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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sun, 14 Oct 2012 08:21:17 -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/14/t1350217370x6irmoyt43svqym.htm/, Retrieved Sun, 28 Apr 2024 15:57:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=176108, Retrieved Sun, 28 Apr 2024 15:57:11 +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] [Prijs Citroenen] [2012-10-14 12:21:17] [725db2a88b228374c3964e39efbe73da] [Current]

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1,94
1,82
1,8
1,79
1,79
1,78
1,81
1,84
1,87
1,87
1,87
1,84
1,82
1,83
1,83
1,82
1,83
1,87
1,88
1,9
1,98
2,03
2,14
2,42
2,73
2,84
2,85
2,94
3,06
3,24
3,18
3,01
2,87
2,73
2,63
2,39
2,26
2,11
2,01
1,99
1,96
1,93
1,98
2,07
2,24
2,31
2,23
2,26
2,28
2,3
2,33
2,26
2,24
2,47
2,55
2,89
3,21
3,21
2,92
2,68
2,4
2,28
2,24
2,2
2,18
2,23
2,24
2,25
2,23
2,25
2,23
2,21

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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=176108&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=176108&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=176108&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.27041666666667	0.0490669744054827	46.2717885945903
Geometric Mean	2.23539264075034
Harmonic Mean	2.20304696715087
Quadratic Mean	2.30775413912892
Winsorized Mean ( 1 / 24 )	2.27013888888889	0.0489332579598774	46.3925555651798
Winsorized Mean ( 2 / 24 )	2.27013888888889	0.0489332579598774	46.3925555651798
Winsorized Mean ( 3 / 24 )	2.26930555555556	0.0485418548683163	46.7494610931473
Winsorized Mean ( 4 / 24 )	2.26319444444444	0.0467842358674359	48.3751503574249
Winsorized Mean ( 5 / 24 )	2.26041666666667	0.0458737284643813	49.2747535971873
Winsorized Mean ( 6 / 24 )	2.25458333333333	0.0445701682988849	50.5850307365732
Winsorized Mean ( 7 / 24 )	2.25263888888889	0.0441525989889463	51.0193950180111
Winsorized Mean ( 8 / 24 )	2.25041666666667	0.0432983054076451	51.9747053719408
Winsorized Mean ( 9 / 24 )	2.24791666666667	0.0427822202386061	52.5432446967344
Winsorized Mean ( 10 / 24 )	2.24513888888889	0.0422174827203607	53.1803116675665
Winsorized Mean ( 11 / 24 )	2.24513888888889	0.0416995143085185	53.8408882242124
Winsorized Mean ( 12 / 24 )	2.22680555555556	0.038148578236607	58.3719147210245
Winsorized Mean ( 13 / 24 )	2.23222222222222	0.0373921099096925	59.6976802756884
Winsorized Mean ( 14 / 24 )	2.2225	0.0356000156054897	62.429747914416
Winsorized Mean ( 15 / 24 )	2.21208333333333	0.0337479713063266	65.5471498791586
Winsorized Mean ( 16 / 24 )	2.19430555555556	0.0307444324189098	71.3724529260107
Winsorized Mean ( 17 / 24 )	2.17777777777778	0.0274255445493278	79.4069110956325
Winsorized Mean ( 18 / 24 )	2.17027777777778	0.0248343275963029	87.3902371369565
Winsorized Mean ( 19 / 24 )	2.17291666666667	0.0228927532082157	94.9172276005167
Winsorized Mean ( 20 / 24 )	2.17291666666667	0.0220926324649911	98.3548099172864
Winsorized Mean ( 21 / 24 )	2.16125	0.018902742491737	114.335261189997
Winsorized Mean ( 22 / 24 )	2.16125	0.017235523852573	125.395086246674
Winsorized Mean ( 23 / 24 )	2.15805555555556	0.016851833938092	128.060575690665
Winsorized Mean ( 24 / 24 )	2.15472222222222	0.0155820462452357	138.28236601987
Trimmed Mean ( 1 / 24 )	2.26357142857143	0.0479898348942725	47.1677269479746
Trimmed Mean ( 2 / 24 )	2.25661764705882	0.0468505976783077	48.1662509954203
Trimmed Mean ( 3 / 24 )	2.24924242424242	0.0454710187709501	49.4654064289272
Trimmed Mean ( 4 / 24 )	2.24171875	0.043978459445657	50.9731077044669
Trimmed Mean ( 5 / 24 )	2.23548387096774	0.0428367934558334	52.1860692787994
Trimmed Mean ( 6 / 24 )	2.2295	0.0417325524285705	53.4235236106397
Trimmed Mean ( 7 / 24 )	2.22431034482759	0.0407552059991036	54.5773304366688
Trimmed Mean ( 8 / 24 )	2.21910714285714	0.0396504833544458	55.9667109987027
Trimmed Mean ( 9 / 24 )	2.21388888888889	0.0384867649178407	57.523382222823
Trimmed Mean ( 10 / 24 )	2.20865384615385	0.0371495985599298	59.4529667013989
Trimmed Mean ( 11 / 24 )	2.2034	0.0355936362117656	61.9043243261463
Trimmed Mean ( 12 / 24 )	2.19770833333333	0.0337192723047754	65.1766240228763
Trimmed Mean ( 13 / 24 )	2.19391304347826	0.0322512453579262	68.0256845628777
Trimmed Mean ( 14 / 24 )	2.18909090909091	0.0304976659797654	71.7789653327349
Trimmed Mean ( 15 / 24 )	2.185	0.0286782989661377	76.1900140095468
Trimmed Mean ( 16 / 24 )	2.18175	0.0267775439309575	81.4768526055028
Trimmed Mean ( 17 / 24 )	2.18026315789474	0.025098630028708	86.8678153110723
