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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 01 Jun 2009 16:35:03 -0600

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/2009/Jun/02/t124389573926n18x6msvs4070.htm/, Retrieved Fri, 10 May 2024 00:42:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41127, Retrieved Fri, 10 May 2024 00:42:21 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

121

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

-       [Central Tendency] [Centrummaten - Ki...] [2009-06-01 22:35:03] [2f928979fcb5db36e984611041f4b2ce] [Current]

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2,98
2,98
2,98
3,03
3,07
3,08
3,08
3,08
3,08
3,08
3,08
3,08
3,08
3,08
3,12
3,15
3,15
3,15
3,15
3,16
3,19
3,2
3,2
3,2
3,21
3,21
3,21
3,21
3,21
3,28
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,45
3,49
3,5
3,54
3,64
3,67
3,67
3,68
3,68
3,68
3,68
3,7
3,83
3,87
3,87
3,87
3,87
3,87
3,87
3,87
3,87
3,87
3,88
3,88
3,88
3,88
3,88
3,88
3,89
3,89
3,91
3,95
3,99
3,99
3,99

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41127&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41127&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41127&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	3.46930555555556	0.0406699213606033	85.3039651784587
Geometric Mean	3.45247833191681
Harmonic Mean	3.43584004701828
Quadratic Mean	3.48618961841658
Winsorized Mean ( 1 / 24 )	3.46930555555556	0.0406699213606033	85.3039651784587
Winsorized Mean ( 2 / 24 )	3.46930555555556	0.0406699213606033	85.3039651784587
Winsorized Mean ( 3 / 24 )	3.46972222222222	0.0400410451687891	86.6541372133507
Winsorized Mean ( 4 / 24 )	3.46972222222222	0.0393471628738531	88.1822720826439
Winsorized Mean ( 5 / 24 )	3.46902777777778	0.0390337920504744	88.8724255458448
Winsorized Mean ( 6 / 24 )	3.46902777777778	0.0390337920504744	88.8724255458448
Winsorized Mean ( 7 / 24 )	3.46805555555556	0.0388874217250628	89.1819360016972
Winsorized Mean ( 8 / 24 )	3.46805555555556	0.0388874217250628	89.1819360016972
Winsorized Mean ( 9 / 24 )	3.46805555555556	0.0388874217250628	89.1819360016972
Winsorized Mean ( 10 / 24 )	3.46805555555556	0.0388874217250628	89.1819360016972
Winsorized Mean ( 11 / 24 )	3.46805555555556	0.0388874217250628	89.1819360016972
Winsorized Mean ( 12 / 24 )	3.46805555555556	0.0388874217250628	89.1819360016972
Winsorized Mean ( 13 / 24 )	3.46625	0.0386197898117238	89.7532072778852
Winsorized Mean ( 14 / 24 )	3.47402777777778	0.0375552070005864	92.50455676422
Winsorized Mean ( 15 / 24 )	3.48027777777778	0.0367444609125671	94.7157120105543
Winsorized Mean ( 16 / 24 )	3.48027777777778	0.0367444609125671	94.7157120105543
Winsorized Mean ( 17 / 24 )	3.48027777777778	0.0367444609125671	94.7157120105543
Winsorized Mean ( 18 / 24 )	3.48027777777778	0.0367444609125671	94.7157120105543
Winsorized Mean ( 19 / 24 )	3.48291666666667	0.0364126054610656	95.6513993592355
Winsorized Mean ( 20 / 24 )	3.49125	0.0353923556439547	98.6441828038179
Winsorized Mean ( 21 / 24 )	3.49416666666667	0.0350451028415789	99.7048484195359
Winsorized Mean ( 22 / 24 )	3.48194444444444	0.0332196646944772	104.815761280797
Winsorized Mean ( 23 / 24 )	3.44041666666667	0.0273521330487426	125.782390007233
Winsorized Mean ( 24 / 24 )	3.43708333333333	0.0260577767070995	131.902401803792
Trimmed Mean ( 1 / 24 )	3.46885714285714	0.0405574728862762	85.5294202521906
Trimmed Mean ( 2 / 24 )	3.46838235294118	0.0403951130432276	85.8614345064362
Trimmed Mean ( 3 / 24 )	3.46787878787879	0.0401735832392435	86.3223667957803
Trimmed Mean ( 4 / 24 )	3.4671875	0.0401494410492532	86.3570552762275
Trimmed Mean ( 5 / 24 )	3.46645161290323	0.0403108602744376	85.9929951706194
Trimmed Mean ( 6 / 24 )	3.46583333333333	0.0405361606488658	85.499792724704
Trimmed Mean ( 7 / 24 )	3.4651724137931	0.0407434252574899	85.0486278925727
Trimmed Mean ( 8 / 24 )	3.46464285714286	0.0409608335936019	84.5842858452967
Trimmed Mean ( 9 / 24 )	3.46407407407407	0.0411534587139076	84.1745550029166
Trimmed Mean ( 10 / 24 )	3.46346153846154	0.0413140901314855	83.8324534665725
Trimmed Mean ( 11 / 24 )	3.4628	0.0414335366482717	83.5748111341696
Trimmed Mean ( 12 / 24 )	3.46208333333333	0.0414999768577793	83.4237412998546
Trimmed Mean ( 13 / 24 )	3.46130434782609	0.0414980456971334	83.40885190324
Trimmed Mean ( 14 / 24 )	3.46068181818182	0.0414603885528176	83.4695944485218
Trimmed Mean ( 15 / 24 )	3.45904761904762	0.0415199174512414	83.310561084562
Trimmed Mean ( 16 / 24 )	3.4565	0.0416326271213533	83.0238262390885
Trimmed Mean ( 17 / 24 )	3.45368421052632	0.0416471342503959	82.927295543594
