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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 20 Oct 2010 15:30:49 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/20/t1287588585bmev3kuf0z6suxe.htm/, Retrieved Fri, 03 May 2024 17:28:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=87235, Retrieved Fri, 03 May 2024 17:28:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2010-10-20 15:30:49] [c6158409503ffaeb6d7b5957d384c3e1] [Current]
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Dataseries X:
84,9
81,9
95,9
81
89,2
102,5
89,8
88,8
83,2
90,2
100,4
187,1
87,6
85,4
86,1
86,7
89,1
103,7
86,9
85,2
80,8
91,2
102,8
182,5
80,9
83,1
88,3
86,6
93
105,3
93,8
86,4
87
96,7
100,5
196,7
86,8
88,2
93,8
85
90,4
115,9
94,9
87,7
91,7
95,9
106,8
204,5
90,2
90,5
93,2
97,8
99,4
120
108,2
98,5
104,3
102,9
111,1
188,1
93,8
94,5
112,4
102,5
115,8
136,5
122,1
110,6
116,4
112,6
121,5
199,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87235&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=87235&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87235&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean104.5138888888893.4553519903155930.2469586837500
Geometric Mean101.530600039410
Harmonic Mean99.3238126617825
Quadratic Mean108.493568677800
Winsorized Mean ( 1 / 24 )104.4430555555563.4264173394369430.4817087963718
Winsorized Mean ( 2 / 24 )104.3736111111113.3982487625271130.7139407397278
Winsorized Mean ( 3 / 24 )104.0527777777783.2609661938298831.9085729789709
Winsorized Mean ( 4 / 24 )104.0638888888893.2346061973263932.1720427589931
Winsorized Mean ( 5 / 24 )103.7513888888893.1194089220410133.2599513182789
Winsorized Mean ( 6 / 24 )100.0597222222221.8548150970640353.9459282925861
Winsorized Mean ( 7 / 24 )98.66944444444441.5019453203301765.6944318204302
Winsorized Mean ( 8 / 24 )98.6251.4845470979635566.4344028797002
Winsorized Mean ( 9 / 24 )98.46251.4412726910181968.3163572123477
Winsorized Mean ( 10 / 24 )98.05972222222221.3274689987247273.8696890973928
Winsorized Mean ( 11 / 24 )98.02916666666671.306899707199975.0089437824568
Winsorized Mean ( 12 / 24 )98.04583333333331.2995348534339275.446867064977
Winsorized Mean ( 13 / 24 )97.48611111111111.1898177579636881.9336494674231
Winsorized Mean ( 14 / 24 )97.46666666666671.1803954139750582.5712007287811
Winsorized Mean ( 15 / 24 )97.21666666666671.1301564144518986.0205414255115
Winsorized Mean ( 16 / 24 )97.12777777777781.1081717772441187.6468610483141
Winsorized Mean ( 17 / 24 )96.70277777777780.99518200107664397.1709472972375
Winsorized Mean ( 18 / 24 )96.37777777777780.935987637148297102.969071334548
Winsorized Mean ( 19 / 24 )96.11388888888890.857858147227783112.039372942352
Winsorized Mean ( 20 / 24 )95.86388888888890.81297023362795117.918079806056
Winsorized Mean ( 21 / 24 )95.83472222222220.768606343301505124.686353498684
Winsorized Mean ( 22 / 24 )95.68194444444440.721973274025593132.528374507465
Winsorized Mean ( 23 / 24 )95.68194444444450.713384575374457134.123932234196
Winsorized Mean ( 24 / 24 )95.78194444444440.674033030183333142.102745941682
Trimmed Mean ( 1 / 24 )103.4242857142863.2300295402852132.0196098594051
Trimmed Mean ( 2 / 24 )102.3455882352942.9856699260030734.2789359747829
Trimmed Mean ( 3 / 24 )101.2393939393942.6956780385626937.5561890148328
Trimmed Mean ( 4 / 24 )100.1843752.3979180565032641.7797325176711
Trimmed Mean ( 5 / 24 )99.0580645161292.0086533428270949.3156596034184
Trimmed Mean ( 6 / 24 )97.93166666666671.5003794090156465.2712681060567
Trimmed Mean ( 7 / 24 )97.49137931034481.3804930085513570.6206976105222
Trimmed Mean ( 8 / 24 )97.2751.3406972648007372.555529539667
Trimmed Mean ( 9 / 24 )97.051.2951577559734374.9329566629184
Trimmed Mean ( 10 / 24 )96.83269230769231.2488206235797777.5393122753843
Trimmed Mean ( 11 / 24 )96.6561.2182796837159879.3381037966433
Trimmed Mean ( 12 / 24 )96.468751.1833476534319881.5219007873285
Trimmed Mean ( 13 / 24 )96.26304347826091.1391299277205184.505762806962
Trimmed Mean ( 14 / 24 )96.1090909090911.1089384014648186.667655103421
Trimmed Mean ( 15 / 24 )95.94285714285721.0705276893965589.6220229454683
Trimmed Mean ( 16 / 24 )95.791.0318691032073092.8315420068893
Trimmed Mean ( 17 / 24 )95.63157894736840.98475654444284697.1118998772176
Trimmed Mean ( 18 / 24 )95.50555555555560.951364470779219100.387977992631
Trimmed Mean ( 19 / 24 )95.40294117647060.92092417828024103.594783834027
Trimmed Mean ( 20 / 24 )95.318750.898872922187522106.042520190762
