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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Thu, 11 Oct 2012 15:42:06 -0400

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/2012/Oct/11/t1349984533vqurcl5u3t2bfau.htm/, Retrieved Sat, 27 Apr 2024 16:51:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=175224, Retrieved Sat, 27 Apr 2024 16:51:06 +0000

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Estimated Impact

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

-       [Central Tendency] [] [2012-10-11 19:42:06] [f369ceac14ec552c853c67dff6d1d312] [Current]

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0.67
0.66
0.66
0.67
0.67
0.67
0.67
0.68
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0.67
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0.69
0.69
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0.69
0.69
0.69
0.7
0.69
0.68
0.7
0.7
0.71
0.69
0.7
0.7
0.71
0.71
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0.71
0.7
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0.71
0.71
0.71
0.7
0.69
0.7
0.7
0.7
0.71
0.7
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0.69
0.7
0.71
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0.71
0.71
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0.69
0.7
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0.72
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0.69
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0.71
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0.74
0.75

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

\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 & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175224&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=175224&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175224&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	3 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	0.697638888888889	0.00210719253735805	331.07505674995
Geometric Mean	0.697412691492829
Harmonic Mean	0.697186192386214
Quadratic Mean	0.697864799067683
Winsorized Mean ( 1 / 24 )	0.6975	0.00206269116342722	338.15047660411
Winsorized Mean ( 2 / 24 )	0.6975	0.00192534776242106	362.272215759567
Winsorized Mean ( 3 / 24 )	0.697083333333333	0.00183895318762906	379.065295420638
Winsorized Mean ( 4 / 24 )	0.697083333333333	0.00183895318762906	379.065295420638
Winsorized Mean ( 5 / 24 )	0.697083333333333	0.00183895318762906	379.065295420638
Winsorized Mean ( 6 / 24 )	0.697083333333333	0.00183895318762906	379.065295420639
Winsorized Mean ( 7 / 24 )	0.696111111111111	0.00169639629494333	410.346988605256
Winsorized Mean ( 8 / 24 )	0.696111111111111	0.00169639629494333	410.346988605256
Winsorized Mean ( 9 / 24 )	0.696111111111111	0.00169639629494333	410.346988605256
Winsorized Mean ( 10 / 24 )	0.696111111111111	0.00169639629494333	410.346988605256
Winsorized Mean ( 11 / 24 )	0.696111111111111	0.00169639629494333	410.346988605256
Winsorized Mean ( 12 / 24 )	0.697777777777778	0.00135922948091081	513.362745274036
Winsorized Mean ( 13 / 24 )	0.697777777777778	0.00135922948091081	513.362745274037
Winsorized Mean ( 14 / 24 )	0.697777777777778	0.00135922948091081	513.362745274036
Winsorized Mean ( 15 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 16 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 17 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 18 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 19 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 20 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 21 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 22 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 23 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 24 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Trimmed Mean ( 1 / 24 )	0.697428571428571	0.00195906043189228	356.001560786421
Trimmed Mean ( 2 / 24 )	0.697352941176471	0.00183395022947671	380.246382899632
Trimmed Mean ( 3 / 24 )	0.697272727272727	0.00177453437269649	392.932781692579
Trimmed Mean ( 4 / 24 )	0.69734375	0.00174293055502589	400.098413553627
Trimmed Mean ( 5 / 24 )	0.69741935483871	0.00170443605544639	409.178949606331
Trimmed Mean ( 6 / 24 )	0.6975	0.00165746044937517	420.824521190201
Trimmed Mean ( 7 / 24 )	0.697586206896552	0.00159987796017455	436.024637041968
Trimmed Mean ( 8 / 24 )	0.697857142857143	0.0015649215928719	445.937448902123
Trimmed Mean ( 9 / 24 )	0.698148148148148	0.00152028156928259	459.222924393931
Trimmed Mean ( 10 / 24 )	0.698461538461538	0.00146308563024658	477.3893776428
Trimmed Mean ( 11 / 24 )	0.6988	0.00138917094641637	503.033843172929
