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rwasp_centraltendency.wasp

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Central Tendency

Date of computation

Thu, 13 Oct 2016 16:49:49 +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/t1476373810qtoc09285538t3g.htm/, Retrieved Tue, 30 Apr 2024 11:15:38 +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 11:15:38 +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	2 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.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	2 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	100.727361111111	0.18542848836667	543.2140551776
Geometric Mean	100.715176814136
Harmonic Mean	100.702926571527
Quadratic Mean	100.739478462186
Winsorized Mean ( 1 / 24 )	100.727361111111	0.185062903599178	544.287154000748
Winsorized Mean ( 2 / 24 )	100.719027777778	0.18346614477939	548.978820582336
Winsorized Mean ( 3 / 24 )	100.706527777778	0.181160854146817	555.895633480304
Winsorized Mean ( 4 / 24 )	100.688194444444	0.17821266664734	564.988989495867
Winsorized Mean ( 5 / 24 )	100.689583333333	0.177366674728884	567.69166748626
Winsorized Mean ( 6 / 24 )	100.690416666667	0.175939845751783	572.300244077293
Winsorized Mean ( 7 / 24 )	100.705	0.171536369713788	587.076665829109
Winsorized Mean ( 8 / 24 )	100.739444444444	0.163997033362907	614.276016941838
Winsorized Mean ( 9 / 24 )	100.831944444444	0.145959353851932	690.822080143852
Winsorized Mean ( 10 / 24 )	100.840277777778	0.144065844718059	699.959646751282
Winsorized Mean ( 11 / 24 )	100.835694444444	0.142438909617286	707.922397857274
Winsorized Mean ( 12 / 24 )	100.830694444444	0.141208223479661	714.056815954259
Winsorized Mean ( 13 / 24 )	100.814444444444	0.136752361900922	737.204411266295
Winsorized Mean ( 14 / 24 )	100.818333333333	0.133732530340832	753.88039900529
Winsorized Mean ( 15 / 24 )	100.874583333333	0.122093107173374	826.210305141062
Winsorized Mean ( 16 / 24 )	100.879027777778	0.118213448450052	853.363378705609
Winsorized Mean ( 17 / 24 )	100.912083333333	0.111925447727417	901.600890434626
Winsorized Mean ( 18 / 24 )	100.912083333333	0.111925447727417	901.600890434626
Winsorized Mean ( 19 / 24 )	100.917361111111	0.108967625422783	926.122421403256
Winsorized Mean ( 20 / 24 )	100.964583333333	0.10082502730311	1001.38414076302
Winsorized Mean ( 21 / 24 )	100.95875	0.0946521796550849	1066.62889716747
Winsorized Mean ( 22 / 24 )	100.961805555556	0.0934463028565721	1080.42589668335
Winsorized Mean ( 23 / 24 )	100.961805555556	0.0934463028565721	1080.42589668335
Winsorized Mean ( 24 / 24 )	100.958472222222	0.0930208677435751	1085.33143875338
Trimmed Mean ( 1 / 24 )	100.733142857143	0.181260201295802	555.737785443338
Trimmed Mean ( 2 / 24 )	100.739264705882	0.176729919013866	570.018168219602
Trimmed Mean ( 3 / 24 )	100.750303030303	0.172322807841629	584.660291299899
Trimmed Mean ( 4 / 24 )	100.76671875	0.168051546131293	599.617921225636
Trimmed Mean ( 5 / 24 )	100.789516129032	0.163905989264363	614.922716255776
Trimmed Mean ( 6 / 24 )	100.8135	0.159078352758583	633.73487499581
Trimmed Mean ( 7 / 24 )	100.838965517241	0.153523388156794	656.831292794646
Trimmed Mean ( 8 / 24 )	100.863571428571	0.147869156924537	682.11365727909
Trimmed Mean ( 9 / 24 )	100.884259259259	0.142866139732374	706.145343103987
Trimmed Mean ( 10 / 24 )	100.892307692308	0.141074473925689	715.170539962125
Trimmed Mean ( 11 / 24 )	100.8998	0.139131266751062	725.212975890842
Trimmed Mean ( 12 / 24 )	100.908541666667	0.13689502293176	737.123523599308
Trimmed Mean ( 13 / 24 )	100.918695652174	0.134174379540894	752.145797114835
Trimmed Mean ( 14 / 24 )	100.931818181818	0.131487373780797	767.616047682892
Trimmed Mean ( 15 / 24 )	100.945714285714	0.128518830381911	785.454660501816
Trimmed Mean ( 16 / 24 )	100.95425	0.127176380396555	793.812889509904
Trimmed Mean ( 17 / 24 )	100.963157894737	0.125980707764151	801.41761136753
Trimmed Mean ( 18 / 24 )	100.969166666667	0.125508726693368	804.479252772167
Trimmed Mean ( 19 / 24 )	100.975882352941	0.124453971509274	811.351225906171
Trimmed Mean ( 20 / 24 )	100.9828125	0.123310546188926	818.930866993992
Trimmed Mean ( 21 / 24 )	100.985	0.123355154950547	818.652451455997
Trimmed Mean ( 22 / 24 )	100.988214285714	0.124324687528058	812.294133157765
Trimmed Mean ( 23 / 24 )	100.991538461538	0.125175190842143	806.801553743168
Trimmed Mean ( 24 / 24 )	100.995416666667	0.125423888761195	805.232700597891
