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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 11 Oct 2015 10:02:23 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/11/t14445541629yhb5x7yunhfswh.htm/, Retrieved Sat, 18 May 2024 14:23:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282303, Retrieved Sat, 18 May 2024 14:23:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-10-11 09:02:23] [88f551c1d3f4ff2d65b8ab6790c1e3d2] [Current]
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Dataseries X:
94,94
95,11
95,53
95,89
95,99
95,42
95,42
95,45
95,99
95,99
95,97
95,97
95,97
96,22
95,8
96,02
96,04
96,15
96,15
95,99
96,08
96,29
96,3
96,44
96,44
96,83
96,7
97,06
97,64
97,61
97,61
97,61
97,55
97,58
97,79
97,79
97,79
97,79
98
98,37
98,68
98,89
98,89
98,89
98,88
98,97
99,05
99,05
99
99,03
99,2
100,3
100,79
100,75
100,75
100,17
99,98
99,93
100,04
100,04
100,49
100,71
100,7
101,27
101,07
101,17
100,71
100,59
100,52
100,65
100,62
100,62




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282303&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282303&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282303&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean98.07888888888890.229671940251974427.039057454237
Geometric Mean98.0598224308145
Harmonic Mean98.0407856770426
Quadratic Mean98.0979797900491
Winsorized Mean ( 1 / 24 )98.07986111111110.228961089444215428.369123108176
Winsorized Mean ( 2 / 24 )98.08569444444440.226940581731206432.208702807591
Winsorized Mean ( 3 / 24 )98.07402777777780.224867432666343436.141537326569
Winsorized Mean ( 4 / 24 )98.07347222222220.224215739756832437.406724115735
Winsorized Mean ( 5 / 24 )98.07902777777780.22331136109789439.203036046089
Winsorized Mean ( 6 / 24 )98.09819444444450.219280310812554447.364353329018
Winsorized Mean ( 7 / 24 )98.10694444444440.218007824486012450.015703224171
Winsorized Mean ( 8 / 24 )98.11472222222220.216564437079949453.050941997467
Winsorized Mean ( 9 / 24 )98.10847222222220.215519957548735455.217573992131
Winsorized Mean ( 10 / 24 )98.10430555555550.214830320858413456.659493704394
Winsorized Mean ( 11 / 24 )98.10736111111110.214404039281159457.581682882653
Winsorized Mean ( 12 / 24 )98.10236111111110.213581272171052459.320988745415
Winsorized Mean ( 13 / 24 )98.08972222222220.211521887958141463.733201178847
Winsorized Mean ( 14 / 24 )98.08388888888890.21058051474614465.778559840312
Winsorized Mean ( 15 / 24 )98.05055555555560.203434409658768481.976258195558
Winsorized Mean ( 16 / 24 )98.02611111111110.198359622232501494.183796116596
Winsorized Mean ( 17 / 24 )98.00486111111110.192404885049486509.367842120559
Winsorized Mean ( 18 / 24 )98.02236111111110.18995711288639516.023641450775
Winsorized Mean ( 19 / 24 )98.00652777777780.187599755385619522.423537153986
Winsorized Mean ( 20 / 24 )98.01208333333340.182847514386208536.031805859354
Winsorized Mean ( 21 / 24 )97.81958333333330.150289423115244650.874700998245
Winsorized Mean ( 22 / 24 )97.77680555555560.14402956605992678.866209420349
Winsorized Mean ( 23 / 24 )97.82152777777780.137637491327277710.718619138268
Winsorized Mean ( 24 / 24 )97.81486111111110.136801432617425715.013426684335
Trimmed Mean ( 1 / 24 )98.07814285714290.227334021800972431.427474339979
Trimmed Mean ( 2 / 24 )98.07632352941180.225292893395216435.328083595442
Trimmed Mean ( 3 / 24 )98.07121212121210.223986192043567437.844901180946
Trimmed Mean ( 4 / 24 )98.070156250.223166970307626439.447451004128
Trimmed Mean ( 5 / 24 )98.06919354838710.222219501965481441.316773194916
Trimmed Mean ( 6 / 24 )98.06683333333330.221146408500041443.447551323516
Trimmed Mean ( 7 / 24 )98.06034482758620.220678567098947444.358263317969
Trimmed Mean ( 8 / 24 )98.05178571428570.22014149923311445.403461209546
Trimmed Mean ( 9 / 24 )98.04129629629630.219515228288324446.626400640976
Trimmed Mean ( 10 / 24 )98.03096153846150.218670268316258448.304940096756
Trimmed Mean ( 11 / 24 )98.02040.217456157439065450.7593675634
Trimmed Mean ( 12 / 24 )98.00854166666670.215702708956111454.368617533721
Trimmed Mean ( 13 / 24 )97.99630434782610.213348133249233459.325811083366
Trimmed Mean ( 14 / 24 )97.98454545454550.210482043783629465.524486997435
Trimmed Mean ( 15 / 24 )97.9723809523810.206681317956123474.026302528125
Trimmed Mean ( 16 / 24 )97.9630.203062829736298482.427040572698
Trimmed Mean ( 17 / 24 )97.95552631578950.199135649088856491.903517848182
Trimmed Mean ( 18 / 24 )97.94972222222220.194958475884543502.413253785536
Trimmed Mean ( 19 / 24 )97.94117647058820.189474253706006516.910211044065
