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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sat, 12 Oct 2013 05:28:04 -0400

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/12/t13815701034elwupndu0mv5bf.htm/, Retrieved Mon, 29 Apr 2024 01:49:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=214866, Retrieved Mon, 29 Apr 2024 01:49:03 +0000

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Estimated Impact

106

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

-       [Central Tendency] [] [2013-10-12 09:28:04] [43b132fa6864a311b34d1147ccf52151] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214866&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214866&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214866&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.52777777777778	0.522188508218163	4.84073804382096
Geometric Mean	NaN
Harmonic Mean	0
Quadratic Mean	5.07444578254611
Winsorized Mean ( 1 / 24 )	2.61111111111111	0.500217306281718	5.21995356482239
Winsorized Mean ( 2 / 24 )	2.58333333333333	0.492411109841626	5.24629376084591
Winsorized Mean ( 3 / 24 )	2.54166666666667	0.481641648553448	5.27709070488454
Winsorized Mean ( 4 / 24 )	2.43055555555556	0.456575326224249	5.32344920093596
Winsorized Mean ( 5 / 24 )	2.36111111111111	0.443305955751947	5.32614344669955
Winsorized Mean ( 6 / 24 )	2.44444444444444	0.427391956571271	5.71944419369721
Winsorized Mean ( 7 / 24 )	2.44444444444444	0.427391956571271	5.71944419369721
Winsorized Mean ( 8 / 24 )	2.44444444444444	0.427391956571271	5.71944419369721
Winsorized Mean ( 9 / 24 )	2.44444444444444	0.383995594943725	6.36581376617792
Winsorized Mean ( 10 / 24 )	2.44444444444444	0.383995594943725	6.36581376617792
Winsorized Mean ( 11 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 12 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 13 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 14 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 15 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 16 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 17 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 18 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 19 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 20 / 24 )	2.44444444444444	0.257051483435708	9.50955198457679
Winsorized Mean ( 21 / 24 )	2.44444444444444	0.257051483435708	9.50955198457679
Winsorized Mean ( 22 / 24 )	2.44444444444444	0.257051483435708	9.50955198457679
Winsorized Mean ( 23 / 24 )	2.44444444444444	0.257051483435708	9.50955198457679
Winsorized Mean ( 24 / 24 )	2.11111111111111	0.2126253248736	9.92878488188606
Trimmed Mean ( 1 / 24 )	2.55714285714286	0.483104056829306	5.29315128075268
Trimmed Mean ( 2 / 24 )	2.5	0.462605135998837	5.40417692207872
Trimmed Mean ( 3 / 24 )	2.45454545454545	0.443119803203968	5.5392366506708
Trimmed Mean ( 4 / 24 )	2.421875	0.42480427770346	5.70115492502318
Trimmed Mean ( 5 / 24 )	2.41935483870968	0.412360828306619	5.8670821102113
Trimmed Mean ( 6 / 24 )	2.43333333333333	0.401527216339557	6.06019526027733
Trimmed Mean ( 7 / 24 )	2.43103448275862	0.392852096970452	6.18816725558032
Trimmed Mean ( 8 / 24 )	2.42857142857143	0.382114029741669	6.35561963064606
Trimmed Mean ( 9 / 24 )	2.42592592592593	0.368768373242635	6.57845439562617
Trimmed Mean ( 10 / 24 )	2.42307692307692	0.362605530326059	6.68240476337487
Trimmed Mean ( 11 / 24 )	2.42	0.354665694848037	6.82332696720751
Trimmed Mean ( 12 / 24 )	2.41666666666667	0.354596630956329	6.81525557687629
Trimmed Mean ( 13 / 24 )	2.41304347826087	0.353828047099878	6.81981967805881
Trimmed Mean ( 14 / 24 )	2.40909090909091	0.352157622878085	6.84094494221675
Trimmed Mean ( 15 / 24 )	2.4047619047619	0.34931411774589	6.88423909196609
Trimmed Mean ( 16 / 24 )	2.4	0.34492659940103	6.95800209136562
Trimmed Mean ( 17 / 24 )	2.39473684210526	0.338475104581345	7.07507527050559
Trimmed Mean ( 18 / 24 )	2.38888888888889	0.329207267605215	7.25648891735173
Trimmed Mean ( 19 / 24 )	2.38235294117647	0.315987279134151	7.5393950911709
Trimmed Mean ( 20 / 24 )	2.375	0.296994352069682	7.9967850682991
Trimmed Mean ( 21 / 24 )	2.36666666666667	0.293544855815051	8.0623680496646
Trimmed Mean ( 22 / 24 )	2.35714285714286	0.287362968098915	8.2026674234917
Trimmed Mean ( 23 / 24 )	2.34615384615385	0.277029893928756	8.46895550830775
Trimmed Mean ( 24 / 24 )	2.33333333333333	0.260063165868498	8.97217922246318
Median	3
Midrange	1.5
Midmean - Weighted Average at Xnp	2.42
Midmean - Weighted Average at X(n+1)p	2.42
Midmean - Empirical Distribution Function	2.42
Midmean - Empirical Distribution Function - Averaging	2.42
Midmean - Empirical Distribution Function - Interpolation	2.42
Midmean - Closest Observation	2.42
Midmean - True Basic - Statistics Graphics Toolkit	2.42
Midmean - MS Excel (old versions)	2.42
