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rwasp_centraltendency.wasp

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Central Tendency

Date of computation

Wed, 12 Oct 2016 13:05:32 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/12/t1476273956bvk8wu67ewf7qi7.htm/, Retrieved Sun, 05 May 2024 14:56:58 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 14:56:58 +0200

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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	1 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	1 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	99.5359722222222	0.0596687057780394	1668.14364287512
Geometric Mean	99.5347027973844
Harmonic Mean	99.5334337807862
Quadratic Mean	99.5372420322609
Winsorized Mean ( 1 / 24 )	99.5343055555555	0.0591332896629062	1683.21948809137
Winsorized Mean ( 2 / 24 )	99.5318055555556	0.058162838160756	1711.26115408021
Winsorized Mean ( 3 / 24 )	99.5309722222222	0.0580176433293282	1715.5293891765
Winsorized Mean ( 4 / 24 )	99.5304166666667	0.0579225771294283	1718.33543325024
Winsorized Mean ( 5 / 24 )	99.5290277777778	0.0574647472127993	1732.00148969957
Winsorized Mean ( 6 / 24 )	99.5290277777778	0.0574647472127993	1732.00148969957
Winsorized Mean ( 7 / 24 )	99.5290277777778	0.0571541308071301	1741.41442398353
Winsorized Mean ( 8 / 24 )	99.5301388888889	0.0566329964369592	1757.45846327733
Winsorized Mean ( 9 / 24 )	99.5276388888889	0.0562329762295404	1769.91590277245
Winsorized Mean ( 10 / 24 )	99.5331944444444	0.0549835750082884	1810.23504618317
Winsorized Mean ( 11 / 24 )	99.5347222222222	0.0547643880031329	1817.50816272298
Winsorized Mean ( 12 / 24 )	99.5330555555555	0.0540042305799792	1843.06033965522
Winsorized Mean ( 13 / 24 )	99.5348611111111	0.0537498382483119	1851.81694224424
Winsorized Mean ( 14 / 24 )	99.5251388888889	0.0522644477466391	1904.26079638982
Winsorized Mean ( 15 / 24 )	99.5209722222222	0.0516466566287889	1926.9586594449
Winsorized Mean ( 16 / 24 )	99.5209722222222	0.0510063666751659	1951.14803718567
Winsorized Mean ( 17 / 24 )	99.5233333333333	0.0500007824664911	1990.43551768476
Winsorized Mean ( 18 / 24 )	99.5083333333333	0.0464789147341778	2140.93495733369
Winsorized Mean ( 19 / 24 )	99.5056944444444	0.0461192856933772	2157.57232464538
Winsorized Mean ( 20 / 24 )	99.4918055555556	0.0442744174114579	2247.16238795291
Winsorized Mean ( 21 / 24 )	99.4918055555556	0.0434880437892639	2287.79675714265
Winsorized Mean ( 22 / 24 )	99.4948611111111	0.0422448120063713	2355.19715642492
Winsorized Mean ( 23 / 24 )	99.50125	0.0413664950551234	2405.35848800844
Winsorized Mean ( 24 / 24 )	99.49125	0.0400913166871446	2481.61592637096
Trimmed Mean ( 1 / 24 )	99.532	0.0586767824894365	1696.27569504034
Trimmed Mean ( 2 / 24 )	99.5295588235294	0.0581068140236224	1712.87241429322
Trimmed Mean ( 3 / 24 )	99.5283333333333	0.0579914724594132	1716.25808265156
Trimmed Mean ( 4 / 24 )	99.52734375	0.057864717275144	1720.00051908579
Trimmed Mean ( 5 / 24 )	99.5264516129032	0.0576913947366746	1725.15246107638
Trimmed Mean ( 6 / 24 )	99.5258333333333	0.057560722870077	1729.05808632699
Trimmed Mean ( 7 / 24 )	99.5251724137931	0.0573408744702743	1735.67587402922
Trimmed Mean ( 8 / 24 )	99.5244642857143	0.0570861274815071	1743.40892746587
Trimmed Mean ( 9 / 24 )	99.5235185185185	0.0568262381496146	1751.3655972878
Trimmed Mean ( 10 / 24 )	99.5228846153846	0.0565227543566746	1760.75787084555
Trimmed Mean ( 11 / 24 )	99.5214	0.0563284899097269	1766.80397716138
Trimmed Mean ( 12 / 24 )	99.5195833333333	0.0560410487323891	1775.83370733417
Trimmed Mean ( 13 / 24 )	99.5178260869565	0.0557426046683799	1785.30993804472
Trimmed Mean ( 14 / 24 )	99.5156818181818	0.0553142069758685	1799.09804838379
Trimmed Mean ( 15 / 24 )	99.5145238095238	0.0549756596768519	1810.15606532913
Trimmed Mean ( 16 / 24 )	99.51375	0.0545502444235282	1824.25855377246
Trimmed Mean ( 17 / 24 )	99.5128947368421	0.0540058316943997	1842.6323901454
Trimmed Mean ( 18 / 24 )	99.5116666666667	0.053375727198496	1864.36179682571
Trimmed Mean ( 19 / 24 )	99.5120588235294	0.0532002228356423	1870.51958656195
Trimmed Mean ( 20 / 24 )	99.5128125	0.0528449389781543	1883.10961133171
Trimmed Mean ( 21 / 24 )	99.5153333333333	0.0525876025190094	1892.37250923087
Trimmed Mean ( 22 / 24 )	99.5182142857143	0.0521750552904147	1907.39068184557
Trimmed Mean ( 23 / 24 )	99.5211538461539	0.051662594482266	1926.36771040053