Trimmed Mean ( 21 / 24 )95.25333333333330.878514071133796108.425506731384
Trimmed Mean ( 22 / 24 )95.18214285714290.859371826249894110.757811636083
Trimmed Mean ( 23 / 24 )95.11923076923080.842761381152536112.866147994523
Trimmed Mean ( 24 / 24 )95.04583333333330.815941244658155116.486124406119
Median94.15
Midrange142.65
Midmean - Weighted Average at Xnp95.291891891892
Midmean - Weighted Average at X(n+1)p95.5055555555556
Midmean - Empirical Distribution Function95.291891891892
Midmean - Empirical Distribution Function - Averaging95.5055555555556
Midmean - Empirical Distribution Function - Interpolation95.5055555555556
Midmean - Closest Observation95.291891891892
Midmean - True Basic - Statistics Graphics Toolkit95.5055555555556
Midmean - MS Excel (old versions)95.6315789473684
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 104.513888888889 & 3.45535199031559 & 30.2469586837500 \tabularnewline
Geometric Mean & 101.530600039410 &  &  \tabularnewline
Harmonic Mean & 99.3238126617825 &  &  \tabularnewline
Quadratic Mean & 108.493568677800 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 104.443055555556 & 3.42641733943694 & 30.4817087963718 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 104.373611111111 & 3.39824876252711 & 30.7139407397278 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 104.052777777778 & 3.26096619382988 & 31.9085729789709 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 104.063888888889 & 3.23460619732639 & 32.1720427589931 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 103.751388888889 & 3.11940892204101 & 33.2599513182789 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 100.059722222222 & 1.85481509706403 & 53.9459282925861 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 98.6694444444444 & 1.50194532033017 & 65.6944318204302 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 98.625 & 1.48454709796355 & 66.4344028797002 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 98.4625 & 1.44127269101819 & 68.3163572123477 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 98.0597222222222 & 1.32746899872472 & 73.8696890973928 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 98.0291666666667 & 1.3068997071999 & 75.0089437824568 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 98.0458333333333 & 1.29953485343392 & 75.446867064977 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 97.4861111111111 & 1.18981775796368 & 81.9336494674231 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 97.4666666666667 & 1.18039541397505 & 82.5712007287811 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 97.2166666666667 & 1.13015641445189 & 86.0205414255115 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 97.1277777777778 & 1.10817177724411 & 87.6468610483141 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 96.7027777777778 & 0.995182001076643 & 97.1709472972375 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 96.3777777777778 & 0.935987637148297 & 102.969071334548 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 96.1138888888889 & 0.857858147227783 & 112.039372942352 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 95.8638888888889 & 0.81297023362795 & 117.918079806056 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 95.8347222222222 & 0.768606343301505 & 124.686353498684 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 95.6819444444444 & 0.721973274025593 & 132.528374507465 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 95.6819444444445 & 0.713384575374457 & 134.123932234196 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 95.7819444444444 & 0.674033030183333 & 142.102745941682 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 103.424285714286 & 3.23002954028521 & 32.0196098594051 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 102.345588235294 & 2.98566992600307 & 34.2789359747829 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 101.239393939394 & 2.69567803856269 & 37.5561890148328 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 100.184375 & 2.39791805650326 & 41.7797325176711 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 99.058064516129 & 2.00865334282709 & 49.3156596034184 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 97.9316666666667 & 1.50037940901564 & 65.2712681060567 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 97.4913793103448 & 1.38049300855135 & 70.6206976105222 