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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Fri, 13 Mar 2009 01:37:15 -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/2009/Mar/13/t1236929909t3kka9jx5xtu75c.htm/, Retrieved Thu, 18 Apr 2024 22:15:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39025, Retrieved Thu, 18 Apr 2024 22:15:27 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

188

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

-       [Central Tendency] [Centrummaten - Pr...] [2009-03-13 07:37:15] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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4,2
4,19
4,19
4,19
4,19
4,18
4,2
4,19
4,17
4,21
4,22
4,23
4,21
4,23
4,23
4,22
4,25
4,28
4,3
4,32
4,33
4,32
4,34
4,33
4,31
4,31
4,3
4,3
4,29
4,33
4,32
4,32
4,35
4,37
4,39
4,4
4,41
4,44
4,47
4,47
4,47
4,48
4,47
4,48
4,46
4,44
4,43
4,41
4,41
4,38
4,35
4,37
4,4
4,39
4,36
4,34
4,33
4,33
4,34
4,34
4,35
4,37
4,39
4,4
4,38
4,37
4,36
4,33
4,33
4,33
4,32
4,33
4,34

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' @ 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39025&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39025&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39025&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' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	4.32986301369863	0.00986494252237418	438.914165376867
Geometric Mean	4.32905168770462
Harmonic Mean	4.32823819694739
Quadratic Mean	4.33067206654408
Winsorized Mean ( 1 / 24 )	4.33	0.00983501649552635	440.263623550564
Winsorized Mean ( 2 / 24 )	4.33	0.00972216786242684	445.37391878761
Winsorized Mean ( 3 / 24 )	4.33	0.00972216786242684	445.37391878761
Winsorized Mean ( 4 / 24 )	4.33	0.00972216786242684	445.37391878761
Winsorized Mean ( 5 / 24 )	4.33	0.00972216786242684	445.37391878761
Winsorized Mean ( 6 / 24 )	4.32917808219178	0.00956184990161433	452.755285508182
Winsorized Mean ( 7 / 24 )	4.32821917808219	0.00902251214935675	479.713311152567
Winsorized Mean ( 8 / 24 )	4.32821917808219	0.00902251214935675	479.713311152567
Winsorized Mean ( 9 / 24 )	4.32821917808219	0.00857490601444254	504.754124510783
Winsorized Mean ( 10 / 24 )	4.32547945205480	0.00815106863760496	530.664093797369
Winsorized Mean ( 11 / 24 )	4.32698630136986	0.00786028330979911	550.487320981876
Winsorized Mean ( 12 / 24 )	4.32698630136986	0.00786028330979911	550.487320981876
Winsorized Mean ( 13 / 24 )	4.32698630136986	0.00727185974295882	595.031594986357
Winsorized Mean ( 14 / 24 )	4.32698630136986	0.00727185974295882	595.031594986357
Winsorized Mean ( 15 / 24 )	4.32698630136986	0.00727185974295882	595.031594986357
Winsorized Mean ( 16 / 24 )	4.32917808219178	0.00617093343891476	701.543473940487
Winsorized Mean ( 17 / 24 )	4.33616438356164	0.00499478471153132	868.138395144612
Winsorized Mean ( 18 / 24 )	4.3386301369863	0.0046215820744767	938.77595746854
Winsorized Mean ( 19 / 24 )	4.3386301369863	0.00385385152231582	1125.79068286968
Winsorized Mean ( 20 / 24 )	4.3386301369863	0.00385385152231582	1125.79068286968
Winsorized Mean ( 21 / 24 )	4.33575342465753	0.00343961725010413	1260.53369005702
Winsorized Mean ( 22 / 24 )	4.33876712328767	0.00302164443042298	1435.89599080667
Winsorized Mean ( 23 / 24 )	4.33876712328767	0.00302164443042298	1435.89599080667
Winsorized Mean ( 24 / 24 )	4.34205479452055	0.00260954010269032	1663.91571834596
Trimmed Mean ( 1 / 24 )	4.33	0.0096560569913251	448.423202544271
Trimmed Mean ( 2 / 24 )	4.33	0.00944314886722427	458.533489292832
Trimmed Mean ( 3 / 24 )	4.33	0.00926029442929499	467.587724457445
Trimmed Mean ( 4 / 24 )	4.33	0.00904050713349473	478.955432041806
Trimmed Mean ( 5 / 24 )	4.33	0.00877551870960525	493.418126413496
Trimmed Mean ( 6 / 24 )	4.33	0.00845431309072863	512.164613911503
Trimmed Mean ( 7 / 24 )	4.33016949152542	0.0081104716367717	533.898604847227
Trimmed Mean ( 8 / 24 )	4.33052631578947	0.00783772227855536	552.523572778043
Trimmed Mean ( 9 / 24 )	4.33090909090909	0.00749982144466568	577.468293460439
Trimmed Mean ( 10 / 24 )	4.33132075471698	0.00719335756253142	602.127826549018
Trimmed Mean ( 11 / 24 )	4.3321568627451	0.00690730630786007	627.18470408868
Trimmed Mean ( 12 / 24 )	4.33285714285714	0.00661759148080347	654.748356018355
Trimmed Mean ( 13 / 24 )	4.33361702127660	0.00624377974956233	694.069489171262
Trimmed Mean ( 14 / 24 )	4.33444444444444	0.00590801164278373	733.655366055126
Trimmed Mean ( 15 / 24 )	4.3353488372093	0.00546152187351611	793.798676927795
Trimmed Mean ( 16 / 24 )	4.33634146341463	0.00484838541846382	894.388768454917