Trimmed Mean ( 18 / 24 )	2.18055555555556	0.0237645342142394	91.7567134241999
Trimmed Mean ( 19 / 24 )	2.18176470588235	0.0226476954328655	96.3349543599148
Trimmed Mean ( 20 / 24 )	2.1828125	0.0216377543731903	100.879807689496
Trimmed Mean ( 21 / 24 )	2.184	0.0204129776165168	106.990760536222
Trimmed Mean ( 22 / 24 )	2.18678571428571	0.0196130124405122	111.49667706164
Trimmed Mean ( 23 / 24 )	2.19	0.0189168219806117	115.769974588997
Trimmed Mean ( 24 / 24 )	2.19416666666667	0.0178552621507899	122.886275661296
Median	2.23
Midrange	2.51
Midmean - Weighted Average at Xnp	2.17243243243243
Midmean - Weighted Average at X(n+1)p	2.18055555555556
Midmean - Empirical Distribution Function	2.17243243243243
Midmean - Empirical Distribution Function - Averaging	2.18055555555556
Midmean - Empirical Distribution Function - Interpolation	2.18055555555556
Midmean - Closest Observation	2.17243243243243
Midmean - True Basic - Statistics Graphics Toolkit	2.18055555555556
Midmean - MS Excel (old versions)	2.18026315789474
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.27041666666667 & 0.0490669744054827 & 46.2717885945903 \tabularnewline
Geometric Mean & 2.23539264075034 &  &  \tabularnewline
Harmonic Mean & 2.20304696715087 &  &  \tabularnewline
Quadratic Mean & 2.30775413912892 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.27013888888889 & 0.0489332579598774 & 46.3925555651798 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.27013888888889 & 0.0489332579598774 & 46.3925555651798 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.26930555555556 & 0.0485418548683163 & 46.7494610931473 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.26319444444444 & 0.0467842358674359 & 48.3751503574249 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.26041666666667 & 0.0458737284643813 & 49.2747535971873 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.25458333333333 & 0.0445701682988849 & 50.5850307365732 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.25263888888889 & 0.0441525989889463 & 51.0193950180111 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.25041666666667 & 0.0432983054076451 & 51.9747053719408 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.24791666666667 & 0.0427822202386061 & 52.5432446967344 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.24513888888889 & 0.0422174827203607 & 53.1803116675665 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.24513888888889 & 0.0416995143085185 & 53.8408882242124 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.22680555555556 & 0.038148578236607 & 58.3719147210245 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.23222222222222 & 0.0373921099096925 & 59.6976802756884 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.2225 & 0.0356000156054897 & 62.429747914416 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.21208333333333 & 0.0337479713063266 & 65.5471498791586 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.19430555555556 & 0.0307444324189098 & 71.3724529260107 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.17777777777778 & 0.0274255445493278 & 79.4069110956325 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.17027777777778 & 0.0248343275963029 & 87.3902371369565 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.17291666666667 & 0.0228927532082157 & 94.9172276005167 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.17291666666667 & 0.0220926324649911 & 98.3548099172864 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.16125 & 0.018902742491737 & 114.335261189997 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.16125 & 0.017235523852573 & 125.395086246674 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.15805555555556 & 0.016851833938092 & 128.060575690665 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.15472222222222 & 0.0155820462452357 & 138.28236601987 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.26357142857143 & 0.0479898348942725 & 47.1677269479746 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.25661764705882 & 0.0468505976783077 & 48.1662509954203 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.24924242424242 & 0.0454710187709501 & 49.4654064289272 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.24171875 & 0.043978459445657 & 50.9731077044669 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.23548387096774 & 0.0428367934558334 & 52.1860692787994 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.2295 & 0.0417325524285705 & 53.4235236106397 