Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Thu, 06 Dec 2007 07:08:25 -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/06/t1196949537vkt9256czjbncxa.htm/, Retrieved Fri, 03 May 2024 10:02:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2615, Retrieved Fri, 03 May 2024 10:02:20 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

188

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

-       [Central Tendency] [Central Tendency] [2007-12-06 14:08:25] [6d644d07a16de69cd360f404f1ea3fa3] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2615&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2615&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2615&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	43.6661428571429	1.94077617066775	22.4993193533075
Geometric Mean	40.6650118372803
Harmonic Mean	37.8273752848949
Quadratic Mean	46.5470543643741
Winsorized Mean ( 1 / 23 )	43.7042857142857	1.92478810719936	22.7060243934472
Winsorized Mean ( 2 / 23 )	43.6728571428571	1.9048678205542	22.9269751274138
Winsorized Mean ( 3 / 23 )	43.5657142857143	1.87525002966675	23.2319496581777
Winsorized Mean ( 4 / 23 )	43.5657142857143	1.87328376743917	23.2563347011061
Winsorized Mean ( 5 / 23 )	43.5871428571429	1.8676896650687	23.3374653575221
Winsorized Mean ( 6 / 23 )	43.4414285714286	1.83712293392595	23.646446173634
Winsorized Mean ( 7 / 23 )	43.2814285714286	1.80173862761062	24.0220351099573
Winsorized Mean ( 8 / 23 )	43.2471428571429	1.78844661356142	24.1813999530144
Winsorized Mean ( 9 / 23 )	43.2728571428571	1.78064463799670	24.3017928560642
Winsorized Mean ( 10 / 23 )	43.3157142857143	1.77001671011785	24.4719239304979
Winsorized Mean ( 11 / 23 )	43.2371428571429	1.74185019956271	24.82253805063
Winsorized Mean ( 12 / 23 )	42.5685714285714	1.61404875594637	26.3737828685430
Winsorized Mean ( 13 / 23 )	42.55	1.57896728311875	26.9479934479427
Winsorized Mean ( 14 / 23 )	42.55	1.57322939352075	27.0462782956125
Winsorized Mean ( 15 / 23 )	42.4428571428571	1.55760283441137	27.2488314769256
Winsorized Mean ( 16 / 23 )	42.6485714285714	1.52278994098904	28.0068644273231
Winsorized Mean ( 17 / 23 )	42.6485714285714	1.52278994098904	28.0068644273231
Winsorized Mean ( 18 / 23 )	42.6485714285714	1.51557783069664	28.1401394008038
Winsorized Mean ( 19 / 23 )	42.35	1.46533689482007	28.9012036410919
Winsorized Mean ( 20 / 23 )	42.2357142857143	1.38669518760627	30.4578213461765
Winsorized Mean ( 21 / 23 )	42.1757142857143	1.36221478974224	30.9611337384576
Winsorized Mean ( 22 / 23 )	42.1128571428571	1.33672744206237	31.5044457214727
Winsorized Mean ( 23 / 23 )	42.2771428571428	1.31491707762478	32.151945986975
Trimmed Mean ( 1 / 23 )	43.5661764705882	1.90406156420235	22.8806553788291
Trimmed Mean ( 2 / 23 )	43.419696969697	1.87848351734254	23.1142283490047
Trimmed Mean ( 3 / 23 )	43.28125	1.85944856963964	23.2763899505904
Trimmed Mean ( 4 / 23 )	43.1741935483871	1.84854329071320	23.3557925125626
Trimmed Mean ( 5 / 23 )	43.06	1.83450789288014	23.4722347977454
Trimmed Mean ( 6 / 23 )	42.9327586206897	1.81758964315259	23.6207104185647
Trimmed Mean ( 7 / 23 )	42.8267857142857	1.80381718461954	23.7423094088766
Trimmed Mean ( 8 / 23 )	42.7425925925926	1.79396963657865	23.8257056981794
Trimmed Mean ( 9 / 23 )	42.6576923076923	1.78274016330143	23.9281602478149
Trimmed Mean ( 10 / 23 )	42.562	1.76819726021177	24.0708437671160
Trimmed Mean ( 11 / 23 )	42.4520833333333	1.74989865355814	24.2597382694214
Trimmed Mean ( 12 / 23 )	42.3434782608696	1.73059050594439	24.4676473812981
Trimmed Mean ( 13 / 23 )	42.3136363636364	1.73071552406935	24.4486374422448
Trimmed Mean ( 14 / 23 )	42.2833333333333	1.73381989731182	24.3873849866939
Trimmed Mean ( 15 / 23 )	42.25	1.73427366012551	24.3617838242105
Trimmed Mean ( 16 / 23 )	42.2263157894737	1.73316197036297	24.3637447114249
Trimmed Mean ( 17 / 23 )	42.175	1.73353650366060	24.3288790925035
Trimmed Mean ( 18 / 23 )	42.1176470588235	1.72776152970646	24.3770024593493
Trimmed Mean ( 19 / 23 )	42.053125	1.71504246382466	24.5201654693835
Trimmed Mean ( 20 / 23 )	42.0166666666667	1.70368149938332	24.662277944484
Trimmed Mean ( 21 / 23 )	41.9892857142857	1.70079610433202	24.6880185151747
Trimmed Mean ( 22 / 23 )	41.9653846153846	1.69347110359115	24.7806912833608
