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*The author of this computation has been verified*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Fri, 23 Oct 2009 08:17:25 -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/23/t1256307516cmbzdu2076dpoi8.htm/, Retrieved Thu, 02 May 2024 12:06:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49986, Retrieved Thu, 02 May 2024 12:06:11 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

129

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

-       [Central Tendency] [workshop 3 review] [2009-10-23 14:17:25] [6198946fb53eb5eb18db46bb758f7fde] [Current]

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-1,6
-1,8
-1
-0,9
-2
-0,4
-0,4
-0,2
-0,5
-0,8
0,3
-1,3
-1,6
-0,4
0,2
0,6
-0,1
0,4
0,9
0,2
0,5
0,6
0,5
0,3
-0,3
0,6
0,6
0,9
-0,7
1,2
0,8
0,7
0,1
-0,4
0
-0,6
-1
0,2
0,9
1,1
-0,6
1,2
0,3
0,7
0,9
0,7
0,2
0,3
-0,2
0,8
1,2
1,2
-0,5
1,4
0,4
1,1
1
0,7
0,7
0,4
0
0,9
1,1
1,7
-0,2
1,6
1,3
1,3
1
0,7
0,4
0,3

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=49986&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=49986&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49986&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	0.244444444444444	0.0983209765628508	2.48618812576771
Geometric Mean	NaN
Harmonic Mean	0
Quadratic Mean	0.863777234656663
Winsorized Mean ( 1 / 24 )	0.245833333333333	0.097181273513742	2.52963687802024
Winsorized Mean ( 2 / 24 )	0.245833333333333	0.0945696433806287	2.59949519259464
Winsorized Mean ( 3 / 24 )	0.241666666666667	0.0938806470996206	2.57419046558365
Winsorized Mean ( 4 / 24 )	0.258333333333333	0.0895290669789192	2.88546884325469
Winsorized Mean ( 5 / 24 )	0.272222222222222	0.083619747758929	3.25547767743839
Winsorized Mean ( 6 / 24 )	0.272222222222222	0.083619747758929	3.25547767743839
Winsorized Mean ( 7 / 24 )	0.281944444444444	0.0815855779491648	3.45581230815232
Winsorized Mean ( 8 / 24 )	0.293055555555556	0.079373682604347	3.69209977337634
Winsorized Mean ( 9 / 24 )	0.293055555555556	0.0750411047737744	3.90526707248017
Winsorized Mean ( 10 / 24 )	0.306944444444444	0.072522361477518	4.23241105489371
Winsorized Mean ( 11 / 24 )	0.306944444444444	0.072522361477518	4.23241105489371
Winsorized Mean ( 12 / 24 )	0.306944444444444	0.0671440183885027	4.57143393873792
Winsorized Mean ( 13 / 24 )	0.306944444444444	0.0671440183885027	4.57143393873792
Winsorized Mean ( 14 / 24 )	0.306944444444444	0.0611677696517229	5.01807481606939
Winsorized Mean ( 15 / 24 )	0.306944444444444	0.0611677696517229	5.01807481606939
Winsorized Mean ( 16 / 24 )	0.306944444444444	0.0611677696517229	5.01807481606939
Winsorized Mean ( 17 / 24 )	0.306944444444444	0.0611677696517229	5.01807481606939
Winsorized Mean ( 18 / 24 )	0.331944444444444	0.0571844060435839	5.80480706910637
Winsorized Mean ( 19 / 24 )	0.331944444444444	0.0495214338796173	6.70304590233343
Winsorized Mean ( 20 / 24 )	0.331944444444444	0.0495214338796173	6.70304590233343
Winsorized Mean ( 21 / 24 )	0.302777777777778	0.045792116431947	6.61200663716308
Winsorized Mean ( 22 / 24 )	0.333333333333333	0.0411588776345725	8.09869832440087
Winsorized Mean ( 23 / 24 )	0.365277777777778	0.0365341032087834	9.99826862288927
Winsorized Mean ( 24 / 24 )	0.365277777777778	0.0365341032087834	9.99826862288927
Trimmed Mean ( 1 / 24 )	0.255714285714286	0.0935306044682572	2.73401724674057
Trimmed Mean ( 2 / 24 )	0.266176470588235	0.0891529324524502	2.9856165497439
Trimmed Mean ( 3 / 24 )	0.277272727272727	0.0856020895586588	3.23908830616484
Trimmed Mean ( 4 / 24 )	0.290625	0.0816107300538393	3.5611126111514
Trimmed Mean ( 5 / 24 )	0.3	0.0784905185474709	3.82211769716569
Trimmed Mean ( 6 / 24 )	0.306666666666667	0.0766482414607192	4.00096154618012
Trimmed Mean ( 7 / 24 )	0.313793103448276	0.0743777687589104	4.21890987971703
Trimmed Mean ( 8 / 24 )	0.319642857142857	0.0721389191415876	4.43093493701357
Trimmed Mean ( 9 / 24 )	0.324074074074074	0.0699373376906125	4.63377767549155
Trimmed Mean ( 10 / 24 )	0.328846153846154	0.0682321771855529	4.81951723381006
Trimmed Mean ( 11 / 24 )	0.332	0.0666663945572678	4.98002032665506
Trimmed Mean ( 12 / 24 )	0.335416666666667	0.0646519310823072	5.18803786757203
Trimmed Mean ( 13 / 24 )	0.339130434782609	0.0632820739069668	5.35902845537547
Trimmed Mean ( 14 / 24 )	0.343181818181818	0.0614653451986421	5.58333833597993
Trimmed Mean ( 15 / 24 )	0.347619047619048	0.0604126436872559	5.75407772946673
Trimmed Mean ( 16 / 24 )	0.3525	0.0589423338352726	5.98042149103121
Trimmed Mean ( 17 / 24 )	0.357894736842105	0.0569034493285053	6.28950865132917
