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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 15 Oct 2008 08:23:48 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/15/t1224080730f7nrogkrl5v1fqq.htm/, Retrieved Sun, 19 May 2024 14:56:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16285, Retrieved Sun, 19 May 2024 14:56:12 +0000
QR Codes:

Original text written by user:Tijdreeks 4 is het aantal maandelijkse inschrijvingen (x1000) van 2dehands wagens in Belgie
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact193
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Totaal aantal ins...] [2008-10-11 17:28:43] [819b576fab25b35cfda70f80599828ec]
-   P   [Univariate Data Series] [Tijdreeks 3 Insch...] [2008-10-15 13:55:32] [819b576fab25b35cfda70f80599828ec]
- RMPD      [Central Tendency] [Central tendency ...] [2008-10-15 14:23:48] [e08fee3874f3333d6b7a377a061b860d] [Current]
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Dataseries X:
54.281
63.654
68.918
58.686
67.074
60.183
54.326
54.085
53.564
60.873
53.398
45.164
59.672
56.298
62.361
56.930
62.954
62.431
52.528
54.060
53.093
52.695
52.333
41.747
58.576
57.851
63.721
63.384
61.141
59.231
63.472
49.214
55.816
61.713
48.664
45.351
57.888
54.091
59.098
58.962
55.433
60.403
60.721
48.440
57.981
60.258
47.312
46.980
54.846
56.824
67.744
62.849
54.691
65.461
53.724
54.560
57.722
55.458
48.490
46.362




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16285&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16285&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16285&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean56.59566666666670.77305352453053273.2105408885325
Geometric Mean56.2742435428588
Harmonic Mean55.942250131495
Quadratic Mean56.9063140503758
Winsorized Mean ( 1 / 20 )56.633050.75129028161274875.381049623628
Winsorized Mean ( 2 / 20 )56.616950.74422508875070176.0750354372499
Winsorized Mean ( 3 / 20 )56.586850.7134657209210479.3126401741487
Winsorized Mean ( 4 / 20 )56.512050.68089351666106682.9968983654319
Winsorized Mean ( 5 / 20 )56.53413333333330.6733985973293483.9534468256163
Winsorized Mean ( 6 / 20 )56.62873333333330.64488075097301487.8127207982102
Winsorized Mean ( 7 / 20 )56.62430.64178676664590788.2291485938995
Winsorized Mean ( 8 / 20 )56.59016666666670.62675524700012290.2906947130123
Winsorized Mean ( 9 / 20 )56.65691666666670.60661328781666593.3987398637234
Winsorized Mean ( 10 / 20 )57.10708333333330.496730258105268114.965984861005
Winsorized Mean ( 11 / 20 )57.130.488634664169713116.917615939252
Winsorized Mean ( 12 / 20 )57.03380.460362451653754123.888904916372
Winsorized Mean ( 13 / 20 )56.99610.425854176322747133.839476442762
Winsorized Mean ( 14 / 20 )57.00473333333330.404722444382341140.848954943257
Winsorized Mean ( 15 / 20 )57.00823333333330.392374794429002145.290253458543
Winsorized Mean ( 16 / 20 )56.96610.3726211665067152.879399026238
Winsorized Mean ( 17 / 20 )57.02021666666670.352407379418675161.801993933062
Winsorized Mean ( 18 / 20 )57.00521666666670.347845991711985163.880619656146
Winsorized Mean ( 19 / 20 )56.84530.323026108598296175.97741633538
Winsorized Mean ( 20 / 20 )56.76163333333330.292457111604523194.085324244362
Trimmed Mean ( 1 / 20 )56.6392241379310.72612487782687578.0020432675977
Trimmed Mean ( 2 / 20 )56.64583928571430.69509260654479581.4939459179296
Trimmed Mean ( 3 / 20 )56.66188888888890.66134660640182385.676539866392
Trimmed Mean ( 4 / 20 )56.690750.63466487152794689.3239133647305
Trimmed Mean ( 5 / 20 )56.744360.61423836678658692.3816600660432
Trimmed Mean ( 6 / 20 )56.79691666666670.59082537968918596.1314774537034
Trimmed Mean ( 7 / 20 )56.83347826086960.5702173835321599.6698450489543
Trimmed Mean ( 8 / 20 )56.87422727272730.544266703043553104.496980900513
Trimmed Mean ( 9 / 20 )56.92495238095240.514584345588924110.623171631472
Trimmed Mean ( 10 / 20 )56.9696250.481282718085289118.370394072418
Trimmed Mean ( 11 / 20 )56.94792105263160.469560459073018121.279208996974
Trimmed Mean ( 12 / 20 )56.92033333333330.455251746159147125.030455816056
Trimmed Mean ( 13 / 20 )56.90364705882350.443116967457932128.416764055025
Trimmed Mean ( 14 / 20 )56.89031250.435132753282065130.742427617537
Trimmed Mean ( 15 / 20 )56.87396666666670.428522893293495132.720952734989
Trimmed Mean ( 16 / 20 )56.85478571428570.420999504697339135.047155827794
Trimmed Mean ( 17 / 20 )56.83873076923080.414349416120082137.175843763608
Trimmed Mean ( 18 / 20 )56.81204166666670.408615754798373139.035367578276
Trimmed Mean ( 19 / 20 )56.78277272727270.398445925501813142.510612088100
Trimmed Mean ( 20 / 20 )56.77290.389843105418199145.630124557667
Median56.877
Midrange55.3325
Midmean - Weighted Average at Xnp56.7618387096774
Midmean - Weighted Average at X(n+1)p56.8739666666667
Midmean - Empirical Distribution Function56.7618387096774
Midmean - Empirical Distribution Function - Averaging56.8739666666667
