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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Thu, 27 Dec 2007 06:55:30 -0700

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/2007/Dec/27/t11987625213espe0viiwfl94z.htm/, Retrieved Sat, 27 Apr 2024 13:41:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4901, Retrieved Sat, 27 Apr 2024 13:41:21 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

277

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

-       [Central Tendency] [s 0650692 paper] [2007-12-27 13:55:30] [011cc8cdd02d5893b5258ac3f5e21d83] [Current]

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Histogram

Boxplots

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

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4901&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4901&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4901&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.09861111111111	0.0876241139776822	23.9501549955258
Geometric Mean	1.94868785338333
Harmonic Mean	1.74683848253598
Quadratic Mean	2.22470347587168
Winsorized Mean ( 1 / 24 )	2.10138888888889	0.0846721805059124	24.8179375602847
Winsorized Mean ( 2 / 24 )	2.10416666666667	0.0840913296448555	25.0223973809575
Winsorized Mean ( 3 / 24 )	2.1	0.0811449754590728	25.8796060768936
Winsorized Mean ( 4 / 24 )	2.08333333333333	0.0752668700122421	27.6792874872368
Winsorized Mean ( 5 / 24 )	2.07638888888889	0.0739954386667725	28.0610389815999
Winsorized Mean ( 6 / 24 )	2.08472222222222	0.0725043769177483	28.7530534134127
Winsorized Mean ( 7 / 24 )	2.08472222222222	0.0725043769177483	28.7530534134127
Winsorized Mean ( 8 / 24 )	2.08472222222222	0.0725043769177483	28.7530534134127
Winsorized Mean ( 9 / 24 )	2.08472222222222	0.0682516895244004	30.5446244151498
Winsorized Mean ( 10 / 24 )	2.08472222222222	0.0682516895244004	30.5446244151498
Winsorized Mean ( 11 / 24 )	2.06944444444444	0.0657697556225608	31.4649860692894
Winsorized Mean ( 12 / 24 )	2.08611111111111	0.0631187852130764	33.050558626387
Winsorized Mean ( 13 / 24 )	2.08611111111111	0.0631187852130764	33.050558626387
Winsorized Mean ( 14 / 24 )	2.06666666666667	0.0601250652737975	34.3727970565268
Winsorized Mean ( 15 / 24 )	2.06666666666667	0.0601250652737975	34.3727970565268
Winsorized Mean ( 16 / 24 )	2.08888888888889	0.0567630895866252	36.8001267038341
Winsorized Mean ( 17 / 24 )	2.08888888888889	0.0567630895866252	36.8001267038341
Winsorized Mean ( 18 / 24 )	2.08888888888889	0.0494712083144862	42.2243353267201
Winsorized Mean ( 19 / 24 )	2.0625	0.0457692680719662	45.0629884829486
Winsorized Mean ( 20 / 24 )	2.0625	0.0457692680719662	45.0629884829486
Winsorized Mean ( 21 / 24 )	2.09166666666667	0.0417604578189188	50.0872542091499
Winsorized Mean ( 22 / 24 )	2.09166666666667	0.0417604578189188	50.0872542091499
Winsorized Mean ( 23 / 24 )	2.09166666666667	0.0417604578189188	50.0872542091499
Winsorized Mean ( 24 / 24 )	2.05833333333333	0.037307146248264	55.1726288479949
Trimmed Mean ( 1 / 24 )	2.09714285714286	0.0819021136843772	25.6054790627813
Trimmed Mean ( 2 / 24 )	2.09264705882353	0.0785993546070641	26.6242269963302
Trimmed Mean ( 3 / 24 )	2.08636363636364	0.0750100650165201	27.8144491129842
Trimmed Mean ( 4 / 24 )	2.08125	0.0720957187267743	28.8678722780675
Trimmed Mean ( 5 / 24 )	2.08064516129032	0.0707980761149863	29.3884421083852
Trimmed Mean ( 6 / 24 )	2.08166666666667	0.06960305803183	29.9076897701061
Trimmed Mean ( 7 / 24 )	2.08103448275862	0.0685365515787691	30.3638632936891
Trimmed Mean ( 8 / 24 )	2.08035714285714	0.0671990473638193	30.9581344448825
Trimmed Mean ( 9 / 24 )	2.07962962962963	0.0655237262189922	31.7385739431108
Trimmed Mean ( 10 / 24 )	2.07884615384615	0.0644232176221421	32.2685862422938
Trimmed Mean ( 11 / 24 )	2.078	0.0630056686792092	32.9811593712314
Trimmed Mean ( 12 / 24 )	2.07916666666667	0.0617388641962732	33.6767884173706
Trimmed Mean ( 13 / 24 )	2.07826086956522	0.0606656349234023	34.2576299117165
Trimmed Mean ( 14 / 24 )	2.07727272727273	0.0592289816390624	35.0718967266987
Trimmed Mean ( 15 / 24 )	2.07857142857143	0.057989517484158	35.8439166033632
Trimmed Mean ( 16 / 24 )	2.08	0.0562959214262523	36.9476144506277
Trimmed Mean ( 17 / 24 )	2.07894736842105	0.0548057340835157	37.9330265926746
Trimmed Mean ( 18 / 24 )	2.07777777777778	0.0527213566423334	39.4105521956428
Trimmed Mean ( 19 / 24 )	2.07647058823529	0.0517189069799933	40.1491583926657
