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*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 26 Dec 2011 10:30:19 -0500

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/2011/Dec/26/t1324913442adunvcpm6cr6mc3.htm/, Retrieved Fri, 03 May 2024 21:59:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160814, Retrieved Fri, 03 May 2024 21:59:35 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDG2011W52a

Estimated Impact

156

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

-       [Central Tendency] [T5] [2011-12-26 15:30:19] [53dd883843ca194f19e2952e03e3e0b7] [Current]

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0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.7
0.7
0.68
0.68
0.69
0.69
0.7
0.7
0.7
0.7
0.7
0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.76
0.77
0.78
0.85
0.89
0.9
0.91
0.91
0.91
0.9
0.89
0.88
0.87
0.86
0.87
0.87
0.87
0.85
0.84
0.84
0.84
0.84
0.84
0.82
0.87
0.92
0.92
0.92
0.93
0.94
0.87
0.84
0.83
0.81
0.81
0.81
0.8
0.8
0.8
0.8
0.8
0.8

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160814&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160814&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160814&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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	0.791111111111111	0.00970930284013501	81.4797029340688
Geometric Mean	0.786909139953385
Harmonic Mean	0.782757956676745
Quadratic Mean	0.795330120138801
Winsorized Mean ( 1 / 24 )	0.790972222222222	0.00968025538789609	81.7098506730753
Winsorized Mean ( 2 / 24 )	0.790972222222222	0.00958276630741828	82.5411156703163
Winsorized Mean ( 3 / 24 )	0.790972222222222	0.00958276630741828	82.5411156703163
Winsorized Mean ( 4 / 24 )	0.791527777777778	0.00950384923710826	83.2849678093816
Winsorized Mean ( 5 / 24 )	0.790833333333333	0.00937555423505179	84.350568884418
Winsorized Mean ( 6 / 24 )	0.790833333333333	0.00937555423505179	84.3505688844181
Winsorized Mean ( 7 / 24 )	0.790833333333333	0.00937555423505179	84.350568884418
Winsorized Mean ( 8 / 24 )	0.789722222222222	0.00918206607102333	86.0070289315843
Winsorized Mean ( 9 / 24 )	0.789722222222222	0.00918206607102333	86.0070289315843
Winsorized Mean ( 10 / 24 )	0.788333333333333	0.00895345292324846	88.0479676490345
Winsorized Mean ( 11 / 24 )	0.789861111111111	0.00874900632756092	90.2800937088031
Winsorized Mean ( 12 / 24 )	0.788194444444444	0.00848760116800986	92.8642179153262
Winsorized Mean ( 13 / 24 )	0.786388888888889	0.00822061218005385	95.6606237667981
Winsorized Mean ( 14 / 24 )	0.786388888888889	0.00822061218005385	95.6606237667981
Winsorized Mean ( 15 / 24 )	0.786388888888889	0.00822061218005385	95.6606237667981
Winsorized Mean ( 16 / 24 )	0.786388888888889	0.00822061218005385	95.6606237667981
Winsorized Mean ( 17 / 24 )	0.786388888888889	0.00822061218005385	95.6606237667981
Winsorized Mean ( 18 / 24 )	0.786388888888889	0.00822061218005385	95.6606237667981
Winsorized Mean ( 19 / 24 )	0.78375	0.00785091299775246	99.829153656953
Winsorized Mean ( 20 / 24 )	0.780972222222222	0.00748017652034478	104.40558723422
Winsorized Mean ( 21 / 24 )	0.780972222222222	0.00748017652034478	104.40558723422
Winsorized Mean ( 22 / 24 )	0.777916666666667	0.00709299258553584	109.673971498717
Winsorized Mean ( 23 / 24 )	0.777916666666667	0.00709299258553584	109.673971498717
Winsorized Mean ( 24 / 24 )	0.777916666666667	0.00709299258553584	109.673971498717
Trimmed Mean ( 1 / 24 )	0.790571428571429	0.00962417099069877	82.1443664431433
Trimmed Mean ( 2 / 24 )	0.790147058823529	0.00955206757943486	82.7200029996309
Trimmed Mean ( 3 / 24 )	0.78969696969697	0.00951987173761733	82.9524799768592
Trimmed Mean ( 4 / 24 )	0.78921875	0.00947350285398198	83.3080183924016
Trimmed Mean ( 5 / 24 )	0.788548387096774	0.00943638214547441	83.5646940681555
Trimmed Mean ( 6 / 24 )	0.788	0.00942049694612043	83.6473919058501
Trimmed Mean ( 7 / 24 )	0.787413793103448	0.00939024330774019	83.8544611995729
Trimmed Mean ( 8 / 24 )	0.786785714285714	0.0093423596912725	84.2170222819314
Trimmed Mean ( 9 / 24 )	0.786296296296296	0.00931735790723471	84.390478945298
Trimmed Mean ( 10 / 24 )	0.785769230769231	0.00927356219558245	84.7321896588497
Trimmed Mean ( 11 / 24 )	0.7854	0.00925471749533001	84.8648270891378
Trimmed Mean ( 12 / 24 )	0.784791666666667	0.00925404638031297	84.8052445831945
Trimmed Mean ( 13 / 24 )	0.784347826086957	0.00928690405094732	84.4574060186342
Trimmed Mean ( 14 / 24 )	0.784090909090909	0.00935735333857705	83.7940901364043
Trimmed Mean ( 15 / 24 )	0.783809523809524	0.00941958064511862	83.2106601492612
Trimmed Mean ( 16 / 24 )	0.7835	0.00947026385249627	82.7326473901228
