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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Fri, 16 Oct 2009 10:17:52 -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/Oct/16/t125570992385p3vomdffn9ryi.htm/, Retrieved Tue, 30 Apr 2024 00:34:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47061, Retrieved Tue, 30 Apr 2024 00:34:06 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

143

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

-     [Univariate Data Series] [Inflatie] [2009-10-11 21:52:09] [badc6a9acdc45286bea7f74742e15a21]
-    D  [Univariate Data Series] [Inflatie] [2009-10-11 22:00:34] [badc6a9acdc45286bea7f74742e15a21]
-         [Univariate Data Series] [Inflatie] [2009-10-12 20:15:52] [badc6a9acdc45286bea7f74742e15a21]
-   PD      [Univariate Data Series] [ws 3 part 2] [2009-10-16 15:38:58] [badc6a9acdc45286bea7f74742e15a21]
- RM D          [Central Tendency] [ws 3 part 3] [2009-10-16 16:17:52] [0545e25c765ce26b196961216dc11e13] [Current]
- RM              [Percentiles] [ws 3 part 3] [2009-10-16 16:24:56] [badc6a9acdc45286bea7f74742e15a21] 

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Dataseries X:

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Histogram

Boxplots

-0.6
-0.8
-1
-0.3
0.4
0
0.1
0
-0.2
0.7
0.3
-0.1
0
0.3
0.8
0.4
0.3
0.7
0.7
0.9
1
0.2
0.3
0.59
0.55
0.55
-0.25
0.1
0.3
-0.14
-0.35
-0.63
-1.1
-1.47
-1.25
-1.29
-1.8
-1.7
-1.85
-1.95
-2.45
-2.6
-2.7
-2.8
-2.6
-1.8
-1.1
-0.9
-0.5
-0.4
0.4
0.1
1.1
1.8
1.72
1.15
1.25
0.83
-0.22
-0.05
-0.21
-0.1
-1.06
-0.61
-1.29
-2
-2.7
-1.7
-2