Median	101.03
Midrange	100.525
Midmean - Weighted Average at Xnp	100.963157894737
Midmean - Weighted Average at X(n+1)p	100.963157894737
Midmean - Empirical Distribution Function	100.963157894737
Midmean - Empirical Distribution Function - Averaging	100.963157894737
Midmean - Empirical Distribution Function - Interpolation	100.963157894737
Midmean - Closest Observation	100.963157894737
Midmean - True Basic - Statistics Graphics Toolkit	100.963157894737
Midmean - MS Excel (old versions)	100.963157894737
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 100.727361111111 & 0.18542848836667 & 543.2140551776 \tabularnewline
Geometric Mean & 100.715176814136 &  &  \tabularnewline
Harmonic Mean & 100.702926571527 &  &  \tabularnewline
Quadratic Mean & 100.739478462186 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 100.727361111111 & 0.185062903599178 & 544.287154000748 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 100.719027777778 & 0.18346614477939 & 548.978820582336 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 100.706527777778 & 0.181160854146817 & 555.895633480304 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 100.688194444444 & 0.17821266664734 & 564.988989495867 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 100.689583333333 & 0.177366674728884 & 567.69166748626 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 100.690416666667 & 0.175939845751783 & 572.300244077293 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 100.705 & 0.171536369713788 & 587.076665829109 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 100.739444444444 & 0.163997033362907 & 614.276016941838 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 100.831944444444 & 0.145959353851932 & 690.822080143852 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 100.840277777778 & 0.144065844718059 & 699.959646751282 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 100.835694444444 & 0.142438909617286 & 707.922397857274 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 100.830694444444 & 0.141208223479661 & 714.056815954259 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 100.814444444444 & 0.136752361900922 & 737.204411266295 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 100.818333333333 & 0.133732530340832 & 753.88039900529 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 100.874583333333 & 0.122093107173374 & 826.210305141062 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 100.879027777778 & 0.118213448450052 & 853.363378705609 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 100.912083333333 & 0.111925447727417 & 901.600890434626 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 100.912083333333 & 0.111925447727417 & 901.600890434626 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 100.917361111111 & 0.108967625422783 & 926.122421403256 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 100.964583333333 & 0.10082502730311 & 1001.38414076302 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 100.95875 & 0.0946521796550849 & 1066.62889716747 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 100.961805555556 & 0.0934463028565721 & 1080.42589668335 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 100.961805555556 & 0.0934463028565721 & 1080.42589668335 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 100.958472222222 & 0.0930208677435751 & 1085.33143875338 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 100.733142857143 & 0.181260201295802 & 555.737785443338 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 100.739264705882 & 0.176729919013866 & 570.018168219602 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 100.750303030303 & 0.172322807841629 & 584.660291299899 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 100.76671875 & 0.168051546131293 & 599.617921225636 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 100.789516129032 & 0.163905989264363 & 614.922716255776 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 100.8135 & 0.159078352758583 & 633.73487499581 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 100.838965517241 & 0.153523388156794 & 656.831292794646 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 100.863571428571 & 0.147869156924537 & 682.11365727909 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 100.884259259259 & 0.142866139732374 & 706.145343103987 