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rwasp_centraltendency.wasp

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Central Tendency

Date of computation

Thu, 13 Oct 2016 15:26:32 +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/13/t1476368833fqf6gizsr5nf3kk.htm/, Retrieved Tue, 30 Apr 2024 12:21:08 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 12:21:08 +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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.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]'Herman Ole Andreas Wold' @ wold.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	'Herman Ole Andreas Wold' @ wold.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	112.536111111111	1.26217777857957	89.160269671169
Geometric Mean	112.036337792494
Harmonic Mean	111.53976395555
Quadratic Mean	113.037541944652
Winsorized Mean ( 1 / 24 )	112.530694444444	1.25975510149509	89.3274369842928
Winsorized Mean ( 2 / 24 )	112.502638888889	1.24836097540893	90.1202785933262
Winsorized Mean ( 3 / 24 )	112.422222222222	1.22872921271438	91.4947093785379
Winsorized Mean ( 4 / 24 )	112.473333333333	1.19888711762775	93.8147817918717
Winsorized Mean ( 5 / 24 )	112.478194444444	1.15855547784391	97.0848583390828
Winsorized Mean ( 6 / 24 )	112.521527777778	1.13794179471454	98.8816196930394
Winsorized Mean ( 7 / 24 )	112.469027777778	1.12143973525167	100.289854409821
Winsorized Mean ( 8 / 24 )	112.562361111111	1.09980232775494	102.347811302498
Winsorized Mean ( 9 / 24 )	112.629861111111	1.08818980952022	103.502036249328
Winsorized Mean ( 10 / 24 )	112.707638888889	1.059667922949	106.361282103575
Winsorized Mean ( 11 / 24 )	112.788611111111	1.0418851659206	108.254359309792
Winsorized Mean ( 12 / 24 )	112.696944444444	0.999575352695097	112.744821228921
Winsorized Mean ( 13 / 24 )	112.539861111111	0.909691419009257	123.712127826465
Winsorized Mean ( 14 / 24 )	112.240416666667	0.798148861764517	140.625918351283
Winsorized Mean ( 15 / 24 )	111.909166666667	0.736901895346071	151.864403353327
Winsorized Mean ( 16 / 24 )	111.904722222222	0.735563349952084	152.134717192628
Winsorized Mean ( 17 / 24 )	111.833888888889	0.723537609770608	154.565412189623
Winsorized Mean ( 18 / 24 )	111.876388888889	0.696441781030158	160.63997298296
Winsorized Mean ( 19 / 24 )	111.805138888889	0.674344752184467	165.798189318903
Winsorized Mean ( 20 / 24 )	111.810694444444	0.636289872229562	175.722888771841
Winsorized Mean ( 21 / 24 )	111.822361111111	0.563474906962875	198.451359109907
Winsorized Mean ( 22 / 24 )	111.846805555556	0.446162073367533	250.686493164604
Winsorized Mean ( 23 / 24 )	111.735	0.428673710687676	260.652793055014
Winsorized Mean ( 24 / 24 )	111.508333333333	0.393386594229597	283.457380014969
Trimmed Mean ( 1 / 24 )	112.489	1.22749614952612	91.6410206609829
Trimmed Mean ( 2 / 24 )	112.444852941176	1.18912430600395	94.5610583968697
Trimmed Mean ( 3 / 24 )	112.413333333333	1.15064796447512	97.6956782647348
Trimmed Mean ( 4 / 24 )	112.41	1.11365164664691	100.938206609271
Trimmed Mean ( 5 / 24 )	112.391612903226	1.08029162468781	104.038215547312
Trimmed Mean ( 6 / 24 )	112.370833333333	1.0528409050187	106.731067151439
Trimmed Mean ( 7 / 24 )	112.339655172414	1.02515310899665	109.583294618659
Trimmed Mean ( 8 / 24 )	112.315892857143	0.995463175389986	112.827772672898
Trimmed Mean ( 9 / 24 )	112.274814814815	0.964079011116	116.458105114069
Trimmed Mean ( 10 / 24 )	112.220192307692	0.927597835472301	120.979359821979
Trimmed Mean ( 11 / 24 )	112.15	0.888495035760712	126.224678232422
Trimmed Mean ( 12 / 24 )	112.062916666667	0.842785189558271	132.967354024579
Trimmed Mean ( 13 / 24 )	111.980217391304	0.794782593499931	140.894149302119
Trimmed Mean ( 14 / 24 )	111.909772727273	0.75580645143677	148.066707441482
Trimmed Mean ( 15 / 24 )	111.869285714286	0.732816975283266	152.656515183813
Trimmed Mean ( 16 / 24 )	111.8645	0.716709177331918	156.080741726283
Trimmed Mean ( 17 / 24 )	111.859736842105	0.694694739068629	161.019985543686
Trimmed Mean ( 18 / 24 )	111.862777777778	0.66727705522544	167.640677739151
Trimmed Mean ( 19 / 24 )	111.861176470588	0.636420158067476	175.766237213888
Trimmed Mean ( 20 / 24 )	111.8678125	0.599058356246291	186.739424187262
Trimmed Mean ( 21 / 24 )	111.874666666667	0.557398871469712	200.708455637312
Trimmed Mean ( 22 / 24 )	111.881071428571	0.521844089531815	214.395589933668