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47061&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47061&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47061&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	-0.420724637681159	0.137805742978944	-3.05302688107451
Geometric Mean	NaN
Harmonic Mean	0
Quadratic Mean	1.21175821475016
Winsorized Mean ( 1 / 23 )	-0.420434782608696	0.137174233918370	-3.06496905868554
Winsorized Mean ( 2 / 23 )	-0.434057971014493	0.134352401264417	-3.23074218941744
Winsorized Mean ( 3 / 23 )	-0.434057971014493	0.132507510578782	-3.27572353535708
Winsorized Mean ( 4 / 23 )	-0.436956521739131	0.132004563515471	-3.31016224062527
Winsorized Mean ( 5 / 23 )	-0.433333333333333	0.128220768604633	-3.3795877068052
Winsorized Mean ( 6 / 23 )	-0.402898550724638	0.118368617648616	-3.4037615605233
Winsorized Mean ( 7 / 23 )	-0.41	0.117241489765446	-3.49705552889381
Winsorized Mean ( 8 / 23 )	-0.40768115942029	0.115556613769306	-3.52797772556900
Winsorized Mean ( 9 / 23 )	-0.40768115942029	0.111070729469594	-3.67046440918436
Winsorized Mean ( 10 / 23 )	-0.400434782608696	0.109698967065409	-3.65030586267901
Winsorized Mean ( 11 / 23 )	-0.400434782608696	0.109698967065409	-3.65030586267901
Winsorized Mean ( 12 / 23 )	-0.402173913043478	0.103707666219128	-3.87795741342507
Winsorized Mean ( 13 / 23 )	-0.409710144927536	0.102659430625101	-3.99096451668181
Winsorized Mean ( 14 / 23 )	-0.363043478260870	0.0943068905973701	-3.84959652429675
Winsorized Mean ( 15 / 23 )	-0.356521739130435	0.0831805486247881	-4.28611911107533
Winsorized Mean ( 16 / 23 )	-0.356521739130435	0.0831805486247881	-4.28611911107533
Winsorized Mean ( 17 / 23 )	-0.346666666666667	0.0815646926718341	-4.25020502512575
Winsorized Mean ( 18 / 23 )	-0.333623188405797	0.0718501599322416	-4.64331866095247
Winsorized Mean ( 19 / 23 )	-0.333623188405797	0.0718501599322416	-4.64331866095247
Winsorized Mean ( 20 / 23 )	-0.322028985507246	0.0700424848878485	-4.59762365688306
Winsorized Mean ( 21 / 23 )	-0.303768115942029	0.0672369369348047	-4.51787558729175
Winsorized Mean ( 22 / 23 )	-0.271884057971014	0.0624487088300506	-4.35371784404584
Winsorized Mean ( 23 / 23 )	-0.271884057971015	0.0531169451492782	-5.11859364665871
Trimmed Mean ( 1 / 23 )	-0.418358208955224	0.133245775810594	-3.13974838159156
Trimmed Mean ( 2 / 23 )	-0.416153846153846	0.128537762392795	-3.23759989599112
Trimmed Mean ( 3 / 23 )	-0.406349206349206	0.124694465629772	-3.25875895371083
Trimmed Mean ( 4 / 23 )	-0.395901639344262	0.120894068485750	-3.27478133793577
Trimmed Mean ( 5 / 23 )	-0.383898305084746	0.116429447749622	-3.29726123849964
Trimmed Mean ( 6 / 23 )	-0.371929824561403	0.112217185198683	-3.31437492308236
Trimmed Mean ( 7 / 23 )	-0.365454545454545	0.109981883473499	-3.32286131054124
Trimmed Mean ( 8 / 23 )	-0.357169811320755	0.107452145273318	-3.32398958077802
Trimmed Mean ( 9 / 23 )	-0.348627450980392	0.104676539914435	-3.33052134953418
Trimmed Mean ( 10 / 23 )	-0.339387755102041	0.102234560966730	-3.31969689988191
Trimmed Mean ( 11 / 23 )	-0.339387755102041	0.0994094297913163	-3.41403985330663
Trimmed Mean ( 12 / 23 )	-0.320666666666667	0.0957154874900324	-3.35020669147258
Trimmed Mean ( 13 / 23 )	-0.309767441860465	0.0923505577235985	-3.35425631957293
Trimmed Mean ( 14 / 23 )	-0.296829268292683	0.088082167171943	-3.36991331869991
Trimmed Mean ( 15 / 23 )	-0.288461538461538	0.0846828954089106	-3.40637311783727
Trimmed Mean ( 16 / 23 )	-0.28	0.082872600223885	-3.37868003711195
Trimmed Mean ( 17 / 23 )	-0.270571428571429	0.0802432675854935	-3.3718894645355
Trimmed Mean ( 18 / 23 )	-0.261212121212121	0.07693557612832	-3.3952058898792
Trimmed Mean ( 19 / 23 )	-0.252258064516129	0.0749877548102891	-3.3639900961739
Trimmed Mean ( 20 / 23 )	-0.242068965517241	0.0719441136936082	-3.36468062624486
Trimmed Mean ( 21 / 23 )	-0.231851851851852	0.0679073380663564	-3.41423855585821
Trimmed Mean ( 22 / 23 )	-0.231851851851852	0.0627436052518502	-3.6952268031333
Trimmed Mean ( 23 / 23 )	-0.215652173913043	0.056738865415158	-3.80078403639406
Median	-0.2
Midrange	-0.5
Midmean - Weighted Average at Xnp	-0.290294117647059
Midmean - Weighted Average at X(n+1)p	-0.234324324324324
Midmean - Empirical Distribution Function	-0.234324324324324
Midmean - Empirical Distribution Function - Averaging	-0.234324324324324
Midmean - Empirical Distribution Function - Interpolation	-0.234324324324324
Midmean - Closest Observation	-0.288461538461538
Midmean - True Basic - Statistics Graphics Toolkit	-0.234324324324324
Midmean - MS Excel (old versions)	-0.234324324324324
Number of observations	69

