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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 computationMon, 20 Oct 2008 09:59:18 -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/20/t12245184049iezbqwz7yuu0uw.htm/, Retrieved Fri, 17 May 2024 09:59:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17555, Retrieved Fri, 17 May 2024 09:59:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Pearson Correlation] [Q3 Clothing produ...] [2007-10-20 14:22:11] [b731da8b544846036771bbf9bf2f34ce]
- RMPD  [Harrell-Davis Quantiles] [Compute the 95% C...] [2008-10-19 19:58:52] [988ab43f527fc78aae41c84649095267]
- RMPD      [Central Tendency] [Luxemburg/Uitvoer] [2008-10-20 15:59:18] [5d823194959040fa9b19b8c8302177e6] [Current]
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Dataseries X:
335.8
368.9
404.3
382.5
333
344.1
320.3
277.8
357.7
407.8
336.8
349.9
352.2
390
455.9
400.6
376.7
417.4
376.8
351
432.8
430.2
436.6
423.3
382
391.8
463.9
431
406.2
420.4
416
364.1
471.7
449.6
470.6
724.6
472.8
441.5
555.5
468.8
460.9
447.2
432
398.6
459.7
443.5
464.7
444
449.2
432.4
519.5
420
455.5
474.6
424.2
355.2
415.3
496.9
499.7
487




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17555&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17555&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17555&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean422.8833333333338.5832069542558349.2686865861546
Geometric Mean418.124323416126
Harmonic Mean413.580459338933
Quadratic Mean427.991739016849
Winsorized Mean ( 1 / 20 )420.7733333333337.062236992419659.580743861326
Winsorized Mean ( 2 / 20 )419.9966666666676.6155927631835363.4858706847847
Winsorized Mean ( 3 / 20 )419.1466666666676.3514229317534665.9925612213878
Winsorized Mean ( 4 / 20 )419.0266666666676.2970030835529266.5438242774755
Winsorized Mean ( 5 / 20 )418.815.9993086701530969.8097102560507
Winsorized Mean ( 6 / 20 )418.155.6539174459728173.9575708339783
Winsorized Mean ( 7 / 20 )418.0683333333335.5925588635422174.7543912427481
Winsorized Mean ( 8 / 20 )418.0816666666675.5359576982248475.5211093467584
Winsorized Mean ( 9 / 20 )418.3666666666675.4190898534647677.2023860056831
Winsorized Mean ( 10 / 20 )418.4833333333335.2886426476567679.1286840903782
Winsorized Mean ( 11 / 20 )418.9054.9443464404472984.7240388685432
Winsorized Mean ( 12 / 20 )419.7054.7417424060357588.5128216719994
Winsorized Mean ( 13 / 20 )420.7454.340270907866596.9398014389892
Winsorized Mean ( 14 / 20 )420.4883333333334.2926215053213497.9560701571465
Winsorized Mean ( 15 / 20 )420.8383333333333.92584878128081107.196776233453
Winsorized Mean ( 16 / 20 )420.8653.88739148666834108.264115266842
Winsorized Mean ( 17 / 20 )421.3183333333333.28928451312535128.088139427323
Winsorized Mean ( 18 / 20 )421.7383333333333.18517850360253132.406498680163
Winsorized Mean ( 19 / 20 )423.2583333333332.75698219079787153.522331317941
Winsorized Mean ( 20 / 20 )422.8583333333332.50115034739290169.065539692207
Trimmed Mean ( 1 / 20 )420.182758620696.6974135818850362.7380635051698
Trimmed Mean ( 2 / 20 )419.556.2414107213199667.2203799321945
Trimmed Mean ( 3 / 20 )419.3018518518525.9844256816280270.0655124081654
Trimmed Mean ( 4 / 20 )419.3615384615385.7950544225683672.3654184900093
Trimmed Mean ( 5 / 20 )419.4625.5780941006690175.1980860182499
Trimmed Mean ( 6 / 20 )419.6255.4084084620337877.587520052471
Trimmed Mean ( 7 / 20 )419.9456521739135.2979548570063179.2656154135692
Trimmed Mean ( 8 / 20 )420.3113636363645.1688439049800781.3163197347482
Trimmed Mean ( 9 / 20 )420.7095238095245.0122878156205383.9356276585724
Trimmed Mean ( 10 / 20 )421.14.8354460457685287.0860714842434
Trimmed Mean ( 11 / 20 )421.5131578947374.6325786333844190.9888835684572
Trimmed Mean ( 12 / 20 )421.9083333333334.4549657953900494.7051790543308
Trimmed Mean ( 13 / 20 )422.2323529411764.2671604283179298.9492567795527
Trimmed Mean ( 14 / 20 )422.4468754.12264836284754102.469781028866
Trimmed Mean ( 15 / 20 )422.7266666666673.92259570796209107.767075207016
Trimmed Mean ( 16 / 20 )422.9964285714293.74895217157163112.830574841423
Trimmed Mean ( 17 / 20 )423.3038461538463.49205903892831121.218983251714
Trimmed Mean ( 18 / 20 )423.5958333333333.33072259626722127.178358776580
Trimmed Mean ( 19 / 20 )423.8772727272733.10544788592816136.494730646747
Trimmed Mean ( 20 / 20 )423.9752.93453013364374144.477984785101
Median423.75
Midrange501.2
Midmean - Weighted Average at Xnp421.245161290323
Midmean - Weighted Average at X(n+1)p422.726666666667
Midmean - Empirical Distribution Function421.245161290323
Midmean - Empirical Distribution Function - Averaging422.726666666667
Midmean - Empirical Distribution Function - Interpolation422.726666666667
Midmean - Closest Observation421.245161290323
Midmean - True Basic - Statistics Graphics Toolkit422.726666666667
