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*The author of this computation has been verified*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 08 Dec 2008 07:09:30 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/08/t1228745440jzbxqnsvj25dksi.htm/, Retrieved Thu, 16 May 2024 09:59:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30502, Retrieved Thu, 16 May 2024 09:59:01 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

162

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

-       [Central Tendency] [] [2008-12-08 14:09:30] [28deb8481dba3cc87d2d53a86e0e0d0b] [Current]

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4.43
4.61
4.54
4.2
4.08
3.95
4.19
4.23
3.89
3.92
4.14
4.24
4.08
4.37
4.43
4.3
4.27
4.06
3.96
4.21
4.31
4.35
4.25
4.06
4
3.87
3.71
3.63
3.48
3.6
3.66
3.45
3.3
3.14
3.21
3.12
3.14
3.4
3.42
3.29
3.49
3.52
3.81
4.03
3.98
4.1
3.96
3.83
3.72
3.82
3.76
3.98
4.14
4
4.13
4.28
4.46
4.63
4.49
4.41
4.5
4.39
4.33
4.45
4.17
4.13
4.33
4.47
4.63
4.9

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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30502&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30502&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30502&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' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	4.019	0.0492204867377375	81.6529918002339
Geometric Mean	3.99730257916325
Harmonic Mean	3.97468413139924
Quadratic Mean	4.03974309649937
Winsorized Mean ( 1 / 23 )	4.01542857142857	0.0482877356333865	83.1562822062063
Winsorized Mean ( 2 / 23 )	4.01542857142857	0.0482877356333865	83.1562822062063
Winsorized Mean ( 3 / 23 )	4.01757142857143	0.0473659974109748	84.8197366923926
Winsorized Mean ( 4 / 23 )	4.01814285714286	0.0455762700492276	88.1630474104793
Winsorized Mean ( 5 / 23 )	4.016	0.0449510430723462	89.3416420512527
Winsorized Mean ( 6 / 23 )	4.02371428571429	0.0429228068390078	93.7430373741909
Winsorized Mean ( 7 / 23 )	4.02371428571429	0.0421940559964497	95.3621118115038
Winsorized Mean ( 8 / 23 )	4.026	0.0413175352163716	97.4404687723179
Winsorized Mean ( 9 / 23 )	4.02857142857143	0.0403526307963402	99.834170636944
Winsorized Mean ( 10 / 23 )	4.02714285714286	0.0396449787729881	101.580149158428
Winsorized Mean ( 11 / 23 )	4.03185714285714	0.0387305245827792	104.100246157002
Winsorized Mean ( 12 / 23 )	4.04214285714286	0.0356703870994375	113.319287673404
Winsorized Mean ( 13 / 23 )	4.044	0.0341294575956958	118.490016686055
Winsorized Mean ( 14 / 23 )	4.046	0.0325025241892833	124.482639454016
Winsorized Mean ( 15 / 23 )	4.05242857142857	0.0300781836390817	134.729830100615
Winsorized Mean ( 16 / 23 )	4.05014285714286	0.029054452239076	139.398355330056
Winsorized Mean ( 17 / 23 )	4.05985714285714	0.0274857334400746	147.707797272668
Winsorized Mean ( 18 / 23 )	4.06757142857143	0.0247667677180579	164.235053797742
Winsorized Mean ( 19 / 23 )	4.06757142857143	0.0239758640837521	169.652756387117
Winsorized Mean ( 20 / 23 )	4.06471428571429	0.0227550840027888	178.628841151109
Winsorized Mean ( 21 / 23 )	4.07371428571428	0.0205827838455131	197.918528236516
Winsorized Mean ( 22 / 23 )	4.07371428571428	0.0188259670768800	216.38804896866
Winsorized Mean ( 23 / 23 )	4.08028571428571	0.0170080621834738	239.903033647795
Trimmed Mean ( 1 / 23 )	4.01926470588235	0.0471232651124499	85.2925767408352
Trimmed Mean ( 2 / 23 )	4.02333333333333	0.0457261195694322	87.9876396951672
Trimmed Mean ( 3 / 23 )	4.02765625	0.0440405556846741	91.4533476561379
Trimmed Mean ( 4 / 23 )	4.03145161290323	0.0424393970342916	94.9931406811872
Trimmed Mean ( 5 / 23 )	4.03533333333333	0.0411779016668817	97.9975464990447
Trimmed Mean ( 6 / 23 )	4.04	0.0398294913946311	101.432377329945
Trimmed Mean ( 7 / 23 )	4.04339285714286	0.0387794938328171	104.266261818022
Trimmed Mean ( 8 / 23 )	4.04703703703704	0.0376665921129015	107.443673823915
Trimmed Mean ( 9 / 23 )	4.05057692307692	0.0364987380322125	110.978547244620
Trimmed Mean ( 10 / 23 )	4.054	0.0352669122839074	114.951940429723
Trimmed Mean ( 11 / 23 )	4.05791666666667	0.0338631977861306	119.832648183293
Trimmed Mean ( 12 / 23 )	4.06152173913044	0.0322923951073397	125.773319867726
Trimmed Mean ( 13 / 23 )	4.06409090909091	0.0310481420187064	130.896428734522
Trimmed Mean ( 14 / 23 )	4.06666666666667	0.0297973540334457	136.477442329345
Trimmed Mean ( 15 / 23 )	4.06925	0.0285468294974937	142.546477897213