Trimmed Mean ( 17 / 24 )	4.33717948717949	0.00436135522816907	994.456828273598
Trimmed Mean ( 18 / 24 )	4.3372972972973	0.0040760165858968	1064.10197453674
Trimmed Mean ( 19 / 24 )	4.33714285714286	0.00379232813731624	1143.66233619546
Trimmed Mean ( 20 / 24 )	4.3369696969697	0.00362767269509482	1195.52397955691
Trimmed Mean ( 21 / 24 )	4.33677419354839	0.00338837661432016	1279.89733349594
Trimmed Mean ( 22 / 24 )	4.33689655172414	0.00318182369693697	1363.02226798396
Trimmed Mean ( 23 / 24 )	4.33666666666667	0.00301940542438558	1436.26511088657
Trimmed Mean ( 24 / 24 )	4.3364	0.00276164202362772	1570.22523661617
Median	4.33
Midrange	4.325
Midmean - Weighted Average at Xnp	4.33583333333333
Midmean - Weighted Average at X(n+1)p	4.34
Midmean - Empirical Distribution Function	4.34
Midmean - Empirical Distribution Function - Averaging	4.34
Midmean - Empirical Distribution Function - Interpolation	4.34
Midmean - Closest Observation	4.3385
Midmean - True Basic - Statistics Graphics Toolkit	4.34
Midmean - MS Excel (old versions)	4.34
Number of observations	73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.32986301369863 & 0.00986494252237418 & 438.914165376867 \tabularnewline
Geometric Mean & 4.32905168770462 &  &  \tabularnewline
Harmonic Mean & 4.32823819694739 &  &  \tabularnewline
Quadratic Mean & 4.33067206654408 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 4.33 & 0.00983501649552635 & 440.263623550564 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 4.33 & 0.00972216786242684 & 445.37391878761 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 4.33 & 0.00972216786242684 & 445.37391878761 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 4.33 & 0.00972216786242684 & 445.37391878761 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 4.33 & 0.00972216786242684 & 445.37391878761 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 4.32917808219178 & 0.00956184990161433 & 452.755285508182 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 4.32821917808219 & 0.00902251214935675 & 479.713311152567 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 4.32821917808219 & 0.00902251214935675 & 479.713311152567 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 4.32821917808219 & 0.00857490601444254 & 504.754124510783 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 4.32547945205480 & 0.00815106863760496 & 530.664093797369 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 4.32698630136986 & 0.00786028330979911 & 550.487320981876 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 4.32698630136986 & 0.00786028330979911 & 550.487320981876 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 4.32698630136986 & 0.00727185974295882 & 595.031594986357 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 4.32698630136986 & 0.00727185974295882 & 595.031594986357 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 4.32698630136986 & 0.00727185974295882 & 595.031594986357 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 4.32917808219178 & 0.00617093343891476 & 701.543473940487 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 4.33616438356164 & 0.00499478471153132 & 868.138395144612 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 4.3386301369863 & 0.0046215820744767 & 938.77595746854 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 4.3386301369863 & 0.00385385152231582 & 1125.79068286968 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 4.3386301369863 & 0.00385385152231582 & 1125.79068286968 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 4.33575342465753 & 0.00343961725010413 & 1260.53369005702 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 4.33876712328767 & 0.00302164443042298 & 1435.89599080667 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 4.33876712328767 & 0.00302164443042298 & 1435.89599080667 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 4.34205479452055 & 0.00260954010269032 & 1663.91571834596 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 4.33 & 0.0096560569913251 & 448.423202544271 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 4.33 & 0.00944314886722427 & 458.533489292832 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 4.33 & 0.00926029442929499 & 467.587724457445 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 4.33 & 0.00904050713349473 & 478.955432041806 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 4.33 & 0.00877551870960525 & 493.418126413496 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 4.33 & 0.00845431309072863 & 512.164613911503 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 4.33016949152542 & 0.0081104716367717 & 533.898604847227 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 4.33052631578947 & 0.00783772227855536 & 552.523572778043 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 4.33090909090909 & 0.00749982144466568 & 577.468293460439 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 4.33132075471698 & 0.00719335756253142 & 602.127826549018 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 4.3321568627451 & 0.00690730630786007 & 627.18470408868 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 4.33285714285714 & 0.00661759148080347 & 654.748356018355 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 4.33361702127660 & 0.00624377974956233 & 694.069489171262 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 4.33444444444444 & 0.00590801164278373 & 733.655366055126 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 4.3353488372093 & 0.00546152187351611 & 793.798676927795 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 4.33634146341463 & 0.00484838541846382 & 894.388768454917 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 4.33717948717949 & 0.00436135522816907 & 994.456828273598 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 4.3372972972973 & 0.0040760165858968 & 1064.10197453674 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 4.33714285714286 & 0.00379232813731624 & 1143.66233619546 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 4.3369696969697 & 0.00362767269509482 & 1195.52397955691 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 4.33677419354839 & 0.00338837661432016 & 1279.89733349594 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 4.33689655172414 & 0.00318182369693697 & 1363.02226798396 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 4.33666666666667 & 0.00301940542438558 & 1436.26511088657 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 4.3364 & 0.00276164202362772 & 1570.22523661617 \tabularnewline
Median & 4.33 &  &  \tabularnewline
Midrange & 4.325 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.33583333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.34 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.34 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.34 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.34 &  &  \tabularnewline
Midmean - Closest Observation & 4.3385 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.34 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.34 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39025&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]4.32986301369863[/C][C]0.00986494252237418[/C][C]438.914165376867[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.32905168770462[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.32823819694739[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.33067206654408[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]4.33[/C][C]0.00983501649552635[/C][C]440.263623550564[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]4.33[/C][C]0.00972216786242684[/C][C]445.37391878761[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]4.33[/C][C]0.00972216786242684[/C][C]445.37391878761[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]4.33[/C][C]0.00972216786242684[/C][C]445.37391878761[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]4.33[/C][C]0.00972216786242684[/C][C]445.37391878761[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]4.32917808219178[/C][C]0.00956184990161433[/C][C]452.755285508182[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]4.32821917808219[/C][C]0.00902251214935675[/C][C]479.713311152567[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]4.32821917808219[/C][C]0.00902251214935675[/C][C]479.713311152567[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]4.32821917808219[/C][C]0.00857490601444254[/C][C]504.754124510783[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]4.32547945205480[/C][C]0.00815106863760496[/C][C]530.664093797369[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]4.32698630136986[/C][C]0.00786028330979911[/C][C]550.487320981876[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]4.32698630136986[/C][C]0.00786028330979911[/C][C]550.487320981876[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]4.32698630136986[/C][C]0.00727185974295882[/C][C]595.031594986357[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]4.32698630136986[/C][C]0.00727185