Midmean - Empirical Distribution Function - Interpolation56.8739666666667
Midmean - Closest Observation56.7618387096774
Midmean - True Basic - Statistics Graphics Toolkit56.8739666666667
Midmean - MS Excel (old versions)56.8903125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 56.5956666666667 & 0.773053524530532 & 73.2105408885325 \tabularnewline
Geometric Mean & 56.2742435428588 &  &  \tabularnewline
Harmonic Mean & 55.942250131495 &  &  \tabularnewline
Quadratic Mean & 56.9063140503758 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 56.63305 & 0.751290281612748 & 75.381049623628 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 56.61695 & 0.744225088750701 & 76.0750354372499 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 56.58685 & 0.71346572092104 & 79.3126401741487 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 56.51205 & 0.680893516661066 & 82.9968983654319 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 56.5341333333333 & 0.67339859732934 & 83.9534468256163 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 56.6287333333333 & 0.644880750973014 & 87.8127207982102 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 56.6243 & 0.641786766645907 & 88.2291485938995 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 56.5901666666667 & 0.626755247000122 & 90.2906947130123 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 56.6569166666667 & 0.606613287816665 & 93.3987398637234 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 57.1070833333333 & 0.496730258105268 & 114.965984861005 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 57.13 & 0.488634664169713 & 116.917615939252 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 57.0338 & 0.460362451653754 & 123.888904916372 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 56.9961 & 0.425854176322747 & 133.839476442762 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 57.0047333333333 & 0.404722444382341 & 140.848954943257 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 57.0082333333333 & 0.392374794429002 & 145.290253458543 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 56.9661 & 0.3726211665067 & 152.879399026238 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 57.0202166666667 & 0.352407379418675 & 161.801993933062 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 57.0052166666667 & 0.347845991711985 & 163.880619656146 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 56.8453 & 0.323026108598296 & 175.97741633538 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 56.7616333333333 & 0.292457111604523 & 194.085324244362 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 56.639224137931 & 0.726124877826875 & 78.0020432675977 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 56.6458392857143 & 0.695092606544795 & 81.4939459179296 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 56.6618888888889 & 0.661346606401823 & 85.676539866392 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 56.69075 & 0.634664871527946 & 89.3239133647305 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 56.74436 & 0.614238366786586 & 92.3816600660432 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 56.7969166666667 & 0.590825379689185 & 96.1314774537034 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 56.8334782608696 & 0.57021738353215 & 99.6698450489543 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 56.8742272727273 & 0.544266703043553 & 104.496980900513 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 56.9249523809524 & 0.514584345588924 & 110.623171631472 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 56.969625 & 0.481282718085289 & 118.370394072418 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 56.9479210526316 & 0.469560459073018 & 121.279208996974 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 56.9203333333333 & 0.455251746159147 & 125.030455816056 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 56.9036470588235 & 0.443116967457932 & 128.416764055025 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 56.8903125 & 0.435132753282065 & 130.742427617537 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 56.8739666666667 & 0.428522893293495 & 132.720952734989 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 56.8547857142857 & 0.420999504697339 & 135.047155827794 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 56.8387307692308 & 0.414349416120082 & 137.175843763608 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 56.8120416666667 & 0.408615754798373 & 139.035367578276 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 56.7827727272727 & 0.398445925501813 & 142.510612088100 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 56.7729 & 0.389843105418199 & 145.630124557667 \tabularnewline
Median & 56.877 &  &  \tabularnewline