Trimmed Mean ( 20 / 24 )	2.078125	0.0511430581720877	40.6335693303178
Trimmed Mean ( 21 / 24 )	2.08	0.0501492026729801	41.4762327043075
Trimmed Mean ( 22 / 24 )	2.07857142857143	0.0496967371569945	41.8251085982791
Trimmed Mean ( 23 / 24 )	2.07692307692308	0.0487718999512226	42.5844201066645
Trimmed Mean ( 24 / 24 )	2.075	0.0471084164300895	44.0473307583873
Median	2.05
Midrange	2.15
Midmean - Weighted Average at Xnp	2.04736842105263
Midmean - Weighted Average at X(n+1)p	2.07777777777778
Midmean - Empirical Distribution Function	2.04736842105263
Midmean - Empirical Distribution Function - Averaging	2.07777777777778
Midmean - Empirical Distribution Function - Interpolation	2.07777777777778
Midmean - Closest Observation	2.04736842105263
Midmean - True Basic - Statistics Graphics Toolkit	2.07777777777778
Midmean - MS Excel (old versions)	2.10952380952381
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.09861111111111 & 0.0876241139776822 & 23.9501549955258 \tabularnewline
Geometric Mean & 1.94868785338333 &  &  \tabularnewline
Harmonic Mean & 1.74683848253598 &  &  \tabularnewline
Quadratic Mean & 2.22470347587168 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.10138888888889 & 0.0846721805059124 & 24.8179375602847 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.10416666666667 & 0.0840913296448555 & 25.0223973809575 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.1 & 0.0811449754590728 & 25.8796060768936 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.08333333333333 & 0.0752668700122421 & 27.6792874872368 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.07638888888889 & 0.0739954386667725 & 28.0610389815999 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.08472222222222 & 0.0725043769177483 & 28.7530534134127 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.08472222222222 & 0.0725043769177483 & 28.7530534134127 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.08472222222222 & 0.0725043769177483 & 28.7530534134127 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.08472222222222 & 0.0682516895244004 & 30.5446244151498 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.08472222222222 & 0.0682516895244004 & 30.5446244151498 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.06944444444444 & 0.0657697556225608 & 31.4649860692894 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.08611111111111 & 0.0631187852130764 & 33.050558626387 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.08611111111111 & 0.0631187852130764 & 33.050558626387 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.06666666666667 & 0.0601250652737975 & 34.3727970565268 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.06666666666667 & 0.0601250652737975 & 34.3727970565268 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.08888888888889 & 0.0567630895866252 & 36.8001267038341 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.08888888888889 & 0.0567630895866252 & 36.8001267038341 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.08888888888889 & 0.0494712083144862 & 42.2243353267201 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.0625 & 0.0457692680719662 & 45.0629884829486 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.0625 & 0.0457692680719662 & 45.0629884829486 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.09166666666667 & 0.0417604578189188 & 50.0872542091499 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.09166666666667 & 0.0417604578189188 & 50.0872542091499 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.09166666666667 & 0.0417604578189188 & 50.0872542091499 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.05833333333333 & 0.037307146248264 & 55.1726288479949 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.09714285714286 & 0.0819021136843772 & 25.6054790627813 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.09264705882353 & 0.0785993546070641 & 26.6242269963302 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.08636363636364 & 0.0750100650165201 & 27.8144491129842 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.08125 & 0.0720957187267743 & 28.8678722780675 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.08064516129032 & 0.0707980761149863 & 29.3884421083852 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.08166666666667 & 0.06960305803183 & 29.9076897701061 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.08103448275862 & 0.0685365515787691 & 30.3638632936891 