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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Thu, 20 Dec 2007 12:33:24 -0700

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/2007/Dec/20/t1198178286shmb19xus2sazgw.htm/, Retrieved Mon, 29 Apr 2024 12:42:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4758, Retrieved Mon, 29 Apr 2024 12:42:18 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

200

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

-       [Central Tendency] [PAPER, TIM, GIEL,...] [2007-12-20 19:33:24] [5ac545ffb613273067e3916533dda4e8] [Current]

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Summary of compuational 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 compuational 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=4758&T=0

[TABLE]
[ROW][C]Summary of compuational 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=4758&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4758&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 compuational 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	-0.109589041095890	5.43214548616753	-0.0201741726864549
Geometric Mean	NaN
Harmonic Mean	64.9326214075656
Quadratic Mean	46.0934131924077
Winsorized Mean ( 1 / 24 )	-0.109589041095890	5.42608284628349	-0.0201967135778164
Winsorized Mean ( 2 / 24 )	-0.0273972602739726	5.38261946589102	-0.00508994931697951
Winsorized Mean ( 3 / 24 )	0.136986301369863	5.26075455218458	0.0260392877126302
Winsorized Mean ( 4 / 24 )	0.136986301369863	5.23901020766782	0.0261473629445061
Winsorized Mean ( 5 / 24 )	0.136986301369863	5.23901020766782	0.0261473629445061
Winsorized Mean ( 6 / 24 )	-0.109589041095890	5.06902738967335	-0.0216193428583846
Winsorized Mean ( 7 / 24 )	-0.109589041095890	5.03290397197378	-0.0217745146154482
Winsorized Mean ( 8 / 24 )	2.3013698630137	4.53427186646554	0.507550039077744
Winsorized Mean ( 9 / 24 )	2.54794520547945	4.49297782456958	0.567094987993523
Winsorized Mean ( 10 / 24 )	0.904109589041096	4.13702536092924	0.21854098299219
Winsorized Mean ( 11 / 24 )	1.20547945205479	3.99385748422543	0.301833367068326
Winsorized Mean ( 12 / 24 )	1.53424657534247	3.94164444816837	0.389240225879685
Winsorized Mean ( 13 / 24 )	1.35616438356164	3.91579801224272	0.346331547061826
Winsorized Mean ( 14 / 24 )	1.54794520547945	3.88578572571865	0.39836092742689
Winsorized Mean ( 15 / 24 )	1.54794520547945	3.82434130458584	0.404761260095505
Winsorized Mean ( 16 / 24 )	1.32876712328767	3.72836502796883	0.356394052974895
Winsorized Mean ( 17 / 24 )	1.32876712328767	3.66007371124345	0.363043814993618
Winsorized Mean ( 18 / 24 )	2.06849315068493	3.47716670114487	0.59487891391686
Winsorized Mean ( 19 / 24 )	1.80821917808219	3.44104829509785	0.525484975220545
Winsorized Mean ( 20 / 24 )	1.26027397260274	3.21117646054426	0.392464876374043
Winsorized Mean ( 21 / 24 )	0.109589041095890	3.06180387011557	0.0357923125532381
Winsorized Mean ( 22 / 24 )	1.31506849315068	2.88318200518298	0.456117057746143
Winsorized Mean ( 23 / 24 )	1.31506849315068	2.71109372585749	0.485069358026249
Winsorized Mean ( 24 / 24 )	0.328767123287671	2.50076508799052	0.131466615903476
Trimmed Mean ( 1 / 24 )	0.169014084507042	5.30282131033028	0.0318724834604158
Trimmed Mean ( 2 / 24 )	0.463768115942029	5.1563607459556	0.0899409755816225
Trimmed Mean ( 3 / 24 )	0.73134328358209	5.00956038001978	0.145989513670499
Trimmed Mean ( 4 / 24 )	0.953846153846154	4.88976711973148	0.195069853121867
Trimmed Mean ( 5 / 24 )	1.19047619047619	4.75324866096906	0.250455272885615
Trimmed Mean ( 6 / 24 )	1.44262295081967	4.58755292640299	0.314464590155869
Trimmed Mean ( 7 / 24 )	1.76271186440678	4.43541476524058	0.397417594002885
Trimmed Mean ( 8 / 24 )	2.10526315789474	4.25809594587647	0.4944142134546
Trimmed Mean ( 9 / 24 )	2.07272727272727	4.16825057130949	0.49726551637612
Trimmed Mean ( 10 / 24 )	2	4.0651444167671	0.491987441270425
Trimmed Mean ( 11 / 24 )	2.15686274509804	4.01432460063098	0.537291564503533
Trimmed Mean ( 12 / 24 )	2.28571428571429	3.97697454487859	0.57473696648568
Trimmed Mean ( 13 / 24 )	2.38297872340426	3.93583517338011	0.605456940758457
Trimmed Mean ( 14 / 24 )	2.51111111111111	3.88348253351335	0.64661321106531
Trimmed Mean ( 15 / 24 )	2.62790697674419	3.8175475327492	0.68837570565931
Trimmed Mean ( 16 / 24 )	2.75609756097561	3.74031766092669	0.73686189538585
Trimmed Mean ( 17 / 24 )	2.92307692307692	3.65524868315984	0.799693037725144
Trimmed Mean ( 18 / 24 )	3.10810810810811	3.55264647448185	0.874871206699907