Midrange & 55.3325 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 56.7618387096774 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 56.8739666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 56.7618387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 56.8739666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 56.8739666666667 &  &  \tabularnewline
Midmean - Closest Observation & 56.7618387096774 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 56.8739666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 56.8903125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16285&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]56.5956666666667[/C][C]0.773053524530532[/C][C]73.2105408885325[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]56.2742435428588[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]55.942250131495[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]56.9063140503758[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]56.63305[/C][C]0.751290281612748[/C][C]75.381049623628[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]56.61695[/C][C]0.744225088750701[/C][C]76.0750354372499[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]56.58685[/C][C]0.71346572092104[/C][C]79.3126401741487[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]56.51205[/C][C]0.680893516661066[/C][C]82.9968983654319[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]56.5341333333333[/C][C]0.67339859732934[/C][C]83.9534468256163[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]56.6287333333333[/C][C]0.644880750973014[/C][C]87.8127207982102[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]56.6243[/C][C]0.641786766645907[/C][C]88.2291485938995[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]56.5901666666667[/C][C]0.626755247000122[/C][C]90.2906947130123[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]56.6569166666667[/C][C]0.606613287816665[/C][C]93.3987398637234[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]57.1070833333333[/C][C]0.496730258105268[/C][C]114.965984861005[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]57.13[/C][C]0.488634664169713[/C][C]116.917615939252[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]57.0338[/C][C]0.460362451653754[/C][C]123.888904916372[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]56.9961[/C][C]0.425854176322747[/C][C]133.839476442762[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]57.0047333333333[/C][C]0.404722444382341[/C][C]140.848954943257[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]57.0082333333333[/C][C]0.392374794429002[/C][C]145.290253458543[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]56.9661[/C][C]0.3726211665067[/C][C]152.879399026238[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]57.0202166666667[/C][C]0.352407379418675[/C][C]161.801993933062[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]57.0052166666667[/C][C]0.347845991711985[/C][C]163.880619656146[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]56.8453[/C][C]0.323026108598296[/C][C]175.97741633538[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]56.7616333333333[/C][C]0.292457111604523[/C][C]194.085324244362[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]56.639224137931[/C][C]0.726124877826875[/C][C]78.0020432675977[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]56.6458392857143[/C][C]0.695092606544795[/C][C]81.4939459179296[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]56.6618888888889[/C][C]0.661346606401823[/C][C]85.676539866392[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]56.69075[/C][C]0.634664871527946[/C][C]89.3239133647305[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]56.74436[/C][C]0.614238366786586[/C][C]92.3816600660432[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]56.7969166666667[/C][C]0.590825379689185[/C][C]96.1314774537034[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]56.8334782608696[/C][C]0.57021738353215[/C][C]99.6698450489543[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]56.8742272727273[/C][C]0.544266703043553[/C][C]104.496980900513[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]56.9249523809524[/C][C]0.514584345588924[/C][C]110.623171631472[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]56.969625[/C][C]0.481282718085289[/C][C]118.370394072418[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]56.9479210526316[/C][C]0.469560459073018[/C][C]121.279208996974[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]56.9203333333333[/C][C]0.455251746159147[/C][C]125.030455816056[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]56.9036470588235[/C][C]0.443116967457932[/C][C]128.416764055025[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]56.8903125[/C][C]0.435132753282065[/C][C]130.742427617537[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]56.8739666666667[/C][C]0.428522893293495[/C][C]132.720952734989[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]56.8547857142857[/C][C]0.420999504697339[/C][C]135.047155827794[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]56.8387307692308[/C][C]0.414349416120082[/C][C]137.175843763608[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]56.8120416666667[/C][C]0.408615754798373[/C][C]139.035367578276[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]56.7827727272727[/C][C]0.398445925501813[/C][C]142.510612088100[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]56.7729[/C][C]0.389843105418199[/C][C]145.630124557667[/C][/ROW]
