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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 computationMon, 07 Mar 2016 20:26:16 +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/t14573824162cufk4zj7cneh1q.htm/, Retrieved Tue, 30 Apr 2024 23:39:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293619, Retrieved Tue, 30 Apr 2024 23:39:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-07 20:26:16] [809417a83781bff5791db815734e4daf] [Current]
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Dataseries X:
90,18
90,5
90,63
90,75
90,76
90,67
90,5
90,8
91,22
92,19
92,51
92,67
93,75
94,1
94,96
95,21
95,33
95,43
95,44
95,64
95,8
95,87
95,98
96,07
96,23
96,32
96,55
96,73
96,61
96,64
96,86
97,02
97,22
98,1
98,46
98,6
98,78
99,13
99,48
99,62
99,68
99,95
100,12
100,25
100,47
100,7
100,88
100,95
100,92
101,12
101,19
101,28
101,28
101,3
101,3
101,36
101,45
101,58
101,73
101,84
102,01
102,14
102,16
102,32
102,41
102,4
102,43
102,42
102,3
102,65
102,72
102,86




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293619&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293619&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293619&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean97.88166666666670.46573964766307210.163912730653
Geometric Mean97.8017476527816
Harmonic Mean97.7206059167914
Quadratic Mean97.960305849983
Winsorized Mean ( 1 / 24 )97.88416666666670.464435467215993210.759456536389
Winsorized Mean ( 2 / 24 )97.88222222222220.464152230969724210.883877510883
Winsorized Mean ( 3 / 24 )97.87847222222220.461646948771403212.020186600842
Winsorized Mean ( 4 / 24 )97.88013888888890.461079417229596212.284771844737
Winsorized Mean ( 5 / 24 )97.8850.459764177151232212.902624572689
Winsorized Mean ( 6 / 24 )97.8850.459466673887395213.040478369906
Winsorized Mean ( 7 / 24 )97.88111111111110.457548519518358213.925096324531
Winsorized Mean ( 8 / 24 )97.92555555555550.447228287558866218.961005552821
Winsorized Mean ( 9 / 24 )98.02930555555560.420111130240921233.341367317116
Winsorized Mean ( 10 / 24 )98.07097222222220.411140164336831238.534156302658
Winsorized Mean ( 11 / 24 )98.07555555555560.403759518019804242.905866433953
Winsorized Mean ( 12 / 24 )98.22722222222220.36736224155303267.385188545685
Winsorized Mean ( 13 / 24 )98.27055555555550.353948601129245277.64075134647
Winsorized Mean ( 14 / 24 )98.40861111111110.323435762873583304.260141911316
Winsorized Mean ( 15 / 24 )98.43361111111110.312018913291779315.47321946815
Winsorized Mean ( 16 / 24 )98.44027777777780.305458234252318322.270827037071
Winsorized Mean ( 17 / 24 )98.44972222222220.3001914472741327.956452844339
Winsorized Mean ( 18 / 24 )98.45222222222220.299837476987956328.351956570715
Winsorized Mean ( 19 / 24 )98.49972222222220.291752031251753337.614520795665
Winsorized Mean ( 20 / 24 )98.54416666666670.285676978547428344.949625159615
Winsorized Mean ( 21 / 24 )98.53833333333330.279397686627224352.681278513248
Winsorized Mean ( 22 / 24 )98.55055555555560.272048026409445362.254256559951
Winsorized Mean ( 23 / 24 )98.5250.261065215891273377.39612174543
Winsorized Mean ( 24 / 24 )98.56833333333330.252748196862439389.986296863594
Trimmed Mean ( 1 / 24 )97.92057142857140.460591027535876212.59765296002
Trimmed Mean ( 2 / 24 )97.95911764705880.455783136559673214.924839884315
Trimmed Mean ( 3 / 24 )98.00106060606060.449992651003855217.78369132793
Trimmed Mean ( 4 / 24 )98.047031250.443933238474654220.859856285796
Trimmed Mean ( 5 / 24 )98.09548387096770.436600351122976224.680267935326
Trimmed Mean ( 6 / 24 )98.1460.427910453170057229.361071394523
Trimmed Mean ( 7 / 24 )98.20.417182886512077235.38837084382
Trimmed Mean ( 8 / 24 )98.25857142857140.404301098784884243.033154557049
Trimmed Mean ( 9 / 24 )98.31407407407410.390941231794342251.480442783771
Trimmed Mean ( 10 / 24 )98.35788461538460.381025580442598258.139845889435
Trimmed Mean ( 11 / 24 )98.39920.370565573254765265.537888843091
Trimmed Mean ( 12 / 24 )98.44333333333330.358827426138818274.347293886195
Trimmed Mean ( 13 / 24 )98.47152173913040.352269929357581279.534281903394
Trimmed Mean ( 14 / 24 )98.49681818181820.34647023685163284.286520761083
Trimmed Mean ( 15 / 24 )98.5076190476190.345115882089087285.433456296835
Trimmed Mean ( 16 / 24 )98.51650.344892876345462285.643765808955
Trimmed Mean ( 17 / 24 )98.52552631578950.34497133230068285.604967980104
Trimmed Mean ( 18 / 24 )98.53444444444440.345077043259665285.54331958356