Trimmed Mean ( 17 / 24 )	0.783157894736842	0.0095048483784179	82.3956220611696
Trimmed Mean ( 18 / 24 )	0.782777777777778	0.0095169949164565	82.2505196912759
Trimmed Mean ( 19 / 24 )	0.782352941176471	0.00949771361481204	82.3727660051111
Trimmed Mean ( 20 / 24 )	0.7821875	0.00952219790931661	82.1435877986426
Trimmed Mean ( 21 / 24 )	0.782333333333333	0.00959745336592531	81.5146793117975
Trimmed Mean ( 22 / 24 )	0.7825	0.00964481657536766	81.1316621612548
Trimmed Mean ( 23 / 24 )	0.783076923076923	0.00974709788397364	80.3394951398275
Trimmed Mean ( 24 / 24 )	0.78375	0.00981370861660332	79.8627746776599
Median	0.8
Midrange	0.81
Midmean - Weighted Average at Xnp	0.78125
Midmean - Weighted Average at X(n+1)p	0.78125
Midmean - Empirical Distribution Function	0.78125
Midmean - Empirical Distribution Function - Averaging	0.78125
Midmean - Empirical Distribution Function - Interpolation	0.78125
Midmean - Closest Observation	0.78125
Midmean - True Basic - Statistics Graphics Toolkit	0.78125
Midmean - MS Excel (old versions)	0.78125
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.791111111111111 & 0.00970930284013501 & 81.4797029340688 \tabularnewline
Geometric Mean & 0.786909139953385 &  &  \tabularnewline
Harmonic Mean & 0.782757956676745 &  &  \tabularnewline
Quadratic Mean & 0.795330120138801 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 0.790972222222222 & 0.00968025538789609 & 81.7098506730753 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 0.790972222222222 & 0.00958276630741828 & 82.5411156703163 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 0.790972222222222 & 0.00958276630741828 & 82.5411156703163 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 0.791527777777778 & 0.00950384923710826 & 83.2849678093816 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 0.790833333333333 & 0.00937555423505179 & 84.350568884418 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 0.790833333333333 & 0.00937555423505179 & 84.3505688844181 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 0.790833333333333 & 0.00937555423505179 & 84.350568884418 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 0.789722222222222 & 0.00918206607102333 & 86.0070289315843 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 0.789722222222222 & 0.00918206607102333 & 86.0070289315843 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 0.788333333333333 & 0.00895345292324846 & 88.0479676490345 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 0.789861111111111 & 0.00874900632756092 & 90.2800937088031 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 0.788194444444444 & 0.00848760116800986 & 92.8642179153262 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 0.786388888888889 & 0.00822061218005385 & 95.6606237667981 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 0.786388888888889 & 0.00822061218005385 & 95.6606237667981 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 0.786388888888889 & 0.00822061218005385 & 95.6606237667981 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 0.786388888888889 & 0.00822061218005385 & 95.6606237667981 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 0.786388888888889 & 0.00822061218005385 & 95.6606237667981 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 0.786388888888889 & 0.00822061218005385 & 95.6606237667981 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 0.78375 & 0.00785091299775246 & 99.829153656953 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 0.780972222222222 & 0.00748017652034478 & 104.40558723422 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 0.780972222222222 & 0.00748017652034478 & 104.40558723422 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 0.777916666666667 & 0.00709299258553584 & 109.673971498717 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 0.777916666666667 & 0.00709299258553584 & 109.673971498717 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 0.777916666666667 & 0.00709299258553584 & 109.673971498717 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 0.790571428571429 & 0.00962417099069877 & 82.1443664431433 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 0.790147058823529 & 0.00955206757943486 & 82.7200029996309 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 0.78969696969697 & 0.00951987173761733 & 82.9524799768592 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 0.78921875 & 0.00947350285398198 & 83.3080183924016 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 0.788548387096774 & 0.00943638214547441 & 83.5646940681555 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 