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 97.275 & 1.34069726480073 & 72.555529539667 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 97.05 & 1.29515775597343 & 74.9329566629184 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 96.8326923076923 & 1.24882062357977 & 77.5393122753843 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 96.656 & 1.21827968371598 & 79.3381037966433 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 96.46875 & 1.18334765343198 & 81.5219007873285 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 96.2630434782609 & 1.13912992772051 & 84.505762806962 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 96.109090909091 & 1.10893840146481 & 86.667655103421 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 95.9428571428572 & 1.07052768939655 & 89.6220229454683 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 95.79 & 1.03186910320730 & 92.8315420068893 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 95.6315789473684 & 0.984756544442846 & 97.1118998772176 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 95.5055555555556 & 0.951364470779219 & 100.387977992631 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 95.4029411764706 & 0.92092417828024 & 103.594783834027 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 95.31875 & 0.898872922187522 & 106.042520190762 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 95.2533333333333 & 0.878514071133796 & 108.425506731384 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 95.1821428571429 & 0.859371826249894 & 110.757811636083 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 95.1192307692308 & 0.842761381152536 & 112.866147994523 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 95.0458333333333 & 0.815941244658155 & 116.486124406119 \tabularnewline
Median & 94.15 &  &  \tabularnewline
Midrange & 142.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 95.291891891892 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 95.5055555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 95.291891891892 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 95.5055555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 95.5055555555556 &  &  \tabularnewline
Midmean - Closest Observation & 95.291891891892 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 95.5055555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 95.6315789473684 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87235&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]104.513888888889[/C][C]3.45535199031559[/C][C]30.2469586837500[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.530600039410[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.3238126617825[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]108.493568677800[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]104.443055555556[/C][C]3.42641733943694[/C][C]30.4817087963718[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]104.373611111111[/C][C]3.39824876252711[/C][C]30.7139407397278[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]104.052777777778[/C][C]3.26096619382988[/C][C]31.9085729789709[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]104.063888888889[/C][C]3.23460619732639[/C][C]32.1720427589931[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]103.751388888889[/C][C]3.11940892204101[/C][C]33.2599513182789[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]100.059722222222[/C][C]1.85481509706403[/C][C]53.9459282925861[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]98.6694444444444[/C][C]1.50194532033017[/C][C]65.6944318204302[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]98.625[/C][C]1.48454709796355[/C][C]66.4344028797002[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]98.4625[/C][C]1.44127269101819[/C][C]68.3163572123477[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]98.0597222222222[/C][C]1.32746899872472[/C][C]73.8696890973928[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]98.0291666666667[/C][C]1.3068997071999[/C][C]75.0089437824568[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]98.0458333333333[/C][C]1.29953485343392[/C][C]75.446867064977[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]97.4861111111111[/C][C]1.18981775796368[/C][C]81.9336494674231[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]97.4666666666667[/C][C]1.18039541397505[/C][C]82.5712007287811[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