Midmean - MS Excel (old versions)422.446875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 422.883333333333 & 8.58320695425583 & 49.2686865861546 \tabularnewline
Geometric Mean & 418.124323416126 &  &  \tabularnewline
Harmonic Mean & 413.580459338933 &  &  \tabularnewline
Quadratic Mean & 427.991739016849 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 420.773333333333 & 7.0622369924196 & 59.580743861326 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 419.996666666667 & 6.61559276318353 & 63.4858706847847 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 419.146666666667 & 6.35142293175346 & 65.9925612213878 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 419.026666666667 & 6.29700308355292 & 66.5438242774755 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 418.81 & 5.99930867015309 & 69.8097102560507 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 418.15 & 5.65391744597281 & 73.9575708339783 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 418.068333333333 & 5.59255886354221 & 74.7543912427481 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 418.081666666667 & 5.53595769822484 & 75.5211093467584 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 418.366666666667 & 5.41908985346476 & 77.2023860056831 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 418.483333333333 & 5.28864264765676 & 79.1286840903782 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 418.905 & 4.94434644044729 & 84.7240388685432 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 419.705 & 4.74174240603575 & 88.5128216719994 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 420.745 & 4.3402709078665 & 96.9398014389892 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 420.488333333333 & 4.29262150532134 & 97.9560701571465 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 420.838333333333 & 3.92584878128081 & 107.196776233453 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 420.865 & 3.88739148666834 & 108.264115266842 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 421.318333333333 & 3.28928451312535 & 128.088139427323 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 421.738333333333 & 3.18517850360253 & 132.406498680163 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 423.258333333333 & 2.75698219079787 & 153.522331317941 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 422.858333333333 & 2.50115034739290 & 169.065539692207 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 420.18275862069 & 6.69741358188503 & 62.7380635051698 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 419.55 & 6.24141072131996 & 67.2203799321945 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 419.301851851852 & 5.98442568162802 & 70.0655124081654 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 419.361538461538 & 5.79505442256836 & 72.3654184900093 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 419.462 & 5.57809410066901 & 75.1980860182499 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 419.625 & 5.40840846203378 & 77.587520052471 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 419.945652173913 & 5.29795485700631 & 79.2656154135692 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 420.311363636364 & 5.16884390498007 & 81.3163197347482 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 420.709523809524 & 5.01228781562053 & 83.9356276585724 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 421.1 & 4.83544604576852 & 87.0860714842434 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 421.513157894737 & 4.63257863338441 & 90.9888835684572 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 421.908333333333 & 4.45496579539004 & 94.7051790543308 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 422.232352941176 & 4.26716042831792 & 98.9492567795527 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 422.446875 & 4.12264836284754 & 102.469781028866 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 422.726666666667 & 3.92259570796209 & 107.767075207016 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 422.996428571429 & 3.74895217157163 & 112.830574841423 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 423.303846153846 & 3.49205903892831 & 121.218983251714 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 423.595833333333 & 3.33072259626722 & 127.178358776580 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 423.877272727273 & 3.10544788592816 & 136.494730646747 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 423.975 & 2.93453013364374 & 144.477984785101 \tabularnewline
Median & 423.75 &  &  \tabularnewline
Midrange & 501.2 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 421.245161290323 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 422.726666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 421.245161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 422.726666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 422.726666666667 &  &  \tabularnewline