Trimmed Mean ( 18 / 24 )	3.45055555555556	0.0415263244954606	83.0932088856731
Trimmed Mean ( 19 / 24 )	3.44705882352941	0.0412170668226466	83.6318323756953
Trimmed Mean ( 20 / 24 )	3.4428125	0.0407124910861955	84.5640344804979
Trimmed Mean ( 21 / 24 )	3.437	0.0400693364574201	85.7763143558005
Trimmed Mean ( 22 / 24 )	3.43	0.0390326142289365	87.8752312074757
Trimmed Mean ( 23 / 24 )	3.42346153846154	0.0379835685433839	90.1300659665862
Trimmed Mean ( 24 / 24 )	3.42125	0.0383363853542426	89.242894664856
Median	3.3
Midrange	3.485
Midmean - Weighted Average at Xnp	3.47772727272727
Midmean - Weighted Average at X(n+1)p	3.47772727272727
Midmean - Empirical Distribution Function	3.47772727272727
Midmean - Empirical Distribution Function - Averaging	3.47772727272727
Midmean - Empirical Distribution Function - Interpolation	3.47772727272727
Midmean - Closest Observation	3.47772727272727
Midmean - True Basic - Statistics Graphics Toolkit	3.47772727272727
Midmean - MS Excel (old versions)	3.47772727272727
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.46930555555556 & 0.0406699213606033 & 85.3039651784587 \tabularnewline
Geometric Mean & 3.45247833191681 &  &  \tabularnewline
Harmonic Mean & 3.43584004701828 &  &  \tabularnewline
Quadratic Mean & 3.48618961841658 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 3.46930555555556 & 0.0406699213606033 & 85.3039651784587 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 3.46930555555556 & 0.0406699213606033 & 85.3039651784587 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 3.46972222222222 & 0.0400410451687891 & 86.6541372133507 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 3.46972222222222 & 0.0393471628738531 & 88.1822720826439 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3.46902777777778 & 0.0390337920504744 & 88.8724255458448 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3.46902777777778 & 0.0390337920504744 & 88.8724255458448 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3.46805555555556 & 0.0388874217250628 & 89.1819360016972 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3.46805555555556 & 0.0388874217250628 & 89.1819360016972 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3.46805555555556 & 0.0388874217250628 & 89.1819360016972 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 3.46805555555556 & 0.0388874217250628 & 89.1819360016972 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 3.46805555555556 & 0.0388874217250628 & 89.1819360016972 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 3.46805555555556 & 0.0388874217250628 & 89.1819360016972 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 3.46625 & 0.0386197898117238 & 89.7532072778852 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 3.47402777777778 & 0.0375552070005864 & 92.50455676422 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 3.48027777777778 & 0.0367444609125671 & 94.7157120105543 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 3.48027777777778 & 0.0367444609125671 & 94.7157120105543 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 3.48027777777778 & 0.0367444609125671 & 94.7157120105543 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 3.48027777777778 & 0.0367444609125671 & 94.7157120105543 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3.48291666666667 & 0.0364126054610656 & 95.6513993592355 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 3.49125 & 0.0353923556439547 & 98.6441828038179 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 3.49416666666667 & 0.0350451028415789 & 99.7048484195359 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 3.48194444444444 & 0.0332196646944772 & 104.815761280797 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 3.44041666666667 & 0.0273521330487426 & 125.782390007233 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 3.43708333333333 & 0.0260577767070995 & 131.902401803792 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 3.46885714285714 & 0.0405574728862762 & 85.5294202521906 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 3.46838235294118 & 0.0403951130432276 & 85.8614345064362 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 3.46787878787879 & 0.0401735832392435 & 86.3223667957803 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 3.4671875 & 0.0401494410492532 & 86.3570552762275 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 3.46645161290323 & 0.0403108602744376 & 85.9929951706194 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 3.46583333333333 & 