Trimmed Mean ( 16 / 23 )	4.07131578947368	0.0274993108736404	148.051556934696
Trimmed Mean ( 17 / 23 )	4.07388888888889	0.0263169864203795	154.800736825023
Trimmed Mean ( 18 / 23 )	4.07558823529412	0.0251278058497325	162.194353922768
Trimmed Mean ( 19 / 23 )	4.0765625	0.0242409335188004	168.168544203892
Trimmed Mean ( 20 / 23 )	4.07766666666667	0.0231719377117670	175.974349551094
Trimmed Mean ( 21 / 23 )	4.07928571428571	0.0219663557763279	185.706075045992
Trimmed Mean ( 22 / 23 )	4.08	0.0209247736868563	194.984187693404
Trimmed Mean ( 23 / 23 )	4.08083333333333	0.0199448212255665	204.606162531167
Median	4.08
Midrange	4.01
Midmean - Weighted Average at Xnp	4.06657142857143
Midmean - Weighted Average at X(n+1)p	4.08081081081081
Midmean - Empirical Distribution Function	4.08081081081081
Midmean - Empirical Distribution Function - Averaging	4.08081081081081
Midmean - Empirical Distribution Function - Interpolation	4.07558823529412
Midmean - Closest Observation	4.08081081081081
Midmean - True Basic - Statistics Graphics Toolkit	4.08081081081081
Midmean - MS Excel (old versions)	4.08081081081081
Number of observations	70

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.019 & 0.0492204867377375 & 81.6529918002339 \tabularnewline
Geometric Mean & 3.99730257916325 &  &  \tabularnewline
Harmonic Mean & 3.97468413139924 &  &  \tabularnewline
Quadratic Mean & 4.03974309649937 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 4.01542857142857 & 0.0482877356333865 & 83.1562822062063 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 4.01542857142857 & 0.0482877356333865 & 83.1562822062063 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 4.01757142857143 & 0.0473659974109748 & 84.8197366923926 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 4.01814285714286 & 0.0455762700492276 & 88.1630474104793 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 4.016 & 0.0449510430723462 & 89.3416420512527 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 4.02371428571429 & 0.0429228068390078 & 93.7430373741909 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 4.02371428571429 & 0.0421940559964497 & 95.3621118115038 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 4.026 & 0.0413175352163716 & 97.4404687723179 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 4.02857142857143 & 0.0403526307963402 & 99.834170636944 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 4.02714285714286 & 0.0396449787729881 & 101.580149158428 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 4.03185714285714 & 0.0387305245827792 & 104.100246157002 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 4.04214285714286 & 0.0356703870994375 & 113.319287673404 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 4.044 & 0.0341294575956958 & 118.490016686055 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 4.046 & 0.0325025241892833 & 124.482639454016 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 4.05242857142857 & 0.0300781836390817 & 134.729830100615 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 4.05014285714286 & 0.029054452239076 & 139.398355330056 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 4.05985714285714 & 0.0274857334400746 & 147.707797272668 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 4.06757142857143 & 0.0247667677180579 & 164.235053797742 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 4.06757142857143 & 0.0239758640837521 & 169.652756387117 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 4.06471428571429 & 0.0227550840027888 & 178.628841151109 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 4.07371428571428 & 0.0205827838455131 & 197.918528236516 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 4.07371428571428 & 0.0188259670768800 & 216.38804896866 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 4.08028571428571 & 0.0170080621834738 & 239.903033647795 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 4.01926470588235 & 0.0471232651124499 & 85.2925767408352 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 4.02333333333333 & 0.0457261195694322 & 87.9876396951672 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 4.02765625 & 0.0440405556846741 & 91.4533476561379 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 4.03145161290323 & 0.0424393970342916 & 94.9931406811872 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 4.03533333333333 & 0.0411779016668817 & 97.9975464990447 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 