Midmean - Closest Observation & 421.245161290323 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 422.726666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 422.446875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17555&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]422.883333333333[/C][C]8.58320695425583[/C][C]49.2686865861546[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]418.124323416126[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]413.580459338933[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]427.991739016849[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]420.773333333333[/C][C]7.0622369924196[/C][C]59.580743861326[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]419.996666666667[/C][C]6.61559276318353[/C][C]63.4858706847847[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]419.146666666667[/C][C]6.35142293175346[/C][C]65.9925612213878[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]419.026666666667[/C][C]6.29700308355292[/C][C]66.5438242774755[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]418.81[/C][C]5.99930867015309[/C][C]69.8097102560507[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]418.15[/C][C]5.65391744597281[/C][C]73.9575708339783[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]418.068333333333[/C][C]5.59255886354221[/C][C]74.7543912427481[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]418.081666666667[/C][C]5.53595769822484[/C][C]75.5211093467584[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]418.366666666667[/C][C]5.41908985346476[/C][C]77.2023860056831[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]418.483333333333[/C][C]5.28864264765676[/C][C]79.1286840903782[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]418.905[/C][C]4.94434644044729[/C][C]84.7240388685432[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]419.705[/C][C]4.74174240603575[/C][C]88.5128216719994[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]420.745[/C][C]4.3402709078665[/C][C]96.9398014389892[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]420.488333333333[/C][C]4.29262150532134[/C][C]97.9560701571465[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]420.838333333333[/C][C]3.92584878128081[/C][C]107.196776233453[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]420.865[/C][C]3.88739148666834[/C][C]108.264115266842[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]421.318333333333[/C][C]3.28928451312535[/C][C]128.088139427323[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]421.738333333333[/C][C]3.18517850360253[/C][C]132.406498680163[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]423.258333333333[/C][C]2.75698219079787[/C][C]153.522331317941[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]422.858333333333[/C][C]2.50115034739290[/C][C]169.065539692207[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]420.18275862069[/C][C]6.69741358188503[/C][C]62.7380635051698[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]419.55[/C][C]6.24141072131996[/C][C]67.2203799321945[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]419.301851851852[/C][C]5.98442568162802[/C][C]70.0655124081654[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]419.361538461538[/C][C]5.79505442256836[/C][C]72.3654184900093[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]419.462[/C][C]5.57809410066901[/C][C]75.1980860182499[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]419.625[/C][C]5.40840846203378[/C][C]77.587520052471[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]419.945652173913[/C][C]5.29795485700631[/C][C]79.2656154135692[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]420.311363636364[/C][C]5.16884390498007[/C][C]81.3163197347482[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]420.709523809524[/C][C]5.01228781562053[/C][C]83.9356276585724[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]421.1[/C][C]4.83544604576852[/C][C]87.0860714842434[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]421.513157894737[/C][C]4.63257863338441[/C][C]90.9888835684572[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]421.908333333333[/C][C]4.45496579539004[/C][C]94.7051790543308[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]422.232352941176[/C][C]4.26716042831792[/C][C]98.9492567795527[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]422.446875[/C][C]4.12264836284754[/C][C]102.469781028866[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]422.726666666667[/C][C]3.92259570796209[/C][C]107.767075207016[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]422.996428571429[/C][C]3.74895217157163[/C][C]112.830574841423[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]423.303846153846[/C][C]3.49205903892831[/C][C]121.218983251714[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]423.595833333333[/C][C]3.33072259626722[/C][C]127.178358776580[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]423.877272727273[/C][C]3.10544788592816[/C][C]136.494730646747[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]423.975[/C][C]2.93453013364374[/C][C]144.477984785101[/C][/ROW]
