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rwasp_centraltendency.wasp

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Central Tendency

Date of computation

Tue, 14 Mar 2017 15:34:29 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Mar/14/t148950587918seilclghhn2qa.htm/, Retrieved Tue, 14 May 2024 02:02:42 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 02:02:42 +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	100.52	0.585227207325542	171.762349292288
Geometric Mean	100.398466569702
Harmonic Mean	100.276423086807
Quadratic Mean	100.640882611282
Winsorized Mean ( 1 / 24 )	100.521944444444	0.58396781855002	172.136102797648
Winsorized Mean ( 2 / 24 )	100.504166666667	0.580170963619004	173.231983275653
Winsorized Mean ( 3 / 24 )	100.519583333333	0.57712512772165	174.172945354433
Winsorized Mean ( 4 / 24 )	100.51625	0.575834138028286	174.557643185549
Winsorized Mean ( 5 / 24 )	100.498888888889	0.571201598270528	175.942940624076
Winsorized Mean ( 6 / 24 )	100.472222222222	0.56565251082068	177.621808973236
Winsorized Mean ( 7 / 24 )	100.431388888889	0.555163918100503	180.904027827521
Winsorized Mean ( 8 / 24 )	100.545833333333	0.533444851530515	188.484026127266
Winsorized Mean ( 9 / 24 )	100.574583333333	0.52794449404372	190.502191931193
Winsorized Mean ( 10 / 24 )	100.612083333333	0.519559369164732	193.648867299
Winsorized Mean ( 11 / 24 )	100.576944444444	0.506508447578386	198.569135273661
Winsorized Mean ( 12 / 24 )	100.233611111111	0.451013434800692	222.240854433539
Winsorized Mean ( 13 / 24 )	100.240833333333	0.43997700315134	227.831983524951
Winsorized Mean ( 14 / 24 )	100.394444444444	0.410007962482745	244.859743299911
Winsorized Mean ( 15 / 24 )	100.327777777778	0.385100347785768	260.523726749762
Winsorized Mean ( 16 / 24 )	100.312222222222	0.379763033674663	264.144251354802
Winsorized Mean ( 17 / 24 )	100.300416666667	0.374063956306496	268.137079169648
Winsorized Mean ( 18 / 24 )	100.325416666667	0.367769199068186	272.794505143064
Winsorized Mean ( 19 / 24 )	100.301666666667	0.362423269090287	276.752833554072
Winsorized Mean ( 20 / 24 )	100.443333333333	0.300721420016872	334.007911134824
Winsorized Mean ( 21 / 24 )	100.592083333333	0.272080673153098	369.714181340366
Winsorized Mean ( 22 / 24 )	100.705138888889	0.248523731485989	405.213370516958
Winsorized Mean ( 23 / 24 )	100.823333333333	0.228018613851832	442.17150358983
Winsorized Mean ( 24 / 24 )	100.873333333333	0.206756757586087	487.884093903596
Trimmed Mean ( 1 / 24 )	100.517714285714	0.575450176513324	174.676659054577
Trimmed Mean ( 2 / 24 )	100.513235294118	0.565225775597855	177.828470734198
Trimmed Mean ( 3 / 24 )	100.518181818182	0.555325474571625	181.007690842422
Trimmed Mean ( 4 / 24 )	100.51765625	0.544728741571639	184.527910093359
Trimmed Mean ( 5 / 24 )	100.518064516129	0.532336321026236	188.824358860862
Trimmed Mean ( 6 / 24 )	100.522666666667	0.518721367280955	193.78933085712
Trimmed Mean ( 7 / 24 )	100.533103448276	0.503653212231352	199.607787673746
Trimmed Mean ( 8 / 24 )	100.551785714286	0.487912203829377	206.085818155613
Trimmed Mean ( 9 / 24 )	100.552777777778	0.47400478084279	212.13452235438
Trimmed Mean ( 10 / 24 )	100.549423076923	0.457946298683858	219.565969559975
Trimmed Mean ( 11 / 24 )	100.5404	0.439737116273543	228.637511547826
Trimmed Mean ( 12 / 24 )	100.535416666667	0.419803331015463	239.482179485049
Trimmed Mean ( 13 / 24 )	100.574782608696	0.407327894260329	246.913565277257
Trimmed Mean ( 14 / 24 )	100.616818181818	0.393558167166794	255.659332154517
Trimmed Mean ( 15 / 24 )	100.644047619048	0.382782626111661	262.927418209647
Trimmed Mean ( 16 / 24 )	100.682	0.373868755252222	269.297710989722
Trimmed Mean ( 17 / 24 )	100.725789473684	0.362655103734155	277.745407238282
Trimmed Mean ( 18 / 24 )	100.775833333333	0.348306874137489	289.33058982222
Trimmed Mean ( 19 / 24 )	100.828823529412	0.329794070870118	305.732675130843
Trimmed Mean ( 20 / 24 )	100.89125	0.304433222059532	331.406833056711
Trimmed Mean ( 21 / 24 )	100.945	0.288896732136382	349.415513472634
Trimmed Mean ( 22 / 24 )	100.988214285714	0.275952440869928	365.962388183099
Trimmed Mean ( 23 / 24 )	101.023846153846	0.264688540871416	381.670645133531
Trimmed Mean ( 24 / 24 )	101.05	0.254740561401573	396.678092581828
Median	101.565
Midrange	100.6
Midmean - Weighted Average at Xnp	100.644864864865