4.04 & 0.0398294913946311 & 101.432377329945 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 4.04339285714286 & 0.0387794938328171 & 104.266261818022 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 4.04703703703704 & 0.0376665921129015 & 107.443673823915 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 4.05057692307692 & 0.0364987380322125 & 110.978547244620 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 4.054 & 0.0352669122839074 & 114.951940429723 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 4.05791666666667 & 0.0338631977861306 & 119.832648183293 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 4.06152173913044 & 0.0322923951073397 & 125.773319867726 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 4.06409090909091 & 0.0310481420187064 & 130.896428734522 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 4.06666666666667 & 0.0297973540334457 & 136.477442329345 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 4.06925 & 0.0285468294974937 & 142.546477897213 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 4.07131578947368 & 0.0274993108736404 & 148.051556934696 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 4.07388888888889 & 0.0263169864203795 & 154.800736825023 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 4.07558823529412 & 0.0251278058497325 & 162.194353922768 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 4.0765625 & 0.0242409335188004 & 168.168544203892 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 4.07766666666667 & 0.0231719377117670 & 175.974349551094 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 4.07928571428571 & 0.0219663557763279 & 185.706075045992 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 4.08 & 0.0209247736868563 & 194.984187693404 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 4.08083333333333 & 0.0199448212255665 & 204.606162531167 \tabularnewline
Median & 4.08 &  &  \tabularnewline
Midrange & 4.01 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.06657142857143 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.08081081081081 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.08081081081081 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.08081081081081 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.07558823529412 &  &  \tabularnewline
Midmean - Closest Observation & 4.08081081081081 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.08081081081081 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.08081081081081 &  &  \tabularnewline
Number of observations & 70 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30502&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]4.019[/C][C]0.0492204867377375[/C][C]81.6529918002339[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.99730257916325[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.97468413139924[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.03974309649937[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]4.01542857142857[/C][C]0.0482877356333865[/C][C]83.1562822062063[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]4.01542857142857[/C][C]0.0482877356333865[/C][C]83.1562822062063[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]4.01757142857143[/C][C]0.0473659974109748[/C][C]84.8197366923926[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]4.01814285714286[/C][C]0.0455762700492276[/C][C]88.1630474104793[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]4.016[/C][C]0.0449510430723462[/C][C]89.3416420512527[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]4.02371428571429[/C][C]0.0429228068390078[/C][C]93.7430373741909[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]4.02371428571429[/C][C]0.0421940559964497[/C][C]95.3621118115038[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]4.026[/C][C]0.0413175352163716[/C][C]97.4404687723179[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]4.02857142857143[/C][C]0.0403526307963402[/C][C]99.834170636944[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]4.02714285714286[/C][C]0.0396449787729881[/C][C]101.580149158428[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]4.03185714285714[/C][C]0.0387305245827792[/C][C]104.100246157002[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]4.04214285714286[/C][C]0.0356703870994375[/C][C]113.319287673404[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]4.044[/C][C]0.0341294