Trimmed Mean ( 19 / 24 )	3.22857142857143	3.45562158347978	0.93429542285712
Trimmed Mean ( 20 / 24 )	3.39393939393939	3.32487735987638	1.02077130269418
Trimmed Mean ( 21 / 24 )	3.64516129032258	3.20099056815424	1.13876039704311
Trimmed Mean ( 22 / 24 )	4.06896551724138	3.05690328934379	1.33107433638008
Trimmed Mean ( 23 / 24 )	4.40740740740741	2.90360776630861	1.51790729400431
Trimmed Mean ( 24 / 24 )	4.8	2.72702524129621	1.76015972544444
Median	9
Midrange	-10
Midmean - Weighted Average at Xnp	2.16666666666667
Midmean - Weighted Average at X(n+1)p	3.10810810810811
Midmean - Empirical Distribution Function	3.10810810810811
Midmean - Empirical Distribution Function - Averaging	3.10810810810811
Midmean - Empirical Distribution Function - Interpolation	3.10810810810811
Midmean - Closest Observation	2
Midmean - True Basic - Statistics Graphics Toolkit	3.10810810810811
Midmean - MS Excel (old versions)	3.10810810810811
Number of observations	73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.109589041095890 & 5.43214548616753 & -0.0201741726864549 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 64.9326214075656 &  &  \tabularnewline
Quadratic Mean & 46.0934131924077 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & -0.109589041095890 & 5.42608284628349 & -0.0201967135778164 \tabularnewline
Winsorized Mean ( 2 / 24 ) & -0.0273972602739726 & 5.38261946589102 & -0.00508994931697951 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 0.136986301369863 & 5.26075455218458 & 0.0260392877126302 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 0.136986301369863 & 5.23901020766782 & 0.0261473629445061 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 0.136986301369863 & 5.23901020766782 & 0.0261473629445061 \tabularnewline
Winsorized Mean ( 6 / 24 ) & -0.109589041095890 & 5.06902738967335 & -0.0216193428583846 \tabularnewline
Winsorized Mean ( 7 / 24 ) & -0.109589041095890 & 5.03290397197378 & -0.0217745146154482 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.3013698630137 & 4.53427186646554 & 0.507550039077744 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.54794520547945 & 4.49297782456958 & 0.567094987993523 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 0.904109589041096 & 4.13702536092924 & 0.21854098299219 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.20547945205479 & 3.99385748422543 & 0.301833367068326 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.53424657534247 & 3.94164444816837 & 0.389240225879685 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.35616438356164 & 3.91579801224272 & 0.346331547061826 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.54794520547945 & 3.88578572571865 & 0.39836092742689 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.54794520547945 & 3.82434130458584 & 0.404761260095505 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.32876712328767 & 3.72836502796883 & 0.356394052974895 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.32876712328767 & 3.66007371124345 & 0.363043814993618 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.06849315068493 & 3.47716670114487 & 0.59487891391686 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.80821917808219 & 3.44104829509785 & 0.525484975220545 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.26027397260274 & 3.21117646054426 & 0.392464876374043 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 0.109589041095890 & 3.06180387011557 & 0.0357923125532381 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.31506849315068 & 2.88318200518298 & 0.456117057746143 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.31506849315068 & 2.71109372585749 & 0.485069358026249 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 0.328767123287671 & 2.50076508799052 & 0.131466615903476 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 0.169014084507042 & 5.30282131033028 & 0.0318724834604158 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 0.463768115942029 & 5.1563607459556 & 0.0899409755816225 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 0.73134328358209 & 5.00956038001978 & 0.145989513670499 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 0.953846153846154 & 4.88976711973148 & 0.195069853121867 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.19047619047619 & 4.75324866096906 & 0.250455272885615 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.44262295081967 & 4.58755292640299 & 0.314464590155869 