]97.2166666666667[/C][C]1.13015641445189[/C][C]86.0205414255115[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]97.1277777777778[/C][C]1.10817177724411[/C][C]87.6468610483141[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]96.7027777777778[/C][C]0.995182001076643[/C][C]97.1709472972375[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]96.3777777777778[/C][C]0.935987637148297[/C][C]102.969071334548[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]96.1138888888889[/C][C]0.857858147227783[/C][C]112.039372942352[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]95.8638888888889[/C][C]0.81297023362795[/C][C]117.918079806056[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]95.8347222222222[/C][C]0.768606343301505[/C][C]124.686353498684[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]95.6819444444444[/C][C]0.721973274025593[/C][C]132.528374507465[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]95.6819444444445[/C][C]0.713384575374457[/C][C]134.123932234196[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]95.7819444444444[/C][C]0.674033030183333[/C][C]142.102745941682[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]103.424285714286[/C][C]3.23002954028521[/C][C]32.0196098594051[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]102.345588235294[/C][C]2.98566992600307[/C][C]34.2789359747829[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]101.239393939394[/C][C]2.69567803856269[/C][C]37.5561890148328[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]100.184375[/C][C]2.39791805650326[/C][C]41.7797325176711[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]99.058064516129[/C][C]2.00865334282709[/C][C]49.3156596034184[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]97.9316666666667[/C][C]1.50037940901564[/C][C]65.2712681060567[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]97.4913793103448[/C][C]1.38049300855135[/C][C]70.6206976105222[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]97.275[/C][C]1.34069726480073[/C][C]72.555529539667[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]97.05[/C][C]1.29515775597343[/C][C]74.9329566629184[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]96.8326923076923[/C][C]1.24882062357977[/C][C]77.5393122753843[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]96.656[/C][C]1.21827968371598[/C][C]79.3381037966433[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]96.46875[/C][C]1.18334765343198[/C][C]81.5219007873285[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]96.2630434782609[/C][C]1.13912992772051[/C][C]84.505762806962[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]96.109090909091[/C][C]1.10893840146481[/C][C]86.667655103421[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]95.9428571428572[/C][C]1.07052768939655[/C][C]89.6220229454683[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]95.79[/C][C]1.03186910320730[/C][C]92.8315420068893[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]95.6315789473684[/C][C]0.984756544442846[/C][C]97.1118998772176[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]95.5055555555556[/C][C]0.951364470779219[/C][C]100.387977992631[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]95.4029411764706[/C][C]0.92092417828024[/C][C]103.594783834027[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]95.31875[/C][C]0.898872922187522[/C][C]106.042520190762[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]95.2533333333333[/C][C]0.878514071133796[/C][C]108.425506731384[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]95.1821428571429[/C][C]0.859371826249894[/C][C]110.757811636083[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]95.1192307692308[/C][C]0.842761381152536[/C][C]112.866147994523[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]95.0458333333333[/C][C]0.815941244658155[/C][C]116.486124406119[/C][/ROW]
[ROW][C]Median[/C][C]94.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]142.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]95.291891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]95.5055555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]95.291891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]95.5055555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]95.5055555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]95.291891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]95.5055555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]95.6315789473684[/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=87235&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87235&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
