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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 computationWed, 21 Oct 2009 10:01:44 -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/2009/Oct/21/t1256141069v2in83id0dsln4x.htm/, Retrieved Thu, 02 May 2024 11:05:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49466, Retrieved Thu, 02 May 2024 11:05:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [SHw WS3 - Vr2] [2009-10-21 16:01:44] [d9efc2d105d810fc0b0ac636e31105d1] [Current]
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Dataseries X:
1,76
1,80
1,86
1,75
2,01
1,75
1,83
1,93
1,82
1,77
2,04
1,78
1,84
1,93
1,78
1,87
2,05
1,85
1,89
1,85
1,95
2,09
1,88
1,80
2,03
1,97
1,80
1,86
2,26
1,89
1,75
1,77
2,06
2,09
1,80
2,09
1,80
1,91
1,85
2,01
1,84
2,05
1,78
1,51
2,03
2,00
1,95
2,11
1,90
1,89
2,20
1,82
2,09
2,15
2,00
1,70
2,14
1,88
1,98
1,99




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49466&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49466&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49466&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 time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.913833333333330.0180631216944469105.952523916267
Geometric Mean1.90879743744916
Harmonic Mean1.90374370457076
Quadratic Mean1.91885599598650
Winsorized Mean ( 1 / 20 )1.9160.0168026094287708114.029907564194
Winsorized Mean ( 2 / 20 )1.9160.0160282236945414119.539135247564
Winsorized Mean ( 3 / 20 )1.91550.0159065509014972120.422083446117
Winsorized Mean ( 4 / 20 )1.91350.0154514457298093123.839544432300
Winsorized Mean ( 5 / 20 )1.912666666666670.0149573152872645127.874998282293
Winsorized Mean ( 6 / 20 )1.913666666666670.0147884644819055129.402661717053
Winsorized Mean ( 7 / 20 )1.913666666666670.0147884644819055129.402661717053
Winsorized Mean ( 8 / 20 )1.9150.0145739881276026131.398487718887
Winsorized Mean ( 9 / 20 )1.91050.0136985813113440139.466997098297
Winsorized Mean ( 10 / 20 )1.908833333333330.0133955293720072142.497790144990
Winsorized Mean ( 11 / 20 )1.91250.0128234975882354149.140278371056
Winsorized Mean ( 12 / 20 )1.91050.0124656023896903153.261747027972
Winsorized Mean ( 13 / 20 )1.908333333333330.0120899796644267157.844213663019
Winsorized Mean ( 14 / 20 )1.908333333333330.0120899796644267157.844213663019
Winsorized Mean ( 15 / 20 )1.903333333333330.0112613198960147169.015119977802
Winsorized Mean ( 16 / 20 )1.908666666666670.0104623799203139182.431404824134
Winsorized Mean ( 17 / 20 )1.905833333333330.0100036481104590190.513831783101
Winsorized Mean ( 18 / 20 )1.908833333333330.0095760166124521199.334797607932
Winsorized Mean ( 19 / 20 )1.908833333333330.00863278361358726221.114465365377
Winsorized Mean ( 20 / 20 )1.90550.00810741796065187235.031672136315
Trimmed Mean ( 1 / 20 )1.914827586206900.0162412271061491117.899194050548
Trimmed Mean ( 2 / 20 )1.913571428571430.0155472229353623123.081236856712
Trimmed Mean ( 3 / 20 )1.912222222222220.0152057095704425125.756855565575
Trimmed Mean ( 4 / 20 )1.910961538461540.0148325485295411128.835684215399
Trimmed Mean ( 5 / 20 )1.91020.0145391519276576131.383178984894
Trimmed Mean ( 6 / 20 )1.909583333333330.0143257391641923133.297368564856
Trimmed Mean ( 7 / 20 )1.908695652173910.0140894612194475135.469740286404
Trimmed Mean ( 8 / 20 )1.907727272727270.0137704820977865138.537435304021
Trimmed Mean ( 9 / 20 )1.906428571428570.0133991758226417142.279539925666
Trimmed Mean ( 10 / 20 )1.905750.0131455730093286144.972759928198
Trimmed Mean ( 11 / 20 )1.905263157894740.0128717099242267148.019429361806
Trimmed Mean ( 12 / 20 )1.904166666666670.0126263455985730150.809008972626
Trimmed Mean ( 13 / 20 )1.903235294117650.0123649250079377153.922105705927
Trimmed Mean ( 14 / 20 )1.90250.0120817110516468157.469417358784
Trimmed Mean ( 15 / 20 )1.901666666666670.0116469455650899163.275998504418
Trimmed Mean ( 16 / 20 )1.901428571428570.0112653691104311168.785288150741
Trimmed Mean ( 17 / 20 )1.900384615384620.0109190133286394174.043620809593
Trimmed Mean ( 18 / 20 )1.899583333333330.0105204970171529180.560227357720
Trimmed Mean ( 19 / 20 )1.898181818181820.009992125983031189.967762756933
Trimmed Mean ( 20 / 20 )1.89650.00949445821740794199.748101110477
Median1.89
Midrange1.885
Midmean - Weighted Average at Xnp1.88970588235294
Midmean - Weighted Average at X(n+1)p1.88970588235294
Midmean - Empirical Distribution Function1.88970588235294
Midmean - Empirical Distribution Function - Averaging1.88970588235294
Midmean - Empirical Distribution Function - Interpolation1.88970588235294
Midmean - Closest Observation1.88970588235294
Midmean - True Basic - Statistics Graphics Toolkit1.88970588235294
Midmean - MS Excel (old versions)1.8975
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.91383333333333 & 0.0180631216944469 & 105.952523916267 \tabularnewline