Midmean - Weighted Average at X(n+1)p	100.775833333333
Midmean - Empirical Distribution Function	100.644864864865
Midmean - Empirical Distribution Function - Averaging	100.775833333333
Midmean - Empirical Distribution Function - Interpolation	100.775833333333
Midmean - Closest Observation	100.644864864865
Midmean - True Basic - Statistics Graphics Toolkit	100.775833333333
Midmean - MS Excel (old versions)	100.725789473684
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 100.52 & 0.585227207325542 & 171.762349292288 \tabularnewline
Geometric Mean & 100.398466569702 &  &  \tabularnewline
Harmonic Mean & 100.276423086807 &  &  \tabularnewline
Quadratic Mean & 100.640882611282 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 100.521944444444 & 0.58396781855002 & 172.136102797648 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 100.504166666667 & 0.580170963619004 & 173.231983275653 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 100.519583333333 & 0.57712512772165 & 174.172945354433 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 100.51625 & 0.575834138028286 & 174.557643185549 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 100.498888888889 & 0.571201598270528 & 175.942940624076 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 100.472222222222 & 0.56565251082068 & 177.621808973236 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 100.431388888889 & 0.555163918100503 & 180.904027827521 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 100.545833333333 & 0.533444851530515 & 188.484026127266 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 100.574583333333 & 0.52794449404372 & 190.502191931193 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 100.612083333333 & 0.519559369164732 & 193.648867299 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 100.576944444444 & 0.506508447578386 & 198.569135273661 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 100.233611111111 & 0.451013434800692 & 222.240854433539 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 100.240833333333 & 0.43997700315134 & 227.831983524951 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 100.394444444444 & 0.410007962482745 & 244.859743299911 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 100.327777777778 & 0.385100347785768 & 260.523726749762 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 100.312222222222 & 0.379763033674663 & 264.144251354802 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 100.300416666667 & 0.374063956306496 & 268.137079169648 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 100.325416666667 & 0.367769199068186 & 272.794505143064 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 100.301666666667 & 0.362423269090287 & 276.752833554072 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 100.443333333333 & 0.300721420016872 & 334.007911134824 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 100.592083333333 & 0.272080673153098 & 369.714181340366 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 100.705138888889 & 0.248523731485989 & 405.213370516958 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 100.823333333333 & 0.228018613851832 & 442.17150358983 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 100.873333333333 & 0.206756757586087 & 487.884093903596 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 100.517714285714 & 0.575450176513324 & 174.676659054577 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 100.513235294118 & 0.565225775597855 & 177.828470734198 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 100.518181818182 & 0.555325474571625 & 181.007690842422 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 100.51765625 & 0.544728741571639 & 184.527910093359 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 100.518064516129 & 0.532336321026236 & 188.824358860862 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 100.522666666667 & 0.518721367280955 & 193.78933085712 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 100.533103448276 & 0.503653212231352 & 199.607787673746 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 100.551785714286 & 0.487912203829377 & 206.085818155613 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 100.552777777778 & 0.47400478084279 & 212.13452235438 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 100.549423076923 & 0.457946298683858 & 