Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 07 Mar 2016 10:07:16 +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/2016/Mar/07/t1457345254tnirm0vvarkq32n.htm/, Retrieved Wed, 01 May 2024 07:57:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293570, Retrieved Wed, 01 May 2024 07:57:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-07 10:07:16] [e1772292a6a44abe5991636299c33e7e] [Current]
Feedback Forum

Post a new message
Dataseries X:
92,8
92,9
93,06
93,28
93,41
93,49
93,49
93,5
93,56
94,12
94,3
94,36
94,36
94,5
94,85
95,16
95,73
95,76
95,76
95,81
96,09
96,48
96,71
96,69
96,69
96,66
96,73
96,84
97,87
98
97,98
98,03
98,11
98,18
98,32
98,34
98,28
98,52
98,56
99,6
100,16
100,46
100,46
100,68
100,83
100,64
100,9
100,92
100,75
100,96
101,05
101,33
101,38
101,44
101,51
101,4
101,26
100,83
100,75
100,81
100,82
100,85
100,79
100,84
101,04
101,11
101,15
101,11
101,28
101,62
102,07
102,14




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293570&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293570&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293570&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 time1 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean98.19750.34972276914467280.786693529178
Geometric Mean98.1529042053958
Harmonic Mean98.1079438412916
Quadratic Mean98.2417056719463
Winsorized Mean ( 1 / 24 )98.19791666666670.349270362738048281.151586687345
Winsorized Mean ( 2 / 24 )98.18986111111110.346484383112468283.388994993286
Winsorized Mean ( 3 / 24 )98.19444444444440.343975531443677285.469271701737
Winsorized Mean ( 4 / 24 )98.19777777777780.342013234411487287.116894604239
Winsorized Mean ( 5 / 24 )98.20055555555560.340555153469065288.354337191012
Winsorized Mean ( 6 / 24 )98.19888888888890.340335179279063288.535816652586
Winsorized Mean ( 7 / 24 )98.1950.339509680511748289.2259208986
Winsorized Mean ( 8 / 24 )98.19611111111110.337496742901779290.954248230149
Winsorized Mean ( 9 / 24 )98.26361111111110.324089328763854303.199156497715
Winsorized Mean ( 10 / 24 )98.27333333333330.317666570602334309.360009606914
Winsorized Mean ( 11 / 24 )98.27638888888890.315280714621662311.710752770974
Winsorized Mean ( 12 / 24 )98.27638888888890.315280714621662311.710752770974
Winsorized Mean ( 13 / 24 )98.29083333333330.309523192681117317.555632849124
Winsorized Mean ( 14 / 24 )98.35694444444440.297759016456953330.323983517939
Winsorized Mean ( 15 / 24 )98.40486111111110.285112612148678345.14383762089
Winsorized Mean ( 16 / 24 )98.52263888888890.264382381309297372.652059494195
Winsorized Mean ( 17 / 24 )98.5250.262728326811024375.007145959055
Winsorized Mean ( 18 / 24 )98.51250.261144611692377377.233515796396
Winsorized Mean ( 19 / 24 )98.52305555555560.258858669157818380.605586345996
Winsorized Mean ( 20 / 24 )98.59805555555550.247205005027244398.851372546803
Winsorized Mean ( 21 / 24 )98.71180555555560.231336384820162426.70246460492
Winsorized Mean ( 22 / 24 )98.763750.223558365142518441.780605870141
Winsorized Mean ( 23 / 24 )98.77013888888890.221876819180142445.1575394575
Winsorized Mean ( 24 / 24 )98.76347222222220.221014710679064446.863794354562
Trimmed Mean ( 1 / 24 )98.21828571428570.346685516972085283.306572977475
Trimmed Mean ( 2 / 24 )98.23985294117650.343435331202955286.050513781067
Trimmed Mean ( 3 / 24 )98.26712121212120.341075001844932288.110007126227
Trimmed Mean ( 4 / 24 )98.2943750.339098132408272289.869998109144
Trimmed Mean ( 5 / 24 )98.32241935483870.337121975101669291.652359135553
Trimmed Mean ( 6 / 24 )98.35166666666670.334863929416271293.706362575723
Trimmed Mean ( 7 / 24 )98.3832758620690.331858174571165296.461812306424
Trimmed Mean ( 8 / 24 )98.41785714285710.328066325481078299.993780216658
Trimmed Mean ( 9 / 24 )98.45481481481480.323561347420279304.284846134388
Trimmed Mean ( 10 / 24 )98.48423076923080.320799616784761306.996098549919
Trimmed Mean ( 11 / 24 )98.51460.318326902951757309.476199110102
Trimmed Mean ( 12 / 24 )98.54708333333330.315256278492343312.593562940657
Trimmed Mean ( 13 / 24 )98.58239130434780.310880343382629317.107187388215
Trimmed Mean ( 14 / 24 )98.61909090909090.306073271600004322.207458343414
Trimmed Mean ( 15 / 24 )98.65119047619050.302077630064651326.575623805963
Trimmed Mean ( 16 / 24 )98.680750.299122731757127329.900537549664
Trimmed Mean ( 17 / 24 )98.69947368421050.299175716187406329.904695949267
Trimmed Mean ( 18 / 24 )98.720.298604691699179330.604316490287