Geometric Mean & 1.90879743744916 &  &  \tabularnewline
Harmonic Mean & 1.90374370457076 &  &  \tabularnewline
Quadratic Mean & 1.91885599598650 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.916 & 0.0168026094287708 & 114.029907564194 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.916 & 0.0160282236945414 & 119.539135247564 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.9155 & 0.0159065509014972 & 120.422083446117 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.9135 & 0.0154514457298093 & 123.839544432300 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.91266666666667 & 0.0149573152872645 & 127.874998282293 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.91366666666667 & 0.0147884644819055 & 129.402661717053 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.91366666666667 & 0.0147884644819055 & 129.402661717053 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.915 & 0.0145739881276026 & 131.398487718887 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.9105 & 0.0136985813113440 & 139.466997098297 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.90883333333333 & 0.0133955293720072 & 142.497790144990 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.9125 & 0.0128234975882354 & 149.140278371056 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.9105 & 0.0124656023896903 & 153.261747027972 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.90833333333333 & 0.0120899796644267 & 157.844213663019 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.90833333333333 & 0.0120899796644267 & 157.844213663019 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.90333333333333 & 0.0112613198960147 & 169.015119977802 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.90866666666667 & 0.0104623799203139 & 182.431404824134 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.90583333333333 & 0.0100036481104590 & 190.513831783101 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.90883333333333 & 0.0095760166124521 & 199.334797607932 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.90883333333333 & 0.00863278361358726 & 221.114465365377 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.9055 & 0.00810741796065187 & 235.031672136315 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.91482758620690 & 0.0162412271061491 & 117.899194050548 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.91357142857143 & 0.0155472229353623 & 123.081236856712 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.91222222222222 & 0.0152057095704425 & 125.756855565575 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.91096153846154 & 0.0148325485295411 & 128.835684215399 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.9102 & 0.0145391519276576 & 131.383178984894 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.90958333333333 & 0.0143257391641923 & 133.297368564856 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.90869565217391 & 0.0140894612194475 & 135.469740286404 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.90772727272727 & 0.0137704820977865 & 138.537435304021 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.90642857142857 & 0.0133991758226417 & 142.279539925666 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.90575 & 0.0131455730093286 & 144.972759928198 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.90526315789474 & 0.0128717099242267 & 148.019429361806 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.90416666666667 & 0.0126263455985730 & 150.809008972626 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.90323529411765 & 0.0123649250079377 & 153.922105705927 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.9025 & 0.0120817110516468 & 157.469417358784 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.90166666666667 & 0.0116469455650899 & 163.275998504418 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.90142857142857 & 0.0112653691104311 & 168.785288150741 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.90038461538462 & 0.0109190133286394 & 174.043620809593 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.89958333333333 & 0.0105204970171529 & 180.560227357720 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.89818181818182 & 0.009992125983031 & 189.967762756933 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.8965 & 0.00949445821740794 & 199.748101110477 \tabularnewline
Median & 1.89 &  &  \tabularnewline
Midrange & 1.885 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.88970588235294 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.88970588235294 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.88970588235294 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.88970588235294 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.88970588235294 &  &  \tabularnewline