0.0405361606488658 & 85.499792724704 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 3.4651724137931 & 0.0407434252574899 & 85.0486278925727 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 3.46464285714286 & 0.0409608335936019 & 84.5842858452967 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 3.46407407407407 & 0.0411534587139076 & 84.1745550029166 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 3.46346153846154 & 0.0413140901314855 & 83.8324534665725 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 3.4628 & 0.0414335366482717 & 83.5748111341696 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 3.46208333333333 & 0.0414999768577793 & 83.4237412998546 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 3.46130434782609 & 0.0414980456971334 & 83.40885190324 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 3.46068181818182 & 0.0414603885528176 & 83.4695944485218 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 3.45904761904762 & 0.0415199174512414 & 83.310561084562 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 3.4565 & 0.0416326271213533 & 83.0238262390885 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 3.45368421052632 & 0.0416471342503959 & 82.927295543594 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3.45055555555556 & 0.0415263244954606 & 83.0932088856731 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 3.44705882352941 & 0.0412170668226466 & 83.6318323756953 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 3.4428125 & 0.0407124910861955 & 84.5640344804979 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 3.437 & 0.0400693364574201 & 85.7763143558005 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 3.43 & 0.0390326142289365 & 87.8752312074757 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 3.42346153846154 & 0.0379835685433839 & 90.1300659665862 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 3.42125 & 0.0383363853542426 & 89.242894664856 \tabularnewline
Median & 3.3 &  &  \tabularnewline
Midrange & 3.485 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.47772727272727 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.47772727272727 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.47772727272727 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.47772727272727 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.47772727272727 &  &  \tabularnewline
Midmean - Closest Observation & 3.47772727272727 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.47772727272727 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.47772727272727 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41127&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]3.46930555555556[/C][C]0.0406699213606033[/C][C]85.3039651784587[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.45247833191681[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.43584004701828[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.48618961841658[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]3.46930555555556[/C][C]0.0406699213606033[/C][C]85.3039651784587[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]3.46930555555556[/C][C]0.0406699213606033[/C][C]85.3039651784587[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]3.46972222222222[/C][C]0.0400410451687891[/C][C]86.6541372133507[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]3.46972222222222[/C][C]0.0393471628738531[/C][C]88.1822720826439[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3.46902777777778[/C][C]0.0390337920504744[/C][C]88.8724255458448[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3.46902777777778[/C][C]0.0390337920504744[/C][C]88.8724255458448[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3.46805555555556[/C][C]0.0388874217250628[/C][C]89.1819360016972[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3.46805555555556[/C][C]0.0388874217250628[/C][C]89.1819360016972[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3.46805555555556[/C][C]0.0388874217250628[/C][C]89.1819360016972[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]3.46805555555556[/C][C]0.0388874217250628[/C][C]89.1819360016972[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]3.46805555555556[/C][C]0.0388874217250628[/C][C]89.1819360016972[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]3.46805555555556[/C][C]0.0388874217250628[/C][C]89.1819360016972[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]3.46625[/C][C]0.0386197898117238[/C][C]89.7532072778852[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]3.47402777