Trimmed Mean ( 19 / 24 )98.74441176470590.297087523542553332.374818663707
Trimmed Mean ( 20 / 24 )98.7706250.294445534663143335.446163627502
Trimmed Mean ( 21 / 24 )98.79133333333330.292757297516291337.4513092294
Trimmed Mean ( 22 / 24 )98.80107142857140.293365501160844336.784901556648
Trimmed Mean ( 23 / 24 )98.80576923076920.294574098332294335.419067019638
Trimmed Mean ( 24 / 24 )98.81041666666670.294604548976722335.400172909326
Median98.33
Midrange97.47
Midmean - Weighted Average at Xnp98.64
Midmean - Weighted Average at X(n+1)p98.64
Midmean - Empirical Distribution Function98.64
Midmean - Empirical Distribution Function - Averaging98.64
Midmean - Empirical Distribution Function - Interpolation98.64
Midmean - Closest Observation98.64
Midmean - True Basic - Statistics Graphics Toolkit98.64
Midmean - MS Excel (old versions)98.6994736842105
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 98.1975 & 0.34972276914467 & 280.786693529178 \tabularnewline
Geometric Mean & 98.1529042053958 &  &  \tabularnewline
Harmonic Mean & 98.1079438412916 &  &  \tabularnewline
Quadratic Mean & 98.2417056719463 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 98.1979166666667 & 0.349270362738048 & 281.151586687345 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 98.1898611111111 & 0.346484383112468 & 283.388994993286 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 98.1944444444444 & 0.343975531443677 & 285.469271701737 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 98.1977777777778 & 0.342013234411487 & 287.116894604239 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 98.2005555555556 & 0.340555153469065 & 288.354337191012 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 98.1988888888889 & 0.340335179279063 & 288.535816652586 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 98.195 & 0.339509680511748 & 289.2259208986 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 98.1961111111111 & 0.337496742901779 & 290.954248230149 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 98.2636111111111 & 0.324089328763854 & 303.199156497715 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 98.2733333333333 & 0.317666570602334 & 309.360009606914 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 98.2763888888889 & 0.315280714621662 & 311.710752770974 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 98.2763888888889 & 0.315280714621662 & 311.710752770974 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 98.2908333333333 & 0.309523192681117 & 317.555632849124 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 98.3569444444444 & 0.297759016456953 & 330.323983517939 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 98.4048611111111 & 0.285112612148678 & 345.14383762089 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 98.5226388888889 & 0.264382381309297 & 372.652059494195 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 98.525 & 0.262728326811024 & 375.007145959055 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 98.5125 & 0.261144611692377 & 377.233515796396 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 98.5230555555556 & 0.258858669157818 & 380.605586345996 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 98.5980555555555 & 0.247205005027244 & 398.851372546803 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 98.7118055555556 & 0.231336384820162 & 426.70246460492 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 98.76375 & 0.223558365142518 & 441.780605870141 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 98.7701388888889 & 0.221876819180142 & 445.1575394575 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 98.7634722222222 & 0.221014710679064 & 446.863794354562 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 98.2182857142857 & 0.346685516972085 & 283.306572977475 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 98.2398529411765 & 0.343435331202955 & 286.050513781067 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 98.2671212121212 & 0.341075001844932 & 288.110007126227 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 98.294375 & 0.339098132408272 & 289.869998109144 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 98.3224193548387 & 0.337121975101669 & 291.652359135553 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 98.3516666666667 & 0.334863929416271 & 293.706362575723 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 98.383275862069 & 0.331858174571165 & 296.461812306424 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 98.4178571428571 & 0.328066325481078 & 299.993780216658 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 98.4548148148148 & 0.323561347420279 & 304.284846134388 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 98.4842307692308 & 0.320799616784761 & 306.996098549919 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 98.5146 & 0.318326902951757 & 309.476199110102 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 98.5470833333333 & 0.315256278492343 & 312.593562940657 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 98.5823913043478 & 0.310880343382629 & 317.107187388215 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 98.6190909090909 & 0.306073271600004 & 322.207458343414 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 98.6511904761905 & 0.302077630064651 & 326.575623805963 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 98.68075 & 0.299122731757127 & 329.900537549664 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 98.6994736842105 & 0.299175716187406 & 329.904695949267 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 98.72 & 0.298604691699179 & 330.604316490287 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 98.7444117647059 & 0.297087523542553 & 332.374818663707 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 98.770625 & 0.294445534663143 & 335.446163627502 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 98.7913333333333 & 0.292757297516291 & 337.4513092294 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 98.8010714285714 & 0.293365501160844 & 336.784901556648 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 98.8057692307692 & 0.294574098332294 & 335.419067019638 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 98.8104166666667 & 0.294604548976722 & 335.400172909326 \tabularnewline
Median & 98.33 &  &  \tabularnewline
Midrange & 97.47 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 98.64 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 98.64 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 98.64 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 98.64 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 98.64 &  &  \tabularnewline
Midmean - Closest Observation & 98.64 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 98.64 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 98.6994736842105 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293570&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]98.1975[/C][C]0.34972276914467[/C][C]280.786693529178[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]98.1529042053958[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]98.1079438412916[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]98.2417056719463[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]98.1979166666667[/C][C]0.349270362738048[/C][C]281.151586687345[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]98.1898611111111[/C][C]0.346484383112468[/C][C]283.388994993286[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]98.1944444444444[/C][C]0.343975531443677[/C][C]285.469271701737[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]98.1977777777778[/C][C]0.342013234411487[/C][C]287.116894604239[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]98.2005555555556[/C][C]0.340555153469065[/C][C]288.354337191012[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]98.1988888888889[/C][C]0.340335179279063[/C][C]288.535816652586[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]98.195[/C][C]0.339509680511748[/C][C]289.2259208986[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]98.1961111111111[/C][C]0.337496742901779[/C][C]290.954248230149[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]98.2636111111111[/C][C]0.324089328763854[/C][C]303.199156497715[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]98.2733333333333[/C][C]0.317666570602334[/C][C]309.360009606914[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]98.2763888888889[/C][C]0.315280714621662[/C][C]311.710752770974[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]98.2763888888889[/C][C]0.315280714621662[/C][C]311.710752770974[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]98.2908333333333[/C][C]0.309523192681117[/C][C]317.555632849124[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]98.3569444444444[/C][C]0.297759016