[ROW][C]Median[/C][C]423.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]501.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]421.245161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]422.726666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]421.245161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]422.726666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]422.726666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]421.245161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]422.726666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]422.446875[/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=17555&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17555&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 Mean422.8833333333338.5832069542558349.2686865861546
Geometric Mean418.124323416126
Harmonic Mean413.580459338933
Quadratic Mean427.991739016849
Winsorized Mean ( 1 / 20 )420.7733333333337.062236992419659.580743861326
Winsorized Mean ( 2 / 20 )419.9966666666676.6155927631835363.4858706847847
Winsorized Mean ( 3 / 20 )419.1466666666676.3514229317534665.9925612213878
Winsorized Mean ( 4 / 20 )419.0266666666676.2970030835529266.5438242774755
Winsorized Mean ( 5 / 20 )418.815.9993086701530969.8097102560507
Winsorized Mean ( 6 / 20 )418.155.6539174459728173.9575708339783
Winsorized Mean ( 7 / 20 )418.0683333333335.5925588635422174.7543912427481
Winsorized Mean ( 8 / 20 )418.0816666666675.5359576982248475.5211093467584
Winsorized Mean ( 9 / 20 )418.3666666666675.4190898534647677.2023860056831
Winsorized Mean ( 10 / 20 )418.4833333333335.2886426476567679.1286840903782
Winsorized Mean ( 11 / 20 )418.9054.9443464404472984.7240388685432
Winsorized Mean ( 12 / 20 )419.7054.7417424060357588.5128216719994
Winsorized Mean ( 13 / 20 )420.7454.340270907866596.9398014389892
Winsorized Mean ( 14 / 20 )420.4883333333334.2926215053213497.9560701571465
Winsorized Mean ( 15 / 20 )420.8383333333333.92584878128081107.196776233453
Winsorized Mean ( 16 / 20 )420.8653.88739148666834108.264115266842
Winsorized Mean ( 17 / 20 )421.3183333333333.28928451312535128.088139427323
Winsorized Mean ( 18 / 20 )421.7383333333333.18517850360253132.406498680163
Winsorized Mean ( 19 / 20 )423.2583333333332.75698219079787153.522331317941
Winsorized Mean ( 20 / 20 )422.8583333333332.50115034739290169.065539692207
Trimmed Mean ( 1 / 20 )420.182758620696.6974135818850362.7380635051698
Trimmed Mean ( 2 / 20 )419.556.2414107213199667.2203799321945
Trimmed Mean ( 3 / 20 )419.3018518518525.9844256816280270.0655124081654
Trimmed Mean ( 4 / 20 )419.3615384615385.7950544225683672.3654184900093
Trimmed Mean ( 5 / 20 )419.4625.5780941006690175.1980860182499
Trimmed Mean ( 6 / 20 )419.6255.4084084620337877.587520052471
Trimmed Mean ( 7 / 20 )419.9456521739135.2979548570063179.2656154135692
Trimmed Mean ( 8 / 20 )420.3113636363645.1688439049800781.3163197347482
Trimmed Mean ( 9 / 20 )420.7095238095245.0122878156205383.9356276585724
Trimmed Mean ( 10 / 20 )421.14.8354460457685287.0860714842434
Trimmed Mean ( 11 / 20 )421.5131578947374.6325786333844190.9888835684572
Trimmed Mean ( 12 / 20 )421.9083333333334.4549657953900494.7051790543308
Trimmed Mean ( 13 / 20 )422.2323529411764.2671604283179298.9492567795527
Trimmed Mean ( 14 / 20 )422.4468754.12264836284754102.469781028866
Trimmed Mean ( 15 / 20 )422.7266666666673.92259570796209107.767075207016
Trimmed Mean ( 16 / 20 )422.9964285714293.74895217157163112.830574841423
Trimmed Mean ( 17 / 20 )423.3038461538463.49205903892831121.218983251714
Trimmed Mean ( 18 / 20 )423.5958333333333.33072259626722127.178358776580
Trimmed Mean ( 19 / 20 )423.8772727272733.10544788592816136.494730646747
Trimmed Mean ( 20 / 20 )423.9752.93453013364374144.477984785101
Median423.75
Midrange501.2
Midmean - Weighted Average at Xnp421.245161290323
Midmean - Weighted Average at X(n+1)p422.726666666667
Midmean - Empirical Distribution Function421.245161290323
Midmean - Empirical Distribution Function - Averaging422.726666666667
Midmean - Empirical Distribution Function - Interpolation422.726666666667
Midmean - Closest Observation421.245161290323
Midmean - True Basic - Statistics Graphics Toolkit422.726666666667
Midmean - MS Excel (old versions)422.446875
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')