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 100.892307692308 & 0.141074473925689 & 715.170539962125 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 100.8998 & 0.139131266751062 & 725.212975890842 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 100.908541666667 & 0.13689502293176 & 737.123523599308 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 100.918695652174 & 0.134174379540894 & 752.145797114835 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 100.931818181818 & 0.131487373780797 & 767.616047682892 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 100.945714285714 & 0.128518830381911 & 785.454660501816 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 100.95425 & 0.127176380396555 & 793.812889509904 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 100.963157894737 & 0.125980707764151 & 801.41761136753 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 100.969166666667 & 0.125508726693368 & 804.479252772167 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 100.975882352941 & 0.124453971509274 & 811.351225906171 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 100.9828125 & 0.123310546188926 & 818.930866993992 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 100.985 & 0.123355154950547 & 818.652451455997 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 100.988214285714 & 0.124324687528058 & 812.294133157765 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 100.991538461538 & 0.125175190842143 & 806.801553743168 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 100.995416666667 & 0.125423888761195 & 805.232700597891 \tabularnewline
Median & 101.03 &  &  \tabularnewline
Midrange & 100.525 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 100.963157894737 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 100.963157894737 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 100.963157894737 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 100.963157894737 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 100.963157894737 &  &  \tabularnewline
Midmean - Closest Observation & 100.963157894737 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 100.963157894737 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 100.963157894737 &  &  \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]100.727361111111[/C][C]0.18542848836667[/C][C]543.2140551776[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]100.715176814136[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]100.702926571527[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]100.739478462186[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]100.727361111111[/C][C]0.185062903599178[/C][C]544.287154000748[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]100.719027777778[/C][C]0.18346614477939[/C][C]548.978820582336[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]100.706527777778[/C][C]0.181160854146817[/C][C]555.895633480304[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]100.688194444444[/C][C]0.17821266664734[/C][C]564.988989495867[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]100.689583333333[/C][C]0.177366674728884[/C][C]567.69166748626[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]100.690416666667[/C][C]0.175939845751783[/C][C]572.300244077293[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]100.705[/C][C]0.171536369713788[/C][C]587.076665829109[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]100.739444444444[/C][C]0.163997033362907[/C][C]614.276016941838[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]100.831944444444[/C][C]0.145959353851932[/C][C]690.822080143852[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]100.840277777778[/C][C]0.144065844718059[/C][C]699.959646751282[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]100.835694444444[/C][C]0.142438909617286[/C][C]707.922397857274[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]100.830694444444[/C][C]0.141208223479661[/C][C]714.056815954259[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]100.814444444444[/C][C]0.136752361900922[/C][C]737.204411266295[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]100.818333333333[/C][C]0.133732530340832[/C][C]753.88039900529[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]100.874583333333[/C][C]0.122093107173374[/C][C]826.210305141062[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]100.879027777778[/C][C]0.118