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.420724637681159 & 0.137805742978944 & -3.05302688107451 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 1.21175821475016 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & -0.420434782608696 & 0.137174233918370 & -3.06496905868554 \tabularnewline
Winsorized Mean ( 2 / 23 ) & -0.434057971014493 & 0.134352401264417 & -3.23074218941744 \tabularnewline
Winsorized Mean ( 3 / 23 ) & -0.434057971014493 & 0.132507510578782 & -3.27572353535708 \tabularnewline
Winsorized Mean ( 4 / 23 ) & -0.436956521739131 & 0.132004563515471 & -3.31016224062527 \tabularnewline
Winsorized Mean ( 5 / 23 ) & -0.433333333333333 & 0.128220768604633 & -3.3795877068052 \tabularnewline
Winsorized Mean ( 6 / 23 ) & -0.402898550724638 & 0.118368617648616 & -3.4037615605233 \tabularnewline
Winsorized Mean ( 7 / 23 ) & -0.41 & 0.117241489765446 & -3.49705552889381 \tabularnewline
Winsorized Mean ( 8 / 23 ) & -0.40768115942029 & 0.115556613769306 & -3.52797772556900 \tabularnewline
Winsorized Mean ( 9 / 23 ) & -0.40768115942029 & 0.111070729469594 & -3.67046440918436 \tabularnewline
Winsorized Mean ( 10 / 23 ) & -0.400434782608696 & 0.109698967065409 & -3.65030586267901 \tabularnewline
Winsorized Mean ( 11 / 23 ) & -0.400434782608696 & 0.109698967065409 & -3.65030586267901 \tabularnewline
Winsorized Mean ( 12 / 23 ) & -0.402173913043478 & 0.103707666219128 & -3.87795741342507 \tabularnewline
Winsorized Mean ( 13 / 23 ) & -0.409710144927536 & 0.102659430625101 & -3.99096451668181 \tabularnewline
Winsorized Mean ( 14 / 23 ) & -0.363043478260870 & 0.0943068905973701 & -3.84959652429675 \tabularnewline
Winsorized Mean ( 15 / 23 ) & -0.356521739130435 & 0.0831805486247881 & -4.28611911107533 \tabularnewline
Winsorized Mean ( 16 / 23 ) & -0.356521739130435 & 0.0831805486247881 & -4.28611911107533 \tabularnewline
Winsorized Mean ( 17 / 23 ) & -0.346666666666667 & 0.0815646926718341 & -4.25020502512575 \tabularnewline
Winsorized Mean ( 18 / 23 ) & -0.333623188405797 & 0.0718501599322416 & -4.64331866095247 \tabularnewline
Winsorized Mean ( 19 / 23 ) & -0.333623188405797 & 0.0718501599322416 & -4.64331866095247 \tabularnewline
Winsorized Mean ( 20 / 23 ) & -0.322028985507246 & 0.0700424848878485 & -4.59762365688306 \tabularnewline
Winsorized Mean ( 21 / 23 ) & -0.303768115942029 & 0.0672369369348047 & -4.51787558729175 \tabularnewline
Winsorized Mean ( 22 / 23 ) & -0.271884057971014 & 0.0624487088300506 & -4.35371784404584 \tabularnewline
Winsorized Mean ( 23 / 23 ) & -0.271884057971015 & 0.0531169451492782 & -5.11859364665871 \tabularnewline
Trimmed Mean ( 1 / 23 ) & -0.418358208955224 & 0.133245775810594 & -3.13974838159156 \tabularnewline
Trimmed Mean ( 2 / 23 ) & -0.416153846153846 & 0.128537762392795 & -3.23759989599112 \tabularnewline
Trimmed Mean ( 3 / 23 ) & -0.406349206349206 & 0.124694465629772 & -3.25875895371083 \tabularnewline
Trimmed Mean ( 4 / 23 ) & -0.395901639344262 & 0.120894068485750 & -3.27478133793577 \tabularnewline
Trimmed Mean ( 5 / 23 ) & -0.383898305084746 & 0.116429447749622 & -3.29726123849964 \tabularnewline
Trimmed Mean ( 6 / 23 ) & -0.371929824561403 & 0.112217185198683 & -3.31437492308236 \tabularnewline
Trimmed Mean ( 7 / 23 ) & -0.365454545454545 & 0.109981883473499 & -3.32286131054124 \tabularnewline
Trimmed Mean ( 8 / 23 ) & -0.357169811320755 & 0.107452145273318 & -3.32398958077802 \tabularnewline
Trimmed Mean ( 9 / 23 ) & -0.348627450980392 & 0.104676539914435 & -3.33052134953418 \tabularnewline
Trimmed Mean ( 10 / 23 ) & -0.339387755102041 & 0.102234560966730 & -3.31969689988191 \tabularnewline
Trimmed Mean ( 11 / 23 ) & -0.339387755102041 & 0.0994094297913163 & -3.41403985330663 \tabularnewline
Trimmed Mean ( 12 / 23 ) & -0.320666666666667 & 0.0957154874900324 & -3.35020669147258 \tabularnewline
Trimmed Mean ( 13 / 23 ) & -0.309767441860465 & 0.0923505577235985 & -3.35425631957293 \tabularnewline
Trimmed Mean ( 14 / 23 ) & -0.296829268292683 & 0.088082167171943 & -3.36991331869991 \tabularnewline
Trimmed Mean ( 15 / 23 ) & -0.288461538461538 & 0.0846828954089106 & -3.40637311783727 \tabularnewline
Trimmed Mean ( 16 / 23 ) & -0.28 & 0.082872600223885 & -3.37868003711195 \tabularnewline