777778[/C][C]0.0375552070005864[/C][C]92.50455676422[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]3.48027777777778[/C][C]0.0367444609125671[/C][C]94.7157120105543[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]3.48027777777778[/C][C]0.0367444609125671[/C][C]94.7157120105543[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]3.48027777777778[/C][C]0.0367444609125671[/C][C]94.7157120105543[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]3.48027777777778[/C][C]0.0367444609125671[/C][C]94.7157120105543[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3.48291666666667[/C][C]0.0364126054610656[/C][C]95.6513993592355[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]3.49125[/C][C]0.0353923556439547[/C][C]98.6441828038179[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]3.49416666666667[/C][C]0.0350451028415789[/C][C]99.7048484195359[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]3.48194444444444[/C][C]0.0332196646944772[/C][C]104.815761280797[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]3.44041666666667[/C][C]0.0273521330487426[/C][C]125.782390007233[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]3.43708333333333[/C][C]0.0260577767070995[/C][C]131.902401803792[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]3.46885714285714[/C][C]0.0405574728862762[/C][C]85.5294202521906[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]3.46838235294118[/C][C]0.0403951130432276[/C][C]85.8614345064362[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]3.46787878787879[/C][C]0.0401735832392435[/C][C]86.3223667957803[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]3.4671875[/C][C]0.0401494410492532[/C][C]86.3570552762275[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]3.46645161290323[/C][C]0.0403108602744376[/C][C]85.9929951706194[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]3.46583333333333[/C][C]0.0405361606488658[/C][C]85.499792724704[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]3.4651724137931[/C][C]0.0407434252574899[/C][C]85.0486278925727[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]3.46464285714286[/C][C]0.0409608335936019[/C][C]84.5842858452967[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]3.46407407407407[/C][C]0.0411534587139076[/C][C]84.1745550029166[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]3.46346153846154[/C][C]0.0413140901314855[/C][C]83.8324534665725[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]3.4628[/C][C]0.0414335366482717[/C][C]83.5748111341696[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]3.46208333333333[/C][C]0.0414999768577793[/C][C]83.4237412998546[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]3.46130434782609[/C][C]0.0414980456971334[/C][C]83.40885190324[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]3.46068181818182[/C][C]0.0414603885528176[/C][C]83.4695944485218[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]3.45904761904762[/C][C]0.0415199174512414[/C][C]83.310561084562[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]3.4565[/C][C]0.0416326271213533[/C][C]83.0238262390885[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]3.45368421052632[/C][C]0.0416471342503959[/C][C]82.927295543594[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3.45055555555556[/C][C]0.0415263244954606[/C][C]83.0932088856731[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]3.44705882352941[/C][C]0.0412170668226466[/C][C]83.6318323756953[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]3.4428125[/C][C]0.0407124910861955[/C][C]84.5640344804979[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]3.437[/C][C]0.0400693364574201[/C][C]85.7763143558005[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]3.43[/C][C]0.0390326142289365[/C][C]87.8752312074757[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]3.42346153846154[/C][C]0.0379835685433839[/C][C]90.1300659665862[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]3.42125[/C][C]0.0383363853542426[/C][C]89.242894664856[/C][/ROW]
[ROW][C]Median[/C][C]3.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.47772727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.47772727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.47772727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.47772727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.47772727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.47772727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.47772727272727[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.47772727272727[/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=41127&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41127&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	3.46930555555556	0.0406699213606033	85.3039651784587