Midmean - Closest Observation & 1.88970588235294 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.88970588235294 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.8975 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49466&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]1.91383333333333[/C][C]0.0180631216944469[/C][C]105.952523916267[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.90879743744916[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.90374370457076[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.91885599598650[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.916[/C][C]0.0168026094287708[/C][C]114.029907564194[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.916[/C][C]0.0160282236945414[/C][C]119.539135247564[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.9155[/C][C]0.0159065509014972[/C][C]120.422083446117[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.9135[/C][C]0.0154514457298093[/C][C]123.839544432300[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.91266666666667[/C][C]0.0149573152872645[/C][C]127.874998282293[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.91366666666667[/C][C]0.0147884644819055[/C][C]129.402661717053[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.91366666666667[/C][C]0.0147884644819055[/C][C]129.402661717053[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.915[/C][C]0.0145739881276026[/C][C]131.398487718887[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.9105[/C][C]0.0136985813113440[/C][C]139.466997098297[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.90883333333333[/C][C]0.0133955293720072[/C][C]142.497790144990[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.9125[/C][C]0.0128234975882354[/C][C]149.140278371056[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.9105[/C][C]0.0124656023896903[/C][C]153.261747027972[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.90833333333333[/C][C]0.0120899796644267[/C][C]157.844213663019[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.90833333333333[/C][C]0.0120899796644267[/C][C]157.844213663019[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.90333333333333[/C][C]0.0112613198960147[/C][C]169.015119977802[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.90866666666667[/C][C]0.0104623799203139[/C][C]182.431404824134[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.90583333333333[/C][C]0.0100036481104590[/C][C]190.513831783101[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.90883333333333[/C][C]0.0095760166124521[/C][C]199.334797607932[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.90883333333333[/C][C]0.00863278361358726[/C][C]221.114465365377[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.9055[/C][C]0.00810741796065187[/C][C]235.031672136315[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.91482758620690[/C][C]0.0162412271061491[/C][C]117.899194050548[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.91357142857143[/C][C]0.0155472229353623[/C][C]123.081236856712[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.91222222222222[/C][C]0.0152057095704425[/C][C]125.756855565575[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.91096153846154[/C][C]0.0148325485295411[/C][C]128.835684215399[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.9102[/C][C]0.0145391519276576[/C][C]131.383178984894[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.90958333333333[/C][C]0.0143257391641923[/C][C]133.297368564856[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.90869565217391[/C][C]0.0140894612194475[/C][C]135.469740286404[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.90772727272727[/C][C]0.0137704820977865[/C][C]138.537435304021[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.90642857142857[/C][C]0.0133991758226417[/C][C]142.279539925666[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.90575[/C][C]0.0131455730093286[/C][C]144.972759928198[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.90526315789474[/C][C]0.0128717099242267[/C][C]148.019429361806[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.90416666666667[/C][C]0.0126263455985730[/C][C]150.809008972626[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.90323529411765[/C][C]0.0123649250079377[/C][C]153.922105705927[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.9025[/C][C]0.0120817110516468[/C][C]157.469417358784[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.90166666666667[/C][C]0.0116469455650899[/C][C]163.275998504418[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.90142857142857[/C][C]0.0112653691104311[/C][C]168.785288150741[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.90038461538462[/C][C]0.0109190133286394[/C][C]174.043620809593[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.89958333333333[/C][C]0.0105204970171529[/C][C]180.560227357720[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.89818181818182[/C][C]0.009992125983031[/C][C]189.967762756933[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.8965[/C][C]0.00949445821740794[/C][C]199.748101110477[/C][/ROW]