Trimmed Mean ( 20 / 24 )97.93343750.182150355174293537.651641723626
Trimmed Mean ( 21 / 24 )97.9240.172834782578524566.575769871498
Trimmed Mean ( 22 / 24 )97.93678571428570.169366274113993578.254355695212
Trimmed Mean ( 23 / 24 )97.95692307692310.165282759332437592.662679837647
Trimmed Mean ( 24 / 24 )97.97458333333330.160691417263417609.706386326323
Median97.79
Midrange98.105
Midmean - Weighted Average at Xnp97.9555263157895
Midmean - Weighted Average at X(n+1)p98.0062162162162
Midmean - Empirical Distribution Function97.9555263157895
Midmean - Empirical Distribution Function - Averaging98.0062162162162
Midmean - Empirical Distribution Function - Interpolation98.0062162162162
Midmean - Closest Observation97.9555263157895
Midmean - True Basic - Statistics Graphics Toolkit98.0062162162162
Midmean - MS Excel (old versions)97.9555263157895
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 98.0788888888889 & 0.229671940251974 & 427.039057454237 \tabularnewline
Geometric Mean & 98.0598224308145 &  &  \tabularnewline
Harmonic Mean & 98.0407856770426 &  &  \tabularnewline
Quadratic Mean & 98.0979797900491 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 98.0798611111111 & 0.228961089444215 & 428.369123108176 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 98.0856944444444 & 0.226940581731206 & 432.208702807591 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 98.0740277777778 & 0.224867432666343 & 436.141537326569 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 98.0734722222222 & 0.224215739756832 & 437.406724115735 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 98.0790277777778 & 0.22331136109789 & 439.203036046089 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 98.0981944444445 & 0.219280310812554 & 447.364353329018 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 98.1069444444444 & 0.218007824486012 & 450.015703224171 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 98.1147222222222 & 0.216564437079949 & 453.050941997467 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 98.1084722222222 & 0.215519957548735 & 455.217573992131 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 98.1043055555555 & 0.214830320858413 & 456.659493704394 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 98.1073611111111 & 0.214404039281159 & 457.581682882653 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 98.1023611111111 & 0.213581272171052 & 459.320988745415 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 98.0897222222222 & 0.211521887958141 & 463.733201178847 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 98.0838888888889 & 0.21058051474614 & 465.778559840312 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 98.0505555555556 & 0.203434409658768 & 481.976258195558 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 98.0261111111111 & 0.198359622232501 & 494.183796116596 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 98.0048611111111 & 0.192404885049486 & 509.367842120559 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 98.0223611111111 & 0.18995711288639 & 516.023641450775 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 98.0065277777778 & 0.187599755385619 & 522.423537153986 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 98.0120833333334 & 0.182847514386208 & 536.031805859354 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 97.8195833333333 & 0.150289423115244 & 650.874700998245 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 97.7768055555556 & 0.14402956605992 & 678.866209420349 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 97.8215277777778 & 0.137637491327277 & 710.718619138268 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 97.8148611111111 & 0.136801432617425 & 715.013426684335 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 98.0781428571429 & 0.227334021800972 & 431.427474339979 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 98.0763235294118 & 0.225292893395216 & 435.328083595442 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 98.0712121212121 & 0.223986192043567 & 437.844901180946 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 98.07015625 & 0.223166970307626 & 439.447451004128 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 98.0691935483871 & 0.222219501965481 & 441.316773194916 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 98.0668333333333 & 0.221146408500041 & 443.447551323516 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 98.0603448275862 & 0.220678567098947 & 