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.08035714285714 & 0.0671990473638193 & 30.9581344448825 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.07962962962963 & 0.0655237262189922 & 31.7385739431108 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.07884615384615 & 0.0644232176221421 & 32.2685862422938 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.078 & 0.0630056686792092 & 32.9811593712314 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.07916666666667 & 0.0617388641962732 & 33.6767884173706 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.07826086956522 & 0.0606656349234023 & 34.2576299117165 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.07727272727273 & 0.0592289816390624 & 35.0718967266987 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.07857142857143 & 0.057989517484158 & 35.8439166033632 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.08 & 0.0562959214262523 & 36.9476144506277 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.07894736842105 & 0.0548057340835157 & 37.9330265926746 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.07777777777778 & 0.0527213566423334 & 39.4105521956428 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.07647058823529 & 0.0517189069799933 & 40.1491583926657 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.078125 & 0.0511430581720877 & 40.6335693303178 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.08 & 0.0501492026729801 & 41.4762327043075 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.07857142857143 & 0.0496967371569945 & 41.8251085982791 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.07692307692308 & 0.0487718999512226 & 42.5844201066645 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.075 & 0.0471084164300895 & 44.0473307583873 \tabularnewline
Median & 2.05 &  &  \tabularnewline
Midrange & 2.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.04736842105263 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.07777777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.04736842105263 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.07777777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.07777777777778 &  &  \tabularnewline
Midmean - Closest Observation & 2.04736842105263 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.07777777777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.10952380952381 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4901&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]2.09861111111111[/C][C]0.0876241139776822[/C][C]23.9501549955258[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.94868785338333[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.74683848253598[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.22470347587168[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.10138888888889[/C][C]0.0846721805059124[/C][C]24.8179375602847[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.10416666666667[/C][C]0.0840913296448555[/C][C]25.0223973809575[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.1[/C][C]0.0811449754590728[/C][C]25.8796060768936[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.08333333333333[/C][C]0.0752668700122421[/C][C]27.6792874872368[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.07638888888889[/C][C]0.0739954386667725[/C][C]28.0610389815999[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.08472222222222[/C][C]0.0725043769177483[/C][C]28.7530534134127[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.08472222222222[/C][C]0.0725043769177483[/C][C]28.7530534134127[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.08472222222222[/C][C]0.0725043769177483[/C][C]28.7530534134127[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.08472222222222[/C][C]0.0682516895244004[/C][C]30.5446244151498[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.08472222222222[/C][C]0.0682516895244004[/C][C]30.5446244151498[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.06944444444444[/C][C]0.0657697556225608[/C][C]31.4649860692894[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.08611111111111[/C][C]0.0631187852130764[/C][C]33.050558626387[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.08611111111111[/C][C]0.0631187852130764[/C][C]33.050558626387[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.06666666666667[/C][C]0.0601250652737975[/C][C]34.3727970565268[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.06666666666