Trimmed Mean ( 19 / 24 )98.54411764705880.344049782299031286.424008143709
Trimmed Mean ( 20 / 24 )98.5493750.343269954398491287.090011045934
Trimmed Mean ( 21 / 24 )98.550.34219742906657287.991643504804
Trimmed Mean ( 22 / 24 )98.55142857142860.340642372586723289.310539446582
Trimmed Mean ( 23 / 24 )98.55153846153850.33858151719635291.07182009698
Trimmed Mean ( 24 / 24 )98.5550.336766917202001292.650480097142
Median98.69
Midrange96.52
Midmean - Weighted Average at Xnp98.5255263157895
Midmean - Weighted Average at X(n+1)p98.6091891891892
Midmean - Empirical Distribution Function98.5255263157895
Midmean - Empirical Distribution Function - Averaging98.6091891891892
Midmean - Empirical Distribution Function - Interpolation98.6091891891892
Midmean - Closest Observation98.5255263157895
Midmean - True Basic - Statistics Graphics Toolkit98.6091891891892
Midmean - MS Excel (old versions)98.5255263157895
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 97.8816666666667 & 0.46573964766307 & 210.163912730653 \tabularnewline
Geometric Mean & 97.8017476527816 &  &  \tabularnewline
Harmonic Mean & 97.7206059167914 &  &  \tabularnewline
Quadratic Mean & 97.960305849983 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 97.8841666666667 & 0.464435467215993 & 210.759456536389 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 97.8822222222222 & 0.464152230969724 & 210.883877510883 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 97.8784722222222 & 0.461646948771403 & 212.020186600842 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 97.8801388888889 & 0.461079417229596 & 212.284771844737 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 97.885 & 0.459764177151232 & 212.902624572689 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 97.885 & 0.459466673887395 & 213.040478369906 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 97.8811111111111 & 0.457548519518358 & 213.925096324531 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 97.9255555555555 & 0.447228287558866 & 218.961005552821 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 98.0293055555556 & 0.420111130240921 & 233.341367317116 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 98.0709722222222 & 0.411140164336831 & 238.534156302658 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 98.0755555555556 & 0.403759518019804 & 242.905866433953 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 98.2272222222222 & 0.36736224155303 & 267.385188545685 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 98.2705555555555 & 0.353948601129245 & 277.64075134647 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 98.4086111111111 & 0.323435762873583 & 304.260141911316 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 98.4336111111111 & 0.312018913291779 & 315.47321946815 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 98.4402777777778 & 0.305458234252318 & 322.270827037071 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 98.4497222222222 & 0.3001914472741 & 327.956452844339 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 98.4522222222222 & 0.299837476987956 & 328.351956570715 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 98.4997222222222 & 0.291752031251753 & 337.614520795665 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 98.5441666666667 & 0.285676978547428 & 344.949625159615 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 98.5383333333333 & 0.279397686627224 & 352.681278513248 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 98.5505555555556 & 0.272048026409445 & 362.254256559951 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 98.525 & 0.261065215891273 & 377.39612174543 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 98.5683333333333 & 0.252748196862439 & 389.986296863594 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 97.9205714285714 & 0.460591027535876 & 212.59765296002 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 97.9591176470588 & 0.455783136559673 & 214.924839884315 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 98.0010606060606 & 0.449992651003855 & 217.78369132793 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 98.04703125 & 0.443933238474654 & 220.859856285796 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 98.0954838709677 & 0.436600351122976 & 224.680267935326 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 98.146 & 0.427910453170057 & 229.361071394523 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 98.2 & 