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*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 08 Oct 2012 03:50:29 -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/08/t13496826711cq5hlptsly1hb0.htm/, Retrieved Thu, 02 May 2024 00:53:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=173254, Retrieved Thu, 02 May 2024 00:53:13 +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] [Betrouwbaarheid r...] [2012-10-08 07:50:29] [91a4a62a2651e4f95a22762c3a012f20] [Current]

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2,07
2,08
2,08
2,08
2,09
2,09
2,09
2,1
2,1
2,1
2,11
2,11
2,11
2,13
2,18
2,2
2,21
2,21
2,22
2,22
2,23
2,23
2,23
2,23
2,24
2,25
2,26
2,27
2,28
2,29
2,3
2,3
2,3
2,32
2,32
2,32
2,33
2,34
2,34
2,34
2,35
2,35
2,36
2,37
2,37
2,37
2,38
2,38
2,38
2,39
2,4
2,41
2,42
2,43
2,43
2,43
2,43
2,44
2,44
2,45
2,45
2,48
2,49
2,49
2,5
2,51
2,52
2,53
2,54
2,54
2,56
2,56

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' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173254&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173254&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173254&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' @ jenkins.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.31180555555556	0.0168177732073224	137.462048456511
Geometric Mean	2.30742553056476
Harmonic Mean	2.30301297468395
Quadratic Mean	2.31614472537639
Winsorized Mean ( 1 / 24 )	2.31194444444444	0.0167901981718908	137.696078436702
Winsorized Mean ( 2 / 24 )	2.31138888888889	0.0166787580031372	138.582794261667
Winsorized Mean ( 3 / 24 )	2.31138888888889	0.0166787580031372	138.582794261667
Winsorized Mean ( 4 / 24 )	2.31138888888889	0.0164662902624145	140.37095496639
Winsorized Mean ( 5 / 24 )	2.31069444444444	0.0163387056280393	141.424571630632
Winsorized Mean ( 6 / 24 )	2.30986111111111	0.0161909732762445	142.663512050888
Winsorized Mean ( 7 / 24 )	2.30986111111111	0.0158404271921225	145.820632429649
Winsorized Mean ( 8 / 24 )	2.30875	0.0156558966826869	147.468397805226
Winsorized Mean ( 9 / 24 )	2.30875	0.0156558966826869	147.468397805226
Winsorized Mean ( 10 / 24 )	2.30875	0.0151736653872179	152.155062147664
Winsorized Mean ( 11 / 24 )	2.30416666666667	0.0144834777163692	159.089323143881
Winsorized Mean ( 12 / 24 )	2.30416666666667	0.0144834777163692	159.089323143881
Winsorized Mean ( 13 / 24 )	2.30597222222222	0.0135583416253603	170.077748882577
Winsorized Mean ( 14 / 24 )	2.31569444444444	0.0118807098765573	194.912128021383
Winsorized Mean ( 15 / 24 )	2.31777777777778	0.0109240911609422	212.171222633579
Winsorized Mean ( 16 / 24 )	2.32	0.0105927603942482	219.01750947371
Winsorized Mean ( 17 / 24 )	2.32	0.0105927603942482	219.01750947371
Winsorized Mean ( 18 / 24 )	2.3225	0.0102334831999547	226.951073707755
Winsorized Mean ( 19 / 24 )	2.31986111111111	0.00984920151898829	235.537988195149
Winsorized Mean ( 20 / 24 )	2.31986111111111	0.0090631005128449	255.967713016448
Winsorized Mean ( 21 / 24 )	2.31694444444444	0.0086616970423197	267.49312901666
Winsorized Mean ( 22 / 24 )	2.31388888888889	0.00825682142126205	280.239667401601
Winsorized Mean ( 23 / 24 )	2.31069444444444	0.00785063614162596	294.332128347229
Winsorized Mean ( 24 / 24 )	2.31402777777778	0.00737350213489245	313.830217370857
Trimmed Mean ( 1 / 24 )	2.31171428571429	0.016567787134716	139.530660728393
Trimmed Mean ( 2 / 24 )	2.31147058823529	0.0162997933082366	141.809809764106
Trimmed Mean ( 3 / 24 )	2.31151515151515	0.0160466139516099	144.050025661847
Trimmed Mean ( 4 / 24 )	2.3115625	0.0157394124624364	146.864599013258
Trimmed Mean ( 5 / 24 )	2.31161290322581	0.0154437166630114	149.679831200364
Trimmed Mean ( 6 / 24 )	2.31183333333333	0.0151218995359177	152.879823585803
Trimmed Mean ( 7 / 24 )	2.31224137931034	0.0147679020801213	156.572095803831
Trimmed Mean ( 8 / 24 )	2.31267857142857	0.0144228603523058	160.34812200472
Trimmed Mean ( 9 / 24 )	2.31333333333333	0.0140379838124219	164.790995932501
Trimmed Mean ( 10 / 24 )	2.31403846153846	0.013554703466962	170.71848655182
Trimmed Mean ( 11 / 24 )	2.3148	0.0130626121711813	177.208047645088
Trimmed Mean ( 12 / 24 )	2.31625	0.0125923010645112	183.941758391392
Trimmed Mean ( 13 / 24 )	2.31782608695652	0.0119819229521288	193.443581319702
Trimmed Mean ( 14 / 24 )	2.31931818181818	0.0114230476529736	203.038475569558
Trimmed Mean ( 15 / 24 )	2.3197619047619	0.0111190793285578	208.628955349201
Trimmed Mean ( 16 / 24 )	2.32	0.0109310191422017	212.240045490645
Trimmed Mean ( 17 / 24 )	2.32	0.0107407044067047	216.000730692466