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.22431034482759 & 0.0407552059991036 & 54.5773304366688 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.21910714285714 & 0.0396504833544458 & 55.9667109987027 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.21388888888889 & 0.0384867649178407 & 57.523382222823 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.20865384615385 & 0.0371495985599298 & 59.4529667013989 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.2034 & 0.0355936362117656 & 61.9043243261463 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.19770833333333 & 0.0337192723047754 & 65.1766240228763 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.19391304347826 & 0.0322512453579262 & 68.0256845628777 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.18909090909091 & 0.0304976659797654 & 71.7789653327349 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.185 & 0.0286782989661377 & 76.1900140095468 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.18175 & 0.0267775439309575 & 81.4768526055028 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.18026315789474 & 0.025098630028708 & 86.8678153110723 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.18055555555556 & 0.0237645342142394 & 91.7567134241999 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.18176470588235 & 0.0226476954328655 & 96.3349543599148 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.1828125 & 0.0216377543731903 & 100.879807689496 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.184 & 0.0204129776165168 & 106.990760536222 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.18678571428571 & 0.0196130124405122 & 111.49667706164 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.19 & 0.0189168219806117 & 115.769974588997 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.19416666666667 & 0.0178552621507899 & 122.886275661296 \tabularnewline
Median & 2.23 &  &  \tabularnewline
Midrange & 2.51 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.17243243243243 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.18055555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.17243243243243 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.18055555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.18055555555556 &  &  \tabularnewline
Midmean - Closest Observation & 2.17243243243243 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.18055555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.18026315789474 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=176108&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]2.27041666666667[/C][C]0.0490669744054827[/C][C]46.2717885945903[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.23539264075034[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.20304696715087[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.30775413912892[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.27013888888889[/C][C]0.0489332579598774[/C][C]46.3925555651798[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.27013888888889[/C][C]0.0489332579598774[/C][C]46.3925555651798[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.26930555555556[/C][C]0.0485418548683163[/C][C]46.7494610931473[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.26319444444444[/C][C]0.0467842358674359[/C][C]48.3751503574249[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.26041666666667[/C][C]0.0458737284643813[/C][C]49.2747535971873[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.25458333333333[/C][C]0.0445701682988849[/C][C]50.5850307365732[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.25263888888889[/C][C]0.0441525989889463[/C][C]51.0193950180111[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.25041666666667[/C][C]0.0432983054076451[/C][C]51.9747053719408[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.24791666666667[/C][C]0.0427822202386061[/C][C]52.5432446967344[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.24513888888889[/C][C]0.0422174827203607[/C][C]53.1803116675665[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.24513888888889[/C][C]0.0416995143085185[/C][C]53.8408882242124[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.22680555555556[/C][C]0.038148578236607[/C][C]58.3719147210245[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.23222222222222[/C][C]0.0373921099096925[/C][C]59.6976802756884[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.2225[/C][C]0.0356000156054897[/C][C]62.429747914416[