Trimmed Mean ( 23 / 24 )	111.885384615385	0.509862796255931	219.44214293922
Trimmed Mean ( 24 / 24 )	111.905	0.495263434512601	225.950458285151
Median	112.045
Midrange	114.185
Midmean - Weighted Average at Xnp	111.654054054054
Midmean - Weighted Average at X(n+1)p	111.862777777778
Midmean - Empirical Distribution Function	111.654054054054
Midmean - Empirical Distribution Function - Averaging	111.862777777778
Midmean - Empirical Distribution Function - Interpolation	111.862777777778
Midmean - Closest Observation	111.654054054054
Midmean - True Basic - Statistics Graphics Toolkit	111.862777777778
Midmean - MS Excel (old versions)	111.859736842105
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 112.536111111111 & 1.26217777857957 & 89.160269671169 \tabularnewline
Geometric Mean & 112.036337792494 &  &  \tabularnewline
Harmonic Mean & 111.53976395555 &  &  \tabularnewline
Quadratic Mean & 113.037541944652 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 112.530694444444 & 1.25975510149509 & 89.3274369842928 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 112.502638888889 & 1.24836097540893 & 90.1202785933262 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 112.422222222222 & 1.22872921271438 & 91.4947093785379 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 112.473333333333 & 1.19888711762775 & 93.8147817918717 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 112.478194444444 & 1.15855547784391 & 97.0848583390828 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 112.521527777778 & 1.13794179471454 & 98.8816196930394 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 112.469027777778 & 1.12143973525167 & 100.289854409821 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 112.562361111111 & 1.09980232775494 & 102.347811302498 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 112.629861111111 & 1.08818980952022 & 103.502036249328 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 112.707638888889 & 1.059667922949 & 106.361282103575 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 112.788611111111 & 1.0418851659206 & 108.254359309792 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 112.696944444444 & 0.999575352695097 & 112.744821228921 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 112.539861111111 & 0.909691419009257 & 123.712127826465 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 112.240416666667 & 0.798148861764517 & 140.625918351283 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 111.909166666667 & 0.736901895346071 & 151.864403353327 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 111.904722222222 & 0.735563349952084 & 152.134717192628 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 111.833888888889 & 0.723537609770608 & 154.565412189623 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 111.876388888889 & 0.696441781030158 & 160.63997298296 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 111.805138888889 & 0.674344752184467 & 165.798189318903 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 111.810694444444 & 0.636289872229562 & 175.722888771841 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 111.822361111111 & 0.563474906962875 & 198.451359109907 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 111.846805555556 & 0.446162073367533 & 250.686493164604 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 111.735 & 0.428673710687676 & 260.652793055014 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 111.508333333333 & 0.393386594229597 & 283.457380014969 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 112.489 & 1.22749614952612 & 91.6410206609829 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 112.444852941176 & 1.18912430600395 & 94.5610583968697 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 112.413333333333 & 1.15064796447512 & 97.6956782647348 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 112.41 & 1.11365164664691 & 100.938206609271 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 112.391612903226 & 1.08029162468781 & 104.038215547312 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 112.370833333333 & 1.0528409050187 & 106.731067151439 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 112.339655172414 & 1.02515310899665 & 109.583294618659 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 112.315892857143 & 0.995463175389986 & 112.827772672898 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 