Trimmed Mean ( 18 / 24 )	0.363888888888889	0.0540653305245296	6.73054035476194
Trimmed Mean ( 19 / 24 )	0.367647058823529	0.0513143797165231	7.16460105051505
Trimmed Mean ( 20 / 24 )	0.371875	0.0496427509488968	7.4910232187337
Trimmed Mean ( 21 / 24 )	0.376666666666667	0.0471445157360289	7.98961789692984
Trimmed Mean ( 22 / 24 )	0.385714285714286	0.0444586145211458	8.6758053499582
Trimmed Mean ( 23 / 24 )	0.392307692307692	0.0422166853354223	9.2927165927573
Trimmed Mean ( 24 / 24 )	0.395833333333333	0.0405930522838553	9.75125818490779
Median	0.4
Midrange	-0.15
Midmean - Weighted Average at Xnp	0.343181818181818
Midmean - Weighted Average at X(n+1)p	0.4175
Midmean - Empirical Distribution Function	0.343181818181818
Midmean - Empirical Distribution Function - Averaging	0.4175
Midmean - Empirical Distribution Function - Interpolation	0.4175
Midmean - Closest Observation	0.343181818181818
Midmean - True Basic - Statistics Graphics Toolkit	0.4175
Midmean - MS Excel (old versions)	0.343181818181818
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.244444444444444 & 0.0983209765628508 & 2.48618812576771 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 0.863777234656663 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 0.245833333333333 & 0.097181273513742 & 2.52963687802024 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 0.245833333333333 & 0.0945696433806287 & 2.59949519259464 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 0.241666666666667 & 0.0938806470996206 & 2.57419046558365 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 0.258333333333333 & 0.0895290669789192 & 2.88546884325469 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 0.272222222222222 & 0.083619747758929 & 3.25547767743839 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 0.272222222222222 & 0.083619747758929 & 3.25547767743839 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 0.281944444444444 & 0.0815855779491648 & 3.45581230815232 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 0.293055555555556 & 0.079373682604347 & 3.69209977337634 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 0.293055555555556 & 0.0750411047737744 & 3.90526707248017 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 0.306944444444444 & 0.072522361477518 & 4.23241105489371 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 0.306944444444444 & 0.072522361477518 & 4.23241105489371 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 0.306944444444444 & 0.0671440183885027 & 4.57143393873792 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 0.306944444444444 & 0.0671440183885027 & 4.57143393873792 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 0.306944444444444 & 0.0611677696517229 & 5.01807481606939 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 0.306944444444444 & 0.0611677696517229 & 5.01807481606939 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 0.306944444444444 & 0.0611677696517229 & 5.01807481606939 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 0.306944444444444 & 0.0611677696517229 & 5.01807481606939 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 0.331944444444444 & 0.0571844060435839 & 5.80480706910637 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 0.331944444444444 & 0.0495214338796173 & 6.70304590233343 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 0.331944444444444 & 0.0495214338796173 & 6.70304590233343 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 0.302777777777778 & 0.045792116431947 & 6.61200663716308 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 0.333333333333333 & 0.0411588776345725 & 8.09869832440087 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 0.365277777777778 & 0.0365341032087834 & 9.99826862288927 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 0.365277777777778 & 0.0365341032087834 & 9.99826862288927 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 0.255714285714286 & 0.0935306044682572 & 2.73401724674057 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 0.266176470588235 & 0.0891529324524502 & 2.9856165497439 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 0.277272727272727 & 0.0856020895586588 & 3.23908830616484 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 0.290625 & 0.0816107300538393 & 3.5611126111514 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 0.3 & 0.0784905185474709 & 3.82211769716569 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 0.306666666666667 & 0.0766482414607192 & 4.00096154618012 