219.565969559975 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 100.5404 & 0.439737116273543 & 228.637511547826 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 100.535416666667 & 0.419803331015463 & 239.482179485049 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 100.574782608696 & 0.407327894260329 & 246.913565277257 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 100.616818181818 & 0.393558167166794 & 255.659332154517 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 100.644047619048 & 0.382782626111661 & 262.927418209647 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 100.682 & 0.373868755252222 & 269.297710989722 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 100.725789473684 & 0.362655103734155 & 277.745407238282 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 100.775833333333 & 0.348306874137489 & 289.33058982222 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 100.828823529412 & 0.329794070870118 & 305.732675130843 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 100.89125 & 0.304433222059532 & 331.406833056711 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 100.945 & 0.288896732136382 & 349.415513472634 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 100.988214285714 & 0.275952440869928 & 365.962388183099 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 101.023846153846 & 0.264688540871416 & 381.670645133531 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 101.05 & 0.254740561401573 & 396.678092581828 \tabularnewline
Median & 101.565 &  &  \tabularnewline
Midrange & 100.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 100.644864864865 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 100.775833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 100.644864864865 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 100.775833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 100.775833333333 &  &  \tabularnewline
Midmean - Closest Observation & 100.644864864865 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 100.775833333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 100.725789473684 &  &  \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]100.52[/C][C]0.585227207325542[/C][C]171.762349292288[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]100.398466569702[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]100.276423086807[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]100.640882611282[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]100.521944444444[/C][C]0.58396781855002[/C][C]172.136102797648[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]100.504166666667[/C][C]0.580170963619004[/C][C]173.231983275653[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]100.519583333333[/C][C]0.57712512772165[/C][C]174.172945354433[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]100.51625[/C][C]0.575834138028286[/C][C]174.557643185549[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]100.498888888889[/C][C]0.571201598270528[/C][C]175.942940624076[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]100.472222222222[/C][C]0.56565251082068[/C][C]177.621808973236[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]100.431388888889[/C][C]0.555163918100503[/C][C]180.904027827521[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]100.545833333333[/C][C]0.533444851530515[/C][C]188.484026127266[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]100.574583333333[/C][C]0.52794449404372[/C][C]190.502191931193[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]100.612083333333[/C][C]0.519559369164732[/C][C]193.648867299[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]100.576944444444[/C][C]0.506508447578386[/C][C]198.569135273661[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]100.233611111111[/C][C]0.451013434800692[/C][C]222.240854433539[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]100.240833333333[/C][C]0.43997700315134[/C][C]227.831983524951[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]100.394444444444[/C][C]0.410007962482745[/C][C]244.859743299911[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]100.327777777778[/C][C]0.385100347785768[/C][C]260.523726749762[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]100.312222222222[/C][C]0.379763033674663[/C][C]264.144251354802[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