Trimmed Mean ( 18 / 24 )	2.32	0.0104653623694457	221.683675930171
Trimmed Mean ( 19 / 24 )	2.31970588235294	0.0101634177981644	228.240728504924
Trimmed Mean ( 20 / 24 )	2.3196875	0.00983210236394848	235.929958225988
Trimmed Mean ( 21 / 24 )	2.31966666666667	0.00957106911398483	242.362335810246
Trimmed Mean ( 22 / 24 )	2.32	0.00928673173099052	249.818780945075
Trimmed Mean ( 23 / 24 )	2.32076923076923	0.00896013524834525	259.010513395747
Trimmed Mean ( 24 / 24 )	2.32208333333333	0.00855458108196554	271.443254916207
Median	2.325
Midrange	2.315
Midmean - Weighted Average at Xnp	2.32268292682927
Midmean - Weighted Average at X(n+1)p	2.32846153846154
Midmean - Empirical Distribution Function	2.32268292682927
Midmean - Empirical Distribution Function - Averaging	2.32846153846154
Midmean - Empirical Distribution Function - Interpolation	2.32846153846154
Midmean - Closest Observation	2.32268292682927
Midmean - True Basic - Statistics Graphics Toolkit	2.32846153846154
Midmean - MS Excel (old versions)	2.32268292682927
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.31180555555556 & 0.0168177732073224 & 137.462048456511 \tabularnewline
Geometric Mean & 2.30742553056476 &  &  \tabularnewline
Harmonic Mean & 2.30301297468395 &  &  \tabularnewline
Quadratic Mean & 2.31614472537639 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.31194444444444 & 0.0167901981718908 & 137.696078436702 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.31138888888889 & 0.0166787580031372 & 138.582794261667 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.31138888888889 & 0.0166787580031372 & 138.582794261667 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.31138888888889 & 0.0164662902624145 & 140.37095496639 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.31069444444444 & 0.0163387056280393 & 141.424571630632 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.30986111111111 & 0.0161909732762445 & 142.663512050888 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.30986111111111 & 0.0158404271921225 & 145.820632429649 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.30875 & 0.0156558966826869 & 147.468397805226 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.30875 & 0.0156558966826869 & 147.468397805226 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.30875 & 0.0151736653872179 & 152.155062147664 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.30416666666667 & 0.0144834777163692 & 159.089323143881 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.30416666666667 & 0.0144834777163692 & 159.089323143881 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.30597222222222 & 0.0135583416253603 & 170.077748882577 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.31569444444444 & 0.0118807098765573 & 194.912128021383 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.31777777777778 & 0.0109240911609422 & 212.171222633579 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.32 & 0.0105927603942482 & 219.01750947371 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.32 & 0.0105927603942482 & 219.01750947371 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.3225 & 0.0102334831999547 & 226.951073707755 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.31986111111111 & 0.00984920151898829 & 235.537988195149 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.31986111111111 & 0.0090631005128449 & 255.967713016448 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.31694444444444 & 0.0086616970423197 & 267.49312901666 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.31388888888889 & 0.00825682142126205 & 280.239667401601 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.31069444444444 & 0.00785063614162596 & 294.332128347229 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.31402777777778 & 0.00737350213489245 & 313.830217370857 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.31171428571429 & 0.016567787134716 & 139.530660728393 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.31147058823529 & 0.0162997933082366 & 141.809809764106 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.31151515151515 & 0.0160466139516099 & 144.050025661847 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.3115625 & 0.0157394124624364 & 146.864599013258 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.31161290322581 & 0.0154437166630114 & 149.679831200364 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.31183333333333 & 0.0151218995359177 & 