667[/C][C]0.0601250652737975[/C][C]34.3727970565268[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.08888888888889[/C][C]0.0567630895866252[/C][C]36.8001267038341[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.08888888888889[/C][C]0.0567630895866252[/C][C]36.8001267038341[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.08888888888889[/C][C]0.0494712083144862[/C][C]42.2243353267201[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.0625[/C][C]0.0457692680719662[/C][C]45.0629884829486[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.0625[/C][C]0.0457692680719662[/C][C]45.0629884829486[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.09166666666667[/C][C]0.0417604578189188[/C][C]50.0872542091499[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.09166666666667[/C][C]0.0417604578189188[/C][C]50.0872542091499[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.09166666666667[/C][C]0.0417604578189188[/C][C]50.0872542091499[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.05833333333333[/C][C]0.037307146248264[/C][C]55.1726288479949[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.09714285714286[/C][C]0.0819021136843772[/C][C]25.6054790627813[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.09264705882353[/C][C]0.0785993546070641[/C][C]26.6242269963302[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.08636363636364[/C][C]0.0750100650165201[/C][C]27.8144491129842[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.08125[/C][C]0.0720957187267743[/C][C]28.8678722780675[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.08064516129032[/C][C]0.0707980761149863[/C][C]29.3884421083852[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.08166666666667[/C][C]0.06960305803183[/C][C]29.9076897701061[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.08103448275862[/C][C]0.0685365515787691[/C][C]30.3638632936891[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.08035714285714[/C][C]0.0671990473638193[/C][C]30.9581344448825[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.07962962962963[/C][C]0.0655237262189922[/C][C]31.7385739431108[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.07884615384615[/C][C]0.0644232176221421[/C][C]32.2685862422938[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.078[/C][C]0.0630056686792092[/C][C]32.9811593712314[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.07916666666667[/C][C]0.0617388641962732[/C][C]33.6767884173706[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.07826086956522[/C][C]0.0606656349234023[/C][C]34.2576299117165[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.07727272727273[/C][C]0.0592289816390624[/C][C]35.0718967266987[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.07857142857143[/C][C]0.057989517484158[/C][C]35.8439166033632[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.08[/C][C]0.0562959214262523[/C][C]36.9476144506277[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.07894736842105[/C][C]0.0548057340835157[/C][C]37.9330265926746[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.07777777777778[/C][C]0.0527213566423334[/C][C]39.4105521956428[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.07647058823529[/C][C]0.0517189069799933[/C][C]40.1491583926657[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.078125[/C][C]0.0511430581720877[/C][C]40.6335693303178[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.08[/C][C]0.0501492026729801[/C][C]41.4762327043075[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.07857142857143[/C][C]0.0496967371569945[/C][C]41.8251085982791[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.07692307692308[/C][C]0.0487718999512226[/C][C]42.5844201066645[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.075[/C][C]0.0471084164300895[/C][C]44.0473307583873[/C][/ROW]
[ROW][C]Median[/C][C]2.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.04736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.07777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.04736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.07777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.07777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.04736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.07777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.10952380952381[/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=4901&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4901&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	2.09861111111111	0.0876241139776822	23.9501549955258