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.52777777777778 & 0.522188508218163 & 4.84073804382096 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 5.07444578254611 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.61111111111111 & 0.500217306281718 & 5.21995356482239 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.58333333333333 & 0.492411109841626 & 5.24629376084591 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.54166666666667 & 0.481641648553448 & 5.27709070488454 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.43055555555556 & 0.456575326224249 & 5.32344920093596 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.36111111111111 & 0.443305955751947 & 5.32614344669955 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.44444444444444 & 0.427391956571271 & 5.71944419369721 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.44444444444444 & 0.427391956571271 & 5.71944419369721 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.44444444444444 & 0.427391956571271 & 5.71944419369721 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.44444444444444 & 0.383995594943725 & 6.36581376617792 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.44444444444444 & 0.383995594943725 & 6.36581376617792 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.44444444444444 & 0.336190157416915 & 7.27101728148767 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.44444444444444 & 0.336190157416915 & 7.27101728148767 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.44444444444444 & 0.336190157416915 & 7.27101728148767 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.44444444444444 & 0.336190157416915 & 7.27101728148767 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.44444444444444 & 0.336190157416915 & 7.27101728148767 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.44444444444444 & 0.336190157416915 & 7.27101728148767 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.44444444444444 & 0.336190157416915 & 7.27101728148767 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.44444444444444 & 0.336190157416915 & 7.27101728148767 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.44444444444444 & 0.336190157416915 & 7.27101728148767 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.44444444444444 & 0.257051483435708 & 9.50955198457679 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.44444444444444 & 0.257051483435708 & 9.50955198457679 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.44444444444444 & 0.257051483435708 & 9.50955198457679 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.44444444444444 & 0.257051483435708 & 9.50955198457679 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.11111111111111 & 0.2126253248736 & 9.92878488188606 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.55714285714286 & 0.483104056829306 & 5.29315128075268 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.5 & 0.462605135998837 & 5.40417692207872 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.45454545454545 & 0.443119803203968 & 5.5392366506708 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.421875 & 0.42480427770346 & 5.70115492502318 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.41935483870968 & 0.412360828306619 & 5.8670821102113 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.43333333333333 & 0.401527216339557 & 6.06019526027733 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.43103448275862 & 0.392852096970452 & 6.18816725558032 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.42857142857143 & 0.382114029741669 & 6.35561963064606 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.42592592592593 & 0.368768373242635 & 6.57845439562617 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.42307692307692 & 0.362605530326059 & 6.68240476337487 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.42 & 0.354665694848037 & 6.82332696720751 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.41666666666667 & 0.354596630956329 & 6.81525557687629 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.41304347826087 & 0.353828047099878 & 6.81981967805881 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.40909090909091 & 0.352157622878085 & 6.84094494221675 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.4047619047619 & 0.34931411774589 & 6.88423909196609 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.4 & 0.34492659940103 & 6.95800209136562 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.39473684210526 & 0.338475104581345 & 7.07507527050559 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.38888888888889 & 0.329207267605215 & 7.25648891735173 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.38235294117647 & 0.315987279134151 & 7.5393950911709 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.375 & 0.296994352069682 & 7.9967850682991 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.36666666666667 & 0.293544855815051 & 8.0623680496646 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.35714285714286 & 0.287362968098915 & 8.2026674234917 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.34615384615385 & 0.277029893928756 & 8.46895550830775 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.33333333333333 & 0.260063165868498 & 8.97217922246318 \tabularnewline
Median & 3 &  &  \tabularnewline
Midrange & 1.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.42 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.42 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.42 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.42 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.42 &  &  \tabularnewline