456953[/C][C]330.323983517939[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]98.4048611111111[/C][C]0.285112612148678[/C][C]345.14383762089[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]98.5226388888889[/C][C]0.264382381309297[/C][C]372.652059494195[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]98.525[/C][C]0.262728326811024[/C][C]375.007145959055[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]98.5125[/C][C]0.261144611692377[/C][C]377.233515796396[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]98.5230555555556[/C][C]0.258858669157818[/C][C]380.605586345996[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]98.5980555555555[/C][C]0.247205005027244[/C][C]398.851372546803[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]98.7118055555556[/C][C]0.231336384820162[/C][C]426.70246460492[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]98.76375[/C][C]0.223558365142518[/C][C]441.780605870141[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]98.7701388888889[/C][C]0.221876819180142[/C][C]445.1575394575[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]98.7634722222222[/C][C]0.221014710679064[/C][C]446.863794354562[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]98.2182857142857[/C][C]0.346685516972085[/C][C]283.306572977475[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]98.2398529411765[/C][C]0.343435331202955[/C][C]286.050513781067[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]98.2671212121212[/C][C]0.341075001844932[/C][C]288.110007126227[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]98.294375[/C][C]0.339098132408272[/C][C]289.869998109144[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]98.3224193548387[/C][C]0.337121975101669[/C][C]291.652359135553[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]98.3516666666667[/C][C]0.334863929416271[/C][C]293.706362575723[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]98.383275862069[/C][C]0.331858174571165[/C][C]296.461812306424[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]98.4178571428571[/C][C]0.328066325481078[/C][C]299.993780216658[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]98.4548148148148[/C][C]0.323561347420279[/C][C]304.284846134388[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]98.4842307692308[/C][C]0.320799616784761[/C][C]306.996098549919[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]98.5146[/C][C]0.318326902951757[/C][C]309.476199110102[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]98.5470833333333[/C][C]0.315256278492343[/C][C]312.593562940657[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]98.5823913043478[/C][C]0.310880343382629[/C][C]317.107187388215[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]98.6190909090909[/C][C]0.306073271600004[/C][C]322.207458343414[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]98.6511904761905[/C][C]0.302077630064651[/C][C]326.575623805963[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]98.68075[/C][C]0.299122731757127[/C][C]329.900537549664[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]98.6994736842105[/C][C]0.299175716187406[/C][C]329.904695949267[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]98.72[/C][C]0.298604691699179[/C][C]330.604316490287[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]98.7444117647059[/C][C]0.297087523542553[/C][C]332.374818663707[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]98.770625[/C][C]0.294445534663143[/C][C]335.446163627502[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]98.7913333333333[/C][C]0.292757297516291[/C][C]337.4513092294[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]98.8010714285714[/C][C]0.293365501160844[/C][C]336.784901556648[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]98.8057692307692[/C][C]0.294574098332294[/C][C]335.419067019638[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]98.8104166666667[/C][C]0.294604548976722[/C][C]335.400172909326[/C][/ROW]
[ROW][C]Median[/C][C]98.33[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]97.47[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]98.64[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]98.64[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]98.64[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]98.64[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]98.64[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]98.64[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]98.64[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]98.6994736842105[/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=293570&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293570&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 Mean98.19750.34972276914467280.786693529178