Geometric Mean	1.94868785338333
Harmonic Mean	1.74683848253598
Quadratic Mean	2.22470347587168
Winsorized Mean ( 1 / 24 )	2.10138888888889	0.0846721805059124	24.8179375602847
Winsorized Mean ( 2 / 24 )	2.10416666666667	0.0840913296448555	25.0223973809575
Winsorized Mean ( 3 / 24 )	2.1	0.0811449754590728	25.8796060768936
Winsorized Mean ( 4 / 24 )	2.08333333333333	0.0752668700122421	27.6792874872368
Winsorized Mean ( 5 / 24 )	2.07638888888889	0.0739954386667725	28.0610389815999
Winsorized Mean ( 6 / 24 )	2.08472222222222	0.0725043769177483	28.7530534134127
Winsorized Mean ( 7 / 24 )	2.08472222222222	0.0725043769177483	28.7530534134127
Winsorized Mean ( 8 / 24 )	2.08472222222222	0.0725043769177483	28.7530534134127
Winsorized Mean ( 9 / 24 )	2.08472222222222	0.0682516895244004	30.5446244151498
Winsorized Mean ( 10 / 24 )	2.08472222222222	0.0682516895244004	30.5446244151498
Winsorized Mean ( 11 / 24 )	2.06944444444444	0.0657697556225608	31.4649860692894
Winsorized Mean ( 12 / 24 )	2.08611111111111	0.0631187852130764	33.050558626387
Winsorized Mean ( 13 / 24 )	2.08611111111111	0.0631187852130764	33.050558626387
Winsorized Mean ( 14 / 24 )	2.06666666666667	0.0601250652737975	34.3727970565268
Winsorized Mean ( 15 / 24 )	2.06666666666667	0.0601250652737975	34.3727970565268
Winsorized Mean ( 16 / 24 )	2.08888888888889	0.0567630895866252	36.8001267038341
Winsorized Mean ( 17 / 24 )	2.08888888888889	0.0567630895866252	36.8001267038341
Winsorized Mean ( 18 / 24 )	2.08888888888889	0.0494712083144862	42.2243353267201
Winsorized Mean ( 19 / 24 )	2.0625	0.0457692680719662	45.0629884829486
Winsorized Mean ( 20 / 24 )	2.0625	0.0457692680719662	45.0629884829486
Winsorized Mean ( 21 / 24 )	2.09166666666667	0.0417604578189188	50.0872542091499
Winsorized Mean ( 22 / 24 )	2.09166666666667	0.0417604578189188	50.0872542091499
Winsorized Mean ( 23 / 24 )	2.09166666666667	0.0417604578189188	50.0872542091499
Winsorized Mean ( 24 / 24 )	2.05833333333333	0.037307146248264	55.1726288479949
Trimmed Mean ( 1 / 24 )	2.09714285714286	0.0819021136843772	25.6054790627813
Trimmed Mean ( 2 / 24 )	2.09264705882353	0.0785993546070641	26.6242269963302
Trimmed Mean ( 3 / 24 )	2.08636363636364	0.0750100650165201	27.8144491129842
Trimmed Mean ( 4 / 24 )	2.08125	0.0720957187267743	28.8678722780675
Trimmed Mean ( 5 / 24 )	2.08064516129032	0.0707980761149863	29.3884421083852
Trimmed Mean ( 6 / 24 )	2.08166666666667	0.06960305803183	29.9076897701061
Trimmed Mean ( 7 / 24 )	2.08103448275862	0.0685365515787691	30.3638632936891
Trimmed Mean ( 8 / 24 )	2.08035714285714	0.0671990473638193	30.9581344448825
Trimmed Mean ( 9 / 24 )	2.07962962962963	0.0655237262189922	31.7385739431108
Trimmed Mean ( 10 / 24 )	2.07884615384615	0.0644232176221421	32.2685862422938
Trimmed Mean ( 11 / 24 )	2.078	0.0630056686792092	32.9811593712314
Trimmed Mean ( 12 / 24 )	2.07916666666667	0.0617388641962732	33.6767884173706
Trimmed Mean ( 13 / 24 )	2.07826086956522	0.0606656349234023	34.2576299117165
Trimmed Mean ( 14 / 24 )	2.07727272727273	0.0592289816390624	35.0718967266987
Trimmed Mean ( 15 / 24 )	2.07857142857143	0.057989517484158	35.8439166033632
Trimmed Mean ( 16 / 24 )	2.08	0.0562959214262523	36.9476144506277
Trimmed Mean ( 17 / 24 )	2.07894736842105	0.0548057340835157	37.9330265926746
Trimmed Mean ( 18 / 24 )	2.07777777777778	0.0527213566423334	39.4105521956428
Trimmed Mean ( 19 / 24 )	2.07647058823529	0.0517189069799933	40.1491583926657
Trimmed Mean ( 20 / 24 )	2.078125	0.0511430581720877	40.6335693303178
Trimmed Mean ( 21 / 24 )	2.08	0.0501492026729801	41.4762327043075
Trimmed Mean ( 22 / 24 )	2.07857142857143	0.0496967371569945	41.8251085982791
Trimmed Mean ( 23 / 24 )	2.07692307692308	0.0487718999512226	42.5844201066645
Trimmed Mean ( 24 / 24 )	2.075	0.0471084164300895	44.0473307583873
Median	2.05
Midrange	2.15
Midmean - Weighted Average at Xnp	2.04736842105263
Midmean - Weighted Average at X(n+1)p	2.07777777777778
Midmean - Empirical Distribution Function	2.04736842105263
Midmean - Empirical Distribution Function - Averaging	2.07777777777778
Midmean - Empirical Distribution Function - Interpolation	2.07777777777778
Midmean - Closest Observation	2.04736842105263
Midmean - True Basic - Statistics Graphics Toolkit	2.07777777777778
Midmean - MS Excel (old versions)	2.10952380952381
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