575956958[/C][C]118.490016686055[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]4.046[/C][C]0.0325025241892833[/C][C]124.482639454016[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]4.05242857142857[/C][C]0.0300781836390817[/C][C]134.729830100615[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]4.05014285714286[/C][C]0.029054452239076[/C][C]139.398355330056[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]4.05985714285714[/C][C]0.0274857334400746[/C][C]147.707797272668[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]4.06757142857143[/C][C]0.0247667677180579[/C][C]164.235053797742[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]4.06757142857143[/C][C]0.0239758640837521[/C][C]169.652756387117[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]4.06471428571429[/C][C]0.0227550840027888[/C][C]178.628841151109[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]4.07371428571428[/C][C]0.0205827838455131[/C][C]197.918528236516[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]4.07371428571428[/C][C]0.0188259670768800[/C][C]216.38804896866[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]4.08028571428571[/C][C]0.0170080621834738[/C][C]239.903033647795[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]4.01926470588235[/C][C]0.0471232651124499[/C][C]85.2925767408352[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]4.02333333333333[/C][C]0.0457261195694322[/C][C]87.9876396951672[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]4.02765625[/C][C]0.0440405556846741[/C][C]91.4533476561379[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]4.03145161290323[/C][C]0.0424393970342916[/C][C]94.9931406811872[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]4.03533333333333[/C][C]0.0411779016668817[/C][C]97.9975464990447[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]4.04[/C][C]0.0398294913946311[/C][C]101.432377329945[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]4.04339285714286[/C][C]0.0387794938328171[/C][C]104.266261818022[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]4.04703703703704[/C][C]0.0376665921129015[/C][C]107.443673823915[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]4.05057692307692[/C][C]0.0364987380322125[/C][C]110.978547244620[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]4.054[/C][C]0.0352669122839074[/C][C]114.951940429723[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]4.05791666666667[/C][C]0.0338631977861306[/C][C]119.832648183293[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]4.06152173913044[/C][C]0.0322923951073397[/C][C]125.773319867726[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]4.06409090909091[/C][C]0.0310481420187064[/C][C]130.896428734522[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]4.06666666666667[/C][C]0.0297973540334457[/C][C]136.477442329345[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]4.06925[/C][C]0.0285468294974937[/C][C]142.546477897213[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]4.07131578947368[/C][C]0.0274993108736404[/C][C]148.051556934696[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]4.07388888888889[/C][C]0.0263169864203795[/C][C]154.800736825023[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]4.07558823529412[/C][C]0.0251278058497325[/C][C]162.194353922768[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]4.0765625[/C][C]0.0242409335188004[/C][C]168.168544203892[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]4.07766666666667[/C][C]0.0231719377117670[/C][C]175.974349551094[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]4.07928571428571[/C][C]0.0219663557763279[/C][C]185.706075045992[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]4.08[/C][C]0.0209247736868563[/C][C]194.984187693404[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]4.08083333333333[/C][C]0.0199448212255665[/C][C]204.606162531167[/C][/ROW]
[ROW][C]Median[/C][C]4.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.01[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.06657142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.08081081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.08081081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.08081081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.07558823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.08081081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.08081081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.08081081081081[/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=30502&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30502&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	4.019	0.0492204867377375	81.6529918002339