Trimmed Mean ( 17 / 23 ) & -0.270571428571429 & 0.0802432675854935 & -3.3718894645355 \tabularnewline
Trimmed Mean ( 18 / 23 ) & -0.261212121212121 & 0.07693557612832 & -3.3952058898792 \tabularnewline
Trimmed Mean ( 19 / 23 ) & -0.252258064516129 & 0.0749877548102891 & -3.3639900961739 \tabularnewline
Trimmed Mean ( 20 / 23 ) & -0.242068965517241 & 0.0719441136936082 & -3.36468062624486 \tabularnewline
Trimmed Mean ( 21 / 23 ) & -0.231851851851852 & 0.0679073380663564 & -3.41423855585821 \tabularnewline
Trimmed Mean ( 22 / 23 ) & -0.231851851851852 & 0.0627436052518502 & -3.6952268031333 \tabularnewline
Trimmed Mean ( 23 / 23 ) & -0.215652173913043 & 0.056738865415158 & -3.80078403639406 \tabularnewline
Median & -0.2 &  &  \tabularnewline
Midrange & -0.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.290294117647059 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -0.234324324324324 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.234324324324324 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -0.234324324324324 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -0.234324324324324 &  &  \tabularnewline
Midmean - Closest Observation & -0.288461538461538 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -0.234324324324324 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -0.234324324324324 &  &  \tabularnewline
Number of observations & 69 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47061&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]-0.420724637681159[/C][C]0.137805742978944[/C][C]-3.05302688107451[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.21175821475016[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]-0.420434782608696[/C][C]0.137174233918370[/C][C]-3.06496905868554[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]-0.434057971014493[/C][C]0.134352401264417[/C][C]-3.23074218941744[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]-0.434057971014493[/C][C]0.132507510578782[/C][C]-3.27572353535708[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]-0.436956521739131[/C][C]0.132004563515471[/C][C]-3.31016224062527[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]-0.433333333333333[/C][C]0.128220768604633[/C][C]-3.3795877068052[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]-0.402898550724638[/C][C]0.118368617648616[/C][C]-3.4037615605233[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]-0.41[/C][C]0.117241489765446[/C][C]-3.49705552889381[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]-0.40768115942029[/C][C]0.115556613769306[/C][C]-3.52797772556900[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]-0.40768115942029[/C][C]0.111070729469594[/C][C]-3.67046440918436[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]-0.400434782608696[/C][C]0.109698967065409[/C][C]-3.65030586267901[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]-0.400434782608696[/C][C]0.109698967065409[/C][C]-3.65030586267901[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]-0.402173913043478[/C][C]0.103707666219128[/C][C]-3.87795741342507[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]-0.409710144927536[/C][C]0.102659430625101[/C][C]-3.99096451668181[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]-0.363043478260870[/C][C]0.0943068905973701[/C][C]-3.84959652429675[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]-0.356521739130435[/C][C]0.0831805486247881[/C][C]-4.28611911107533[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]-0.356521739130435[/C][C]0.0831805486247881[/C][C]-4.28611911107533[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]-0.346666666666667[/C][C]0.0815646926718341[/C][C]-4.25020502512575[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]-0.333623188405797[/C][C]0.0718501599322416[/C][C]-4.64331866095247[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]-0.333623188405797[/C][C]0.0718501599322416[/C][C]-4.64331866095247[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]-0.322028985507246[/C][C]0.0700424848878485[/C][C]-4.59762365688306[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]-0.303768115942029[/C][C]0.0672369369348047