Trimmed Mean ( 12 / 24 )	0.699166666666667	0.0012921384404966	541.092691583389
Trimmed Mean ( 13 / 24 )	0.699347826086956	0.00125886897757849	555.536627355925
Trimmed Mean ( 14 / 24 )	0.699545454545454	0.00121454127684714	575.975035086023
Trimmed Mean ( 15 / 24 )	0.699761904761905	0.00115510759101354	605.798031461212
Trimmed Mean ( 16 / 24 )	0.69975	0.00115954787829192	603.467966351483
Trimmed Mean ( 17 / 24 )	0.699736842105263	0.00116167106944238	602.353678689053
Trimmed Mean ( 18 / 24 )	0.699722222222222	0.00116060405120283	602.894864529414
Trimmed Mean ( 19 / 24 )	0.699705882352941	0.00115510909714994	605.748741897506
Trimmed Mean ( 20 / 24 )	0.6996875	0.00114338692897673	611.942888507727
Trimmed Mean ( 21 / 24 )	0.699666666666667	0.00112273612147621	623.179973711654
Trimmed Mean ( 22 / 24 )	0.699642857142857	0.00108892243920732	642.509357830995
Trimmed Mean ( 23 / 24 )	0.699615384615385	0.00103489415746721	676.026026011797
Trimmed Mean ( 24 / 24 )	0.699583333333333	0.000947759881125242	738.144067147833
Median	0.7
Midrange	0.705
Midmean - Weighted Average at Xnp	0.7014
Midmean - Weighted Average at X(n+1)p	0.7014
Midmean - Empirical Distribution Function	0.7014
Midmean - Empirical Distribution Function - Averaging	0.7014
Midmean - Empirical Distribution Function - Interpolation	0.7014
Midmean - Closest Observation	0.7014
Midmean - True Basic - Statistics Graphics Toolkit	0.7014
Midmean - MS Excel (old versions)	0.7014
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.697638888888889 & 0.00210719253735805 & 331.07505674995 \tabularnewline
Geometric Mean & 0.697412691492829 &  &  \tabularnewline
Harmonic Mean & 0.697186192386214 &  &  \tabularnewline
Quadratic Mean & 0.697864799067683 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 0.6975 & 0.00206269116342722 & 338.15047660411 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 0.6975 & 0.00192534776242106 & 362.272215759567 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 0.697083333333333 & 0.00183895318762906 & 379.065295420638 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 0.697083333333333 & 0.00183895318762906 & 379.065295420638 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 0.697083333333333 & 0.00183895318762906 & 379.065295420638 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 0.697083333333333 & 0.00183895318762906 & 379.065295420639 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 0.696111111111111 & 0.00169639629494333 & 410.346988605256 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 0.696111111111111 & 0.00169639629494333 & 410.346988605256 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 0.696111111111111 & 0.00169639629494333 & 410.346988605256 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 0.696111111111111 & 0.00169639629494333 & 410.346988605256 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 0.696111111111111 & 0.00169639629494333 & 410.346988605256 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 0.697777777777778 & 0.00135922948091081 & 513.362745274036 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 0.697777777777778 & 0.00135922948091081 & 513.362745274037 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 0.697777777777778 & 0.00135922948091081 & 513.362745274036 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 0.699861111111111 & 0.00101808866065431 & 687.426486668974 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 0.699861111111111 & 0.00101808866065431 & 687.426486668974 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 0.699861111111111 & 0.00101808866065431 & 687.426486668974 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 0.699861111111111 & 0.00101808866065431 & 687.426486668974 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 0.699861111111111 & 0.00101808866065431 & 687.426486668974 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 0.699861111111111 & 0.00101808866065431 & 687.426486668974 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 0.699861111111111 & 0.00101808866065431 & 687.426486668974 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 0.699861111111111 & 0.00101808866065431 & 687.426486668974 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 0.699861111111111 & 0.00101808866065431 & 687.426486668974 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 0.699861111111111 & 0.00101808866065431 & 687.426486668974 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 0.697428571428571 & 0.00195906043189228 & 356.001560786421 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 0.697352941176471 & 0.00183395022947671 & 380.246382899632 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 0.697272727272727 & 0.00177453437269649 & 392.932781692579 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 0.69734375 & 0.00174293055502589 & 400.098413553627 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 0.69741935483871 & 0.00170443605544639 & 409.178949606331 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 0.6975 & 0.00165746044937517 & 420.824521190201 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 0.697586206896552 & 0.00159987796017455 & 436.024637041968 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 0.697857142857143 & 0.0015649215928719 & 445.937448902123 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 0.698148148148148 & 0.00152028156928259 & 459.222924393931 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 0.698461538461538 & 0.00146308563024658 & 477.3893776428 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 0.6988 & 0.00138917094641637 & 503.033843172929 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 0.699166666666667 & 0.0012921384404966 & 541.092691583389 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 0.699347826086956 & 0.00125886897757849 & 555.536627355925 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 0.699545454545454 & 0.00121454127684714 & 575.975035086023 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 0.699761904761905 & 0.00115510759101354 & 605.798031461212 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 0.69975 & 0.00115954787829192 & 603.467966351483 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 0.699736842105263 & 0.00116167106944238 & 602.353678689053 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 0.699722222222222 & 0.00116060405120283 & 602.894864529414 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 0.699705882352941 & 0.00115510909714994 & 605.748741897506 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 0.6996875 & 0.00114338692897673 & 611.942888507727 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 0.699666666666667 & 0.00112273612147621 & 623.179973711654 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 0.699642857142857 & 0.00108892243920732 & 642.509357830995 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 0.699615384615385 & 0.00103489415746721 & 676.026026011797 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 0.699583333333333 & 0.000947759881125242 & 738.144067147833 \tabularnewline
Median & 0.7 &  &  \tabularnewline
Midrange & 0.705 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.7014 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.7014 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.7014 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.7014 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.7014 &  &  \tabularnewline
Midmean - Closest Observation & 0.7014 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.7014 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.7014 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175224&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]0.697638888888889[/C][C]0.00210719253735805[/C][C]331.07505674995[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.697412691492829[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.697186192386214[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.697864799067683[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]0.6975[/C][C]0.00206269116342722[/C][C]338.15047660411[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]0.6975[/C][C]0.00192534776242106[/C][C]362.272215759567[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]0.697083333333333[/C][C]0.00183895318762906[/C][C]379.065295420638[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]0.697083333333333[/C][C]0.00183895318762906[/C][C]379.065295420638[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]0.697083333333333[/C][C]0.00183895318762906[/C][C]379.065295420638[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]0.697083333333333[/C][C]0.00183895318762906[/C][C]379.065295420639[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]0.696111111111111[/C][C]0.00169639629494333[/C][C]410.346988605256[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]0.696111111111111[/C][C]0.00169639629494333[/C][C]410.346988605256[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]0.696111111111111[/C][C]0.00169639629494333[/C][C]410.346988605256[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]0.696111111111111[/C][C]0.00169639629494333[/C][C]410.346988605256[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]0.696111111111111[/C][C]0.00169639629494333[/C][C]410.346988605256[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]0.697777