213448450052[/C][C]853.363378705609[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]100.912083333333[/C][C]0.111925447727417[/C][C]901.600890434626[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]100.912083333333[/C][C]0.111925447727417[/C][C]901.600890434626[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]100.917361111111[/C][C]0.108967625422783[/C][C]926.122421403256[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]100.964583333333[/C][C]0.10082502730311[/C][C]1001.38414076302[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]100.95875[/C][C]0.0946521796550849[/C][C]1066.62889716747[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]100.961805555556[/C][C]0.0934463028565721[/C][C]1080.42589668335[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]100.961805555556[/C][C]0.0934463028565721[/C][C]1080.42589668335[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]100.958472222222[/C][C]0.0930208677435751[/C][C]1085.33143875338[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]100.733142857143[/C][C]0.181260201295802[/C][C]555.737785443338[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]100.739264705882[/C][C]0.176729919013866[/C][C]570.018168219602[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]100.750303030303[/C][C]0.172322807841629[/C][C]584.660291299899[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]100.76671875[/C][C]0.168051546131293[/C][C]599.617921225636[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]100.789516129032[/C][C]0.163905989264363[/C][C]614.922716255776[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]100.8135[/C][C]0.159078352758583[/C][C]633.73487499581[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]100.838965517241[/C][C]0.153523388156794[/C][C]656.831292794646[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]100.863571428571[/C][C]0.147869156924537[/C][C]682.11365727909[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]100.884259259259[/C][C]0.142866139732374[/C][C]706.145343103987[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]100.892307692308[/C][C]0.141074473925689[/C][C]715.170539962125[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]100.8998[/C][C]0.139131266751062[/C][C]725.212975890842[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]100.908541666667[/C][C]0.13689502293176[/C][C]737.123523599308[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]100.918695652174[/C][C]0.134174379540894[/C][C]752.145797114835[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]100.931818181818[/C][C]0.131487373780797[/C][C]767.616047682892[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]100.945714285714[/C][C]0.128518830381911[/C][C]785.454660501816[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]100.95425[/C][C]0.127176380396555[/C][C]793.812889509904[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]100.963157894737[/C][C]0.125980707764151[/C][C]801.41761136753[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]100.969166666667[/C][C]0.125508726693368[/C][C]804.479252772167[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]100.975882352941[/C][C]0.124453971509274[/C][C]811.351225906171[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]100.9828125[/C][C]0.123310546188926[/C][C]818.930866993992[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]100.985[/C][C]0.123355154950547[/C][C]818.652451455997[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]100.988214285714[/C][C]0.124324687528058[/C][C]812.294133157765[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]100.991538461538[/C][C]0.125175190842143[/C][C]806.801553743168[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]100.995416666667[/C][C]0.125423888761195[/C][C]805.232700597891[/C][/ROW]
[ROW][C]Median[/C][C]101.03[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]100.525[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]100.963157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]100.963157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]100.963157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]100.963157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]100.963157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]100.963157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]100.963157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]100.963157894737[/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	100.727361111111	0.18542848836667	543.2140551776