Trimmed Mean ( 24 / 24 )	99.52375	0.0508721489960692	1956.35041892352
Median	99.6
Midrange	99.675
Midmean - Weighted Average at Xnp	99.4986486486487
Midmean - Weighted Average at X(n+1)p	99.5116666666667
Midmean - Empirical Distribution Function	99.4986486486487
Midmean - Empirical Distribution Function - Averaging	99.5116666666667
Midmean - Empirical Distribution Function - Interpolation	99.5116666666667
Midmean - Closest Observation	99.4986486486487
Midmean - True Basic - Statistics Graphics Toolkit	99.5116666666667
Midmean - MS Excel (old versions)	99.5128947368421
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 99.5359722222222 & 0.0596687057780394 & 1668.14364287512 \tabularnewline
Geometric Mean & 99.5347027973844 &  &  \tabularnewline
Harmonic Mean & 99.5334337807862 &  &  \tabularnewline
Quadratic Mean & 99.5372420322609 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 99.5343055555555 & 0.0591332896629062 & 1683.21948809137 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 99.5318055555556 & 0.058162838160756 & 1711.26115408021 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 99.5309722222222 & 0.0580176433293282 & 1715.5293891765 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 99.5304166666667 & 0.0579225771294283 & 1718.33543325024 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 99.5290277777778 & 0.0574647472127993 & 1732.00148969957 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 99.5290277777778 & 0.0574647472127993 & 1732.00148969957 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 99.5290277777778 & 0.0571541308071301 & 1741.41442398353 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 99.5301388888889 & 0.0566329964369592 & 1757.45846327733 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 99.5276388888889 & 0.0562329762295404 & 1769.91590277245 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 99.5331944444444 & 0.0549835750082884 & 1810.23504618317 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 99.5347222222222 & 0.0547643880031329 & 1817.50816272298 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 99.5330555555555 & 0.0540042305799792 & 1843.06033965522 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 99.5348611111111 & 0.0537498382483119 & 1851.81694224424 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 99.5251388888889 & 0.0522644477466391 & 1904.26079638982 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 99.5209722222222 & 0.0516466566287889 & 1926.9586594449 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 99.5209722222222 & 0.0510063666751659 & 1951.14803718567 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 99.5233333333333 & 0.0500007824664911 & 1990.43551768476 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 99.5083333333333 & 0.0464789147341778 & 2140.93495733369 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 99.5056944444444 & 0.0461192856933772 & 2157.57232464538 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 99.4918055555556 & 0.0442744174114579 & 2247.16238795291 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 99.4918055555556 & 0.0434880437892639 & 2287.79675714265 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 99.4948611111111 & 0.0422448120063713 & 2355.19715642492 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 99.50125 & 0.0413664950551234 & 2405.35848800844 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 99.49125 & 0.0400913166871446 & 2481.61592637096 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 99.532 & 0.0586767824894365 & 1696.27569504034 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 99.5295588235294 & 0.0581068140236224 & 1712.87241429322 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 99.5283333333333 & 0.0579914724594132 & 1716.25808265156 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 99.52734375 & 0.057864717275144 & 1720.00051908579 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 99.5264516129032 & 0.0576913947366746 & 1725.15246107638 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 99.5258333333333 & 0.057560722870077 & 1729.05808632699 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 99.5251724137931 & 0.0573408744702743 & 1735.67587402922 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 99.5244642857143 & 0.0570861274815071 & 1743.40892746587 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 99.5235185185185 & 0.0568262381496146 & 1751.3655972878 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 99.5228846153846 & 0.0565227543566746 & 1760.75787084555 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 99.5214 & 0.0563284899097269 & 1766.80397716138 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 99.5195833333333 & 0.0560410487323891 & 1775.83370733417 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 99.5178260869565 & 0.0557426046683799 & 1785.30993804472 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 99.5156818181818 & 0.0553142069758685 & 1799.09804838379 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 99.5145238095238 & 0.0549756596768519 & 1810.15606532913 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 99.51375 & 0.0545502444235282 & 1824.25855377246 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 99.5128947368421 & 0.0540058316943997 & 1842.6323901454 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 99.5116666666667 & 0.053375727198496 & 1864.36179682571 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 99.5120588235294 & 0.0532002228356423 & 1870.51958656195 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 99.5128125 & 0.0528449389781543 & 1883.10961133171 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 99.5153333333333 & 0.0525876025190094 & 1892.37250923087 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 99.5182142857143 & 0.0521750552904147 & 1907.39068184557 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 99.5211538461539 & 0.051662594482266 & 1926.36771040053 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 99.52375 & 0.0508721489960692 & 1956.35041892352 \tabularnewline
Median & 99.6 &  &  \tabularnewline
Midrange & 99.675 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.4986486486487 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.5116666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.4986486486487 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.5116666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.5116666666667 &  &  \tabularnewline
Midmean - Closest Observation & 99.4986486486487 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.5116666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.5128947368421 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]99.5359722222222[/C][C]0.0596687057780394[/C][C]1668.14364287512[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]99.5347027973844[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.5334337807862[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]99.5372420322609[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]99.5343055555555[/C][C]0.0591332896629062[/C][C]1683.21948809137[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]99.5318055555556[/C][C]0.058162838160756[/C][C]1711.26115408021[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]99.5309722222222[/C][C]0.0580176433293282[/C][C]1715.5293891765[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]99.5304166666667[/C][C]0.0579225771294283[/C][C]1718.33543325024[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]99.5290277777778[/C][C]0.0574647472127993[/C][C]1732.00148969957[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]99.5290277777778[/C][C]0.0574647472127993[/C][C]1732.00148969957[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]99.5290277777778[/C][C]0.0571541308071301[/C][C]1741.41442398353[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]99.5301388888889[/C][C]0.0566329964369592[/C][C]1757.45846327733[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]99.5276388888889[/C][C]0.0562329762295404[/C][C]1769.91590277245[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]99.5331944444444[/C][C]0.0549835750082884[/C][C]1810.23504618317[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]99.5347222222222[/C][C]0.0547643880031329[/C][C]1817.50816272298[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]99.5330555555555[/C][C]0.0540042305799792[/C][C]1843.06033965522[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]99.5348611111111[/C][C]0.0537498382483119[/C][C]1851.81694224424[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]99.5251388888889[/C][C]0.0522644477466391[/C][C]1904.26079638982[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]99.5209722222222[/C][C]0.0516466566287889[/C][C]1926.9586594449[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]99.5209722222222[/C