0.417182886512077 & 235.38837084382 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 98.2585714285714 & 0.404301098784884 & 243.033154557049 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 98.3140740740741 & 0.390941231794342 & 251.480442783771 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 98.3578846153846 & 0.381025580442598 & 258.139845889435 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 98.3992 & 0.370565573254765 & 265.537888843091 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 98.4433333333333 & 0.358827426138818 & 274.347293886195 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 98.4715217391304 & 0.352269929357581 & 279.534281903394 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 98.4968181818182 & 0.34647023685163 & 284.286520761083 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 98.507619047619 & 0.345115882089087 & 285.433456296835 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 98.5165 & 0.344892876345462 & 285.643765808955 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 98.5255263157895 & 0.34497133230068 & 285.604967980104 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 98.5344444444444 & 0.345077043259665 & 285.54331958356 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 98.5441176470588 & 0.344049782299031 & 286.424008143709 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 98.549375 & 0.343269954398491 & 287.090011045934 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 98.55 & 0.34219742906657 & 287.991643504804 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 98.5514285714286 & 0.340642372586723 & 289.310539446582 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 98.5515384615385 & 0.33858151719635 & 291.07182009698 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 98.555 & 0.336766917202001 & 292.650480097142 \tabularnewline
Median & 98.69 &  &  \tabularnewline
Midrange & 96.52 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 98.5255263157895 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 98.6091891891892 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 98.5255263157895 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 98.6091891891892 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 98.6091891891892 &  &  \tabularnewline
Midmean - Closest Observation & 98.5255263157895 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 98.6091891891892 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 98.5255263157895 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293619&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]97.8816666666667[/C][C]0.46573964766307[/C][C]210.163912730653[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]97.8017476527816[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]97.7206059167914[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]97.960305849983[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]97.8841666666667[/C][C]0.464435467215993[/C][C]210.759456536389[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]97.8822222222222[/C][C]0.464152230969724[/C][C]210.883877510883[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]97.8784722222222[/C][C]0.461646948771403[/C][C]212.020186600842[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]97.8801388888889[/C][C]0.461079417229596[/C][C]212.284771844737[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]97.885[/C][C]0.459764177151232[/C][C]212.902624572689[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]97.885[/C][C]0.459466673887395[/C][C]213.040478369906[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]97.8811111111111[/C][C]0.457548519518358[/C][C]213.925096324531[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]97.9255555555555[/C][C]0.447228287558866[/C][C]218.961005552821[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]98.0293055555556[/C][C]0.420111130240921[/C][C]233.341367317116[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]98.0709722222222[/C][C]0.411140164336831[/C][C]238.534156302658[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]98.0755555555556[/C][C]0.403759518019804[/C][C]242.905866433953[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]98.2272222222222[/C][C]0.36736224155303[/C][C]267.385188545685[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]98.2705555555555[/C][C]0.353948601129245[/C][C]277.64075134647[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]98.4086111111111[/C][C