152.879823585803 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.31224137931034 & 0.0147679020801213 & 156.572095803831 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.31267857142857 & 0.0144228603523058 & 160.34812200472 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.31333333333333 & 0.0140379838124219 & 164.790995932501 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.31403846153846 & 0.013554703466962 & 170.71848655182 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.3148 & 0.0130626121711813 & 177.208047645088 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.31625 & 0.0125923010645112 & 183.941758391392 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.31782608695652 & 0.0119819229521288 & 193.443581319702 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.31931818181818 & 0.0114230476529736 & 203.038475569558 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.3197619047619 & 0.0111190793285578 & 208.628955349201 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.32 & 0.0109310191422017 & 212.240045490645 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.32 & 0.0107407044067047 & 216.000730692466 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.32 & 0.0104653623694457 & 221.683675930171 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.31970588235294 & 0.0101634177981644 & 228.240728504924 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.3196875 & 0.00983210236394848 & 235.929958225988 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.31966666666667 & 0.00957106911398483 & 242.362335810246 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.32 & 0.00928673173099052 & 249.818780945075 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.32076923076923 & 0.00896013524834525 & 259.010513395747 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.32208333333333 & 0.00855458108196554 & 271.443254916207 \tabularnewline
Median & 2.325 &  &  \tabularnewline
Midrange & 2.315 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.32268292682927 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.32846153846154 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.32268292682927 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.32846153846154 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.32846153846154 &  &  \tabularnewline
Midmean - Closest Observation & 2.32268292682927 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.32846153846154 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.32268292682927 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173254&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]2.31180555555556[/C][C]0.0168177732073224[/C][C]137.462048456511[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.30742553056476[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.30301297468395[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.31614472537639[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.31194444444444[/C][C]0.0167901981718908[/C][C]137.696078436702[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.31138888888889[/C][C]0.0166787580031372[/C][C]138.582794261667[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.31138888888889[/C][C]0.0166787580031372[/C][C]138.582794261667[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.31138888888889[/C][C]0.0164662902624145[/C][C]140.37095496639[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.31069444444444[/C][C]0.0163387056280393[/C][C]141.424571630632[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.30986111111111[/C][C]0.0161909732762445[/C][C]142.663512050888[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.30986111111111[/C][C]0.0158404271921225[/C][C]145.820632429649[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.30875[/C][C]0.0156558966826869[/C][C]147.468397805226[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.30875[/C][C]0.0156558966826869[/C][C]147.468397805226[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.30875[/C][C]0.0151736653872179[/C][C]152.155062147664[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.30416666666667[/C][C]0.0144834777163692[/C][C]159.089323143881[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.30416666666667[/C][C]0.0144834777163692[/C][C]159.089323143881[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.30597222222222[/C][C]0.0135583416253603[/C][C]170.077748882577[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.31569444444444[/C][C]0.0118807098765573[/C][C]194.912