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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Dec 2008 15:31:04 -0700
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/Dec/21/t1229898793w91h82pzph7w8r4.htm/, Retrieved Sun, 26 May 2024 02:56:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35890, Retrieved Sun, 26 May 2024 02:56:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Paper central ten...] [2007-11-09 08:56:17] [74be16979710d4c4e7c6647856088456]
-    D    [Central Tendency] [] [2008-12-21 22:31:04] [0e4dd4b7713a9edf1ca3fab1bbbafcc9] [Current]
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Dataseries X:
403537
488968
516209
554104
510945
397922
537144
512773
510602
464522
429335
369309
326831
401511
439797
451401
449830
336249
477772
442862
474578
495272
410547
359886
338612
356662
415506
549174
392468
289850
420099
387181
442850
471590
327695
300903
278253
291787
386715
440427
376759
256370
390839
387535
410787
406736
322972
267222
260452
365963
389214
389815
397823
244832
354586
333837
974019
523735
403636
308037




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35890&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35890&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35890&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean410280.78333333313882.960804446329.5528302004521
Geometric Mean398829.534563071
Harmonic Mean388586.353484088
Quadratic Mean423912.468103715
Winsorized Mean ( 1 / 20 )403474.510343.091896715339.0090800728680
Winsorized Mean ( 2 / 20 )403446.23333333310270.59262884439.2816897634799
Winsorized Mean ( 3 / 20 )403183.23333333310051.528449120840.1116343026021
Winsorized Mean ( 4 / 20 )403024.79691.4764848637341.5854798419466
Winsorized Mean ( 5 / 20 )403363.959356.2241741447343.1118304235022
Winsorized Mean ( 6 / 20 )403214.059246.9031287843343.6053070292096
Winsorized Mean ( 7 / 20 )404064.3166666678991.9234861662844.9363606450059
Winsorized Mean ( 8 / 20 )404969.7833333338801.365610209146.0121532576252
Winsorized Mean ( 9 / 20 )404910.5333333337939.3615181982951.000389943853
Winsorized Mean ( 10 / 20 )404503.0333333337627.5967688242353.0315177365736
Winsorized Mean ( 11 / 20 )402608.8333333337226.1429895722355.7155918329215
Winsorized Mean ( 12 / 20 )403198.4333333336901.2061979517658.4243423204773
Winsorized Mean ( 13 / 20 )403073.6333333336699.6492528128460.1633933543765
Winsorized Mean ( 14 / 20 )401975.86324.960988772363.5538781525394
Winsorized Mean ( 15 / 20 )402689.055125.882060593178.5599522657386
Winsorized Mean ( 16 / 20 )402823.7166666674970.9679405110381.0352674745383
Winsorized Mean ( 17 / 20 )401762.9166666674516.5551748049688.9533950360778
Winsorized Mean ( 18 / 20 )403582.4166666674235.3193761797895.2897245332876
Winsorized Mean ( 19 / 20 )403874.73956.70982691513102.073368446855
Winsorized Mean ( 20 / 20 )406148.0333333333565.64211893456113.906000598482
Trimmed Mean ( 1 / 20 )403413.72413793110056.982425079740.1127999519929
Trimmed Mean ( 2 / 20 )403348.6071428579704.209138597341.5642945635402
Trimmed Mean ( 3 / 20 )403294.370370379315.5737487205843.2924886055204
Trimmed Mean ( 4 / 20 )403337.1153846158939.47737659845.1186460229188
Trimmed Mean ( 5 / 20 )403430.848613.9535718180446.8345733043988
Trimmed Mean ( 6 / 20 )403447.56258320.1388413569148.4904843768452
Trimmed Mean ( 7 / 20 )403498.3260869577977.9495472101350.5766956408065
Trimmed Mean ( 8 / 20 )403388.0681818187613.8147751736852.9810719190521
Trimmed Mean ( 9 / 20 )403105.6190476197192.7812518520756.0430805460438
Trimmed Mean ( 10 / 20 )402804.86895.2747438056558.4175127121451
Trimmed Mean ( 11 / 20 )402536.6578947376585.2037898193761.1274412672016
Trimmed Mean ( 12 / 20 )402525.7222222226281.0768478998964.0854636823635
Trimmed Mean ( 13 / 20 )402426.7941176475955.8254396897867.5686012279447
Trimmed Mean ( 14 / 20 )402333.55557.2619572675872.3977928508198
Trimmed Mean ( 15 / 20 )402384.65108.9483979008678.7607485261213
Trimmed Mean ( 16 / 20 )402341.1071428574882.3203281443882.4077651815555
Trimmed Mean ( 17 / 20 )402271.54587.4258581307087.6900275754907
Trimmed Mean ( 18 / 20 )402346.2916666674305.9311662238593.4400193906283
Trimmed Mean ( 19 / 20 )4021593966.74210430650101.382693763579
Trimmed Mean ( 20 / 20 )401888.13526.05332146147113.976750593614
Median399716.5
Midrange609425.5
Midmean - Weighted Average at Xnp400327.419354839
Midmean - Weighted Average at X(n+1)p402384.6
Midmean - Empirical Distribution Function400327.419354839
Midmean - Empirical Distribution Function - Averaging402384.6
Midmean - Empirical Distribution Function - Interpolation402384.6
Midmean - Closest Observation400327.419354839
Midmean - True Basic - Statistics Graphics Toolkit402384.6
Midmean - MS Excel (old versions)402333.5