Geometric Mean98.1529042053958
Harmonic Mean98.1079438412916
Quadratic Mean98.2417056719463
Winsorized Mean ( 1 / 24 )98.19791666666670.349270362738048281.151586687345
Winsorized Mean ( 2 / 24 )98.18986111111110.346484383112468283.388994993286
Winsorized Mean ( 3 / 24 )98.19444444444440.343975531443677285.469271701737
Winsorized Mean ( 4 / 24 )98.19777777777780.342013234411487287.116894604239
Winsorized Mean ( 5 / 24 )98.20055555555560.340555153469065288.354337191012
Winsorized Mean ( 6 / 24 )98.19888888888890.340335179279063288.535816652586
Winsorized Mean ( 7 / 24 )98.1950.339509680511748289.2259208986
Winsorized Mean ( 8 / 24 )98.19611111111110.337496742901779290.954248230149
Winsorized Mean ( 9 / 24 )98.26361111111110.324089328763854303.199156497715
Winsorized Mean ( 10 / 24 )98.27333333333330.317666570602334309.360009606914
Winsorized Mean ( 11 / 24 )98.27638888888890.315280714621662311.710752770974
Winsorized Mean ( 12 / 24 )98.27638888888890.315280714621662311.710752770974
Winsorized Mean ( 13 / 24 )98.29083333333330.309523192681117317.555632849124
Winsorized Mean ( 14 / 24 )98.35694444444440.297759016456953330.323983517939
Winsorized Mean ( 15 / 24 )98.40486111111110.285112612148678345.14383762089
Winsorized Mean ( 16 / 24 )98.52263888888890.264382381309297372.652059494195
Winsorized Mean ( 17 / 24 )98.5250.262728326811024375.007145959055
Winsorized Mean ( 18 / 24 )98.51250.261144611692377377.233515796396
Winsorized Mean ( 19 / 24 )98.52305555555560.258858669157818380.605586345996
Winsorized Mean ( 20 / 24 )98.59805555555550.247205005027244398.851372546803
Winsorized Mean ( 21 / 24 )98.71180555555560.231336384820162426.70246460492
Winsorized Mean ( 22 / 24 )98.763750.223558365142518441.780605870141
Winsorized Mean ( 23 / 24 )98.77013888888890.221876819180142445.1575394575
Winsorized Mean ( 24 / 24 )98.76347222222220.221014710679064446.863794354562
Trimmed Mean ( 1 / 24 )98.21828571428570.346685516972085283.306572977475
Trimmed Mean ( 2 / 24 )98.23985294117650.343435331202955286.050513781067
Trimmed Mean ( 3 / 24 )98.26712121212120.341075001844932288.110007126227
Trimmed Mean ( 4 / 24 )98.2943750.339098132408272289.869998109144
Trimmed Mean ( 5 / 24 )98.32241935483870.337121975101669291.652359135553
Trimmed Mean ( 6 / 24 )98.35166666666670.334863929416271293.706362575723
Trimmed Mean ( 7 / 24 )98.3832758620690.331858174571165296.461812306424
Trimmed Mean ( 8 / 24 )98.41785714285710.328066325481078299.993780216658
Trimmed Mean ( 9 / 24 )98.45481481481480.323561347420279304.284846134388
Trimmed Mean ( 10 / 24 )98.48423076923080.320799616784761306.996098549919
Trimmed Mean ( 11 / 24 )98.51460.318326902951757309.476199110102
Trimmed Mean ( 12 / 24 )98.54708333333330.315256278492343312.593562940657
Trimmed Mean ( 13 / 24 )98.58239130434780.310880343382629317.107187388215
Trimmed Mean ( 14 / 24 )98.61909090909090.306073271600004322.207458343414
Trimmed Mean ( 15 / 24 )98.65119047619050.302077630064651326.575623805963
Trimmed Mean ( 16 / 24 )98.680750.299122731757127329.900537549664
Trimmed Mean ( 17 / 24 )98.69947368421050.299175716187406329.904695949267
Trimmed Mean ( 18 / 24 )98.720.298604691699179330.604316490287
Trimmed Mean ( 19 / 24 )98.74441176470590.297087523542553332.374818663707
Trimmed Mean ( 20 / 24 )98.7706250.294445534663143335.446163627502
Trimmed Mean ( 21 / 24 )98.79133333333330.292757297516291337.4513092294
Trimmed Mean ( 22 / 24 )98.80107142857140.293365501160844336.784901556648
Trimmed Mean ( 23 / 24 )98.80576923076920.294574098332294335.419067019638
Trimmed Mean ( 24 / 24 )98.81041666666670.294604548976722335.400172909326
Median98.33
Midrange97.47
Midmean - Weighted Average at Xnp98.64
Midmean - Weighted Average at X(n+1)p98.64
Midmean - Empirical Distribution Function98.64
Midmean - Empirical Distribution Function - Averaging98.64
Midmean - Empirical Distribution Function - Interpolation98.64
Midmean - Closest Observation98.64
Midmean - True Basic - Statistics Graphics Toolkit98.64
Midmean - MS Excel (old versions)98.6994736842105
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')