Geometric Mean	100.715176814136
Harmonic Mean	100.702926571527
Quadratic Mean	100.739478462186
Winsorized Mean ( 1 / 24 )	100.727361111111	0.185062903599178	544.287154000748
Winsorized Mean ( 2 / 24 )	100.719027777778	0.18346614477939	548.978820582336
Winsorized Mean ( 3 / 24 )	100.706527777778	0.181160854146817	555.895633480304
Winsorized Mean ( 4 / 24 )	100.688194444444	0.17821266664734	564.988989495867
Winsorized Mean ( 5 / 24 )	100.689583333333	0.177366674728884	567.69166748626
Winsorized Mean ( 6 / 24 )	100.690416666667	0.175939845751783	572.300244077293
Winsorized Mean ( 7 / 24 )	100.705	0.171536369713788	587.076665829109
Winsorized Mean ( 8 / 24 )	100.739444444444	0.163997033362907	614.276016941838
Winsorized Mean ( 9 / 24 )	100.831944444444	0.145959353851932	690.822080143852
Winsorized Mean ( 10 / 24 )	100.840277777778	0.144065844718059	699.959646751282
Winsorized Mean ( 11 / 24 )	100.835694444444	0.142438909617286	707.922397857274
Winsorized Mean ( 12 / 24 )	100.830694444444	0.141208223479661	714.056815954259
Winsorized Mean ( 13 / 24 )	100.814444444444	0.136752361900922	737.204411266295
Winsorized Mean ( 14 / 24 )	100.818333333333	0.133732530340832	753.88039900529
Winsorized Mean ( 15 / 24 )	100.874583333333	0.122093107173374	826.210305141062
Winsorized Mean ( 16 / 24 )	100.879027777778	0.118213448450052	853.363378705609
Winsorized Mean ( 17 / 24 )	100.912083333333	0.111925447727417	901.600890434626
Winsorized Mean ( 18 / 24 )	100.912083333333	0.111925447727417	901.600890434626
Winsorized Mean ( 19 / 24 )	100.917361111111	0.108967625422783	926.122421403256
Winsorized Mean ( 20 / 24 )	100.964583333333	0.10082502730311	1001.38414076302
Winsorized Mean ( 21 / 24 )	100.95875	0.0946521796550849	1066.62889716747
Winsorized Mean ( 22 / 24 )	100.961805555556	0.0934463028565721	1080.42589668335
Winsorized Mean ( 23 / 24 )	100.961805555556	0.0934463028565721	1080.42589668335
Winsorized Mean ( 24 / 24 )	100.958472222222	0.0930208677435751	1085.33143875338
Trimmed Mean ( 1 / 24 )	100.733142857143	0.181260201295802	555.737785443338
Trimmed Mean ( 2 / 24 )	100.739264705882	0.176729919013866	570.018168219602
Trimmed Mean ( 3 / 24 )	100.750303030303	0.172322807841629	584.660291299899
Trimmed Mean ( 4 / 24 )	100.76671875	0.168051546131293	599.617921225636
Trimmed Mean ( 5 / 24 )	100.789516129032	0.163905989264363	614.922716255776
Trimmed Mean ( 6 / 24 )	100.8135	0.159078352758583	633.73487499581
Trimmed Mean ( 7 / 24 )	100.838965517241	0.153523388156794	656.831292794646
Trimmed Mean ( 8 / 24 )	100.863571428571	0.147869156924537	682.11365727909
Trimmed Mean ( 9 / 24 )	100.884259259259	0.142866139732374	706.145343103987
Trimmed Mean ( 10 / 24 )	100.892307692308	0.141074473925689	715.170539962125
Trimmed Mean ( 11 / 24 )	100.8998	0.139131266751062	725.212975890842
Trimmed Mean ( 12 / 24 )	100.908541666667	0.13689502293176	737.123523599308
Trimmed Mean ( 13 / 24 )	100.918695652174	0.134174379540894	752.145797114835
Trimmed Mean ( 14 / 24 )	100.931818181818	0.131487373780797	767.616047682892
Trimmed Mean ( 15 / 24 )	100.945714285714	0.128518830381911	785.454660501816
Trimmed Mean ( 16 / 24 )	100.95425	0.127176380396555	793.812889509904
Trimmed Mean ( 17 / 24 )	100.963157894737	0.125980707764151	801.41761136753
Trimmed Mean ( 18 / 24 )	100.969166666667	0.125508726693368	804.479252772167
Trimmed Mean ( 19 / 24 )	100.975882352941	0.124453971509274	811.351225906171
Trimmed Mean ( 20 / 24 )	100.9828125	0.123310546188926	818.930866993992
Trimmed Mean ( 21 / 24 )	100.985	0.123355154950547	818.652451455997
Trimmed Mean ( 22 / 24 )	100.988214285714	0.124324687528058	812.294133157765
Trimmed Mean ( 23 / 24 )	100.991538461538	0.125175190842143	806.801553743168
Trimmed Mean ( 24 / 24 )	100.995416666667	0.125423888761195	805.232700597891
Median	101.03
Midrange	100.525
Midmean - Weighted Average at Xnp	100.963157894737
Midmean - Weighted Average at X(n+1)p	100.963157894737
Midmean - Empirical Distribution Function	100.963157894737
Midmean - Empirical Distribution Function - Averaging	100.963157894737
Midmean - Empirical Distribution Function - Interpolation	100.963157894737
Midmean - Closest Observation	100.963157894737
Midmean - True Basic - Statistics Graphics Toolkit	100.963157894737
Midmean - MS Excel (old versions)	100.963157894737
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