Geometric Mean	3.99730257916325
Harmonic Mean	3.97468413139924
Quadratic Mean	4.03974309649937
Winsorized Mean ( 1 / 23 )	4.01542857142857	0.0482877356333865	83.1562822062063
Winsorized Mean ( 2 / 23 )	4.01542857142857	0.0482877356333865	83.1562822062063
Winsorized Mean ( 3 / 23 )	4.01757142857143	0.0473659974109748	84.8197366923926
Winsorized Mean ( 4 / 23 )	4.01814285714286	0.0455762700492276	88.1630474104793
Winsorized Mean ( 5 / 23 )	4.016	0.0449510430723462	89.3416420512527
Winsorized Mean ( 6 / 23 )	4.02371428571429	0.0429228068390078	93.7430373741909
Winsorized Mean ( 7 / 23 )	4.02371428571429	0.0421940559964497	95.3621118115038
Winsorized Mean ( 8 / 23 )	4.026	0.0413175352163716	97.4404687723179
Winsorized Mean ( 9 / 23 )	4.02857142857143	0.0403526307963402	99.834170636944
Winsorized Mean ( 10 / 23 )	4.02714285714286	0.0396449787729881	101.580149158428
Winsorized Mean ( 11 / 23 )	4.03185714285714	0.0387305245827792	104.100246157002
Winsorized Mean ( 12 / 23 )	4.04214285714286	0.0356703870994375	113.319287673404
Winsorized Mean ( 13 / 23 )	4.044	0.0341294575956958	118.490016686055
Winsorized Mean ( 14 / 23 )	4.046	0.0325025241892833	124.482639454016
Winsorized Mean ( 15 / 23 )	4.05242857142857	0.0300781836390817	134.729830100615
Winsorized Mean ( 16 / 23 )	4.05014285714286	0.029054452239076	139.398355330056
Winsorized Mean ( 17 / 23 )	4.05985714285714	0.0274857334400746	147.707797272668
Winsorized Mean ( 18 / 23 )	4.06757142857143	0.0247667677180579	164.235053797742
Winsorized Mean ( 19 / 23 )	4.06757142857143	0.0239758640837521	169.652756387117
Winsorized Mean ( 20 / 23 )	4.06471428571429	0.0227550840027888	178.628841151109
Winsorized Mean ( 21 / 23 )	4.07371428571428	0.0205827838455131	197.918528236516
Winsorized Mean ( 22 / 23 )	4.07371428571428	0.0188259670768800	216.38804896866
Winsorized Mean ( 23 / 23 )	4.08028571428571	0.0170080621834738	239.903033647795
Trimmed Mean ( 1 / 23 )	4.01926470588235	0.0471232651124499	85.2925767408352
Trimmed Mean ( 2 / 23 )	4.02333333333333	0.0457261195694322	87.9876396951672
Trimmed Mean ( 3 / 23 )	4.02765625	0.0440405556846741	91.4533476561379
Trimmed Mean ( 4 / 23 )	4.03145161290323	0.0424393970342916	94.9931406811872
Trimmed Mean ( 5 / 23 )	4.03533333333333	0.0411779016668817	97.9975464990447
Trimmed Mean ( 6 / 23 )	4.04	0.0398294913946311	101.432377329945
Trimmed Mean ( 7 / 23 )	4.04339285714286	0.0387794938328171	104.266261818022
Trimmed Mean ( 8 / 23 )	4.04703703703704	0.0376665921129015	107.443673823915
Trimmed Mean ( 9 / 23 )	4.05057692307692	0.0364987380322125	110.978547244620
Trimmed Mean ( 10 / 23 )	4.054	0.0352669122839074	114.951940429723
Trimmed Mean ( 11 / 23 )	4.05791666666667	0.0338631977861306	119.832648183293
Trimmed Mean ( 12 / 23 )	4.06152173913044	0.0322923951073397	125.773319867726
Trimmed Mean ( 13 / 23 )	4.06409090909091	0.0310481420187064	130.896428734522
Trimmed Mean ( 14 / 23 )	4.06666666666667	0.0297973540334457	136.477442329345
Trimmed Mean ( 15 / 23 )	4.06925	0.0285468294974937	142.546477897213
Trimmed Mean ( 16 / 23 )	4.07131578947368	0.0274993108736404	148.051556934696
Trimmed Mean ( 17 / 23 )	4.07388888888889	0.0263169864203795	154.800736825023
Trimmed Mean ( 18 / 23 )	4.07558823529412	0.0251278058497325	162.194353922768
Trimmed Mean ( 19 / 23 )	4.0765625	0.0242409335188004	168.168544203892
Trimmed Mean ( 20 / 23 )	4.07766666666667	0.0231719377117670	175.974349551094
Trimmed Mean ( 21 / 23 )	4.07928571428571	0.0219663557763279	185.706075045992
Trimmed Mean ( 22 / 23 )	4.08	0.0209247736868563	194.984187693404
Trimmed Mean ( 23 / 23 )	4.08083333333333	0.0199448212255665	204.606162531167
Median	4.08
Midrange	4.01
Midmean - Weighted Average at Xnp	4.06657142857143
Midmean - Weighted Average at X(n+1)p	4.08081081081081
Midmean - Empirical Distribution Function	4.08081081081081
Midmean - Empirical Distribution Function - Averaging	4.08081081081081
Midmean - Empirical Distribution Function - Interpolation	4.07558823529412
Midmean - Closest Observation	4.08081081081081
Midmean - True Basic - Statistics Graphics Toolkit	4.08081081081081
Midmean - MS Excel (old versions)	4.08081081081081
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