0.788 & 0.00942049694612043 & 83.6473919058501 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 0.787413793103448 & 0.00939024330774019 & 83.8544611995729 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 0.786785714285714 & 0.0093423596912725 & 84.2170222819314 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 0.786296296296296 & 0.00931735790723471 & 84.390478945298 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 0.785769230769231 & 0.00927356219558245 & 84.7321896588497 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 0.7854 & 0.00925471749533001 & 84.8648270891378 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 0.784791666666667 & 0.00925404638031297 & 84.8052445831945 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 0.784347826086957 & 0.00928690405094732 & 84.4574060186342 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 0.784090909090909 & 0.00935735333857705 & 83.7940901364043 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 0.783809523809524 & 0.00941958064511862 & 83.2106601492612 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 0.7835 & 0.00947026385249627 & 82.7326473901228 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 0.783157894736842 & 0.0095048483784179 & 82.3956220611696 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 0.782777777777778 & 0.0095169949164565 & 82.2505196912759 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 0.782352941176471 & 0.00949771361481204 & 82.3727660051111 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 0.7821875 & 0.00952219790931661 & 82.1435877986426 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 0.782333333333333 & 0.00959745336592531 & 81.5146793117975 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 0.7825 & 0.00964481657536766 & 81.1316621612548 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 0.783076923076923 & 0.00974709788397364 & 80.3394951398275 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 0.78375 & 0.00981370861660332 & 79.8627746776599 \tabularnewline
Median & 0.8 &  &  \tabularnewline
Midrange & 0.81 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.78125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.78125 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.78125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.78125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.78125 &  &  \tabularnewline
Midmean - Closest Observation & 0.78125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.78125 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.78125 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160814&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]0.791111111111111[/C][C]0.00970930284013501[/C][C]81.4797029340688[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.786909139953385[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.782757956676745[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.795330120138801[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]0.790972222222222[/C][C]0.00968025538789609[/C][C]81.7098506730753[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]0.790972222222222[/C][C]0.00958276630741828[/C][C]82.5411156703163[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]0.790972222222222[/C][C]0.00958276630741828[/C][C]82.5411156703163[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]0.791527777777778[/C][C]0.00950384923710826[/C][C]83.2849678093816[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]0.790833333333333[/C][C]0.00937555423505179[/C][C]84.350568884418[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]0.790833333333333[/C][C]0.00937555423505179[/C][C]84.3505688844181[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]0.790833333333333[/C][C]0.00937555423505179[/C][C]84.350568884418[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]0.789722222222222[/C][C]0.00918206607102333[/C][C]86.0070289315843[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]0.789722222222222[/C][C]0.00918206607102333[/C][C]86.0070289315843[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]0.788333333333333[/C][C]0.00895345292324846[/C][C]88.0479676490345[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]0.789861111111111[/C][C]0.00874900632756092[/C][C]90.2800937088031[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]0.788194444444444[/C][C]0.00848760116800986[/C][C]92.8642179153262[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]0.786388888888889[/C][C]0.00822061218005385[/C][C]95.6606237667981[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]0.786388888888889[/C][C]0.00822061218005385[/C][C]95