Trimmed Mean ( 23 / 23 )	41.9458333333333	1.67918824382871	24.9798278945145
Median	40.35
Midrange	47.065
Midmean - Weighted Average at Xnp	41.3555555555555
Midmean - Weighted Average at X(n+1)p	42.2263157894737
Midmean - Empirical Distribution Function	42.2263157894737
Midmean - Empirical Distribution Function - Averaging	42.2263157894737
Midmean - Empirical Distribution Function - Interpolation	42.1176470588235
Midmean - Closest Observation	42.2263157894737
Midmean - True Basic - Statistics Graphics Toolkit	42.2263157894737
Midmean - MS Excel (old versions)	42.2263157894737
Number of observations	70

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 43.6661428571429 & 1.94077617066775 & 22.4993193533075 \tabularnewline
Geometric Mean & 40.6650118372803 &  &  \tabularnewline
Harmonic Mean & 37.8273752848949 &  &  \tabularnewline
Quadratic Mean & 46.5470543643741 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 43.7042857142857 & 1.92478810719936 & 22.7060243934472 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 43.6728571428571 & 1.9048678205542 & 22.9269751274138 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 43.5657142857143 & 1.87525002966675 & 23.2319496581777 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 43.5657142857143 & 1.87328376743917 & 23.2563347011061 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 43.5871428571429 & 1.8676896650687 & 23.3374653575221 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 43.4414285714286 & 1.83712293392595 & 23.646446173634 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 43.2814285714286 & 1.80173862761062 & 24.0220351099573 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 43.2471428571429 & 1.78844661356142 & 24.1813999530144 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 43.2728571428571 & 1.78064463799670 & 24.3017928560642 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 43.3157142857143 & 1.77001671011785 & 24.4719239304979 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 43.2371428571429 & 1.74185019956271 & 24.82253805063 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 42.5685714285714 & 1.61404875594637 & 26.3737828685430 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 42.55 & 1.57896728311875 & 26.9479934479427 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 42.55 & 1.57322939352075 & 27.0462782956125 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 42.4428571428571 & 1.55760283441137 & 27.2488314769256 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 42.6485714285714 & 1.52278994098904 & 28.0068644273231 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 42.6485714285714 & 1.52278994098904 & 28.0068644273231 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 42.6485714285714 & 1.51557783069664 & 28.1401394008038 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 42.35 & 1.46533689482007 & 28.9012036410919 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 42.2357142857143 & 1.38669518760627 & 30.4578213461765 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 42.1757142857143 & 1.36221478974224 & 30.9611337384576 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 42.1128571428571 & 1.33672744206237 & 31.5044457214727 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 42.2771428571428 & 1.31491707762478 & 32.151945986975 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 43.5661764705882 & 1.90406156420235 & 22.8806553788291 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 43.419696969697 & 1.87848351734254 & 23.1142283490047 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 43.28125 & 1.85944856963964 & 23.2763899505904 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 43.1741935483871 & 1.84854329071320 & 23.3557925125626 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 43.06 & 1.83450789288014 & 23.4722347977454 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 42.9327586206897 & 1.81758964315259 & 23.6207104185647 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 42.8267857142857 & 1.80381718461954 & 23.7423094088766 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 42.7425925925926 & 1.79396963657865 & 23.8257056981794 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 42.6576923076923 & 1.78274016330143 & 23.9281602478149 