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.76271186440678 & 4.43541476524058 & 0.397417594002885 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.10526315789474 & 4.25809594587647 & 0.4944142134546 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.07272727272727 & 4.16825057130949 & 0.49726551637612 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2 & 4.0651444167671 & 0.491987441270425 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.15686274509804 & 4.01432460063098 & 0.537291564503533 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.28571428571429 & 3.97697454487859 & 0.57473696648568 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.38297872340426 & 3.93583517338011 & 0.605456940758457 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.51111111111111 & 3.88348253351335 & 0.64661321106531 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.62790697674419 & 3.8175475327492 & 0.68837570565931 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.75609756097561 & 3.74031766092669 & 0.73686189538585 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.92307692307692 & 3.65524868315984 & 0.799693037725144 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3.10810810810811 & 3.55264647448185 & 0.874871206699907 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 3.22857142857143 & 3.45562158347978 & 0.93429542285712 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 3.39393939393939 & 3.32487735987638 & 1.02077130269418 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 3.64516129032258 & 3.20099056815424 & 1.13876039704311 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 4.06896551724138 & 3.05690328934379 & 1.33107433638008 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 4.40740740740741 & 2.90360776630861 & 1.51790729400431 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 4.8 & 2.72702524129621 & 1.76015972544444 \tabularnewline
Median & 9 &  &  \tabularnewline
Midrange & -10 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.16666666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.10810810810811 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.10810810810811 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.10810810810811 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.10810810810811 &  &  \tabularnewline
Midmean - Closest Observation & 2 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.10810810810811 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.10810810810811 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4758&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]-0.109589041095890[/C][C]5.43214548616753[/C][C]-0.0201741726864549[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]64.9326214075656[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]46.0934131924077[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]-0.109589041095890[/C][C]5.42608284628349[/C][C]-0.0201967135778164[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]-0.0273972602739726[/C][C]5.38261946589102[/C][C]-0.00508994931697951[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]0.136986301369863[/C][C]5.26075455218458[/C][C]0.0260392877126302[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]0.136986301369863[/C][C]5.23901020766782[/C][C]0.0261473629445061[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]0.136986301369863[/C][C]5.23901020766782[/C][C]0.0261473629445061[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]-0.109589041095890[/C][C]5.06902738967335[/C][C]-0.0216193428583846[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]-0.109589041095890[/C][C]5.03290397197378[/C][C]-0.0217745146154482[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.3013698630137[/C][C]4.53427186646554[/C][C]0.507550039077744[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.54794520547945[/C][C]4.49297782456958[/C][C]0.567094987993523[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]0.904109589041096[/C][C]4.13702536092924[/C][C]0.21854098299219[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.20547945205479[/C][C]3.99385748422543[/C][C]0.301833367068326[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.53424657534247[/C][C]3.94164444816837[/C][C]0.389240225879685[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.35616438356164[/C][C]3.91579801224272[/C][C]0.346331547061826[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.54794520547945[/C][C]3.88578572571865[/C][C]0.39836092742689[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