128021383[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.31777777777778[/C][C]0.0109240911609422[/C][C]212.171222633579[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.32[/C][C]0.0105927603942482[/C][C]219.01750947371[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.32[/C][C]0.0105927603942482[/C][C]219.01750947371[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.3225[/C][C]0.0102334831999547[/C][C]226.951073707755[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.31986111111111[/C][C]0.00984920151898829[/C][C]235.537988195149[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.31986111111111[/C][C]0.0090631005128449[/C][C]255.967713016448[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.31694444444444[/C][C]0.0086616970423197[/C][C]267.49312901666[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.31388888888889[/C][C]0.00825682142126205[/C][C]280.239667401601[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.31069444444444[/C][C]0.00785063614162596[/C][C]294.332128347229[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.31402777777778[/C][C]0.00737350213489245[/C][C]313.830217370857[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.31171428571429[/C][C]0.016567787134716[/C][C]139.530660728393[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.31147058823529[/C][C]0.0162997933082366[/C][C]141.809809764106[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.31151515151515[/C][C]0.0160466139516099[/C][C]144.050025661847[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.3115625[/C][C]0.0157394124624364[/C][C]146.864599013258[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.31161290322581[/C][C]0.0154437166630114[/C][C]149.679831200364[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.31183333333333[/C][C]0.0151218995359177[/C][C]152.879823585803[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.31224137931034[/C][C]0.0147679020801213[/C][C]156.572095803831[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.31267857142857[/C][C]0.0144228603523058[/C][C]160.34812200472[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.31333333333333[/C][C]0.0140379838124219[/C][C]164.790995932501[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.31403846153846[/C][C]0.013554703466962[/C][C]170.71848655182[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.3148[/C][C]0.0130626121711813[/C][C]177.208047645088[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.31625[/C][C]0.0125923010645112[/C][C]183.941758391392[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.31782608695652[/C][C]0.0119819229521288[/C][C]193.443581319702[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.31931818181818[/C][C]0.0114230476529736[/C][C]203.038475569558[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.3197619047619[/C][C]0.0111190793285578[/C][C]208.628955349201[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.32[/C][C]0.0109310191422017[/C][C]212.240045490645[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.32[/C][C]0.0107407044067047[/C][C]216.000730692466[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.32[/C][C]0.0104653623694457[/C][C]221.683675930171[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.31970588235294[/C][C]0.0101634177981644[/C][C]228.240728504924[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.3196875[/C][C]0.00983210236394848[/C][C]235.929958225988[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.31966666666667[/C][C]0.00957106911398483[/C][C]242.362335810246[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.32[/C][C]0.00928673173099052[/C][C]249.818780945075[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.32076923076923[/C][C]0.00896013524834525[/C][C]259.010513395747[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.32208333333333[/C][C]0.00855458108196554[/C][C]271.443254916207[/C][/ROW]
[ROW][C]Median[/C][C]2.325[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.315[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.32268292682927[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.32846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.32268292682927[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.32846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.32846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.32268292682927[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.32846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.32268292682927[/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=173254&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173254&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	2.31180555555556	0.0168177732073224	137.462048456511