]100.300416666667[/C][C]0.374063956306496[/C][C]268.137079169648[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]100.325416666667[/C][C]0.367769199068186[/C][C]272.794505143064[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]100.301666666667[/C][C]0.362423269090287[/C][C]276.752833554072[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]100.443333333333[/C][C]0.300721420016872[/C][C]334.007911134824[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]100.592083333333[/C][C]0.272080673153098[/C][C]369.714181340366[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]100.705138888889[/C][C]0.248523731485989[/C][C]405.213370516958[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]100.823333333333[/C][C]0.228018613851832[/C][C]442.17150358983[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]100.873333333333[/C][C]0.206756757586087[/C][C]487.884093903596[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]100.517714285714[/C][C]0.575450176513324[/C][C]174.676659054577[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]100.513235294118[/C][C]0.565225775597855[/C][C]177.828470734198[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]100.518181818182[/C][C]0.555325474571625[/C][C]181.007690842422[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]100.51765625[/C][C]0.544728741571639[/C][C]184.527910093359[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]100.518064516129[/C][C]0.532336321026236[/C][C]188.824358860862[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]100.522666666667[/C][C]0.518721367280955[/C][C]193.78933085712[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]100.533103448276[/C][C]0.503653212231352[/C][C]199.607787673746[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]100.551785714286[/C][C]0.487912203829377[/C][C]206.085818155613[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]100.552777777778[/C][C]0.47400478084279[/C][C]212.13452235438[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]100.549423076923[/C][C]0.457946298683858[/C][C]219.565969559975[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]100.5404[/C][C]0.439737116273543[/C][C]228.637511547826[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]100.535416666667[/C][C]0.419803331015463[/C][C]239.482179485049[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]100.574782608696[/C][C]0.407327894260329[/C][C]246.913565277257[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]100.616818181818[/C][C]0.393558167166794[/C][C]255.659332154517[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]100.644047619048[/C][C]0.382782626111661[/C][C]262.927418209647[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]100.682[/C][C]0.373868755252222[/C][C]269.297710989722[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]100.725789473684[/C][C]0.362655103734155[/C][C]277.745407238282[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]100.775833333333[/C][C]0.348306874137489[/C][C]289.33058982222[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]100.828823529412[/C][C]0.329794070870118[/C][C]305.732675130843[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]100.89125[/C][C]0.304433222059532[/C][C]331.406833056711[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]100.945[/C][C]0.288896732136382[/C][C]349.415513472634[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]100.988214285714[/C][C]0.275952440869928[/C][C]365.962388183099[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]101.023846153846[/C][C]0.264688540871416[/C][C]381.670645133531[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]101.05[/C][C]0.254740561401573[/C][C]396.678092581828[/C][/ROW]
[ROW][C]Median[/C][C]101.565[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]100.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]100.644864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]100.775833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]100.644864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]100.775833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]100.775833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]100.644864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]100.775833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]100.725789473684[/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	100.52	0.585227207325542	171.762349292288