[ROW][C]Median[/C][C]1.89[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.885[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.88970588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.88970588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.88970588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.88970588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.88970588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.88970588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.88970588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.8975[/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=49466&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49466&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 Mean1.913833333333330.0180631216944469105.952523916267
Geometric Mean1.90879743744916
Harmonic Mean1.90374370457076
Quadratic Mean1.91885599598650
Winsorized Mean ( 1 / 20 )1.9160.0168026094287708114.029907564194
Winsorized Mean ( 2 / 20 )1.9160.0160282236945414119.539135247564
Winsorized Mean ( 3 / 20 )1.91550.0159065509014972120.422083446117
Winsorized Mean ( 4 / 20 )1.91350.0154514457298093123.839544432300
Winsorized Mean ( 5 / 20 )1.912666666666670.0149573152872645127.874998282293
Winsorized Mean ( 6 / 20 )1.913666666666670.0147884644819055129.402661717053
Winsorized Mean ( 7 / 20 )1.913666666666670.0147884644819055129.402661717053
Winsorized Mean ( 8 / 20 )1.9150.0145739881276026131.398487718887
Winsorized Mean ( 9 / 20 )1.91050.0136985813113440139.466997098297
Winsorized Mean ( 10 / 20 )1.908833333333330.0133955293720072142.497790144990
Winsorized Mean ( 11 / 20 )1.91250.0128234975882354149.140278371056
Winsorized Mean ( 12 / 20 )1.91050.0124656023896903153.261747027972
Winsorized Mean ( 13 / 20 )1.908333333333330.0120899796644267157.844213663019
Winsorized Mean ( 14 / 20 )1.908333333333330.0120899796644267157.844213663019
Winsorized Mean ( 15 / 20 )1.903333333333330.0112613198960147169.015119977802
Winsorized Mean ( 16 / 20 )1.908666666666670.0104623799203139182.431404824134
Winsorized Mean ( 17 / 20 )1.905833333333330.0100036481104590190.513831783101
Winsorized Mean ( 18 / 20 )1.908833333333330.0095760166124521199.334797607932
Winsorized Mean ( 19 / 20 )1.908833333333330.00863278361358726221.114465365377
Winsorized Mean ( 20 / 20 )1.90550.00810741796065187235.031672136315
Trimmed Mean ( 1 / 20 )1.914827586206900.0162412271061491117.899194050548
Trimmed Mean ( 2 / 20 )1.913571428571430.0155472229353623123.081236856712
Trimmed Mean ( 3 / 20 )1.912222222222220.0152057095704425125.756855565575
Trimmed Mean ( 4 / 20 )1.910961538461540.0148325485295411128.835684215399
Trimmed Mean ( 5 / 20 )1.91020.0145391519276576131.383178984894
Trimmed Mean ( 6 / 20 )1.909583333333330.0143257391641923133.297368564856
Trimmed Mean ( 7 / 20 )1.908695652173910.0140894612194475135.469740286404
Trimmed Mean ( 8 / 20 )1.907727272727270.0137704820977865138.537435304021
Trimmed Mean ( 9 / 20 )1.906428571428570.0133991758226417142.279539925666
Trimmed Mean ( 10 / 20 )1.905750.0131455730093286144.972759928198
Trimmed Mean ( 11 / 20 )1.905263157894740.0128717099242267148.019429361806
Trimmed Mean ( 12 / 20 )1.904166666666670.0126263455985730150.809008972626
Trimmed Mean ( 13 / 20 )1.903235294117650.0123649250079377153.922105705927
Trimmed Mean ( 14 / 20 )1.90250.0120817110516468157.469417358784
Trimmed Mean ( 15 / 20 )1.901666666666670.0116469455650899163.275998504418
Trimmed Mean ( 16 / 20 )1.901428571428570.0112653691104311168.785288150741
Trimmed Mean ( 17 / 20 )1.900384615384620.0109190133286394174.043620809593
Trimmed Mean ( 18 / 20 )1.899583333333330.0105204970171529180.560227357720
Trimmed Mean ( 19 / 20 )1.898181818181820.009992125983031189.967762756933
Trimmed Mean ( 20 / 20 )1.89650.00949445821740794199.748101110477
Median1.89
Midrange1.885
Midmean - Weighted Average at Xnp1.88970588235294
Midmean - Weighted Average at X(n+1)p1.88970588235294
Midmean - Empirical Distribution Function1.88970588235294
Midmean - Empirical Distribution Function - Averaging1.88970588235294
Midmean - Empirical Distribution Function - Interpolation1.88970588235294
Midmean - Closest Observation1.88970588235294
Midmean - True Basic - Statistics Graphics Toolkit1.88970588235294
Midmean - MS Excel (old versions)1.8975
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')