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.21208333333333[/C][C]0.0337479713063266[/C][C]65.5471498791586[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.19430555555556[/C][C]0.0307444324189098[/C][C]71.3724529260107[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.17777777777778[/C][C]0.0274255445493278[/C][C]79.4069110956325[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.17027777777778[/C][C]0.0248343275963029[/C][C]87.3902371369565[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.17291666666667[/C][C]0.0228927532082157[/C][C]94.9172276005167[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.17291666666667[/C][C]0.0220926324649911[/C][C]98.3548099172864[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.16125[/C][C]0.018902742491737[/C][C]114.335261189997[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.16125[/C][C]0.017235523852573[/C][C]125.395086246674[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.15805555555556[/C][C]0.016851833938092[/C][C]128.060575690665[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.15472222222222[/C][C]0.0155820462452357[/C][C]138.28236601987[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.26357142857143[/C][C]0.0479898348942725[/C][C]47.1677269479746[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.25661764705882[/C][C]0.0468505976783077[/C][C]48.1662509954203[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.24924242424242[/C][C]0.0454710187709501[/C][C]49.4654064289272[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.24171875[/C][C]0.043978459445657[/C][C]50.9731077044669[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.23548387096774[/C][C]0.0428367934558334[/C][C]52.1860692787994[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.2295[/C][C]0.0417325524285705[/C][C]53.4235236106397[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.22431034482759[/C][C]0.0407552059991036[/C][C]54.5773304366688[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.21910714285714[/C][C]0.0396504833544458[/C][C]55.9667109987027[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.21388888888889[/C][C]0.0384867649178407[/C][C]57.523382222823[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.20865384615385[/C][C]0.0371495985599298[/C][C]59.4529667013989[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.2034[/C][C]0.0355936362117656[/C][C]61.9043243261463[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.19770833333333[/C][C]0.0337192723047754[/C][C]65.1766240228763[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.19391304347826[/C][C]0.0322512453579262[/C][C]68.0256845628777[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.18909090909091[/C][C]0.0304976659797654[/C][C]71.7789653327349[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.185[/C][C]0.0286782989661377[/C][C]76.1900140095468[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.18175[/C][C]0.0267775439309575[/C][C]81.4768526055028[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.18026315789474[/C][C]0.025098630028708[/C][C]86.8678153110723[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.18055555555556[/C][C]0.0237645342142394[/C][C]91.7567134241999[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.18176470588235[/C][C]0.0226476954328655[/C][C]96.3349543599148[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.1828125[/C][C]0.0216377543731903[/C][C]100.879807689496[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.184[/C][C]0.0204129776165168[/C][C]106.990760536222[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.18678571428571[/C][C]0.0196130124405122[/C][C]111.49667706164[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.19[/C][C]0.0189168219806117[/C][C]115.769974588997[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.19416666666667[/C][C]0.0178552621507899[/C][C]122.886275661296[/C][/ROW]
[ROW][C]Median[/C][C]2.23[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.51[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.17243243243243[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.18055555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.17243243243243[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.18055555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.18055555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.17243243243243[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.18055555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.18026315789474[/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=176108&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=176108&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	2.27041666666667	0.0490669744054827	46.2717885945903