Geometric Mean	3.45247833191681
Harmonic Mean	3.43584004701828
Quadratic Mean	3.48618961841658
Winsorized Mean ( 1 / 24 )	3.46930555555556	0.0406699213606033	85.3039651784587
Winsorized Mean ( 2 / 24 )	3.46930555555556	0.0406699213606033	85.3039651784587
Winsorized Mean ( 3 / 24 )	3.46972222222222	0.0400410451687891	86.6541372133507
Winsorized Mean ( 4 / 24 )	3.46972222222222	0.0393471628738531	88.1822720826439
Winsorized Mean ( 5 / 24 )	3.46902777777778	0.0390337920504744	88.8724255458448
Winsorized Mean ( 6 / 24 )	3.46902777777778	0.0390337920504744	88.8724255458448
Winsorized Mean ( 7 / 24 )	3.46805555555556	0.0388874217250628	89.1819360016972
Winsorized Mean ( 8 / 24 )	3.46805555555556	0.0388874217250628	89.1819360016972
Winsorized Mean ( 9 / 24 )	3.46805555555556	0.0388874217250628	89.1819360016972
Winsorized Mean ( 10 / 24 )	3.46805555555556	0.0388874217250628	89.1819360016972
Winsorized Mean ( 11 / 24 )	3.46805555555556	0.0388874217250628	89.1819360016972
Winsorized Mean ( 12 / 24 )	3.46805555555556	0.0388874217250628	89.1819360016972
Winsorized Mean ( 13 / 24 )	3.46625	0.0386197898117238	89.7532072778852
Winsorized Mean ( 14 / 24 )	3.47402777777778	0.0375552070005864	92.50455676422
Winsorized Mean ( 15 / 24 )	3.48027777777778	0.0367444609125671	94.7157120105543
Winsorized Mean ( 16 / 24 )	3.48027777777778	0.0367444609125671	94.7157120105543
Winsorized Mean ( 17 / 24 )	3.48027777777778	0.0367444609125671	94.7157120105543
Winsorized Mean ( 18 / 24 )	3.48027777777778	0.0367444609125671	94.7157120105543
Winsorized Mean ( 19 / 24 )	3.48291666666667	0.0364126054610656	95.6513993592355
Winsorized Mean ( 20 / 24 )	3.49125	0.0353923556439547	98.6441828038179
Winsorized Mean ( 21 / 24 )	3.49416666666667	0.0350451028415789	99.7048484195359
Winsorized Mean ( 22 / 24 )	3.48194444444444	0.0332196646944772	104.815761280797
Winsorized Mean ( 23 / 24 )	3.44041666666667	0.0273521330487426	125.782390007233
Winsorized Mean ( 24 / 24 )	3.43708333333333	0.0260577767070995	131.902401803792
Trimmed Mean ( 1 / 24 )	3.46885714285714	0.0405574728862762	85.5294202521906
Trimmed Mean ( 2 / 24 )	3.46838235294118	0.0403951130432276	85.8614345064362
Trimmed Mean ( 3 / 24 )	3.46787878787879	0.0401735832392435	86.3223667957803
Trimmed Mean ( 4 / 24 )	3.4671875	0.0401494410492532	86.3570552762275
Trimmed Mean ( 5 / 24 )	3.46645161290323	0.0403108602744376	85.9929951706194
Trimmed Mean ( 6 / 24 )	3.46583333333333	0.0405361606488658	85.499792724704
Trimmed Mean ( 7 / 24 )	3.4651724137931	0.0407434252574899	85.0486278925727
Trimmed Mean ( 8 / 24 )	3.46464285714286	0.0409608335936019	84.5842858452967
Trimmed Mean ( 9 / 24 )	3.46407407407407	0.0411534587139076	84.1745550029166
Trimmed Mean ( 10 / 24 )	3.46346153846154	0.0413140901314855	83.8324534665725
Trimmed Mean ( 11 / 24 )	3.4628	0.0414335366482717	83.5748111341696
Trimmed Mean ( 12 / 24 )	3.46208333333333	0.0414999768577793	83.4237412998546
Trimmed Mean ( 13 / 24 )	3.46130434782609	0.0414980456971334	83.40885190324
Trimmed Mean ( 14 / 24 )	3.46068181818182	0.0414603885528176	83.4695944485218
Trimmed Mean ( 15 / 24 )	3.45904761904762	0.0415199174512414	83.310561084562
Trimmed Mean ( 16 / 24 )	3.4565	0.0416326271213533	83.0238262390885
Trimmed Mean ( 17 / 24 )	3.45368421052632	0.0416471342503959	82.927295543594
Trimmed Mean ( 18 / 24 )	3.45055555555556	0.0415263244954606	83.0932088856731
Trimmed Mean ( 19 / 24 )	3.44705882352941	0.0412170668226466	83.6318323756953
Trimmed Mean ( 20 / 24 )	3.4428125	0.0407124910861955	84.5640344804979
Trimmed Mean ( 21 / 24 )	3.437	0.0400693364574201	85.7763143558005
Trimmed Mean ( 22 / 24 )	3.43	0.0390326142289365	87.8752312074757
Trimmed Mean ( 23 / 24 )	3.42346153846154	0.0379835685433839	90.1300659665862
Trimmed Mean ( 24 / 24 )	3.42125	0.0383363853542426	89.242894664856
Median	3.3
Midrange	3.485
Midmean - Weighted Average at Xnp	3.47772727272727
Midmean - Weighted Average at X(n+1)p	3.47772727272727
Midmean - Empirical Distribution Function	3.47772727272727
Midmean - Empirical Distribution Function - Averaging	3.47772727272727
Midmean - Empirical Distribution Function - Interpolation	3.47772727272727
Midmean - Closest Observation	3.47772727272727
Midmean - True Basic - Statistics Graphics Toolkit	3.47772727272727
Midmean - MS Excel (old versions)	3.47772727272727
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