]0.323435762873583[/C][C]304.260141911316[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]98.4336111111111[/C][C]0.312018913291779[/C][C]315.47321946815[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]98.4402777777778[/C][C]0.305458234252318[/C][C]322.270827037071[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]98.4497222222222[/C][C]0.3001914472741[/C][C]327.956452844339[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]98.4522222222222[/C][C]0.299837476987956[/C][C]328.351956570715[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]98.4997222222222[/C][C]0.291752031251753[/C][C]337.614520795665[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]98.5441666666667[/C][C]0.285676978547428[/C][C]344.949625159615[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]98.5383333333333[/C][C]0.279397686627224[/C][C]352.681278513248[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]98.5505555555556[/C][C]0.272048026409445[/C][C]362.254256559951[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]98.525[/C][C]0.261065215891273[/C][C]377.39612174543[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]98.5683333333333[/C][C]0.252748196862439[/C][C]389.986296863594[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]97.9205714285714[/C][C]0.460591027535876[/C][C]212.59765296002[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]97.9591176470588[/C][C]0.455783136559673[/C][C]214.924839884315[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]98.0010606060606[/C][C]0.449992651003855[/C][C]217.78369132793[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]98.04703125[/C][C]0.443933238474654[/C][C]220.859856285796[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]98.0954838709677[/C][C]0.436600351122976[/C][C]224.680267935326[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]98.146[/C][C]0.427910453170057[/C][C]229.361071394523[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]98.2[/C][C]0.417182886512077[/C][C]235.38837084382[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]98.2585714285714[/C][C]0.404301098784884[/C][C]243.033154557049[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]98.3140740740741[/C][C]0.390941231794342[/C][C]251.480442783771[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]98.3578846153846[/C][C]0.381025580442598[/C][C]258.139845889435[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]98.3992[/C][C]0.370565573254765[/C][C]265.537888843091[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]98.4433333333333[/C][C]0.358827426138818[/C][C]274.347293886195[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]98.4715217391304[/C][C]0.352269929357581[/C][C]279.534281903394[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]98.4968181818182[/C][C]0.34647023685163[/C][C]284.286520761083[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]98.507619047619[/C][C]0.345115882089087[/C][C]285.433456296835[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]98.5165[/C][C]0.344892876345462[/C][C]285.643765808955[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]98.5255263157895[/C][C]0.34497133230068[/C][C]285.604967980104[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]98.5344444444444[/C][C]0.345077043259665[/C][C]285.54331958356[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]98.5441176470588[/C][C]0.344049782299031[/C][C]286.424008143709[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]98.549375[/C][C]0.343269954398491[/C][C]287.090011045934[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]98.55[/C][C]0.34219742906657[/C][C]287.991643504804[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]98.5514285714286[/C][C]0.340642372586723[/C][C]289.310539446582[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]98.5515384615385[/C][C]0.33858151719635[/C][C]291.07182009698[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]98.555[/C][C]0.336766917202001[/C][C]292.650480097142[/C][/ROW]
[ROW][C]Median[/C][C]98.69[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]96.52[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]98.5255263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]98.6091891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]98.5255263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]98.6091891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]98.6091891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]98.5255263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]98.6091891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]98.5255263157895[/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=293619&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293619&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 Mean97.88166666666670.46573964766307210.163912730653