.54794520547945[/C][C]3.82434130458584[/C][C]0.404761260095505[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.32876712328767[/C][C]3.72836502796883[/C][C]0.356394052974895[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.32876712328767[/C][C]3.66007371124345[/C][C]0.363043814993618[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.06849315068493[/C][C]3.47716670114487[/C][C]0.59487891391686[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.80821917808219[/C][C]3.44104829509785[/C][C]0.525484975220545[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.26027397260274[/C][C]3.21117646054426[/C][C]0.392464876374043[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]0.109589041095890[/C][C]3.06180387011557[/C][C]0.0357923125532381[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.31506849315068[/C][C]2.88318200518298[/C][C]0.456117057746143[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.31506849315068[/C][C]2.71109372585749[/C][C]0.485069358026249[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]0.328767123287671[/C][C]2.50076508799052[/C][C]0.131466615903476[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]0.169014084507042[/C][C]5.30282131033028[/C][C]0.0318724834604158[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]0.463768115942029[/C][C]5.1563607459556[/C][C]0.0899409755816225[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]0.73134328358209[/C][C]5.00956038001978[/C][C]0.145989513670499[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]0.953846153846154[/C][C]4.88976711973148[/C][C]0.195069853121867[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.19047619047619[/C][C]4.75324866096906[/C][C]0.250455272885615[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.44262295081967[/C][C]4.58755292640299[/C][C]0.314464590155869[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.76271186440678[/C][C]4.43541476524058[/C][C]0.397417594002885[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.10526315789474[/C][C]4.25809594587647[/C][C]0.4944142134546[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.07272727272727[/C][C]4.16825057130949[/C][C]0.49726551637612[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2[/C][C]4.0651444167671[/C][C]0.491987441270425[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.15686274509804[/C][C]4.01432460063098[/C][C]0.537291564503533[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.28571428571429[/C][C]3.97697454487859[/C][C]0.57473696648568[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.38297872340426[/C][C]3.93583517338011[/C][C]0.605456940758457[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.51111111111111[/C][C]3.88348253351335[/C][C]0.64661321106531[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.62790697674419[/C][C]3.8175475327492[/C][C]0.68837570565931[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.75609756097561[/C][C]3.74031766092669[/C][C]0.73686189538585[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.92307692307692[/C][C]3.65524868315984[/C][C]0.799693037725144[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3.10810810810811[/C][C]3.55264647448185[/C][C]0.874871206699907[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]3.22857142857143[/C][C]3.45562158347978[/C][C]0.93429542285712[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]3.39393939393939[/C][C]3.32487735987638[/C][C]1.02077130269418[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]3.64516129032258[/C][C]3.20099056815424[/C][C]1.13876039704311[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]4.06896551724138[/C][C]3.05690328934379[/C][C]1.33107433638008[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]4.40740740740741[/C][C]2.90360776630861[/C][C]1.51790729400431[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]4.8[/C][C]2.72702524129621[/C][C]1.76015972544444[/C][/ROW]
[ROW][C]Median[/C][C]9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-10[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.16666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.10810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.10810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.10810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.10810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.10810810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.10810810810811[/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=4758&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4758&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	-0.109589041095890	5.43214548616753	-0.0201741726864549