974295882[/C][C]595.031594986357[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]4.32698630136986[/C][C]0.00727185974295882[/C][C]595.031594986357[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]4.32917808219178[/C][C]0.00617093343891476[/C][C]701.543473940487[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]4.33616438356164[/C][C]0.00499478471153132[/C][C]868.138395144612[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]4.3386301369863[/C][C]0.0046215820744767[/C][C]938.77595746854[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]4.3386301369863[/C][C]0.00385385152231582[/C][C]1125.79068286968[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]4.3386301369863[/C][C]0.00385385152231582[/C][C]1125.79068286968[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]4.33575342465753[/C][C]0.00343961725010413[/C][C]1260.53369005702[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]4.33876712328767[/C][C]0.00302164443042298[/C][C]1435.89599080667[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]4.33876712328767[/C][C]0.00302164443042298[/C][C]1435.89599080667[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]4.34205479452055[/C][C]0.00260954010269032[/C][C]1663.91571834596[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]4.33[/C][C]0.0096560569913251[/C][C]448.423202544271[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]4.33[/C][C]0.00944314886722427[/C][C]458.533489292832[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]4.33[/C][C]0.00926029442929499[/C][C]467.587724457445[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]4.33[/C][C]0.00904050713349473[/C][C]478.955432041806[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]4.33[/C][C]0.00877551870960525[/C][C]493.418126413496[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]4.33[/C][C]0.00845431309072863[/C][C]512.164613911503[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]4.33016949152542[/C][C]0.0081104716367717[/C][C]533.898604847227[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]4.33052631578947[/C][C]0.00783772227855536[/C][C]552.523572778043[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]4.33090909090909[/C][C]0.00749982144466568[/C][C]577.468293460439[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]4.33132075471698[/C][C]0.00719335756253142[/C][C]602.127826549018[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]4.3321568627451[/C][C]0.00690730630786007[/C][C]627.18470408868[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]4.33285714285714[/C][C]0.00661759148080347[/C][C]654.748356018355[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]4.33361702127660[/C][C]0.00624377974956233[/C][C]694.069489171262[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]4.33444444444444[/C][C]0.00590801164278373[/C][C]733.655366055126[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]4.3353488372093[/C][C]0.00546152187351611[/C][C]793.798676927795[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]4.33634146341463[/C][C]0.00484838541846382[/C][C]894.388768454917[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]4.33717948717949[/C][C]0.00436135522816907[/C][C]994.456828273598[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]4.3372972972973[/C][C]0.0040760165858968[/C][C]1064.10197453674[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]4.33714285714286[/C][C]0.00379232813731624[/C][C]1143.66233619546[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]4.3369696969697[/C][C]0.00362767269509482[/C][C]1195.52397955691[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]4.33677419354839[/C][C]0.00338837661432016[/C][C]1279.89733349594[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]4.33689655172414[/C][C]0.00318182369693697[/C][C]1363.02226798396[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]4.33666666666667[/C][C]0.00301940542438558[/C][C]1436.26511088657[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]4.3364[/C][C]0.00276164202362772[/C][C]1570.22523661617[/C][/ROW]
[ROW][C]Median[/C][C]4.33[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.325[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.33583333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.34[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.34[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.34[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.34[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.3385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.34[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.34[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39025&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39025&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	4.32986301369863	0.00986494252237418	438.914165376867