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 0.313793103448276 & 0.0743777687589104 & 4.21890987971703 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 0.319642857142857 & 0.0721389191415876 & 4.43093493701357 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 0.324074074074074 & 0.0699373376906125 & 4.63377767549155 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 0.328846153846154 & 0.0682321771855529 & 4.81951723381006 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 0.332 & 0.0666663945572678 & 4.98002032665506 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 0.335416666666667 & 0.0646519310823072 & 5.18803786757203 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 0.339130434782609 & 0.0632820739069668 & 5.35902845537547 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 0.343181818181818 & 0.0614653451986421 & 5.58333833597993 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 0.347619047619048 & 0.0604126436872559 & 5.75407772946673 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 0.3525 & 0.0589423338352726 & 5.98042149103121 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 0.357894736842105 & 0.0569034493285053 & 6.28950865132917 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 0.363888888888889 & 0.0540653305245296 & 6.73054035476194 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 0.367647058823529 & 0.0513143797165231 & 7.16460105051505 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 0.371875 & 0.0496427509488968 & 7.4910232187337 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 0.376666666666667 & 0.0471445157360289 & 7.98961789692984 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 0.385714285714286 & 0.0444586145211458 & 8.6758053499582 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 0.392307692307692 & 0.0422166853354223 & 9.2927165927573 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 0.395833333333333 & 0.0405930522838553 & 9.75125818490779 \tabularnewline
Median & 0.4 &  &  \tabularnewline
Midrange & -0.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.343181818181818 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.4175 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.343181818181818 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.4175 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.4175 &  &  \tabularnewline
Midmean - Closest Observation & 0.343181818181818 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.4175 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.343181818181818 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49986&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]0.244444444444444[/C][C]0.0983209765628508[/C][C]2.48618812576771[/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]0.863777234656663[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]0.245833333333333[/C][C]0.097181273513742[/C][C]2.52963687802024[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]0.245833333333333[/C][C]0.0945696433806287[/C][C]2.59949519259464[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]0.241666666666667[/C][C]0.0938806470996206[/C][C]2.57419046558365[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]0.258333333333333[/C][C]0.0895290669789192[/C][C]2.88546884325469[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]0.272222222222222[/C][C]0.083619747758929[/C][C]3.25547767743839[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]0.272222222222222[/C][C]0.083619747758929[/C][C]3.25547767743839[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]0.281944444444444[/C][C]0.0815855779491648[/C][C]3.45581230815232[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]0.293055555555556[/C][C]0.079373682604347[/C][C]3.69209977337634[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]0.293055555555556[/C][C]0.0750411047737744[/C][C]3.90526707248017[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]0.306944444444444[/C][C]0.072522361477518[/C][C]4.23241105489371[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]0.306944444444444[/C][C]0.072522361477518[/C][C]4.23241105489371[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]0.306944444444444[/C][C]0.0671440183885027[/C][C]4.57143393873792[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]0.306944444444444[/C][C]0.0671440183885027[/C][C]4.57143393873792[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]0.306944444444444[/C][C]0.0611677696517229[/C][C]5.01807481606939[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]0.306944444