.6606237667981[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]0.786388888888889[/C][C]0.00822061218005385[/C][C]95.6606237667981[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]0.786388888888889[/C][C]0.00822061218005385[/C][C]95.6606237667981[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]0.786388888888889[/C][C]0.00822061218005385[/C][C]95.6606237667981[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]0.786388888888889[/C][C]0.00822061218005385[/C][C]95.6606237667981[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]0.78375[/C][C]0.00785091299775246[/C][C]99.829153656953[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]0.780972222222222[/C][C]0.00748017652034478[/C][C]104.40558723422[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]0.780972222222222[/C][C]0.00748017652034478[/C][C]104.40558723422[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]0.777916666666667[/C][C]0.00709299258553584[/C][C]109.673971498717[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]0.777916666666667[/C][C]0.00709299258553584[/C][C]109.673971498717[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]0.777916666666667[/C][C]0.00709299258553584[/C][C]109.673971498717[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]0.790571428571429[/C][C]0.00962417099069877[/C][C]82.1443664431433[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]0.790147058823529[/C][C]0.00955206757943486[/C][C]82.7200029996309[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]0.78969696969697[/C][C]0.00951987173761733[/C][C]82.9524799768592[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]0.78921875[/C][C]0.00947350285398198[/C][C]83.3080183924016[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]0.788548387096774[/C][C]0.00943638214547441[/C][C]83.5646940681555[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]0.788[/C][C]0.00942049694612043[/C][C]83.6473919058501[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]0.787413793103448[/C][C]0.00939024330774019[/C][C]83.8544611995729[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]0.786785714285714[/C][C]0.0093423596912725[/C][C]84.2170222819314[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]0.786296296296296[/C][C]0.00931735790723471[/C][C]84.390478945298[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]0.785769230769231[/C][C]0.00927356219558245[/C][C]84.7321896588497[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]0.7854[/C][C]0.00925471749533001[/C][C]84.8648270891378[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]0.784791666666667[/C][C]0.00925404638031297[/C][C]84.8052445831945[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]0.784347826086957[/C][C]0.00928690405094732[/C][C]84.4574060186342[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]0.784090909090909[/C][C]0.00935735333857705[/C][C]83.7940901364043[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]0.783809523809524[/C][C]0.00941958064511862[/C][C]83.2106601492612[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]0.7835[/C][C]0.00947026385249627[/C][C]82.7326473901228[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]0.783157894736842[/C][C]0.0095048483784179[/C][C]82.3956220611696[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]0.782777777777778[/C][C]0.0095169949164565[/C][C]82.2505196912759[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]0.782352941176471[/C][C]0.00949771361481204[/C][C]82.3727660051111[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]0.7821875[/C][C]0.00952219790931661[/C][C]82.1435877986426[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]0.782333333333333[/C][C]0.00959745336592531[/C][C]81.5146793117975[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]0.7825[/C][C]0.00964481657536766[/C][C]81.1316621612548[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]0.783076923076923[/C][C]0.00974709788397364[/C][C]80.3394951398275[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]0.78375[/C][C]0.00981370861660332[/C][C]79.8627746776599[/C][/ROW]
[ROW][C]Median[/C][C]0.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.78125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.78125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.78125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.78125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.78125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.78125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.78125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.78125[/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=160814&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160814&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	0.791111111111111	0.00970930284013501	81.4797029340688