Geometric Mean97.8017476527816
Harmonic Mean97.7206059167914
Quadratic Mean97.960305849983
Winsorized Mean ( 1 / 24 )97.88416666666670.464435467215993210.759456536389
Winsorized Mean ( 2 / 24 )97.88222222222220.464152230969724210.883877510883
Winsorized Mean ( 3 / 24 )97.87847222222220.461646948771403212.020186600842
Winsorized Mean ( 4 / 24 )97.88013888888890.461079417229596212.284771844737
Winsorized Mean ( 5 / 24 )97.8850.459764177151232212.902624572689
Winsorized Mean ( 6 / 24 )97.8850.459466673887395213.040478369906
Winsorized Mean ( 7 / 24 )97.88111111111110.457548519518358213.925096324531
Winsorized Mean ( 8 / 24 )97.92555555555550.447228287558866218.961005552821
Winsorized Mean ( 9 / 24 )98.02930555555560.420111130240921233.341367317116
Winsorized Mean ( 10 / 24 )98.07097222222220.411140164336831238.534156302658
Winsorized Mean ( 11 / 24 )98.07555555555560.403759518019804242.905866433953
Winsorized Mean ( 12 / 24 )98.22722222222220.36736224155303267.385188545685
Winsorized Mean ( 13 / 24 )98.27055555555550.353948601129245277.64075134647
Winsorized Mean ( 14 / 24 )98.40861111111110.323435762873583304.260141911316
Winsorized Mean ( 15 / 24 )98.43361111111110.312018913291779315.47321946815
Winsorized Mean ( 16 / 24 )98.44027777777780.305458234252318322.270827037071
Winsorized Mean ( 17 / 24 )98.44972222222220.3001914472741327.956452844339
Winsorized Mean ( 18 / 24 )98.45222222222220.299837476987956328.351956570715
Winsorized Mean ( 19 / 24 )98.49972222222220.291752031251753337.614520795665
Winsorized Mean ( 20 / 24 )98.54416666666670.285676978547428344.949625159615
Winsorized Mean ( 21 / 24 )98.53833333333330.279397686627224352.681278513248
Winsorized Mean ( 22 / 24 )98.55055555555560.272048026409445362.254256559951
Winsorized Mean ( 23 / 24 )98.5250.261065215891273377.39612174543
Winsorized Mean ( 24 / 24 )98.56833333333330.252748196862439389.986296863594
Trimmed Mean ( 1 / 24 )97.92057142857140.460591027535876212.59765296002
Trimmed Mean ( 2 / 24 )97.95911764705880.455783136559673214.924839884315
Trimmed Mean ( 3 / 24 )98.00106060606060.449992651003855217.78369132793
Trimmed Mean ( 4 / 24 )98.047031250.443933238474654220.859856285796
Trimmed Mean ( 5 / 24 )98.09548387096770.436600351122976224.680267935326
Trimmed Mean ( 6 / 24 )98.1460.427910453170057229.361071394523
Trimmed Mean ( 7 / 24 )98.20.417182886512077235.38837084382
Trimmed Mean ( 8 / 24 )98.25857142857140.404301098784884243.033154557049
Trimmed Mean ( 9 / 24 )98.31407407407410.390941231794342251.480442783771
Trimmed Mean ( 10 / 24 )98.35788461538460.381025580442598258.139845889435
Trimmed Mean ( 11 / 24 )98.39920.370565573254765265.537888843091
Trimmed Mean ( 12 / 24 )98.44333333333330.358827426138818274.347293886195
Trimmed Mean ( 13 / 24 )98.47152173913040.352269929357581279.534281903394
Trimmed Mean ( 14 / 24 )98.49681818181820.34647023685163284.286520761083
Trimmed Mean ( 15 / 24 )98.5076190476190.345115882089087285.433456296835
Trimmed Mean ( 16 / 24 )98.51650.344892876345462285.643765808955
Trimmed Mean ( 17 / 24 )98.52552631578950.34497133230068285.604967980104
Trimmed Mean ( 18 / 24 )98.53444444444440.345077043259665285.54331958356
Trimmed Mean ( 19 / 24 )98.54411764705880.344049782299031286.424008143709
Trimmed Mean ( 20 / 24 )98.5493750.343269954398491287.090011045934
Trimmed Mean ( 21 / 24 )98.550.34219742906657287.991643504804
Trimmed Mean ( 22 / 24 )98.55142857142860.340642372586723289.310539446582
Trimmed Mean ( 23 / 24 )98.55153846153850.33858151719635291.07182009698
Trimmed Mean ( 24 / 24 )98.5550.336766917202001292.650480097142
Median98.69
Midrange96.52
Midmean - Weighted Average at Xnp98.5255263157895
Midmean - Weighted Average at X(n+1)p98.6091891891892
Midmean - Empirical Distribution Function98.5255263157895
Midmean - Empirical Distribution Function - Averaging98.6091891891892
Midmean - Empirical Distribution Function - Interpolation98.6091891891892
Midmean - Closest Observation98.5255263157895
Midmean - True Basic - Statistics Graphics Toolkit98.6091891891892
Midmean - MS Excel (old versions)98.5255263157895
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')