Geometric Mean	100.398466569702
Harmonic Mean	100.276423086807
Quadratic Mean	100.640882611282
Winsorized Mean ( 1 / 24 )	100.521944444444	0.58396781855002	172.136102797648
Winsorized Mean ( 2 / 24 )	100.504166666667	0.580170963619004	173.231983275653
Winsorized Mean ( 3 / 24 )	100.519583333333	0.57712512772165	174.172945354433
Winsorized Mean ( 4 / 24 )	100.51625	0.575834138028286	174.557643185549
Winsorized Mean ( 5 / 24 )	100.498888888889	0.571201598270528	175.942940624076
Winsorized Mean ( 6 / 24 )	100.472222222222	0.56565251082068	177.621808973236
Winsorized Mean ( 7 / 24 )	100.431388888889	0.555163918100503	180.904027827521
Winsorized Mean ( 8 / 24 )	100.545833333333	0.533444851530515	188.484026127266
Winsorized Mean ( 9 / 24 )	100.574583333333	0.52794449404372	190.502191931193
Winsorized Mean ( 10 / 24 )	100.612083333333	0.519559369164732	193.648867299
Winsorized Mean ( 11 / 24 )	100.576944444444	0.506508447578386	198.569135273661
Winsorized Mean ( 12 / 24 )	100.233611111111	0.451013434800692	222.240854433539
Winsorized Mean ( 13 / 24 )	100.240833333333	0.43997700315134	227.831983524951
Winsorized Mean ( 14 / 24 )	100.394444444444	0.410007962482745	244.859743299911
Winsorized Mean ( 15 / 24 )	100.327777777778	0.385100347785768	260.523726749762
Winsorized Mean ( 16 / 24 )	100.312222222222	0.379763033674663	264.144251354802
Winsorized Mean ( 17 / 24 )	100.300416666667	0.374063956306496	268.137079169648
Winsorized Mean ( 18 / 24 )	100.325416666667	0.367769199068186	272.794505143064
Winsorized Mean ( 19 / 24 )	100.301666666667	0.362423269090287	276.752833554072
Winsorized Mean ( 20 / 24 )	100.443333333333	0.300721420016872	334.007911134824
Winsorized Mean ( 21 / 24 )	100.592083333333	0.272080673153098	369.714181340366
Winsorized Mean ( 22 / 24 )	100.705138888889	0.248523731485989	405.213370516958
Winsorized Mean ( 23 / 24 )	100.823333333333	0.228018613851832	442.17150358983
Winsorized Mean ( 24 / 24 )	100.873333333333	0.206756757586087	487.884093903596
Trimmed Mean ( 1 / 24 )	100.517714285714	0.575450176513324	174.676659054577
Trimmed Mean ( 2 / 24 )	100.513235294118	0.565225775597855	177.828470734198
Trimmed Mean ( 3 / 24 )	100.518181818182	0.555325474571625	181.007690842422
Trimmed Mean ( 4 / 24 )	100.51765625	0.544728741571639	184.527910093359
Trimmed Mean ( 5 / 24 )	100.518064516129	0.532336321026236	188.824358860862
Trimmed Mean ( 6 / 24 )	100.522666666667	0.518721367280955	193.78933085712
Trimmed Mean ( 7 / 24 )	100.533103448276	0.503653212231352	199.607787673746
Trimmed Mean ( 8 / 24 )	100.551785714286	0.487912203829377	206.085818155613
Trimmed Mean ( 9 / 24 )	100.552777777778	0.47400478084279	212.13452235438
Trimmed Mean ( 10 / 24 )	100.549423076923	0.457946298683858	219.565969559975
Trimmed Mean ( 11 / 24 )	100.5404	0.439737116273543	228.637511547826
Trimmed Mean ( 12 / 24 )	100.535416666667	0.419803331015463	239.482179485049
Trimmed Mean ( 13 / 24 )	100.574782608696	0.407327894260329	246.913565277257
Trimmed Mean ( 14 / 24 )	100.616818181818	0.393558167166794	255.659332154517
Trimmed Mean ( 15 / 24 )	100.644047619048	0.382782626111661	262.927418209647
Trimmed Mean ( 16 / 24 )	100.682	0.373868755252222	269.297710989722
Trimmed Mean ( 17 / 24 )	100.725789473684	0.362655103734155	277.745407238282
Trimmed Mean ( 18 / 24 )	100.775833333333	0.348306874137489	289.33058982222
Trimmed Mean ( 19 / 24 )	100.828823529412	0.329794070870118	305.732675130843
Trimmed Mean ( 20 / 24 )	100.89125	0.304433222059532	331.406833056711
Trimmed Mean ( 21 / 24 )	100.945	0.288896732136382	349.415513472634
Trimmed Mean ( 22 / 24 )	100.988214285714	0.275952440869928	365.962388183099
Trimmed Mean ( 23 / 24 )	101.023846153846	0.264688540871416	381.670645133531
Trimmed Mean ( 24 / 24 )	101.05	0.254740561401573	396.678092581828
Median	101.565
Midrange	100.6
Midmean - Weighted Average at Xnp	100.644864864865
Midmean - Weighted Average at X(n+1)p	100.775833333333
Midmean - Empirical Distribution Function	100.644864864865
Midmean - Empirical Distribution Function - Averaging	100.775833333333
Midmean - Empirical Distribution Function - Interpolation	100.775833333333
Midmean - Closest Observation	100.644864864865
Midmean - True Basic - Statistics Graphics Toolkit	100.775833333333
Midmean - MS Excel (old versions)	100.725789473684
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