][C]0.0510063666751659[/C][C]1951.14803718567[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]99.5233333333333[/C][C]0.0500007824664911[/C][C]1990.43551768476[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]99.5083333333333[/C][C]0.0464789147341778[/C][C]2140.93495733369[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]99.5056944444444[/C][C]0.0461192856933772[/C][C]2157.57232464538[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]99.4918055555556[/C][C]0.0442744174114579[/C][C]2247.16238795291[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]99.4918055555556[/C][C]0.0434880437892639[/C][C]2287.79675714265[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]99.4948611111111[/C][C]0.0422448120063713[/C][C]2355.19715642492[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]99.50125[/C][C]0.0413664950551234[/C][C]2405.35848800844[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]99.49125[/C][C]0.0400913166871446[/C][C]2481.61592637096[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]99.532[/C][C]0.0586767824894365[/C][C]1696.27569504034[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]99.5295588235294[/C][C]0.0581068140236224[/C][C]1712.87241429322[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]99.5283333333333[/C][C]0.0579914724594132[/C][C]1716.25808265156[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]99.52734375[/C][C]0.057864717275144[/C][C]1720.00051908579[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]99.5264516129032[/C][C]0.0576913947366746[/C][C]1725.15246107638[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]99.5258333333333[/C][C]0.057560722870077[/C][C]1729.05808632699[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]99.5251724137931[/C][C]0.0573408744702743[/C][C]1735.67587402922[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]99.5244642857143[/C][C]0.0570861274815071[/C][C]1743.40892746587[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]99.5235185185185[/C][C]0.0568262381496146[/C][C]1751.3655972878[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]99.5228846153846[/C][C]0.0565227543566746[/C][C]1760.75787084555[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]99.5214[/C][C]0.0563284899097269[/C][C]1766.80397716138[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]99.5195833333333[/C][C]0.0560410487323891[/C][C]1775.83370733417[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]99.5178260869565[/C][C]0.0557426046683799[/C][C]1785.30993804472[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]99.5156818181818[/C][C]0.0553142069758685[/C][C]1799.09804838379[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]99.5145238095238[/C][C]0.0549756596768519[/C][C]1810.15606532913[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]99.51375[/C][C]0.0545502444235282[/C][C]1824.25855377246[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]99.5128947368421[/C][C]0.0540058316943997[/C][C]1842.6323901454[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]99.5116666666667[/C][C]0.053375727198496[/C][C]1864.36179682571[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]99.5120588235294[/C][C]0.0532002228356423[/C][C]1870.51958656195[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]99.5128125[/C][C]0.0528449389781543[/C][C]1883.10961133171[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]99.5153333333333[/C][C]0.0525876025190094[/C][C]1892.37250923087[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]99.5182142857143[/C][C]0.0521750552904147[/C][C]1907.39068184557[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]99.5211538461539[/C][C]0.051662594482266[/C][C]1926.36771040053[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]99.52375[/C][C]0.0508721489960692[/C][C]1956.35041892352[/C][/ROW]
[ROW][C]Median[/C][C]99.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]99.675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.4986486486487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.5116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.4986486486487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.5116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.5116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.4986486486487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.5116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.5128947368421[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	99.5359722222222	0.0596687057780394	1668.14364287512