112.274814814815 & 0.964079011116 & 116.458105114069 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 112.220192307692 & 0.927597835472301 & 120.979359821979 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 112.15 & 0.888495035760712 & 126.224678232422 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 112.062916666667 & 0.842785189558271 & 132.967354024579 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 111.980217391304 & 0.794782593499931 & 140.894149302119 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 111.909772727273 & 0.75580645143677 & 148.066707441482 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 111.869285714286 & 0.732816975283266 & 152.656515183813 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 111.8645 & 0.716709177331918 & 156.080741726283 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 111.859736842105 & 0.694694739068629 & 161.019985543686 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 111.862777777778 & 0.66727705522544 & 167.640677739151 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 111.861176470588 & 0.636420158067476 & 175.766237213888 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 111.8678125 & 0.599058356246291 & 186.739424187262 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 111.874666666667 & 0.557398871469712 & 200.708455637312 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 111.881071428571 & 0.521844089531815 & 214.395589933668 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 111.885384615385 & 0.509862796255931 & 219.44214293922 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 111.905 & 0.495263434512601 & 225.950458285151 \tabularnewline
Median & 112.045 &  &  \tabularnewline
Midrange & 114.185 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.654054054054 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111.862777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.654054054054 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111.862777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111.862777777778 &  &  \tabularnewline
Midmean - Closest Observation & 111.654054054054 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111.862777777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111.859736842105 &  &  \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]112.536111111111[/C][C]1.26217777857957[/C][C]89.160269671169[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]112.036337792494[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.53976395555[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]113.037541944652[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]112.530694444444[/C][C]1.25975510149509[/C][C]89.3274369842928[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]112.502638888889[/C][C]1.24836097540893[/C][C]90.1202785933262[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]112.422222222222[/C][C]1.22872921271438[/C][C]91.4947093785379[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]112.473333333333[/C][C]1.19888711762775[/C][C]93.8147817918717[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]112.478194444444[/C][C]1.15855547784391[/C][C]97.0848583390828[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]112.521527777778[/C][C]1.13794179471454[/C][C]98.8816196930394[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]112.469027777778[/C][C]1.12143973525167[/C][C]100.289854409821[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]112.562361111111[/C][C]1.09980232775494[/C][C]102.347811302498[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]112.629861111111[/C][C]1.08818980952022[/C][C]103.502036249328[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]112.707638888889[/C][C]1.059667922949[/C][C]106.361282103575[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]112.788611111111[/C][C]1.0418851659206[/C][C]108.254359309792[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]112.696944444444[/C][C]0.999575352695097[/C][C]112.744821228921[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]112.539861111111[/C][C]0.909691419009257[/C][C]123.712127826465[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]112.240416666667[/C][C]0.798148861764517[/C][C]140.625918351283[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]111.909166666667[/C][C]0.736901895346071[/C][C]151.864403353327[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