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 42.562 & 1.76819726021177 & 24.0708437671160 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 42.4520833333333 & 1.74989865355814 & 24.2597382694214 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 42.3434782608696 & 1.73059050594439 & 24.4676473812981 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 42.3136363636364 & 1.73071552406935 & 24.4486374422448 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 42.2833333333333 & 1.73381989731182 & 24.3873849866939 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 42.25 & 1.73427366012551 & 24.3617838242105 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 42.2263157894737 & 1.73316197036297 & 24.3637447114249 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 42.175 & 1.73353650366060 & 24.3288790925035 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 42.1176470588235 & 1.72776152970646 & 24.3770024593493 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 42.053125 & 1.71504246382466 & 24.5201654693835 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 42.0166666666667 & 1.70368149938332 & 24.662277944484 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 41.9892857142857 & 1.70079610433202 & 24.6880185151747 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 41.9653846153846 & 1.69347110359115 & 24.7806912833608 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 41.9458333333333 & 1.67918824382871 & 24.9798278945145 \tabularnewline
Median & 40.35 &  &  \tabularnewline
Midrange & 47.065 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 41.3555555555555 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 42.2263157894737 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 42.2263157894737 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 42.2263157894737 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 42.1176470588235 &  &  \tabularnewline
Midmean - Closest Observation & 42.2263157894737 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 42.2263157894737 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 42.2263157894737 &  &  \tabularnewline
Number of observations & 70 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2615&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]43.6661428571429[/C][C]1.94077617066775[/C][C]22.4993193533075[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]40.6650118372803[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]37.8273752848949[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]46.5470543643741[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]43.7042857142857[/C][C]1.92478810719936[/C][C]22.7060243934472[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]43.6728571428571[/C][C]1.9048678205542[/C][C]22.9269751274138[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]43.5657142857143[/C][C]1.87525002966675[/C][C]23.2319496581777[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]43.5657142857143[/C][C]1.87328376743917[/C][C]23.2563347011061[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]43.5871428571429[/C][C]1.8676896650687[/C][C]23.3374653575221[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]43.4414285714286[/C][C]1.83712293392595[/C][C]23.646446173634[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]43.2814285714286[/C][C]1.80173862761062[/C][C]24.0220351099573[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]43.2471428571429[/C][C]1.78844661356142[/C][C]24.1813999530144[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]43.2728571428571[/C][C]1.78064463799670[/C][C]24.3017928560642[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]43.3157142857143[/C][C]1.77001671011785[/C][C]24.4719239304979[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]43.2371428571429[/C][C]1.74185019956271[/C][C]24.82253805063[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]42.5685714285714[/C][C]1.61404875594637[/C][C]26.3737828685430[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]42.55[/C][C]1.57896728311875[/C][C]26.9479934479427[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]42.55[/C][C]1.57322939352075[/C][C]27.0462782956125[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]42.4428571428571[/C][C]1.55760283441137[/C][C]27.2488