444444[/C][C]0.0611677696517229[/C][C]5.01807481606939[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]0.306944444444444[/C][C]0.0611677696517229[/C][C]5.01807481606939[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]0.306944444444444[/C][C]0.0611677696517229[/C][C]5.01807481606939[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]0.331944444444444[/C][C]0.0571844060435839[/C][C]5.80480706910637[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]0.331944444444444[/C][C]0.0495214338796173[/C][C]6.70304590233343[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]0.331944444444444[/C][C]0.0495214338796173[/C][C]6.70304590233343[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]0.302777777777778[/C][C]0.045792116431947[/C][C]6.61200663716308[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]0.333333333333333[/C][C]0.0411588776345725[/C][C]8.09869832440087[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]0.365277777777778[/C][C]0.0365341032087834[/C][C]9.99826862288927[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]0.365277777777778[/C][C]0.0365341032087834[/C][C]9.99826862288927[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]0.255714285714286[/C][C]0.0935306044682572[/C][C]2.73401724674057[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]0.266176470588235[/C][C]0.0891529324524502[/C][C]2.9856165497439[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]0.277272727272727[/C][C]0.0856020895586588[/C][C]3.23908830616484[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]0.290625[/C][C]0.0816107300538393[/C][C]3.5611126111514[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]0.3[/C][C]0.0784905185474709[/C][C]3.82211769716569[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]0.306666666666667[/C][C]0.0766482414607192[/C][C]4.00096154618012[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]0.313793103448276[/C][C]0.0743777687589104[/C][C]4.21890987971703[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]0.319642857142857[/C][C]0.0721389191415876[/C][C]4.43093493701357[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]0.324074074074074[/C][C]0.0699373376906125[/C][C]4.63377767549155[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]0.328846153846154[/C][C]0.0682321771855529[/C][C]4.81951723381006[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]0.332[/C][C]0.0666663945572678[/C][C]4.98002032665506[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]0.335416666666667[/C][C]0.0646519310823072[/C][C]5.18803786757203[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]0.339130434782609[/C][C]0.0632820739069668[/C][C]5.35902845537547[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]0.343181818181818[/C][C]0.0614653451986421[/C][C]5.58333833597993[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]0.347619047619048[/C][C]0.0604126436872559[/C][C]5.75407772946673[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]0.3525[/C][C]0.0589423338352726[/C][C]5.98042149103121[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]0.357894736842105[/C][C]0.0569034493285053[/C][C]6.28950865132917[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]0.363888888888889[/C][C]0.0540653305245296[/C][C]6.73054035476194[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]0.367647058823529[/C][C]0.0513143797165231[/C][C]7.16460105051505[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]0.371875[/C][C]0.0496427509488968[/C][C]7.4910232187337[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]0.376666666666667[/C][C]0.0471445157360289[/C][C]7.98961789692984[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]0.385714285714286[/C][C]0.0444586145211458[/C][C]8.6758053499582[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]0.392307692307692[/C][C]0.0422166853354223[/C][C]9.2927165927573[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]0.395833333333333[/C][C]0.0405930522838553[/C][C]9.75125818490779[/C][/ROW]
[ROW][C]Median[/C][C]0.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.343181818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.4175[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.343181818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.4175[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.4175[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.343181818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.4175[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.343181818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49986&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49986&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	0.244444444444444	0.0983209765628508	2.48618812576771