444.358263317969 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 98.0517857142857 & 0.22014149923311 & 445.403461209546 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 98.0412962962963 & 0.219515228288324 & 446.626400640976 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 98.0309615384615 & 0.218670268316258 & 448.304940096756 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 98.0204 & 0.217456157439065 & 450.7593675634 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 98.0085416666667 & 0.215702708956111 & 454.368617533721 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 97.9963043478261 & 0.213348133249233 & 459.325811083366 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 97.9845454545455 & 0.210482043783629 & 465.524486997435 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 97.972380952381 & 0.206681317956123 & 474.026302528125 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 97.963 & 0.203062829736298 & 482.427040572698 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 97.9555263157895 & 0.199135649088856 & 491.903517848182 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 97.9497222222222 & 0.194958475884543 & 502.413253785536 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 97.9411764705882 & 0.189474253706006 & 516.910211044065 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 97.9334375 & 0.182150355174293 & 537.651641723626 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 97.924 & 0.172834782578524 & 566.575769871498 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 97.9367857142857 & 0.169366274113993 & 578.254355695212 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 97.9569230769231 & 0.165282759332437 & 592.662679837647 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 97.9745833333333 & 0.160691417263417 & 609.706386326323 \tabularnewline
Median & 97.79 &  &  \tabularnewline
Midrange & 98.105 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.9555263157895 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 98.0062162162162 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.9555263157895 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 98.0062162162162 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 98.0062162162162 &  &  \tabularnewline
Midmean - Closest Observation & 97.9555263157895 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 98.0062162162162 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.9555263157895 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282303&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]98.0788888888889[/C][C]0.229671940251974[/C][C]427.039057454237[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]98.0598224308145[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]98.0407856770426[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]98.0979797900491[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]98.0798611111111[/C][C]0.228961089444215[/C][C]428.369123108176[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]98.0856944444444[/C][C]0.226940581731206[/C][C]432.208702807591[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]98.0740277777778[/C][C]0.224867432666343[/C][C]436.141537326569[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]98.0734722222222[/C][C]0.224215739756832[/C][C]437.406724115735[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]98.0790277777778[/C][C]0.22331136109789[/C][C]439.203036046089[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]98.0981944444445[/C][C]0.219280310812554[/C][C]447.364353329018[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]98.1069444444444[/C][C]0.218007824486012[/C][C]450.015703224171[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]98.1147222222222[/C][C]0.216564437079949[/C][C]453.050941997467[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]98.1084722222222[/C][C]0.215519957548735[/C][C]455.217573992131[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]98.1043055555555[/C][C]0.214830320858413[/C][C]456.659493704394[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]98.1073611111111[/C][C]0.214404039281159[/C][C]457.581682882653[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]98.1023611111111[/C][C]0.213581272171052[/C][C]459.320988745415[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]98.0897222222222[/C][C]0.211521887958141[/C][C]463.733201178847[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]98.0838888888889[/C][C]0.21058051474614[/C][C]465.778559840312[