Geometric Mean	2.23539264075034
Harmonic Mean	2.20304696715087
Quadratic Mean	2.30775413912892
Winsorized Mean ( 1 / 24 )	2.27013888888889	0.0489332579598774	46.3925555651798
Winsorized Mean ( 2 / 24 )	2.27013888888889	0.0489332579598774	46.3925555651798
Winsorized Mean ( 3 / 24 )	2.26930555555556	0.0485418548683163	46.7494610931473
Winsorized Mean ( 4 / 24 )	2.26319444444444	0.0467842358674359	48.3751503574249
Winsorized Mean ( 5 / 24 )	2.26041666666667	0.0458737284643813	49.2747535971873
Winsorized Mean ( 6 / 24 )	2.25458333333333	0.0445701682988849	50.5850307365732
Winsorized Mean ( 7 / 24 )	2.25263888888889	0.0441525989889463	51.0193950180111
Winsorized Mean ( 8 / 24 )	2.25041666666667	0.0432983054076451	51.9747053719408
Winsorized Mean ( 9 / 24 )	2.24791666666667	0.0427822202386061	52.5432446967344
Winsorized Mean ( 10 / 24 )	2.24513888888889	0.0422174827203607	53.1803116675665
Winsorized Mean ( 11 / 24 )	2.24513888888889	0.0416995143085185	53.8408882242124
Winsorized Mean ( 12 / 24 )	2.22680555555556	0.038148578236607	58.3719147210245
Winsorized Mean ( 13 / 24 )	2.23222222222222	0.0373921099096925	59.6976802756884
Winsorized Mean ( 14 / 24 )	2.2225	0.0356000156054897	62.429747914416
Winsorized Mean ( 15 / 24 )	2.21208333333333	0.0337479713063266	65.5471498791586
Winsorized Mean ( 16 / 24 )	2.19430555555556	0.0307444324189098	71.3724529260107
Winsorized Mean ( 17 / 24 )	2.17777777777778	0.0274255445493278	79.4069110956325
Winsorized Mean ( 18 / 24 )	2.17027777777778	0.0248343275963029	87.3902371369565
Winsorized Mean ( 19 / 24 )	2.17291666666667	0.0228927532082157	94.9172276005167
Winsorized Mean ( 20 / 24 )	2.17291666666667	0.0220926324649911	98.3548099172864
Winsorized Mean ( 21 / 24 )	2.16125	0.018902742491737	114.335261189997
Winsorized Mean ( 22 / 24 )	2.16125	0.017235523852573	125.395086246674
Winsorized Mean ( 23 / 24 )	2.15805555555556	0.016851833938092	128.060575690665
Winsorized Mean ( 24 / 24 )	2.15472222222222	0.0155820462452357	138.28236601987
Trimmed Mean ( 1 / 24 )	2.26357142857143	0.0479898348942725	47.1677269479746
Trimmed Mean ( 2 / 24 )	2.25661764705882	0.0468505976783077	48.1662509954203
Trimmed Mean ( 3 / 24 )	2.24924242424242	0.0454710187709501	49.4654064289272
Trimmed Mean ( 4 / 24 )	2.24171875	0.043978459445657	50.9731077044669
Trimmed Mean ( 5 / 24 )	2.23548387096774	0.0428367934558334	52.1860692787994
Trimmed Mean ( 6 / 24 )	2.2295	0.0417325524285705	53.4235236106397
Trimmed Mean ( 7 / 24 )	2.22431034482759	0.0407552059991036	54.5773304366688
Trimmed Mean ( 8 / 24 )	2.21910714285714	0.0396504833544458	55.9667109987027
Trimmed Mean ( 9 / 24 )	2.21388888888889	0.0384867649178407	57.523382222823
Trimmed Mean ( 10 / 24 )	2.20865384615385	0.0371495985599298	59.4529667013989
Trimmed Mean ( 11 / 24 )	2.2034	0.0355936362117656	61.9043243261463
Trimmed Mean ( 12 / 24 )	2.19770833333333	0.0337192723047754	65.1766240228763
Trimmed Mean ( 13 / 24 )	2.19391304347826	0.0322512453579262	68.0256845628777
Trimmed Mean ( 14 / 24 )	2.18909090909091	0.0304976659797654	71.7789653327349
Trimmed Mean ( 15 / 24 )	2.185	0.0286782989661377	76.1900140095468
Trimmed Mean ( 16 / 24 )	2.18175	0.0267775439309575	81.4768526055028
Trimmed Mean ( 17 / 24 )	2.18026315789474	0.025098630028708	86.8678153110723
Trimmed Mean ( 18 / 24 )	2.18055555555556	0.0237645342142394	91.7567134241999
Trimmed Mean ( 19 / 24 )	2.18176470588235	0.0226476954328655	96.3349543599148
Trimmed Mean ( 20 / 24 )	2.1828125	0.0216377543731903	100.879807689496
Trimmed Mean ( 21 / 24 )	2.184	0.0204129776165168	106.990760536222
Trimmed Mean ( 22 / 24 )	2.18678571428571	0.0196130124405122	111.49667706164
Trimmed Mean ( 23 / 24 )	2.19	0.0189168219806117	115.769974588997
Trimmed Mean ( 24 / 24 )	2.19416666666667	0.0178552621507899	122.886275661296
Median	2.23
Midrange	2.51
Midmean - Weighted Average at Xnp	2.17243243243243
Midmean - Weighted Average at X(n+1)p	2.18055555555556
Midmean - Empirical Distribution Function	2.17243243243243
Midmean - Empirical Distribution Function - Averaging	2.18055555555556
Midmean - Empirical Distribution Function - Interpolation	2.18055555555556
Midmean - Closest Observation	2.17243243243243
Midmean - True Basic - Statistics Graphics Toolkit	2.18055555555556
Midmean - MS Excel (old versions)	2.18026315789474
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