Midmean - Closest Observation & 2.42 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.42 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.42 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214866&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]2.52777777777778[/C][C]0.522188508218163[/C][C]4.84073804382096[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.07444578254611[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.61111111111111[/C][C]0.500217306281718[/C][C]5.21995356482239[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.58333333333333[/C][C]0.492411109841626[/C][C]5.24629376084591[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.54166666666667[/C][C]0.481641648553448[/C][C]5.27709070488454[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.43055555555556[/C][C]0.456575326224249[/C][C]5.32344920093596[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.36111111111111[/C][C]0.443305955751947[/C][C]5.32614344669955[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.44444444444444[/C][C]0.427391956571271[/C][C]5.71944419369721[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.44444444444444[/C][C]0.427391956571271[/C][C]5.71944419369721[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.44444444444444[/C][C]0.427391956571271[/C][C]5.71944419369721[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.44444444444444[/C][C]0.383995594943725[/C][C]6.36581376617792[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.44444444444444[/C][C]0.383995594943725[/C][C]6.36581376617792[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.44444444444444[/C][C]0.336190157416915[/C][C]7.27101728148767[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.44444444444444[/C][C]0.336190157416915[/C][C]7.27101728148767[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.44444444444444[/C][C]0.336190157416915[/C][C]7.27101728148767[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.44444444444444[/C][C]0.336190157416915[/C][C]7.27101728148767[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.44444444444444[/C][C]0.336190157416915[/C][C]7.27101728148767[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.44444444444444[/C][C]0.336190157416915[/C][C]7.27101728148767[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.44444444444444[/C][C]0.336190157416915[/C][C]7.27101728148767[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.44444444444444[/C][C]0.336190157416915[/C][C]7.27101728148767[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.44444444444444[/C][C]0.336190157416915[/C][C]7.27101728148767[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.44444444444444[/C][C]0.257051483435708[/C][C]9.50955198457679[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.44444444444444[/C][C]0.257051483435708[/C][C]9.50955198457679[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.44444444444444[/C][C]0.257051483435708[/C][C]9.50955198457679[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.44444444444444[/C][C]0.257051483435708[/C][C]9.50955198457679[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.11111111111111[/C][C]0.2126253248736[/C][C]9.92878488188606[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.55714285714286[/C][C]0.483104056829306[/C][C]5.29315128075268[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.5[/C][C]0.462605135998837[/C][C]5.40417692207872[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.45454545454545[/C][C]0.443119803203968[/C][C]5.5392366506708[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.421875[/C][C]0.42480427770346[/C][C]5.70115492502318[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.41935483870968[/C][C]0.412360828306619[/C][C]5.8670821102113[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.43333333333333[/C][C]0.401527216339557[/C][C]6.06019526027733[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.43103448275862[/C][C]0.392852096970452[/C][C]6.18816725558032[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.42857142857143[/C][C]0.382114029741669[/C][C]6.35561963064606[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.42592592592593[/C][C]0.368768373242635[/C][C]6.57845439562617[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.42307692307692[/C][C]0.362605530326059[/C][C]6.68240476337487[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.42[/C][C]0.354665694848037[/C][C]6.82332696720751[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.41666666666667[/C][C]0.354596630956329[/C][C]6.81525557687629[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.41304347826087[/C][C]0.353828047099878[/C][C]6.81981967805881[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.40909090909091[/C][C]0.352157622878085[/C][C]6.84094494221675[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.4047619047619[/C][C]0.34931411774589[/C][C]6.88423909196609[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.4[/C][C]0.34492659940103[/C][C]6.95800209136562[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.39473684210526[/C][C]0.338475104581345[/C][C]7.07507527050559[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.38888888888889[/C][C]0.329207267605215[/C][C]7.25648891735173[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.38235294117647[/C][C]0.315987279134151[/C][C]7.5393950911709[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.375[/C][C]0.296994352069682[/C][C]7.9967850682991[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.36666666666667[/C][C]0.293544855815051[/C][C]8.0623680496646[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.35714285714286[/C][C]0.287362968098915[/C][C]8.2026674234917[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.34615384615385[/C][C]0.277029893928756[/C][C]8.46895550830775[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.33333333333333[/C][C]0.260063165868498[/C][C]8.97217922246318[/C][/ROW]