314769256[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]42.6485714285714[/C][C]1.52278994098904[/C][C]28.0068644273231[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]42.6485714285714[/C][C]1.52278994098904[/C][C]28.0068644273231[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]42.6485714285714[/C][C]1.51557783069664[/C][C]28.1401394008038[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]42.35[/C][C]1.46533689482007[/C][C]28.9012036410919[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]42.2357142857143[/C][C]1.38669518760627[/C][C]30.4578213461765[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]42.1757142857143[/C][C]1.36221478974224[/C][C]30.9611337384576[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]42.1128571428571[/C][C]1.33672744206237[/C][C]31.5044457214727[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]42.2771428571428[/C][C]1.31491707762478[/C][C]32.151945986975[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]43.5661764705882[/C][C]1.90406156420235[/C][C]22.8806553788291[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]43.419696969697[/C][C]1.87848351734254[/C][C]23.1142283490047[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]43.28125[/C][C]1.85944856963964[/C][C]23.2763899505904[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]43.1741935483871[/C][C]1.84854329071320[/C][C]23.3557925125626[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]43.06[/C][C]1.83450789288014[/C][C]23.4722347977454[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]42.9327586206897[/C][C]1.81758964315259[/C][C]23.6207104185647[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]42.8267857142857[/C][C]1.80381718461954[/C][C]23.7423094088766[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]42.7425925925926[/C][C]1.79396963657865[/C][C]23.8257056981794[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]42.6576923076923[/C][C]1.78274016330143[/C][C]23.9281602478149[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]42.562[/C][C]1.76819726021177[/C][C]24.0708437671160[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]42.4520833333333[/C][C]1.74989865355814[/C][C]24.2597382694214[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]42.3434782608696[/C][C]1.73059050594439[/C][C]24.4676473812981[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]42.3136363636364[/C][C]1.73071552406935[/C][C]24.4486374422448[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]42.2833333333333[/C][C]1.73381989731182[/C][C]24.3873849866939[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]42.25[/C][C]1.73427366012551[/C][C]24.3617838242105[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]42.2263157894737[/C][C]1.73316197036297[/C][C]24.3637447114249[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]42.175[/C][C]1.73353650366060[/C][C]24.3288790925035[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]42.1176470588235[/C][C]1.72776152970646[/C][C]24.3770024593493[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]42.053125[/C][C]1.71504246382466[/C][C]24.5201654693835[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]42.0166666666667[/C][C]1.70368149938332[/C][C]24.662277944484[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]41.9892857142857[/C][C]1.70079610433202[/C][C]24.6880185151747[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]41.9653846153846[/C][C]1.69347110359115[/C][C]24.7806912833608[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]41.9458333333333[/C][C]1.67918824382871[/C][C]24.9798278945145[/C][/ROW]
[ROW][C]Median[/C][C]40.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]47.065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]41.3555555555555[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]42.2263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]42.2263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]42.2263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]42.1176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]42.2263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]42.2263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]42.2263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]70[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2615&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2615&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	43.6661428571429	1.94077617066775	22.4993193533075