MeasureValueS.E.Value/S.E.
Arithmetic Mean104.5138888888893.4553519903155930.2469586837500
Geometric Mean101.530600039410
Harmonic Mean99.3238126617825
Quadratic Mean108.493568677800
Winsorized Mean ( 1 / 24 )104.4430555555563.4264173394369430.4817087963718
Winsorized Mean ( 2 / 24 )104.3736111111113.3982487625271130.7139407397278
Winsorized Mean ( 3 / 24 )104.0527777777783.2609661938298831.9085729789709
Winsorized Mean ( 4 / 24 )104.0638888888893.2346061973263932.1720427589931
Winsorized Mean ( 5 / 24 )103.7513888888893.1194089220410133.2599513182789
Winsorized Mean ( 6 / 24 )100.0597222222221.8548150970640353.9459282925861
Winsorized Mean ( 7 / 24 )98.66944444444441.5019453203301765.6944318204302
Winsorized Mean ( 8 / 24 )98.6251.4845470979635566.4344028797002
Winsorized Mean ( 9 / 24 )98.46251.4412726910181968.3163572123477
Winsorized Mean ( 10 / 24 )98.05972222222221.3274689987247273.8696890973928
Winsorized Mean ( 11 / 24 )98.02916666666671.306899707199975.0089437824568
Winsorized Mean ( 12 / 24 )98.04583333333331.2995348534339275.446867064977
Winsorized Mean ( 13 / 24 )97.48611111111111.1898177579636881.9336494674231
Winsorized Mean ( 14 / 24 )97.46666666666671.1803954139750582.5712007287811
Winsorized Mean ( 15 / 24 )97.21666666666671.1301564144518986.0205414255115
Winsorized Mean ( 16 / 24 )97.12777777777781.1081717772441187.6468610483141
Winsorized Mean ( 17 / 24 )96.70277777777780.99518200107664397.1709472972375
Winsorized Mean ( 18 / 24 )96.37777777777780.935987637148297102.969071334548
Winsorized Mean ( 19 / 24 )96.11388888888890.857858147227783112.039372942352
Winsorized Mean ( 20 / 24 )95.86388888888890.81297023362795117.918079806056
Winsorized Mean ( 21 / 24 )95.83472222222220.768606343301505124.686353498684
Winsorized Mean ( 22 / 24 )95.68194444444440.721973274025593132.528374507465
Winsorized Mean ( 23 / 24 )95.68194444444450.713384575374457134.123932234196
Winsorized Mean ( 24 / 24 )95.78194444444440.674033030183333142.102745941682
Trimmed Mean ( 1 / 24 )103.4242857142863.2300295402852132.0196098594051
Trimmed Mean ( 2 / 24 )102.3455882352942.9856699260030734.2789359747829
Trimmed Mean ( 3 / 24 )101.2393939393942.6956780385626937.5561890148328
Trimmed Mean ( 4 / 24 )100.1843752.3979180565032641.7797325176711
Trimmed Mean ( 5 / 24 )99.0580645161292.0086533428270949.3156596034184
Trimmed Mean ( 6 / 24 )97.93166666666671.5003794090156465.2712681060567
Trimmed Mean ( 7 / 24 )97.49137931034481.3804930085513570.6206976105222
Trimmed Mean ( 8 / 24 )97.2751.3406972648007372.555529539667
Trimmed Mean ( 9 / 24 )97.051.2951577559734374.9329566629184
Trimmed Mean ( 10 / 24 )96.83269230769231.2488206235797777.5393122753843
Trimmed Mean ( 11 / 24 )96.6561.2182796837159879.3381037966433
Trimmed Mean ( 12 / 24 )96.468751.1833476534319881.5219007873285
Trimmed Mean ( 13 / 24 )96.26304347826091.1391299277205184.505762806962
Trimmed Mean ( 14 / 24 )96.1090909090911.1089384014648186.667655103421
Trimmed Mean ( 15 / 24 )95.94285714285721.0705276893965589.6220229454683
Trimmed Mean ( 16 / 24 )95.791.0318691032073092.8315420068893
Trimmed Mean ( 17 / 24 )95.63157894736840.98475654444284697.1118998772176
Trimmed Mean ( 18 / 24 )95.50555555555560.951364470779219100.387977992631
Trimmed Mean ( 19 / 24 )95.40294117647060.92092417828024103.594783834027
Trimmed Mean ( 20 / 24 )95.318750.898872922187522106.042520190762
Trimmed Mean ( 21 / 24 )95.25333333333330.878514071133796108.425506731384
Trimmed Mean ( 22 / 24 )95.18214285714290.859371826249894110.757811636083
Trimmed Mean ( 23 / 24 )95.11923076923080.842761381152536112.866147994523
Trimmed Mean ( 24 / 24 )95.04583333333330.815941244658155116.486124406119
Median94.15
Midrange142.65
Midmean - Weighted Average at Xnp95.291891891892
Midmean - Weighted Average at X(n+1)p95.5055555555556
Midmean - Empirical Distribution Function95.291891891892
Midmean - Empirical Distribution Function - Averaging95.5055555555556
Midmean - Empirical Distribution Function - Interpolation95.5055555555556
Midmean - Closest Observation95.291891891892
Midmean - True Basic - Statistics Graphics Toolkit95.5055555555556
Midmean - MS Excel (old versions)95.6315789473684
Number of observations72



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')