Geometric Mean	NaN
Harmonic Mean	64.9326214075656
Quadratic Mean	46.0934131924077
Winsorized Mean ( 1 / 24 )	-0.109589041095890	5.42608284628349	-0.0201967135778164
Winsorized Mean ( 2 / 24 )	-0.0273972602739726	5.38261946589102	-0.00508994931697951
Winsorized Mean ( 3 / 24 )	0.136986301369863	5.26075455218458	0.0260392877126302
Winsorized Mean ( 4 / 24 )	0.136986301369863	5.23901020766782	0.0261473629445061
Winsorized Mean ( 5 / 24 )	0.136986301369863	5.23901020766782	0.0261473629445061
Winsorized Mean ( 6 / 24 )	-0.109589041095890	5.06902738967335	-0.0216193428583846
Winsorized Mean ( 7 / 24 )	-0.109589041095890	5.03290397197378	-0.0217745146154482
Winsorized Mean ( 8 / 24 )	2.3013698630137	4.53427186646554	0.507550039077744
Winsorized Mean ( 9 / 24 )	2.54794520547945	4.49297782456958	0.567094987993523
Winsorized Mean ( 10 / 24 )	0.904109589041096	4.13702536092924	0.21854098299219
Winsorized Mean ( 11 / 24 )	1.20547945205479	3.99385748422543	0.301833367068326
Winsorized Mean ( 12 / 24 )	1.53424657534247	3.94164444816837	0.389240225879685
Winsorized Mean ( 13 / 24 )	1.35616438356164	3.91579801224272	0.346331547061826
Winsorized Mean ( 14 / 24 )	1.54794520547945	3.88578572571865	0.39836092742689
Winsorized Mean ( 15 / 24 )	1.54794520547945	3.82434130458584	0.404761260095505
Winsorized Mean ( 16 / 24 )	1.32876712328767	3.72836502796883	0.356394052974895
Winsorized Mean ( 17 / 24 )	1.32876712328767	3.66007371124345	0.363043814993618
Winsorized Mean ( 18 / 24 )	2.06849315068493	3.47716670114487	0.59487891391686
Winsorized Mean ( 19 / 24 )	1.80821917808219	3.44104829509785	0.525484975220545
Winsorized Mean ( 20 / 24 )	1.26027397260274	3.21117646054426	0.392464876374043
Winsorized Mean ( 21 / 24 )	0.109589041095890	3.06180387011557	0.0357923125532381
Winsorized Mean ( 22 / 24 )	1.31506849315068	2.88318200518298	0.456117057746143
Winsorized Mean ( 23 / 24 )	1.31506849315068	2.71109372585749	0.485069358026249
Winsorized Mean ( 24 / 24 )	0.328767123287671	2.50076508799052	0.131466615903476
Trimmed Mean ( 1 / 24 )	0.169014084507042	5.30282131033028	0.0318724834604158
Trimmed Mean ( 2 / 24 )	0.463768115942029	5.1563607459556	0.0899409755816225
Trimmed Mean ( 3 / 24 )	0.73134328358209	5.00956038001978	0.145989513670499
Trimmed Mean ( 4 / 24 )	0.953846153846154	4.88976711973148	0.195069853121867
Trimmed Mean ( 5 / 24 )	1.19047619047619	4.75324866096906	0.250455272885615
Trimmed Mean ( 6 / 24 )	1.44262295081967	4.58755292640299	0.314464590155869
Trimmed Mean ( 7 / 24 )	1.76271186440678	4.43541476524058	0.397417594002885
Trimmed Mean ( 8 / 24 )	2.10526315789474	4.25809594587647	0.4944142134546
Trimmed Mean ( 9 / 24 )	2.07272727272727	4.16825057130949	0.49726551637612
Trimmed Mean ( 10 / 24 )	2	4.0651444167671	0.491987441270425
Trimmed Mean ( 11 / 24 )	2.15686274509804	4.01432460063098	0.537291564503533
Trimmed Mean ( 12 / 24 )	2.28571428571429	3.97697454487859	0.57473696648568
Trimmed Mean ( 13 / 24 )	2.38297872340426	3.93583517338011	0.605456940758457
Trimmed Mean ( 14 / 24 )	2.51111111111111	3.88348253351335	0.64661321106531
Trimmed Mean ( 15 / 24 )	2.62790697674419	3.8175475327492	0.68837570565931
Trimmed Mean ( 16 / 24 )	2.75609756097561	3.74031766092669	0.73686189538585
Trimmed Mean ( 17 / 24 )	2.92307692307692	3.65524868315984	0.799693037725144
Trimmed Mean ( 18 / 24 )	3.10810810810811	3.55264647448185	0.874871206699907
Trimmed Mean ( 19 / 24 )	3.22857142857143	3.45562158347978	0.93429542285712
Trimmed Mean ( 20 / 24 )	3.39393939393939	3.32487735987638	1.02077130269418
Trimmed Mean ( 21 / 24 )	3.64516129032258	3.20099056815424	1.13876039704311
Trimmed Mean ( 22 / 24 )	4.06896551724138	3.05690328934379	1.33107433638008
Trimmed Mean ( 23 / 24 )	4.40740740740741	2.90360776630861	1.51790729400431
Trimmed Mean ( 24 / 24 )	4.8	2.72702524129621	1.76015972544444
Median	9
Midrange	-10
Midmean - Weighted Average at Xnp	2.16666666666667
Midmean - Weighted Average at X(n+1)p	3.10810810810811
Midmean - Empirical Distribution Function	3.10810810810811
Midmean - Empirical Distribution Function - Averaging	3.10810810810811
Midmean - Empirical Distribution Function - Interpolation	3.10810810810811
Midmean - Closest Observation	2
Midmean - True Basic - Statistics Graphics Toolkit	3.10810810810811
Midmean - MS Excel (old versions)	3.10810810810811
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