Geometric Mean	40.6650118372803
Harmonic Mean	37.8273752848949
Quadratic Mean	46.5470543643741
Winsorized Mean ( 1 / 23 )	43.7042857142857	1.92478810719936	22.7060243934472
Winsorized Mean ( 2 / 23 )	43.6728571428571	1.9048678205542	22.9269751274138
Winsorized Mean ( 3 / 23 )	43.5657142857143	1.87525002966675	23.2319496581777
Winsorized Mean ( 4 / 23 )	43.5657142857143	1.87328376743917	23.2563347011061
Winsorized Mean ( 5 / 23 )	43.5871428571429	1.8676896650687	23.3374653575221
Winsorized Mean ( 6 / 23 )	43.4414285714286	1.83712293392595	23.646446173634
Winsorized Mean ( 7 / 23 )	43.2814285714286	1.80173862761062	24.0220351099573
Winsorized Mean ( 8 / 23 )	43.2471428571429	1.78844661356142	24.1813999530144
Winsorized Mean ( 9 / 23 )	43.2728571428571	1.78064463799670	24.3017928560642
Winsorized Mean ( 10 / 23 )	43.3157142857143	1.77001671011785	24.4719239304979
Winsorized Mean ( 11 / 23 )	43.2371428571429	1.74185019956271	24.82253805063
Winsorized Mean ( 12 / 23 )	42.5685714285714	1.61404875594637	26.3737828685430
Winsorized Mean ( 13 / 23 )	42.55	1.57896728311875	26.9479934479427
Winsorized Mean ( 14 / 23 )	42.55	1.57322939352075	27.0462782956125
Winsorized Mean ( 15 / 23 )	42.4428571428571	1.55760283441137	27.2488314769256
Winsorized Mean ( 16 / 23 )	42.6485714285714	1.52278994098904	28.0068644273231
Winsorized Mean ( 17 / 23 )	42.6485714285714	1.52278994098904	28.0068644273231
Winsorized Mean ( 18 / 23 )	42.6485714285714	1.51557783069664	28.1401394008038
Winsorized Mean ( 19 / 23 )	42.35	1.46533689482007	28.9012036410919
Winsorized Mean ( 20 / 23 )	42.2357142857143	1.38669518760627	30.4578213461765
Winsorized Mean ( 21 / 23 )	42.1757142857143	1.36221478974224	30.9611337384576
Winsorized Mean ( 22 / 23 )	42.1128571428571	1.33672744206237	31.5044457214727
Winsorized Mean ( 23 / 23 )	42.2771428571428	1.31491707762478	32.151945986975
Trimmed Mean ( 1 / 23 )	43.5661764705882	1.90406156420235	22.8806553788291
Trimmed Mean ( 2 / 23 )	43.419696969697	1.87848351734254	23.1142283490047
Trimmed Mean ( 3 / 23 )	43.28125	1.85944856963964	23.2763899505904
Trimmed Mean ( 4 / 23 )	43.1741935483871	1.84854329071320	23.3557925125626
Trimmed Mean ( 5 / 23 )	43.06	1.83450789288014	23.4722347977454
Trimmed Mean ( 6 / 23 )	42.9327586206897	1.81758964315259	23.6207104185647
Trimmed Mean ( 7 / 23 )	42.8267857142857	1.80381718461954	23.7423094088766
Trimmed Mean ( 8 / 23 )	42.7425925925926	1.79396963657865	23.8257056981794
Trimmed Mean ( 9 / 23 )	42.6576923076923	1.78274016330143	23.9281602478149
Trimmed Mean ( 10 / 23 )	42.562	1.76819726021177	24.0708437671160
Trimmed Mean ( 11 / 23 )	42.4520833333333	1.74989865355814	24.2597382694214
Trimmed Mean ( 12 / 23 )	42.3434782608696	1.73059050594439	24.4676473812981
Trimmed Mean ( 13 / 23 )	42.3136363636364	1.73071552406935	24.4486374422448
Trimmed Mean ( 14 / 23 )	42.2833333333333	1.73381989731182	24.3873849866939
Trimmed Mean ( 15 / 23 )	42.25	1.73427366012551	24.3617838242105
Trimmed Mean ( 16 / 23 )	42.2263157894737	1.73316197036297	24.3637447114249
Trimmed Mean ( 17 / 23 )	42.175	1.73353650366060	24.3288790925035
Trimmed Mean ( 18 / 23 )	42.1176470588235	1.72776152970646	24.3770024593493
Trimmed Mean ( 19 / 23 )	42.053125	1.71504246382466	24.5201654693835
Trimmed Mean ( 20 / 23 )	42.0166666666667	1.70368149938332	24.662277944484
Trimmed Mean ( 21 / 23 )	41.9892857142857	1.70079610433202	24.6880185151747
Trimmed Mean ( 22 / 23 )	41.9653846153846	1.69347110359115	24.7806912833608
Trimmed Mean ( 23 / 23 )	41.9458333333333	1.67918824382871	24.9798278945145
Median	40.35
Midrange	47.065
Midmean - Weighted Average at Xnp	41.3555555555555
Midmean - Weighted Average at X(n+1)p	42.2263157894737
Midmean - Empirical Distribution Function	42.2263157894737
Midmean - Empirical Distribution Function - Averaging	42.2263157894737
Midmean - Empirical Distribution Function - Interpolation	42.1176470588235
Midmean - Closest Observation	42.2263157894737
Midmean - True Basic - Statistics Graphics Toolkit	42.2263157894737
Midmean - MS Excel (old versions)	42.2263157894737
Number of observations	70

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