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]98.0505555555556[/C][C]0.203434409658768[/C][C]481.976258195558[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]98.0261111111111[/C][C]0.198359622232501[/C][C]494.183796116596[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]98.0048611111111[/C][C]0.192404885049486[/C][C]509.367842120559[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]98.0223611111111[/C][C]0.18995711288639[/C][C]516.023641450775[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]98.0065277777778[/C][C]0.187599755385619[/C][C]522.423537153986[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]98.0120833333334[/C][C]0.182847514386208[/C][C]536.031805859354[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]97.8195833333333[/C][C]0.150289423115244[/C][C]650.874700998245[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]97.7768055555556[/C][C]0.14402956605992[/C][C]678.866209420349[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]97.8215277777778[/C][C]0.137637491327277[/C][C]710.718619138268[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]97.8148611111111[/C][C]0.136801432617425[/C][C]715.013426684335[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]98.0781428571429[/C][C]0.227334021800972[/C][C]431.427474339979[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]98.0763235294118[/C][C]0.225292893395216[/C][C]435.328083595442[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]98.0712121212121[/C][C]0.223986192043567[/C][C]437.844901180946[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]98.07015625[/C][C]0.223166970307626[/C][C]439.447451004128[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]98.0691935483871[/C][C]0.222219501965481[/C][C]441.316773194916[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]98.0668333333333[/C][C]0.221146408500041[/C][C]443.447551323516[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]98.0603448275862[/C][C]0.220678567098947[/C][C]444.358263317969[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]98.0517857142857[/C][C]0.22014149923311[/C][C]445.403461209546[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]98.0412962962963[/C][C]0.219515228288324[/C][C]446.626400640976[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]98.0309615384615[/C][C]0.218670268316258[/C][C]448.304940096756[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]98.0204[/C][C]0.217456157439065[/C][C]450.7593675634[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]98.0085416666667[/C][C]0.215702708956111[/C][C]454.368617533721[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]97.9963043478261[/C][C]0.213348133249233[/C][C]459.325811083366[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]97.9845454545455[/C][C]0.210482043783629[/C][C]465.524486997435[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]97.972380952381[/C][C]0.206681317956123[/C][C]474.026302528125[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]97.963[/C][C]0.203062829736298[/C][C]482.427040572698[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]97.9555263157895[/C][C]0.199135649088856[/C][C]491.903517848182[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]97.9497222222222[/C][C]0.194958475884543[/C][C]502.413253785536[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]97.9411764705882[/C][C]0.189474253706006[/C][C]516.910211044065[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]97.9334375[/C][C]0.182150355174293[/C][C]537.651641723626[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]97.924[/C][C]0.172834782578524[/C][C]566.575769871498[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]97.9367857142857[/C][C]0.169366274113993[/C][C]578.254355695212[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]97.9569230769231[/C][C]0.165282759332437[/C][C]592.662679837647[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]97.9745833333333[/C][C]0.160691417263417[/C][C]609.706386326323[/C][/ROW]
[ROW][C]Median[/C][C]97.79[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]98.105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.9555263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]98.0062162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.9555263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]98.0062162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]98.0062162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.9555263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]98.0062162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.9555263157895[/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=282303&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282303&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 Mean98.07888888888890.229671940251974427.039057454237