]111.904722222222[/C][C]0.735563349952084[/C][C]152.134717192628[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]111.833888888889[/C][C]0.723537609770608[/C][C]154.565412189623[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]111.876388888889[/C][C]0.696441781030158[/C][C]160.63997298296[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]111.805138888889[/C][C]0.674344752184467[/C][C]165.798189318903[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]111.810694444444[/C][C]0.636289872229562[/C][C]175.722888771841[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]111.822361111111[/C][C]0.563474906962875[/C][C]198.451359109907[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]111.846805555556[/C][C]0.446162073367533[/C][C]250.686493164604[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]111.735[/C][C]0.428673710687676[/C][C]260.652793055014[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]111.508333333333[/C][C]0.393386594229597[/C][C]283.457380014969[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]112.489[/C][C]1.22749614952612[/C][C]91.6410206609829[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]112.444852941176[/C][C]1.18912430600395[/C][C]94.5610583968697[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]112.413333333333[/C][C]1.15064796447512[/C][C]97.6956782647348[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]112.41[/C][C]1.11365164664691[/C][C]100.938206609271[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]112.391612903226[/C][C]1.08029162468781[/C][C]104.038215547312[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]112.370833333333[/C][C]1.0528409050187[/C][C]106.731067151439[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]112.339655172414[/C][C]1.02515310899665[/C][C]109.583294618659[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]112.315892857143[/C][C]0.995463175389986[/C][C]112.827772672898[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]112.274814814815[/C][C]0.964079011116[/C][C]116.458105114069[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]112.220192307692[/C][C]0.927597835472301[/C][C]120.979359821979[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]112.15[/C][C]0.888495035760712[/C][C]126.224678232422[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]112.062916666667[/C][C]0.842785189558271[/C][C]132.967354024579[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]111.980217391304[/C][C]0.794782593499931[/C][C]140.894149302119[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]111.909772727273[/C][C]0.75580645143677[/C][C]148.066707441482[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]111.869285714286[/C][C]0.732816975283266[/C][C]152.656515183813[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]111.8645[/C][C]0.716709177331918[/C][C]156.080741726283[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]111.859736842105[/C][C]0.694694739068629[/C][C]161.019985543686[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]111.862777777778[/C][C]0.66727705522544[/C][C]167.640677739151[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]111.861176470588[/C][C]0.636420158067476[/C][C]175.766237213888[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]111.8678125[/C][C]0.599058356246291[/C][C]186.739424187262[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]111.874666666667[/C][C]0.557398871469712[/C][C]200.708455637312[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]111.881071428571[/C][C]0.521844089531815[/C][C]214.395589933668[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]111.885384615385[/C][C]0.509862796255931[/C][C]219.44214293922[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]111.905[/C][C]0.495263434512601[/C][C]225.950458285151[/C][/ROW]
[ROW][C]Median[/C][C]112.045[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]114.185[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.654054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111.862777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.654054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111.862777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111.862777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.654054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111.862777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111.859736842105[/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	112.536111111111	1.26217777857957	89.160269671169