[ROW][C]Median[/C][C]3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.42[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.42[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.42[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.42[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.42[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.42[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.42[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.42[/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=214866&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214866&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	2.52777777777778	0.522188508218163	4.84073804382096
Geometric Mean	NaN
Harmonic Mean	0
Quadratic Mean	5.07444578254611
Winsorized Mean ( 1 / 24 )	2.61111111111111	0.500217306281718	5.21995356482239
Winsorized Mean ( 2 / 24 )	2.58333333333333	0.492411109841626	5.24629376084591
Winsorized Mean ( 3 / 24 )	2.54166666666667	0.481641648553448	5.27709070488454
Winsorized Mean ( 4 / 24 )	2.43055555555556	0.456575326224249	5.32344920093596
Winsorized Mean ( 5 / 24 )	2.36111111111111	0.443305955751947	5.32614344669955
Winsorized Mean ( 6 / 24 )	2.44444444444444	0.427391956571271	5.71944419369721
Winsorized Mean ( 7 / 24 )	2.44444444444444	0.427391956571271	5.71944419369721
Winsorized Mean ( 8 / 24 )	2.44444444444444	0.427391956571271	5.71944419369721
Winsorized Mean ( 9 / 24 )	2.44444444444444	0.383995594943725	6.36581376617792
Winsorized Mean ( 10 / 24 )	2.44444444444444	0.383995594943725	6.36581376617792
Winsorized Mean ( 11 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 12 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 13 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 14 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 15 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 16 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 17 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 18 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 19 / 24 )	2.44444444444444	0.336190157416915	7.27101728148767
Winsorized Mean ( 20 / 24 )	2.44444444444444	0.257051483435708	9.50955198457679
Winsorized Mean ( 21 / 24 )	2.44444444444444	0.257051483435708	9.50955198457679
Winsorized Mean ( 22 / 24 )	2.44444444444444	0.257051483435708	9.50955198457679
Winsorized Mean ( 23 / 24 )	2.44444444444444	0.257051483435708	9.50955198457679
Winsorized Mean ( 24 / 24 )	2.11111111111111	0.2126253248736	9.92878488188606
Trimmed Mean ( 1 / 24 )	2.55714285714286	0.483104056829306	5.29315128075268
Trimmed Mean ( 2 / 24 )	2.5	0.462605135998837	5.40417692207872
Trimmed Mean ( 3 / 24 )	2.45454545454545	0.443119803203968	5.5392366506708
Trimmed Mean ( 4 / 24 )	2.421875	0.42480427770346	5.70115492502318
Trimmed Mean ( 5 / 24 )	2.41935483870968	0.412360828306619	5.8670821102113
Trimmed Mean ( 6 / 24 )	2.43333333333333	0.401527216339557	6.06019526027733
Trimmed Mean ( 7 / 24 )	2.43103448275862	0.392852096970452	6.18816725558032
Trimmed Mean ( 8 / 24 )	2.42857142857143	0.382114029741669	6.35561963064606
Trimmed Mean ( 9 / 24 )	2.42592592592593	0.368768373242635	6.57845439562617
Trimmed Mean ( 10 / 24 )	2.42307692307692	0.362605530326059	6.68240476337487
Trimmed Mean ( 11 / 24 )	2.42	0.354665694848037	6.82332696720751
Trimmed Mean ( 12 / 24 )	2.41666666666667	0.354596630956329	6.81525557687629
Trimmed Mean ( 13 / 24 )	2.41304347826087	0.353828047099878	6.81981967805881
Trimmed Mean ( 14 / 24 )	2.40909090909091	0.352157622878085	6.84094494221675
Trimmed Mean ( 15 / 24 )	2.4047619047619	0.34931411774589	6.88423909196609
Trimmed Mean ( 16 / 24 )	2.4	0.34492659940103	6.95800209136562
Trimmed Mean ( 17 / 24 )	2.39473684210526	0.338475104581345	7.07507527050559
Trimmed Mean ( 18 / 24 )	2.38888888888889	0.329207267605215	7.25648891735173
Trimmed Mean ( 19 / 24 )	2.38235294117647	0.315987279134151	7.5393950911709
Trimmed Mean ( 20 / 24 )	2.375	0.296994352069682	7.9967850682991
Trimmed Mean ( 21 / 24 )	2.36666666666667	0.293544855815051	8.0623680496646
Trimmed Mean ( 22 / 24 )	2.35714285714286	0.287362968098915	8.2026674234917
Trimmed Mean ( 23 / 24 )	2.34615384615385	0.277029893928756	8.46895550830775
Trimmed Mean ( 24 / 24 )	2.33333333333333	0.260063165868498	8.97217922246318
Median	3
Midrange	1.5
Midmean - Weighted Average at Xnp	2.42
Midmean - Weighted Average at X(n+1)p	2.42
Midmean - Empirical Distribution Function	2.42
Midmean - Empirical Distribution Function - Averaging	2.42
Midmean - Empirical Distribution Function - Interpolation	2.42
Midmean - Closest Observation	2.42
Midmean - True Basic - Statistics Graphics Toolkit	2.42
Midmean - MS Excel (old versions)	2.42
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