777777778[/C][C]0.00135922948091081[/C][C]513.362745274036[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]0.697777777777778[/C][C]0.00135922948091081[/C][C]513.362745274037[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]0.697777777777778[/C][C]0.00135922948091081[/C][C]513.362745274036[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]0.699861111111111[/C][C]0.00101808866065431[/C][C]687.426486668974[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]0.699861111111111[/C][C]0.00101808866065431[/C][C]687.426486668974[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]0.699861111111111[/C][C]0.00101808866065431[/C][C]687.426486668974[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]0.699861111111111[/C][C]0.00101808866065431[/C][C]687.426486668974[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]0.699861111111111[/C][C]0.00101808866065431[/C][C]687.426486668974[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]0.699861111111111[/C][C]0.00101808866065431[/C][C]687.426486668974[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]0.699861111111111[/C][C]0.00101808866065431[/C][C]687.426486668974[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]0.699861111111111[/C][C]0.00101808866065431[/C][C]687.426486668974[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]0.699861111111111[/C][C]0.00101808866065431[/C][C]687.426486668974[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]0.699861111111111[/C][C]0.00101808866065431[/C][C]687.426486668974[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]0.697428571428571[/C][C]0.00195906043189228[/C][C]356.001560786421[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]0.697352941176471[/C][C]0.00183395022947671[/C][C]380.246382899632[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]0.697272727272727[/C][C]0.00177453437269649[/C][C]392.932781692579[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]0.69734375[/C][C]0.00174293055502589[/C][C]400.098413553627[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]0.69741935483871[/C][C]0.00170443605544639[/C][C]409.178949606331[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]0.6975[/C][C]0.00165746044937517[/C][C]420.824521190201[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]0.697586206896552[/C][C]0.00159987796017455[/C][C]436.024637041968[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]0.697857142857143[/C][C]0.0015649215928719[/C][C]445.937448902123[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]0.698148148148148[/C][C]0.00152028156928259[/C][C]459.222924393931[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]0.698461538461538[/C][C]0.00146308563024658[/C][C]477.3893776428[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]0.6988[/C][C]0.00138917094641637[/C][C]503.033843172929[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]0.699166666666667[/C][C]0.0012921384404966[/C][C]541.092691583389[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]0.699347826086956[/C][C]0.00125886897757849[/C][C]555.536627355925[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]0.699545454545454[/C][C]0.00121454127684714[/C][C]575.975035086023[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]0.699761904761905[/C][C]0.00115510759101354[/C][C]605.798031461212[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]0.69975[/C][C]0.00115954787829192[/C][C]603.467966351483[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]0.699736842105263[/C][C]0.00116167106944238[/C][C]602.353678689053[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]0.699722222222222[/C][C]0.00116060405120283[/C][C]602.894864529414[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]0.699705882352941[/C][C]0.00115510909714994[/C][C]605.748741897506[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]0.6996875[/C][C]0.00114338692897673[/C][C]611.942888507727[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]0.699666666666667[/C][C]0.00112273612147621[/C][C]623.179973711654[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]0.699642857142857[/C][C]0.00108892243920732[/C][C]642.509357830995[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]0.699615384615385[/C][C]0.00103489415746721[/C][C]676.026026011797[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]0.699583333333333[/C][C]0.000947759881125242[/C][C]738.144067147833[/C][/ROW]