Geometric Mean	112.036337792494
Harmonic Mean	111.53976395555
Quadratic Mean	113.037541944652
Winsorized Mean ( 1 / 24 )	112.530694444444	1.25975510149509	89.3274369842928
Winsorized Mean ( 2 / 24 )	112.502638888889	1.24836097540893	90.1202785933262
Winsorized Mean ( 3 / 24 )	112.422222222222	1.22872921271438	91.4947093785379
Winsorized Mean ( 4 / 24 )	112.473333333333	1.19888711762775	93.8147817918717
Winsorized Mean ( 5 / 24 )	112.478194444444	1.15855547784391	97.0848583390828
Winsorized Mean ( 6 / 24 )	112.521527777778	1.13794179471454	98.8816196930394
Winsorized Mean ( 7 / 24 )	112.469027777778	1.12143973525167	100.289854409821
Winsorized Mean ( 8 / 24 )	112.562361111111	1.09980232775494	102.347811302498
Winsorized Mean ( 9 / 24 )	112.629861111111	1.08818980952022	103.502036249328
Winsorized Mean ( 10 / 24 )	112.707638888889	1.059667922949	106.361282103575
Winsorized Mean ( 11 / 24 )	112.788611111111	1.0418851659206	108.254359309792
Winsorized Mean ( 12 / 24 )	112.696944444444	0.999575352695097	112.744821228921
Winsorized Mean ( 13 / 24 )	112.539861111111	0.909691419009257	123.712127826465
Winsorized Mean ( 14 / 24 )	112.240416666667	0.798148861764517	140.625918351283
Winsorized Mean ( 15 / 24 )	111.909166666667	0.736901895346071	151.864403353327
Winsorized Mean ( 16 / 24 )	111.904722222222	0.735563349952084	152.134717192628
Winsorized Mean ( 17 / 24 )	111.833888888889	0.723537609770608	154.565412189623
Winsorized Mean ( 18 / 24 )	111.876388888889	0.696441781030158	160.63997298296
Winsorized Mean ( 19 / 24 )	111.805138888889	0.674344752184467	165.798189318903
Winsorized Mean ( 20 / 24 )	111.810694444444	0.636289872229562	175.722888771841
Winsorized Mean ( 21 / 24 )	111.822361111111	0.563474906962875	198.451359109907
Winsorized Mean ( 22 / 24 )	111.846805555556	0.446162073367533	250.686493164604
Winsorized Mean ( 23 / 24 )	111.735	0.428673710687676	260.652793055014
Winsorized Mean ( 24 / 24 )	111.508333333333	0.393386594229597	283.457380014969
Trimmed Mean ( 1 / 24 )	112.489	1.22749614952612	91.6410206609829
Trimmed Mean ( 2 / 24 )	112.444852941176	1.18912430600395	94.5610583968697
Trimmed Mean ( 3 / 24 )	112.413333333333	1.15064796447512	97.6956782647348
Trimmed Mean ( 4 / 24 )	112.41	1.11365164664691	100.938206609271
Trimmed Mean ( 5 / 24 )	112.391612903226	1.08029162468781	104.038215547312
Trimmed Mean ( 6 / 24 )	112.370833333333	1.0528409050187	106.731067151439
Trimmed Mean ( 7 / 24 )	112.339655172414	1.02515310899665	109.583294618659
Trimmed Mean ( 8 / 24 )	112.315892857143	0.995463175389986	112.827772672898
Trimmed Mean ( 9 / 24 )	112.274814814815	0.964079011116	116.458105114069
Trimmed Mean ( 10 / 24 )	112.220192307692	0.927597835472301	120.979359821979
Trimmed Mean ( 11 / 24 )	112.15	0.888495035760712	126.224678232422
Trimmed Mean ( 12 / 24 )	112.062916666667	0.842785189558271	132.967354024579
Trimmed Mean ( 13 / 24 )	111.980217391304	0.794782593499931	140.894149302119
Trimmed Mean ( 14 / 24 )	111.909772727273	0.75580645143677	148.066707441482
Trimmed Mean ( 15 / 24 )	111.869285714286	0.732816975283266	152.656515183813
Trimmed Mean ( 16 / 24 )	111.8645	0.716709177331918	156.080741726283
Trimmed Mean ( 17 / 24 )	111.859736842105	0.694694739068629	161.019985543686
Trimmed Mean ( 18 / 24 )	111.862777777778	0.66727705522544	167.640677739151
Trimmed Mean ( 19 / 24 )	111.861176470588	0.636420158067476	175.766237213888
Trimmed Mean ( 20 / 24 )	111.8678125	0.599058356246291	186.739424187262
Trimmed Mean ( 21 / 24 )	111.874666666667	0.557398871469712	200.708455637312
Trimmed Mean ( 22 / 24 )	111.881071428571	0.521844089531815	214.395589933668
Trimmed Mean ( 23 / 24 )	111.885384615385	0.509862796255931	219.44214293922
Trimmed Mean ( 24 / 24 )	111.905	0.495263434512601	225.950458285151
Median	112.045
Midrange	114.185
Midmean - Weighted Average at Xnp	111.654054054054
Midmean - Weighted Average at X(n+1)p	111.862777777778
Midmean - Empirical Distribution Function	111.654054054054
Midmean - Empirical Distribution Function - Averaging	111.862777777778
Midmean - Empirical Distribution Function - Interpolation	111.862777777778
Midmean - Closest Observation	111.654054054054
Midmean - True Basic - Statistics Graphics Toolkit	111.862777777778
Midmean - MS Excel (old versions)	111.859736842105
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