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 410280.783333333 & 13882.9608044463 & 29.5528302004521 \tabularnewline
Geometric Mean & 398829.534563071 &  &  \tabularnewline
Harmonic Mean & 388586.353484088 &  &  \tabularnewline
Quadratic Mean & 423912.468103715 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 403474.5 & 10343.0918967153 & 39.0090800728680 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 403446.233333333 & 10270.592628844 & 39.2816897634799 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 403183.233333333 & 10051.5284491208 & 40.1116343026021 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 403024.7 & 9691.47648486373 & 41.5854798419466 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 403363.95 & 9356.22417414473 & 43.1118304235022 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 403214.05 & 9246.90312878433 & 43.6053070292096 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 404064.316666667 & 8991.92348616628 & 44.9363606450059 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 404969.783333333 & 8801.3656102091 & 46.0121532576252 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 404910.533333333 & 7939.36151819829 & 51.000389943853 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 404503.033333333 & 7627.59676882423 & 53.0315177365736 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 402608.833333333 & 7226.14298957223 & 55.7155918329215 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 403198.433333333 & 6901.20619795176 & 58.4243423204773 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 403073.633333333 & 6699.64925281284 & 60.1633933543765 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 401975.8 & 6324.9609887723 & 63.5538781525394 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 402689.05 & 5125.8820605931 & 78.5599522657386 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 402823.716666667 & 4970.96794051103 & 81.0352674745383 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 401762.916666667 & 4516.55517480496 & 88.9533950360778 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 403582.416666667 & 4235.31937617978 & 95.2897245332876 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 403874.7 & 3956.70982691513 & 102.073368446855 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 406148.033333333 & 3565.64211893456 & 113.906000598482 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 403413.724137931 & 10056.9824250797 & 40.1127999519929 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 403348.607142857 & 9704.2091385973 & 41.5642945635402 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 403294.37037037 & 9315.57374872058 & 43.2924886055204 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 403337.115384615 & 8939.477376598 & 45.1186460229188 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 403430.84 & 8613.95357181804 & 46.8345733043988 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 403447.5625 & 8320.13884135691 & 48.4904843768452 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 403498.326086957 & 7977.94954721013 & 50.5766956408065 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 403388.068181818 & 7613.81477517368 & 52.9810719190521 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 403105.619047619 & 7192.78125185207 & 56.0430805460438 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 402804.8 & 6895.27474380565 & 58.4175127121451 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 402536.657894737 & 6585.20378981937 & 61.1274412672016 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 402525.722222222 & 6281.07684789989 & 64.0854636823635 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 402426.794117647 & 5955.82543968978 & 67.5686012279447 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 402333.5 & 5557.26195726758 & 72.3977928508198 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 402384.6 & 5108.94839790086 & 78.7607485261213 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 402341.107142857 & 4882.32032814438 & 82.4077651815555 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 402271.5 & 4587.42585813070 & 87.6900275754907 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 402346.291666667 & 4305.93116622385 & 93.4400193906283 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 402159 & 3966.74210430650 & 101.382693763579 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 401888.1 & 3526.05332146147 & 113.976750593614 \tabularnewline
Median & 399716.5 &  &  \tabularnewline
Midrange & 609425.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 400327.419354839 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 402384.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 400327.419354839 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 402384.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 402384.6 &  &  \tabularnewline