[/C][C]-4.51787558729175[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]-0.271884057971014[/C][C]0.0624487088300506[/C][C]-4.35371784404584[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]-0.271884057971015[/C][C]0.0531169451492782[/C][C]-5.11859364665871[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]-0.418358208955224[/C][C]0.133245775810594[/C][C]-3.13974838159156[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]-0.416153846153846[/C][C]0.128537762392795[/C][C]-3.23759989599112[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]-0.406349206349206[/C][C]0.124694465629772[/C][C]-3.25875895371083[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]-0.395901639344262[/C][C]0.120894068485750[/C][C]-3.27478133793577[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]-0.383898305084746[/C][C]0.116429447749622[/C][C]-3.29726123849964[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]-0.371929824561403[/C][C]0.112217185198683[/C][C]-3.31437492308236[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]-0.365454545454545[/C][C]0.109981883473499[/C][C]-3.32286131054124[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]-0.357169811320755[/C][C]0.107452145273318[/C][C]-3.32398958077802[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]-0.348627450980392[/C][C]0.104676539914435[/C][C]-3.33052134953418[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]-0.339387755102041[/C][C]0.102234560966730[/C][C]-3.31969689988191[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]-0.339387755102041[/C][C]0.0994094297913163[/C][C]-3.41403985330663[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]-0.320666666666667[/C][C]0.0957154874900324[/C][C]-3.35020669147258[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]-0.309767441860465[/C][C]0.0923505577235985[/C][C]-3.35425631957293[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]-0.296829268292683[/C][C]0.088082167171943[/C][C]-3.36991331869991[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]-0.288461538461538[/C][C]0.0846828954089106[/C][C]-3.40637311783727[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]-0.28[/C][C]0.082872600223885[/C][C]-3.37868003711195[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]-0.270571428571429[/C][C]0.0802432675854935[/C][C]-3.3718894645355[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]-0.261212121212121[/C][C]0.07693557612832[/C][C]-3.3952058898792[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]-0.252258064516129[/C][C]0.0749877548102891[/C][C]-3.3639900961739[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]-0.242068965517241[/C][C]0.0719441136936082[/C][C]-3.36468062624486[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]-0.231851851851852[/C][C]0.0679073380663564[/C][C]-3.41423855585821[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]-0.231851851851852[/C][C]0.0627436052518502[/C][C]-3.6952268031333[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]-0.215652173913043[/C][C]0.056738865415158[/C][C]-3.80078403639406[/C][/ROW]
[ROW][C]Median[/C][C]-0.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.290294117647059[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-0.234324324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.234324324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-0.234324324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-0.234324324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.288461538461538[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-0.234324324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-0.234324324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]69[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47061&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47061&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	-0.420724637681159	0.137805742978944	-3.05302688107451
Geometric Mean	NaN
Harmonic Mean	0
Quadratic Mean	1.21175821475016
Winsorized Mean ( 1 / 23 )	-0.420434782608696	0.137174233918370	-3.06496905868554
Winsorized Mean ( 2 / 23 )	-0.434057971014493	0.134352401264417	-3.23074218941744
Winsorized Mean ( 3 / 23 )	-0.434057971014493	0.132507510578782	-3.27572353535708