[ROW][C]Median[/C][C]0.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.705[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.7014[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.7014[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.7014[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.7014[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.7014[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.7014[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.7014[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.7014[/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=175224&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175224&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	0.697638888888889	0.00210719253735805	331.07505674995
Geometric Mean	0.697412691492829
Harmonic Mean	0.697186192386214
Quadratic Mean	0.697864799067683
Winsorized Mean ( 1 / 24 )	0.6975	0.00206269116342722	338.15047660411
Winsorized Mean ( 2 / 24 )	0.6975	0.00192534776242106	362.272215759567
Winsorized Mean ( 3 / 24 )	0.697083333333333	0.00183895318762906	379.065295420638
Winsorized Mean ( 4 / 24 )	0.697083333333333	0.00183895318762906	379.065295420638
Winsorized Mean ( 5 / 24 )	0.697083333333333	0.00183895318762906	379.065295420638
Winsorized Mean ( 6 / 24 )	0.697083333333333	0.00183895318762906	379.065295420639
Winsorized Mean ( 7 / 24 )	0.696111111111111	0.00169639629494333	410.346988605256
Winsorized Mean ( 8 / 24 )	0.696111111111111	0.00169639629494333	410.346988605256
Winsorized Mean ( 9 / 24 )	0.696111111111111	0.00169639629494333	410.346988605256
Winsorized Mean ( 10 / 24 )	0.696111111111111	0.00169639629494333	410.346988605256
Winsorized Mean ( 11 / 24 )	0.696111111111111	0.00169639629494333	410.346988605256
Winsorized Mean ( 12 / 24 )	0.697777777777778	0.00135922948091081	513.362745274036
Winsorized Mean ( 13 / 24 )	0.697777777777778	0.00135922948091081	513.362745274037
Winsorized Mean ( 14 / 24 )	0.697777777777778	0.00135922948091081	513.362745274036
Winsorized Mean ( 15 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 16 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 17 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 18 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 19 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 20 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 21 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 22 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 23 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Winsorized Mean ( 24 / 24 )	0.699861111111111	0.00101808866065431	687.426486668974
Trimmed Mean ( 1 / 24 )	0.697428571428571	0.00195906043189228	356.001560786421
Trimmed Mean ( 2 / 24 )	0.697352941176471	0.00183395022947671	380.246382899632
Trimmed Mean ( 3 / 24 )	0.697272727272727	0.00177453437269649	392.932781692579
Trimmed Mean ( 4 / 24 )	0.69734375	0.00174293055502589	400.098413553627
Trimmed Mean ( 5 / 24 )	0.69741935483871	0.00170443605544639	409.178949606331
Trimmed Mean ( 6 / 24 )	0.6975	0.00165746044937517	420.824521190201
Trimmed Mean ( 7 / 24 )	0.697586206896552	0.00159987796017455	436.024637041968
Trimmed Mean ( 8 / 24 )	0.697857142857143	0.0015649215928719	445.937448902123
Trimmed Mean ( 9 / 24 )	0.698148148148148	0.00152028156928259	459.222924393931
Trimmed Mean ( 10 / 24 )	0.698461538461538	0.00146308563024658	477.3893776428
Trimmed Mean ( 11 / 24 )	0.6988	0.00138917094641637	503.033843172929
Trimmed Mean ( 12 / 24 )	0.699166666666667	0.0012921384404966	541.092691583389
Trimmed Mean ( 13 / 24 )	0.699347826086956	0.00125886897757849	555.536627355925
Trimmed Mean ( 14 / 24 )	0.699545454545454	0.00121454127684714	575.975035086023
Trimmed Mean ( 15 / 24 )	0.699761904761905	0.00115510759101354	605.798031461212
Trimmed Mean ( 16 / 24 )	0.69975	0.00115954787829192	603.467966351483
Trimmed Mean ( 17 / 24 )	0.699736842105263	0.00116167106944238	602.353678689053
Trimmed Mean ( 18 / 24 )	0.699722222222222	0.00116060405120283	602.894864529414
Trimmed Mean ( 19 / 24 )	0.699705882352941	0.00115510909714994	605.748741897506
Trimmed Mean ( 20 / 24 )	0.6996875	0.00114338692897673	611.942888507727
Trimmed Mean ( 21 / 24 )	0.699666666666667	0.00112273612147621	623.179973711654
Trimmed Mean ( 22 / 24 )	0.699642857142857	0.00108892243920732	642.509357830995
Trimmed Mean ( 23 / 24 )	0.699615384615385	0.00103489415746721	676.026026011797
Trimmed Mean ( 24 / 24 )	0.699583333333333	0.000947759881125242	738.144067147833
Median	0.7
Midrange	0.705
Midmean - Weighted Average at Xnp	0.7014
Midmean - Weighted Average at X(n+1)p	0.7014
Midmean - Empirical Distribution Function	0.7014
Midmean - Empirical Distribution Function - Averaging	0.7014
Midmean - Empirical Distribution Function - Interpolation	0.7014
Midmean - Closest Observation	0.7014
Midmean - True Basic - Statistics Graphics Toolkit	0.7014
Midmean - MS Excel (old versions)	0.7014
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