Geometric Mean	4.32905168770462
Harmonic Mean	4.32823819694739
Quadratic Mean	4.33067206654408
Winsorized Mean ( 1 / 24 )	4.33	0.00983501649552635	440.263623550564
Winsorized Mean ( 2 / 24 )	4.33	0.00972216786242684	445.37391878761
Winsorized Mean ( 3 / 24 )	4.33	0.00972216786242684	445.37391878761
Winsorized Mean ( 4 / 24 )	4.33	0.00972216786242684	445.37391878761
Winsorized Mean ( 5 / 24 )	4.33	0.00972216786242684	445.37391878761
Winsorized Mean ( 6 / 24 )	4.32917808219178	0.00956184990161433	452.755285508182
Winsorized Mean ( 7 / 24 )	4.32821917808219	0.00902251214935675	479.713311152567
Winsorized Mean ( 8 / 24 )	4.32821917808219	0.00902251214935675	479.713311152567
Winsorized Mean ( 9 / 24 )	4.32821917808219	0.00857490601444254	504.754124510783
Winsorized Mean ( 10 / 24 )	4.32547945205480	0.00815106863760496	530.664093797369
Winsorized Mean ( 11 / 24 )	4.32698630136986	0.00786028330979911	550.487320981876
Winsorized Mean ( 12 / 24 )	4.32698630136986	0.00786028330979911	550.487320981876
Winsorized Mean ( 13 / 24 )	4.32698630136986	0.00727185974295882	595.031594986357
Winsorized Mean ( 14 / 24 )	4.32698630136986	0.00727185974295882	595.031594986357
Winsorized Mean ( 15 / 24 )	4.32698630136986	0.00727185974295882	595.031594986357
Winsorized Mean ( 16 / 24 )	4.32917808219178	0.00617093343891476	701.543473940487
Winsorized Mean ( 17 / 24 )	4.33616438356164	0.00499478471153132	868.138395144612
Winsorized Mean ( 18 / 24 )	4.3386301369863	0.0046215820744767	938.77595746854
Winsorized Mean ( 19 / 24 )	4.3386301369863	0.00385385152231582	1125.79068286968
Winsorized Mean ( 20 / 24 )	4.3386301369863	0.00385385152231582	1125.79068286968
Winsorized Mean ( 21 / 24 )	4.33575342465753	0.00343961725010413	1260.53369005702
Winsorized Mean ( 22 / 24 )	4.33876712328767	0.00302164443042298	1435.89599080667
Winsorized Mean ( 23 / 24 )	4.33876712328767	0.00302164443042298	1435.89599080667
Winsorized Mean ( 24 / 24 )	4.34205479452055	0.00260954010269032	1663.91571834596
Trimmed Mean ( 1 / 24 )	4.33	0.0096560569913251	448.423202544271
Trimmed Mean ( 2 / 24 )	4.33	0.00944314886722427	458.533489292832
Trimmed Mean ( 3 / 24 )	4.33	0.00926029442929499	467.587724457445
Trimmed Mean ( 4 / 24 )	4.33	0.00904050713349473	478.955432041806
Trimmed Mean ( 5 / 24 )	4.33	0.00877551870960525	493.418126413496
Trimmed Mean ( 6 / 24 )	4.33	0.00845431309072863	512.164613911503
Trimmed Mean ( 7 / 24 )	4.33016949152542	0.0081104716367717	533.898604847227
Trimmed Mean ( 8 / 24 )	4.33052631578947	0.00783772227855536	552.523572778043
Trimmed Mean ( 9 / 24 )	4.33090909090909	0.00749982144466568	577.468293460439
Trimmed Mean ( 10 / 24 )	4.33132075471698	0.00719335756253142	602.127826549018
Trimmed Mean ( 11 / 24 )	4.3321568627451	0.00690730630786007	627.18470408868
Trimmed Mean ( 12 / 24 )	4.33285714285714	0.00661759148080347	654.748356018355
Trimmed Mean ( 13 / 24 )	4.33361702127660	0.00624377974956233	694.069489171262
Trimmed Mean ( 14 / 24 )	4.33444444444444	0.00590801164278373	733.655366055126
Trimmed Mean ( 15 / 24 )	4.3353488372093	0.00546152187351611	793.798676927795
Trimmed Mean ( 16 / 24 )	4.33634146341463	0.00484838541846382	894.388768454917
Trimmed Mean ( 17 / 24 )	4.33717948717949	0.00436135522816907	994.456828273598
Trimmed Mean ( 18 / 24 )	4.3372972972973	0.0040760165858968	1064.10197453674
Trimmed Mean ( 19 / 24 )	4.33714285714286	0.00379232813731624	1143.66233619546
Trimmed Mean ( 20 / 24 )	4.3369696969697	0.00362767269509482	1195.52397955691
Trimmed Mean ( 21 / 24 )	4.33677419354839	0.00338837661432016	1279.89733349594
Trimmed Mean ( 22 / 24 )	4.33689655172414	0.00318182369693697	1363.02226798396
Trimmed Mean ( 23 / 24 )	4.33666666666667	0.00301940542438558	1436.26511088657
Trimmed Mean ( 24 / 24 )	4.3364	0.00276164202362772	1570.22523661617
Median	4.33
Midrange	4.325
Midmean - Weighted Average at Xnp	4.33583333333333
Midmean - Weighted Average at X(n+1)p	4.34
Midmean - Empirical Distribution Function	4.34
Midmean - Empirical Distribution Function - Averaging	4.34
Midmean - Empirical Distribution Function - Interpolation	4.34
Midmean - Closest Observation	4.3385
Midmean - True Basic - Statistics Graphics Toolkit	4.34
Midmean - MS Excel (old versions)	4.34
Number of observations	73

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