Geometric Mean	2.30742553056476
Harmonic Mean	2.30301297468395
Quadratic Mean	2.31614472537639
Winsorized Mean ( 1 / 24 )	2.31194444444444	0.0167901981718908	137.696078436702
Winsorized Mean ( 2 / 24 )	2.31138888888889	0.0166787580031372	138.582794261667
Winsorized Mean ( 3 / 24 )	2.31138888888889	0.0166787580031372	138.582794261667
Winsorized Mean ( 4 / 24 )	2.31138888888889	0.0164662902624145	140.37095496639
Winsorized Mean ( 5 / 24 )	2.31069444444444	0.0163387056280393	141.424571630632
Winsorized Mean ( 6 / 24 )	2.30986111111111	0.0161909732762445	142.663512050888
Winsorized Mean ( 7 / 24 )	2.30986111111111	0.0158404271921225	145.820632429649
Winsorized Mean ( 8 / 24 )	2.30875	0.0156558966826869	147.468397805226
Winsorized Mean ( 9 / 24 )	2.30875	0.0156558966826869	147.468397805226
Winsorized Mean ( 10 / 24 )	2.30875	0.0151736653872179	152.155062147664
Winsorized Mean ( 11 / 24 )	2.30416666666667	0.0144834777163692	159.089323143881
Winsorized Mean ( 12 / 24 )	2.30416666666667	0.0144834777163692	159.089323143881
Winsorized Mean ( 13 / 24 )	2.30597222222222	0.0135583416253603	170.077748882577
Winsorized Mean ( 14 / 24 )	2.31569444444444	0.0118807098765573	194.912128021383
Winsorized Mean ( 15 / 24 )	2.31777777777778	0.0109240911609422	212.171222633579
Winsorized Mean ( 16 / 24 )	2.32	0.0105927603942482	219.01750947371
Winsorized Mean ( 17 / 24 )	2.32	0.0105927603942482	219.01750947371
Winsorized Mean ( 18 / 24 )	2.3225	0.0102334831999547	226.951073707755
Winsorized Mean ( 19 / 24 )	2.31986111111111	0.00984920151898829	235.537988195149
Winsorized Mean ( 20 / 24 )	2.31986111111111	0.0090631005128449	255.967713016448
Winsorized Mean ( 21 / 24 )	2.31694444444444	0.0086616970423197	267.49312901666
Winsorized Mean ( 22 / 24 )	2.31388888888889	0.00825682142126205	280.239667401601
Winsorized Mean ( 23 / 24 )	2.31069444444444	0.00785063614162596	294.332128347229
Winsorized Mean ( 24 / 24 )	2.31402777777778	0.00737350213489245	313.830217370857
Trimmed Mean ( 1 / 24 )	2.31171428571429	0.016567787134716	139.530660728393
Trimmed Mean ( 2 / 24 )	2.31147058823529	0.0162997933082366	141.809809764106
Trimmed Mean ( 3 / 24 )	2.31151515151515	0.0160466139516099	144.050025661847
Trimmed Mean ( 4 / 24 )	2.3115625	0.0157394124624364	146.864599013258
Trimmed Mean ( 5 / 24 )	2.31161290322581	0.0154437166630114	149.679831200364
Trimmed Mean ( 6 / 24 )	2.31183333333333	0.0151218995359177	152.879823585803
Trimmed Mean ( 7 / 24 )	2.31224137931034	0.0147679020801213	156.572095803831
Trimmed Mean ( 8 / 24 )	2.31267857142857	0.0144228603523058	160.34812200472
Trimmed Mean ( 9 / 24 )	2.31333333333333	0.0140379838124219	164.790995932501
Trimmed Mean ( 10 / 24 )	2.31403846153846	0.013554703466962	170.71848655182
Trimmed Mean ( 11 / 24 )	2.3148	0.0130626121711813	177.208047645088
Trimmed Mean ( 12 / 24 )	2.31625	0.0125923010645112	183.941758391392
Trimmed Mean ( 13 / 24 )	2.31782608695652	0.0119819229521288	193.443581319702
Trimmed Mean ( 14 / 24 )	2.31931818181818	0.0114230476529736	203.038475569558
Trimmed Mean ( 15 / 24 )	2.3197619047619	0.0111190793285578	208.628955349201
Trimmed Mean ( 16 / 24 )	2.32	0.0109310191422017	212.240045490645
Trimmed Mean ( 17 / 24 )	2.32	0.0107407044067047	216.000730692466
Trimmed Mean ( 18 / 24 )	2.32	0.0104653623694457	221.683675930171
Trimmed Mean ( 19 / 24 )	2.31970588235294	0.0101634177981644	228.240728504924
Trimmed Mean ( 20 / 24 )	2.3196875	0.00983210236394848	235.929958225988
Trimmed Mean ( 21 / 24 )	2.31966666666667	0.00957106911398483	242.362335810246
Trimmed Mean ( 22 / 24 )	2.32	0.00928673173099052	249.818780945075
Trimmed Mean ( 23 / 24 )	2.32076923076923	0.00896013524834525	259.010513395747
Trimmed Mean ( 24 / 24 )	2.32208333333333	0.00855458108196554	271.443254916207
Median	2.325
Midrange	2.315
Midmean - Weighted Average at Xnp	2.32268292682927
Midmean - Weighted Average at X(n+1)p	2.32846153846154
Midmean - Empirical Distribution Function	2.32268292682927
Midmean - Empirical Distribution Function - Averaging	2.32846153846154
Midmean - Empirical Distribution Function - Interpolation	2.32846153846154
Midmean - Closest Observation	2.32268292682927
Midmean - True Basic - Statistics Graphics Toolkit	2.32846153846154
Midmean - MS Excel (old versions)	2.32268292682927
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