Geometric Mean	NaN
Harmonic Mean	0
Quadratic Mean	0.863777234656663
Winsorized Mean ( 1 / 24 )	0.245833333333333	0.097181273513742	2.52963687802024
Winsorized Mean ( 2 / 24 )	0.245833333333333	0.0945696433806287	2.59949519259464
Winsorized Mean ( 3 / 24 )	0.241666666666667	0.0938806470996206	2.57419046558365
Winsorized Mean ( 4 / 24 )	0.258333333333333	0.0895290669789192	2.88546884325469
Winsorized Mean ( 5 / 24 )	0.272222222222222	0.083619747758929	3.25547767743839
Winsorized Mean ( 6 / 24 )	0.272222222222222	0.083619747758929	3.25547767743839
Winsorized Mean ( 7 / 24 )	0.281944444444444	0.0815855779491648	3.45581230815232
Winsorized Mean ( 8 / 24 )	0.293055555555556	0.079373682604347	3.69209977337634
Winsorized Mean ( 9 / 24 )	0.293055555555556	0.0750411047737744	3.90526707248017
Winsorized Mean ( 10 / 24 )	0.306944444444444	0.072522361477518	4.23241105489371
Winsorized Mean ( 11 / 24 )	0.306944444444444	0.072522361477518	4.23241105489371
Winsorized Mean ( 12 / 24 )	0.306944444444444	0.0671440183885027	4.57143393873792
Winsorized Mean ( 13 / 24 )	0.306944444444444	0.0671440183885027	4.57143393873792
Winsorized Mean ( 14 / 24 )	0.306944444444444	0.0611677696517229	5.01807481606939
Winsorized Mean ( 15 / 24 )	0.306944444444444	0.0611677696517229	5.01807481606939
Winsorized Mean ( 16 / 24 )	0.306944444444444	0.0611677696517229	5.01807481606939
Winsorized Mean ( 17 / 24 )	0.306944444444444	0.0611677696517229	5.01807481606939
Winsorized Mean ( 18 / 24 )	0.331944444444444	0.0571844060435839	5.80480706910637
Winsorized Mean ( 19 / 24 )	0.331944444444444	0.0495214338796173	6.70304590233343
Winsorized Mean ( 20 / 24 )	0.331944444444444	0.0495214338796173	6.70304590233343
Winsorized Mean ( 21 / 24 )	0.302777777777778	0.045792116431947	6.61200663716308
Winsorized Mean ( 22 / 24 )	0.333333333333333	0.0411588776345725	8.09869832440087
Winsorized Mean ( 23 / 24 )	0.365277777777778	0.0365341032087834	9.99826862288927
Winsorized Mean ( 24 / 24 )	0.365277777777778	0.0365341032087834	9.99826862288927
Trimmed Mean ( 1 / 24 )	0.255714285714286	0.0935306044682572	2.73401724674057
Trimmed Mean ( 2 / 24 )	0.266176470588235	0.0891529324524502	2.9856165497439
Trimmed Mean ( 3 / 24 )	0.277272727272727	0.0856020895586588	3.23908830616484
Trimmed Mean ( 4 / 24 )	0.290625	0.0816107300538393	3.5611126111514
Trimmed Mean ( 5 / 24 )	0.3	0.0784905185474709	3.82211769716569
Trimmed Mean ( 6 / 24 )	0.306666666666667	0.0766482414607192	4.00096154618012
Trimmed Mean ( 7 / 24 )	0.313793103448276	0.0743777687589104	4.21890987971703
Trimmed Mean ( 8 / 24 )	0.319642857142857	0.0721389191415876	4.43093493701357
Trimmed Mean ( 9 / 24 )	0.324074074074074	0.0699373376906125	4.63377767549155
Trimmed Mean ( 10 / 24 )	0.328846153846154	0.0682321771855529	4.81951723381006
Trimmed Mean ( 11 / 24 )	0.332	0.0666663945572678	4.98002032665506
Trimmed Mean ( 12 / 24 )	0.335416666666667	0.0646519310823072	5.18803786757203
Trimmed Mean ( 13 / 24 )	0.339130434782609	0.0632820739069668	5.35902845537547
Trimmed Mean ( 14 / 24 )	0.343181818181818	0.0614653451986421	5.58333833597993
Trimmed Mean ( 15 / 24 )	0.347619047619048	0.0604126436872559	5.75407772946673
Trimmed Mean ( 16 / 24 )	0.3525	0.0589423338352726	5.98042149103121
Trimmed Mean ( 17 / 24 )	0.357894736842105	0.0569034493285053	6.28950865132917
Trimmed Mean ( 18 / 24 )	0.363888888888889	0.0540653305245296	6.73054035476194
Trimmed Mean ( 19 / 24 )	0.367647058823529	0.0513143797165231	7.16460105051505
Trimmed Mean ( 20 / 24 )	0.371875	0.0496427509488968	7.4910232187337
Trimmed Mean ( 21 / 24 )	0.376666666666667	0.0471445157360289	7.98961789692984
Trimmed Mean ( 22 / 24 )	0.385714285714286	0.0444586145211458	8.6758053499582
Trimmed Mean ( 23 / 24 )	0.392307692307692	0.0422166853354223	9.2927165927573
Trimmed Mean ( 24 / 24 )	0.395833333333333	0.0405930522838553	9.75125818490779
Median	0.4
Midrange	-0.15
Midmean - Weighted Average at Xnp	0.343181818181818
Midmean - Weighted Average at X(n+1)p	0.4175
Midmean - Empirical Distribution Function	0.343181818181818
Midmean - Empirical Distribution Function - Averaging	0.4175
Midmean - Empirical Distribution Function - Interpolation	0.4175
Midmean - Closest Observation	0.343181818181818
Midmean - True Basic - Statistics Graphics Toolkit	0.4175
Midmean - MS Excel (old versions)	0.343181818181818
Number of observations	72

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code