[ROW][C]Median[/C][C]56.877[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]55.3325[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]56.7618387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]56.8739666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]56.7618387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]56.8739666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]56.8739666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]56.7618387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]56.8739666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]56.8903125[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16285&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16285&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 Mean56.59566666666670.77305352453053273.2105408885325
Geometric Mean56.2742435428588
Harmonic Mean55.942250131495
Quadratic Mean56.9063140503758
Winsorized Mean ( 1 / 20 )56.633050.75129028161274875.381049623628
Winsorized Mean ( 2 / 20 )56.616950.74422508875070176.0750354372499
Winsorized Mean ( 3 / 20 )56.586850.7134657209210479.3126401741487
Winsorized Mean ( 4 / 20 )56.512050.68089351666106682.9968983654319
Winsorized Mean ( 5 / 20 )56.53413333333330.6733985973293483.9534468256163
Winsorized Mean ( 6 / 20 )56.62873333333330.64488075097301487.8127207982102
Winsorized Mean ( 7 / 20 )56.62430.64178676664590788.2291485938995
Winsorized Mean ( 8 / 20 )56.59016666666670.62675524700012290.2906947130123
Winsorized Mean ( 9 / 20 )56.65691666666670.60661328781666593.3987398637234
Winsorized Mean ( 10 / 20 )57.10708333333330.496730258105268114.965984861005
Winsorized Mean ( 11 / 20 )57.130.488634664169713116.917615939252
Winsorized Mean ( 12 / 20 )57.03380.460362451653754123.888904916372
Winsorized Mean ( 13 / 20 )56.99610.425854176322747133.839476442762
Winsorized Mean ( 14 / 20 )57.00473333333330.404722444382341140.848954943257
Winsorized Mean ( 15 / 20 )57.00823333333330.392374794429002145.290253458543
Winsorized Mean ( 16 / 20 )56.96610.3726211665067152.879399026238
Winsorized Mean ( 17 / 20 )57.02021666666670.352407379418675161.801993933062
Winsorized Mean ( 18 / 20 )57.00521666666670.347845991711985163.880619656146
Winsorized Mean ( 19 / 20 )56.84530.323026108598296175.97741633538
Winsorized Mean ( 20 / 20 )56.76163333333330.292457111604523194.085324244362
Trimmed Mean ( 1 / 20 )56.6392241379310.72612487782687578.0020432675977
Trimmed Mean ( 2 / 20 )56.64583928571430.69509260654479581.4939459179296
Trimmed Mean ( 3 / 20 )56.66188888888890.66134660640182385.676539866392
Trimmed Mean ( 4 / 20 )56.690750.63466487152794689.3239133647305
Trimmed Mean ( 5 / 20 )56.744360.61423836678658692.3816600660432
Trimmed Mean ( 6 / 20 )56.79691666666670.59082537968918596.1314774537034
Trimmed Mean ( 7 / 20 )56.83347826086960.5702173835321599.6698450489543
Trimmed Mean ( 8 / 20 )56.87422727272730.544266703043553104.496980900513
Trimmed Mean ( 9 / 20 )56.92495238095240.514584345588924110.623171631472
Trimmed Mean ( 10 / 20 )56.9696250.481282718085289118.370394072418
Trimmed Mean ( 11 / 20 )56.94792105263160.469560459073018121.279208996974
Trimmed Mean ( 12 / 20 )56.92033333333330.455251746159147125.030455816056
Trimmed Mean ( 13 / 20 )56.90364705882350.443116967457932128.416764055025
Trimmed Mean ( 14 / 20 )56.89031250.435132753282065130.742427617537
Trimmed Mean ( 15 / 20 )56.87396666666670.428522893293495132.720952734989
Trimmed Mean ( 16 / 20 )56.85478571428570.420999504697339135.047155827794
Trimmed Mean ( 17 / 20 )56.83873076923080.414349416120082137.175843763608
Trimmed Mean ( 18 / 20 )56.81204166666670.408615754798373139.035367578276
Trimmed Mean ( 19 / 20 )56.78277272727270.398445925501813142.510612088100
Trimmed Mean ( 20 / 20 )56.77290.389843105418199145.630124557667
Median56.877
Midrange55.3325
Midmean - Weighted Average at Xnp56.7618387096774
Midmean - Weighted Average at X(n+1)p56.8739666666667
Midmean - Empirical Distribution Function56.7618387096774
Midmean - Empirical Distribution Function - Averaging56.8739666666667
Midmean - Empirical Distribution Function - Interpolation56.8739666666667
Midmean - Closest Observation56.7618387096774
Midmean - True Basic - Statistics Graphics Toolkit56.8739666666667
Midmean - MS Excel (old versions)56.8903125
Number of observations60



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')