Geometric Mean	0.786909139953385
Harmonic Mean	0.782757956676745
Quadratic Mean	0.795330120138801
Winsorized Mean ( 1 / 24 )	0.790972222222222	0.00968025538789609	81.7098506730753
Winsorized Mean ( 2 / 24 )	0.790972222222222	0.00958276630741828	82.5411156703163
Winsorized Mean ( 3 / 24 )	0.790972222222222	0.00958276630741828	82.5411156703163
Winsorized Mean ( 4 / 24 )	0.791527777777778	0.00950384923710826	83.2849678093816
Winsorized Mean ( 5 / 24 )	0.790833333333333	0.00937555423505179	84.350568884418
Winsorized Mean ( 6 / 24 )	0.790833333333333	0.00937555423505179	84.3505688844181
Winsorized Mean ( 7 / 24 )	0.790833333333333	0.00937555423505179	84.350568884418
Winsorized Mean ( 8 / 24 )	0.789722222222222	0.00918206607102333	86.0070289315843
Winsorized Mean ( 9 / 24 )	0.789722222222222	0.00918206607102333	86.0070289315843
Winsorized Mean ( 10 / 24 )	0.788333333333333	0.00895345292324846	88.0479676490345
Winsorized Mean ( 11 / 24 )	0.789861111111111	0.00874900632756092	90.2800937088031
Winsorized Mean ( 12 / 24 )	0.788194444444444	0.00848760116800986	92.8642179153262
Winsorized Mean ( 13 / 24 )	0.786388888888889	0.00822061218005385	95.6606237667981
Winsorized Mean ( 14 / 24 )	0.786388888888889	0.00822061218005385	95.6606237667981
Winsorized Mean ( 15 / 24 )	0.786388888888889	0.00822061218005385	95.6606237667981
Winsorized Mean ( 16 / 24 )	0.786388888888889	0.00822061218005385	95.6606237667981
Winsorized Mean ( 17 / 24 )	0.786388888888889	0.00822061218005385	95.6606237667981
Winsorized Mean ( 18 / 24 )	0.786388888888889	0.00822061218005385	95.6606237667981
Winsorized Mean ( 19 / 24 )	0.78375	0.00785091299775246	99.829153656953
Winsorized Mean ( 20 / 24 )	0.780972222222222	0.00748017652034478	104.40558723422
Winsorized Mean ( 21 / 24 )	0.780972222222222	0.00748017652034478	104.40558723422
Winsorized Mean ( 22 / 24 )	0.777916666666667	0.00709299258553584	109.673971498717
Winsorized Mean ( 23 / 24 )	0.777916666666667	0.00709299258553584	109.673971498717
Winsorized Mean ( 24 / 24 )	0.777916666666667	0.00709299258553584	109.673971498717
Trimmed Mean ( 1 / 24 )	0.790571428571429	0.00962417099069877	82.1443664431433
Trimmed Mean ( 2 / 24 )	0.790147058823529	0.00955206757943486	82.7200029996309
Trimmed Mean ( 3 / 24 )	0.78969696969697	0.00951987173761733	82.9524799768592
Trimmed Mean ( 4 / 24 )	0.78921875	0.00947350285398198	83.3080183924016
Trimmed Mean ( 5 / 24 )	0.788548387096774	0.00943638214547441	83.5646940681555
Trimmed Mean ( 6 / 24 )	0.788	0.00942049694612043	83.6473919058501
Trimmed Mean ( 7 / 24 )	0.787413793103448	0.00939024330774019	83.8544611995729
Trimmed Mean ( 8 / 24 )	0.786785714285714	0.0093423596912725	84.2170222819314
Trimmed Mean ( 9 / 24 )	0.786296296296296	0.00931735790723471	84.390478945298
Trimmed Mean ( 10 / 24 )	0.785769230769231	0.00927356219558245	84.7321896588497
Trimmed Mean ( 11 / 24 )	0.7854	0.00925471749533001	84.8648270891378
Trimmed Mean ( 12 / 24 )	0.784791666666667	0.00925404638031297	84.8052445831945
Trimmed Mean ( 13 / 24 )	0.784347826086957	0.00928690405094732	84.4574060186342
Trimmed Mean ( 14 / 24 )	0.784090909090909	0.00935735333857705	83.7940901364043
Trimmed Mean ( 15 / 24 )	0.783809523809524	0.00941958064511862	83.2106601492612
Trimmed Mean ( 16 / 24 )	0.7835	0.00947026385249627	82.7326473901228
Trimmed Mean ( 17 / 24 )	0.783157894736842	0.0095048483784179	82.3956220611696
Trimmed Mean ( 18 / 24 )	0.782777777777778	0.0095169949164565	82.2505196912759
Trimmed Mean ( 19 / 24 )	0.782352941176471	0.00949771361481204	82.3727660051111
Trimmed Mean ( 20 / 24 )	0.7821875	0.00952219790931661	82.1435877986426
Trimmed Mean ( 21 / 24 )	0.782333333333333	0.00959745336592531	81.5146793117975
Trimmed Mean ( 22 / 24 )	0.7825	0.00964481657536766	81.1316621612548
Trimmed Mean ( 23 / 24 )	0.783076923076923	0.00974709788397364	80.3394951398275
Trimmed Mean ( 24 / 24 )	0.78375	0.00981370861660332	79.8627746776599
Median	0.8
Midrange	0.81
Midmean - Weighted Average at Xnp	0.78125
Midmean - Weighted Average at X(n+1)p	0.78125
Midmean - Empirical Distribution Function	0.78125
Midmean - Empirical Distribution Function - Averaging	0.78125
Midmean - Empirical Distribution Function - Interpolation	0.78125
Midmean - Closest Observation	0.78125
Midmean - True Basic - Statistics Graphics Toolkit	0.78125
Midmean - MS Excel (old versions)	0.78125
Number of observations	72

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 0.1 ; par2 = 1 ; par3 = 0.1 ;

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