Midmean - Closest Observation & 400327.419354839 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 402384.6 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 402333.5 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35890&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]410280.783333333[/C][C]13882.9608044463[/C][C]29.5528302004521[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]398829.534563071[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]388586.353484088[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]423912.468103715[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]403474.5[/C][C]10343.0918967153[/C][C]39.0090800728680[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]403446.233333333[/C][C]10270.592628844[/C][C]39.2816897634799[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]403183.233333333[/C][C]10051.5284491208[/C][C]40.1116343026021[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]403024.7[/C][C]9691.47648486373[/C][C]41.5854798419466[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]403363.95[/C][C]9356.22417414473[/C][C]43.1118304235022[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]403214.05[/C][C]9246.90312878433[/C][C]43.6053070292096[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]404064.316666667[/C][C]8991.92348616628[/C][C]44.9363606450059[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]404969.783333333[/C][C]8801.3656102091[/C][C]46.0121532576252[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]404910.533333333[/C][C]7939.36151819829[/C][C]51.000389943853[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]404503.033333333[/C][C]7627.59676882423[/C][C]53.0315177365736[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]402608.833333333[/C][C]7226.14298957223[/C][C]55.7155918329215[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]403198.433333333[/C][C]6901.20619795176[/C][C]58.4243423204773[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]403073.633333333[/C][C]6699.64925281284[/C][C]60.1633933543765[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]401975.8[/C][C]6324.9609887723[/C][C]63.5538781525394[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]402689.05[/C][C]5125.8820605931[/C][C]78.5599522657386[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]402823.716666667[/C][C]4970.96794051103[/C][C]81.0352674745383[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]401762.916666667[/C][C]4516.55517480496[/C][C]88.9533950360778[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]403582.416666667[/C][C]4235.31937617978[/C][C]95.2897245332876[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]403874.7[/C][C]3956.70982691513[/C][C]102.073368446855[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]406148.033333333[/C][C]3565.64211893456[/C][C]113.906000598482[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]403413.724137931[/C][C]10056.9824250797[/C][C]40.1127999519929[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]403348.607142857[/C][C]9704.2091385973[/C][C]41.5642945635402[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]403294.37037037[/C][C]9315.57374872058[/C][C]43.2924886055204[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]403337.115384615[/C][C]8939.477376598[/C][C]45.1186460229188[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]403430.84[/C][C]8613.95357181804[/C][C]46.8345733043988[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]403447.5625[/C][C]8320.13884135691[/C][C]48.4904843768452[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]403498.326086957[/C][C]7977.94954721013[/C][C]50.5766956408065[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]403388.068181818[/C][C]7613.81477517368[/C][C]52.9810719190521[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]403105.619047619[/C][C]7192.78125185207[/C][C]56.0430805460438[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]402804.8[/C][C]6895.27474380565[/C][C]58.4175127121451[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]402536.657894737[/C][C]6585.20378981937[/C][C]61.1274412672016[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]402525.722222222[/C][C]6281.07684789989[/C][C]64.0854636823635[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]402426.794117647[/C][C]5955.82543968978[/C][C]67.5686012279447[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]402333.5[/C][C]5557.26195726758[/C][C]72.3977928508198[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]402384.6[/C][C]5108.94839790086[/C][C]78.7607485261213[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]402341.107142857[/C][C]4882.32032814438[/C][C]82.4077651815555[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]402271.5[/C][C]4587.42585813070[/C][C]87.6900275754907[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]402346.291666667[/C][C]4305.93116622385[/C][C]93.4400193906283[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]402159[/C][C]3966.74210430650[/C][C]101.382693763579[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]401888.1[/C][C]3526.05332146147[/C][C]113.976750593614[/C][/ROW]