Winsorized Mean ( 4 / 23 )	-0.436956521739131	0.132004563515471	-3.31016224062527
Winsorized Mean ( 5 / 23 )	-0.433333333333333	0.128220768604633	-3.3795877068052
Winsorized Mean ( 6 / 23 )	-0.402898550724638	0.118368617648616	-3.4037615605233
Winsorized Mean ( 7 / 23 )	-0.41	0.117241489765446	-3.49705552889381
Winsorized Mean ( 8 / 23 )	-0.40768115942029	0.115556613769306	-3.52797772556900
Winsorized Mean ( 9 / 23 )	-0.40768115942029	0.111070729469594	-3.67046440918436
Winsorized Mean ( 10 / 23 )	-0.400434782608696	0.109698967065409	-3.65030586267901
Winsorized Mean ( 11 / 23 )	-0.400434782608696	0.109698967065409	-3.65030586267901
Winsorized Mean ( 12 / 23 )	-0.402173913043478	0.103707666219128	-3.87795741342507
Winsorized Mean ( 13 / 23 )	-0.409710144927536	0.102659430625101	-3.99096451668181
Winsorized Mean ( 14 / 23 )	-0.363043478260870	0.0943068905973701	-3.84959652429675
Winsorized Mean ( 15 / 23 )	-0.356521739130435	0.0831805486247881	-4.28611911107533
Winsorized Mean ( 16 / 23 )	-0.356521739130435	0.0831805486247881	-4.28611911107533
Winsorized Mean ( 17 / 23 )	-0.346666666666667	0.0815646926718341	-4.25020502512575
Winsorized Mean ( 18 / 23 )	-0.333623188405797	0.0718501599322416	-4.64331866095247
Winsorized Mean ( 19 / 23 )	-0.333623188405797	0.0718501599322416	-4.64331866095247
Winsorized Mean ( 20 / 23 )	-0.322028985507246	0.0700424848878485	-4.59762365688306
Winsorized Mean ( 21 / 23 )	-0.303768115942029	0.0672369369348047	-4.51787558729175
Winsorized Mean ( 22 / 23 )	-0.271884057971014	0.0624487088300506	-4.35371784404584
Winsorized Mean ( 23 / 23 )	-0.271884057971015	0.0531169451492782	-5.11859364665871
Trimmed Mean ( 1 / 23 )	-0.418358208955224	0.133245775810594	-3.13974838159156
Trimmed Mean ( 2 / 23 )	-0.416153846153846	0.128537762392795	-3.23759989599112
Trimmed Mean ( 3 / 23 )	-0.406349206349206	0.124694465629772	-3.25875895371083
Trimmed Mean ( 4 / 23 )	-0.395901639344262	0.120894068485750	-3.27478133793577
Trimmed Mean ( 5 / 23 )	-0.383898305084746	0.116429447749622	-3.29726123849964
Trimmed Mean ( 6 / 23 )	-0.371929824561403	0.112217185198683	-3.31437492308236
Trimmed Mean ( 7 / 23 )	-0.365454545454545	0.109981883473499	-3.32286131054124
Trimmed Mean ( 8 / 23 )	-0.357169811320755	0.107452145273318	-3.32398958077802
Trimmed Mean ( 9 / 23 )	-0.348627450980392	0.104676539914435	-3.33052134953418
Trimmed Mean ( 10 / 23 )	-0.339387755102041	0.102234560966730	-3.31969689988191
Trimmed Mean ( 11 / 23 )	-0.339387755102041	0.0994094297913163	-3.41403985330663
Trimmed Mean ( 12 / 23 )	-0.320666666666667	0.0957154874900324	-3.35020669147258
Trimmed Mean ( 13 / 23 )	-0.309767441860465	0.0923505577235985	-3.35425631957293
Trimmed Mean ( 14 / 23 )	-0.296829268292683	0.088082167171943	-3.36991331869991
Trimmed Mean ( 15 / 23 )	-0.288461538461538	0.0846828954089106	-3.40637311783727
Trimmed Mean ( 16 / 23 )	-0.28	0.082872600223885	-3.37868003711195
Trimmed Mean ( 17 / 23 )	-0.270571428571429	0.0802432675854935	-3.3718894645355
Trimmed Mean ( 18 / 23 )	-0.261212121212121	0.07693557612832	-3.3952058898792
Trimmed Mean ( 19 / 23 )	-0.252258064516129	0.0749877548102891	-3.3639900961739
Trimmed Mean ( 20 / 23 )	-0.242068965517241	0.0719441136936082	-3.36468062624486
Trimmed Mean ( 21 / 23 )	-0.231851851851852	0.0679073380663564	-3.41423855585821
Trimmed Mean ( 22 / 23 )	-0.231851851851852	0.0627436052518502	-3.6952268031333
Trimmed Mean ( 23 / 23 )	-0.215652173913043	0.056738865415158	-3.80078403639406
Median	-0.2
Midrange	-0.5
Midmean - Weighted Average at Xnp	-0.290294117647059
Midmean - Weighted Average at X(n+1)p	-0.234324324324324
Midmean - Empirical Distribution Function	-0.234324324324324
Midmean - Empirical Distribution Function - Averaging	-0.234324324324324
Midmean - Empirical Distribution Function - Interpolation	-0.234324324324324
Midmean - Closest Observation	-0.288461538461538
Midmean - True Basic - Statistics Graphics Toolkit	-0.234324324324324
Midmean - MS Excel (old versions)	-0.234324324324324
Number of observations	69

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 0.01 ; par2 = 0.99 ; par3 = 0.005 ;

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