Geometric Mean98.0598224308145
Harmonic Mean98.0407856770426
Quadratic Mean98.0979797900491
Winsorized Mean ( 1 / 24 )98.07986111111110.228961089444215428.369123108176
Winsorized Mean ( 2 / 24 )98.08569444444440.226940581731206432.208702807591
Winsorized Mean ( 3 / 24 )98.07402777777780.224867432666343436.141537326569
Winsorized Mean ( 4 / 24 )98.07347222222220.224215739756832437.406724115735
Winsorized Mean ( 5 / 24 )98.07902777777780.22331136109789439.203036046089
Winsorized Mean ( 6 / 24 )98.09819444444450.219280310812554447.364353329018
Winsorized Mean ( 7 / 24 )98.10694444444440.218007824486012450.015703224171
Winsorized Mean ( 8 / 24 )98.11472222222220.216564437079949453.050941997467
Winsorized Mean ( 9 / 24 )98.10847222222220.215519957548735455.217573992131
Winsorized Mean ( 10 / 24 )98.10430555555550.214830320858413456.659493704394
Winsorized Mean ( 11 / 24 )98.10736111111110.214404039281159457.581682882653
Winsorized Mean ( 12 / 24 )98.10236111111110.213581272171052459.320988745415
Winsorized Mean ( 13 / 24 )98.08972222222220.211521887958141463.733201178847
Winsorized Mean ( 14 / 24 )98.08388888888890.21058051474614465.778559840312
Winsorized Mean ( 15 / 24 )98.05055555555560.203434409658768481.976258195558
Winsorized Mean ( 16 / 24 )98.02611111111110.198359622232501494.183796116596
Winsorized Mean ( 17 / 24 )98.00486111111110.192404885049486509.367842120559
Winsorized Mean ( 18 / 24 )98.02236111111110.18995711288639516.023641450775
Winsorized Mean ( 19 / 24 )98.00652777777780.187599755385619522.423537153986
Winsorized Mean ( 20 / 24 )98.01208333333340.182847514386208536.031805859354
Winsorized Mean ( 21 / 24 )97.81958333333330.150289423115244650.874700998245
Winsorized Mean ( 22 / 24 )97.77680555555560.14402956605992678.866209420349
Winsorized Mean ( 23 / 24 )97.82152777777780.137637491327277710.718619138268
Winsorized Mean ( 24 / 24 )97.81486111111110.136801432617425715.013426684335
Trimmed Mean ( 1 / 24 )98.07814285714290.227334021800972431.427474339979
Trimmed Mean ( 2 / 24 )98.07632352941180.225292893395216435.328083595442
Trimmed Mean ( 3 / 24 )98.07121212121210.223986192043567437.844901180946
Trimmed Mean ( 4 / 24 )98.070156250.223166970307626439.447451004128
Trimmed Mean ( 5 / 24 )98.06919354838710.222219501965481441.316773194916
Trimmed Mean ( 6 / 24 )98.06683333333330.221146408500041443.447551323516
Trimmed Mean ( 7 / 24 )98.06034482758620.220678567098947444.358263317969
Trimmed Mean ( 8 / 24 )98.05178571428570.22014149923311445.403461209546
Trimmed Mean ( 9 / 24 )98.04129629629630.219515228288324446.626400640976
Trimmed Mean ( 10 / 24 )98.03096153846150.218670268316258448.304940096756
Trimmed Mean ( 11 / 24 )98.02040.217456157439065450.7593675634
Trimmed Mean ( 12 / 24 )98.00854166666670.215702708956111454.368617533721
Trimmed Mean ( 13 / 24 )97.99630434782610.213348133249233459.325811083366
Trimmed Mean ( 14 / 24 )97.98454545454550.210482043783629465.524486997435
Trimmed Mean ( 15 / 24 )97.9723809523810.206681317956123474.026302528125
Trimmed Mean ( 16 / 24 )97.9630.203062829736298482.427040572698
Trimmed Mean ( 17 / 24 )97.95552631578950.199135649088856491.903517848182
Trimmed Mean ( 18 / 24 )97.94972222222220.194958475884543502.413253785536
Trimmed Mean ( 19 / 24 )97.94117647058820.189474253706006516.910211044065
Trimmed Mean ( 20 / 24 )97.93343750.182150355174293537.651641723626
Trimmed Mean ( 21 / 24 )97.9240.172834782578524566.575769871498
Trimmed Mean ( 22 / 24 )97.93678571428570.169366274113993578.254355695212
Trimmed Mean ( 23 / 24 )97.95692307692310.165282759332437592.662679837647
Trimmed Mean ( 24 / 24 )97.97458333333330.160691417263417609.706386326323
Median97.79
Midrange98.105
Midmean - Weighted Average at Xnp97.9555263157895
Midmean - Weighted Average at X(n+1)p98.0062162162162
Midmean - Empirical Distribution Function97.9555263157895
Midmean - Empirical Distribution Function - Averaging98.0062162162162
Midmean - Empirical Distribution Function - Interpolation98.0062162162162
Midmean - Closest Observation97.9555263157895
Midmean - True Basic - Statistics Graphics Toolkit98.0062162162162
Midmean - MS Excel (old versions)97.9555263157895
Number of observations72



Parameters (Session):
par1 = grey ;
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')