[ROW][C]Median[/C][C]399716.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]609425.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]400327.419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]402384.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]400327.419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]402384.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]402384.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]400327.419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]402384.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]402333.5[/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=35890&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35890&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 Mean410280.78333333313882.960804446329.5528302004521
Geometric Mean398829.534563071
Harmonic Mean388586.353484088
Quadratic Mean423912.468103715
Winsorized Mean ( 1 / 20 )403474.510343.091896715339.0090800728680
Winsorized Mean ( 2 / 20 )403446.23333333310270.59262884439.2816897634799
Winsorized Mean ( 3 / 20 )403183.23333333310051.528449120840.1116343026021
Winsorized Mean ( 4 / 20 )403024.79691.4764848637341.5854798419466
Winsorized Mean ( 5 / 20 )403363.959356.2241741447343.1118304235022
Winsorized Mean ( 6 / 20 )403214.059246.9031287843343.6053070292096
Winsorized Mean ( 7 / 20 )404064.3166666678991.9234861662844.9363606450059
Winsorized Mean ( 8 / 20 )404969.7833333338801.365610209146.0121532576252
Winsorized Mean ( 9 / 20 )404910.5333333337939.3615181982951.000389943853
Winsorized Mean ( 10 / 20 )404503.0333333337627.5967688242353.0315177365736
Winsorized Mean ( 11 / 20 )402608.8333333337226.1429895722355.7155918329215
Winsorized Mean ( 12 / 20 )403198.4333333336901.2061979517658.4243423204773
Winsorized Mean ( 13 / 20 )403073.6333333336699.6492528128460.1633933543765
Winsorized Mean ( 14 / 20 )401975.86324.960988772363.5538781525394
Winsorized Mean ( 15 / 20 )402689.055125.882060593178.5599522657386
Winsorized Mean ( 16 / 20 )402823.7166666674970.9679405110381.0352674745383
Winsorized Mean ( 17 / 20 )401762.9166666674516.5551748049688.9533950360778
Winsorized Mean ( 18 / 20 )403582.4166666674235.3193761797895.2897245332876
Winsorized Mean ( 19 / 20 )403874.73956.70982691513102.073368446855
Winsorized Mean ( 20 / 20 )406148.0333333333565.64211893456113.906000598482
Trimmed Mean ( 1 / 20 )403413.72413793110056.982425079740.1127999519929
Trimmed Mean ( 2 / 20 )403348.6071428579704.209138597341.5642945635402
Trimmed Mean ( 3 / 20 )403294.370370379315.5737487205843.2924886055204
Trimmed Mean ( 4 / 20 )403337.1153846158939.47737659845.1186460229188
Trimmed Mean ( 5 / 20 )403430.848613.9535718180446.8345733043988
Trimmed Mean ( 6 / 20 )403447.56258320.1388413569148.4904843768452
Trimmed Mean ( 7 / 20 )403498.3260869577977.9495472101350.5766956408065
Trimmed Mean ( 8 / 20 )403388.0681818187613.8147751736852.9810719190521
Trimmed Mean ( 9 / 20 )403105.6190476197192.7812518520756.0430805460438
Trimmed Mean ( 10 / 20 )402804.86895.2747438056558.4175127121451
Trimmed Mean ( 11 / 20 )402536.6578947376585.2037898193761.1274412672016
Trimmed Mean ( 12 / 20 )402525.7222222226281.0768478998964.0854636823635
Trimmed Mean ( 13 / 20 )402426.7941176475955.8254396897867.5686012279447
Trimmed Mean ( 14 / 20 )402333.55557.2619572675872.3977928508198
Trimmed Mean ( 15 / 20 )402384.65108.9483979008678.7607485261213
Trimmed Mean ( 16 / 20 )402341.1071428574882.3203281443882.4077651815555
Trimmed Mean ( 17 / 20 )402271.54587.4258581307087.6900275754907
Trimmed Mean ( 18 / 20 )402346.2916666674305.9311662238593.4400193906283
Trimmed Mean ( 19 / 20 )4021593966.74210430650101.382693763579
Trimmed Mean ( 20 / 20 )401888.13526.05332146147113.976750593614
Median399716.5
Midrange609425.5
Midmean - Weighted Average at Xnp400327.419354839
Midmean - Weighted Average at X(n+1)p402384.6
Midmean - Empirical Distribution Function400327.419354839
Midmean - Empirical Distribution Function - Averaging402384.6
Midmean - Empirical Distribution Function - Interpolation402384.6
Midmean - Closest Observation400327.419354839
Midmean - True Basic - Statistics Graphics Toolkit402384.6
Midmean - MS Excel (old versions)402333.5
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')