Geometric Mean	99.5347027973844
Harmonic Mean	99.5334337807862
Quadratic Mean	99.5372420322609
Winsorized Mean ( 1 / 24 )	99.5343055555555	0.0591332896629062	1683.21948809137
Winsorized Mean ( 2 / 24 )	99.5318055555556	0.058162838160756	1711.26115408021
Winsorized Mean ( 3 / 24 )	99.5309722222222	0.0580176433293282	1715.5293891765
Winsorized Mean ( 4 / 24 )	99.5304166666667	0.0579225771294283	1718.33543325024
Winsorized Mean ( 5 / 24 )	99.5290277777778	0.0574647472127993	1732.00148969957
Winsorized Mean ( 6 / 24 )	99.5290277777778	0.0574647472127993	1732.00148969957
Winsorized Mean ( 7 / 24 )	99.5290277777778	0.0571541308071301	1741.41442398353
Winsorized Mean ( 8 / 24 )	99.5301388888889	0.0566329964369592	1757.45846327733
Winsorized Mean ( 9 / 24 )	99.5276388888889	0.0562329762295404	1769.91590277245
Winsorized Mean ( 10 / 24 )	99.5331944444444	0.0549835750082884	1810.23504618317
Winsorized Mean ( 11 / 24 )	99.5347222222222	0.0547643880031329	1817.50816272298
Winsorized Mean ( 12 / 24 )	99.5330555555555	0.0540042305799792	1843.06033965522
Winsorized Mean ( 13 / 24 )	99.5348611111111	0.0537498382483119	1851.81694224424
Winsorized Mean ( 14 / 24 )	99.5251388888889	0.0522644477466391	1904.26079638982
Winsorized Mean ( 15 / 24 )	99.5209722222222	0.0516466566287889	1926.9586594449
Winsorized Mean ( 16 / 24 )	99.5209722222222	0.0510063666751659	1951.14803718567
Winsorized Mean ( 17 / 24 )	99.5233333333333	0.0500007824664911	1990.43551768476
Winsorized Mean ( 18 / 24 )	99.5083333333333	0.0464789147341778	2140.93495733369
Winsorized Mean ( 19 / 24 )	99.5056944444444	0.0461192856933772	2157.57232464538
Winsorized Mean ( 20 / 24 )	99.4918055555556	0.0442744174114579	2247.16238795291
Winsorized Mean ( 21 / 24 )	99.4918055555556	0.0434880437892639	2287.79675714265
Winsorized Mean ( 22 / 24 )	99.4948611111111	0.0422448120063713	2355.19715642492
Winsorized Mean ( 23 / 24 )	99.50125	0.0413664950551234	2405.35848800844
Winsorized Mean ( 24 / 24 )	99.49125	0.0400913166871446	2481.61592637096
Trimmed Mean ( 1 / 24 )	99.532	0.0586767824894365	1696.27569504034
Trimmed Mean ( 2 / 24 )	99.5295588235294	0.0581068140236224	1712.87241429322
Trimmed Mean ( 3 / 24 )	99.5283333333333	0.0579914724594132	1716.25808265156
Trimmed Mean ( 4 / 24 )	99.52734375	0.057864717275144	1720.00051908579
Trimmed Mean ( 5 / 24 )	99.5264516129032	0.0576913947366746	1725.15246107638
Trimmed Mean ( 6 / 24 )	99.5258333333333	0.057560722870077	1729.05808632699
Trimmed Mean ( 7 / 24 )	99.5251724137931	0.0573408744702743	1735.67587402922
Trimmed Mean ( 8 / 24 )	99.5244642857143	0.0570861274815071	1743.40892746587
Trimmed Mean ( 9 / 24 )	99.5235185185185	0.0568262381496146	1751.3655972878
Trimmed Mean ( 10 / 24 )	99.5228846153846	0.0565227543566746	1760.75787084555
Trimmed Mean ( 11 / 24 )	99.5214	0.0563284899097269	1766.80397716138
Trimmed Mean ( 12 / 24 )	99.5195833333333	0.0560410487323891	1775.83370733417
Trimmed Mean ( 13 / 24 )	99.5178260869565	0.0557426046683799	1785.30993804472
Trimmed Mean ( 14 / 24 )	99.5156818181818	0.0553142069758685	1799.09804838379
Trimmed Mean ( 15 / 24 )	99.5145238095238	0.0549756596768519	1810.15606532913
Trimmed Mean ( 16 / 24 )	99.51375	0.0545502444235282	1824.25855377246
Trimmed Mean ( 17 / 24 )	99.5128947368421	0.0540058316943997	1842.6323901454
Trimmed Mean ( 18 / 24 )	99.5116666666667	0.053375727198496	1864.36179682571
Trimmed Mean ( 19 / 24 )	99.5120588235294	0.0532002228356423	1870.51958656195
Trimmed Mean ( 20 / 24 )	99.5128125	0.0528449389781543	1883.10961133171
Trimmed Mean ( 21 / 24 )	99.5153333333333	0.0525876025190094	1892.37250923087
Trimmed Mean ( 22 / 24 )	99.5182142857143	0.0521750552904147	1907.39068184557
Trimmed Mean ( 23 / 24 )	99.5211538461539	0.051662594482266	1926.36771040053
Trimmed Mean ( 24 / 24 )	99.52375	0.0508721489960692	1956.35041892352
Median	99.6
Midrange	99.675
Midmean - Weighted Average at Xnp	99.4986486486487
Midmean - Weighted Average at X(n+1)p	99.5116666666667
Midmean - Empirical Distribution Function	99.4986486486487
Midmean - Empirical Distribution Function - Averaging	99.5116666666667
Midmean - Empirical Distribution Function - Interpolation	99.5116666666667
Midmean - Closest Observation	99.4986486486487
Midmean - True Basic - Statistics Graphics Toolkit	99.5116666666667
Midmean - MS Excel (old versions)	99.5128947368421
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