906848769
Winsorized Mean ( 10 / 24 )	0.888685329305555	0.0176456321707983	50.362906848769
Winsorized Mean ( 11 / 24 )	0.888196663472222	0.0173449834443257	51.2076973911894
Winsorized Mean ( 12 / 24 )	0.889094651805556	0.0172226307309629	51.6236262446908
Winsorized Mean ( 13 / 24 )	0.88903805125	0.0170377456234987	52.1804979893483
Winsorized Mean ( 14 / 24 )	0.885230747361111	0.0161805145282118	54.7096784726872
Winsorized Mean ( 15 / 24 )	0.879125741111111	0.0151933579750168	57.8625042967265
Winsorized Mean ( 16 / 24 )	0.870401774444444	0.0133825291154840	65.0401554843143
Winsorized Mean ( 17 / 24 )	0.872968200694444	0.0130346510188289	66.972886303854
Winsorized Mean ( 18 / 24 )	0.872968200694444	0.0130346510188289	66.972886303854
Winsorized Mean ( 19 / 24 )	0.876848919027778	0.0125320156374827	69.9687061038416
Winsorized Mean ( 20 / 24 )	0.876848919027778	0.0125320156374827	69.9687061038416
Winsorized Mean ( 21 / 24 )	0.877420816111111	0.0124601767228791	70.4180073545837
Winsorized Mean ( 22 / 24 )	0.878204291111111	0.0123624973247778	71.0377740063044
Winsorized Mean ( 23 / 24 )	0.878204291111111	0.0123624973247778	71.0377740063044
Winsorized Mean ( 24 / 24 )	0.879858551111111	0.0121585518652705	72.3654067409398
Trimmed Mean ( 1 / 24 )	0.898137421142857	0.0216396202052605	41.5043061118293
Trimmed Mean ( 2 / 24 )	0.895587095735294	0.0209696679908977	42.7086921988484
Trimmed Mean ( 3 / 24 )	0.893270705454545	0.0202893662343817	44.0265454886825
Trimmed Mean ( 4 / 24 )	0.8903883134375	0.0195760431253164	45.4835692656407
Trimmed Mean ( 5 / 24 )	0.888563107419355	0.0191116837480304	46.4931881007569
Trimmed Mean ( 6 / 24 )	0.886558689333333	0.0186366710967749	47.5706570518783
Trimmed Mean ( 7 / 24 )	0.884578646551724	0.0182356786519553	48.5081286764655
Trimmed Mean ( 8 / 24 )	0.882379532321429	0.0177495189031381	49.7128703677386
Trimmed Mean ( 9 / 24 )	0.880680969074074	0.0174276889036289	50.5334341199246
Trimmed Mean ( 10 / 24 )	0.879449529038462	0.0172418994835339	51.0065338148119
Trimmed Mean ( 11 / 24 )	0.8781195738	0.0169917166026487	51.6792737505473
Trimmed Mean ( 12 / 24 )	0.876745425208333	0.0167254879998393	52.4197216378235
Trimmed Mean ( 13 / 24 )	0.875134656521739	0.0163933422051657	53.3835410479002
Trimmed Mean ( 14 / 24 )	0.873384578863636	0.0159897714422212	54.621454848157
Trimmed Mean ( 15 / 24 )	0.871934027619048	0.0156522437529979	55.7066476460952
Trimmed Mean ( 16 / 24 )	0.871071022	0.0154225727527754	56.4802666820454
Trimmed Mean ( 17 / 24 )	0.871150275	0.0154823749337395	56.267225069041
Trimmed Mean ( 18 / 24 )	0.870936401388889	0.0155773146806514	55.9105609178378
Trimmed Mean ( 19 / 24 )	0.87069736617647	0.0156401568140331	55.6706289156408
Trimmed Mean ( 20 / 24 )	0.8699688928125	0.0157630874641827	55.1902598262725
Trimmed Mean ( 21 / 24 )	0.869143289666667	0.0158469072247386	54.8462408052624
Trimmed Mean ( 22 / 24 )	0.868129715	0.0158875257260598	54.6422224560768
Trimmed Mean ( 23 / 24 )	0.866861586538462	0.0158653953783103	54.6385114186031
Trimmed Mean ( 24 / 24 )	0.865382103333333	0.0157138044211552	55.0714569266424
Median	0.844129555
Midrange	0.98245614
Midmean - Weighted Average at Xnp	0.874454114102564
Midmean - Weighted Average at X(n+1)p	0.874454114102564
Midmean - Empirical Distribution Function	0.874454114102564
Midmean - Empirical Distribution Function - Averaging	0.874454114102564
Midmean - Empirical Distribution Function - Interpolation	0.874454114102564
Midmean - Closest Observation	0.874454114102564
Midmean - True Basic - Statistics Graphics Toolkit	0.874454114102564
Midmean - MS Excel (old versions)	0.874454114102564
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