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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 computationThu, 05 Nov 2009 02:49:33 -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/2009/Nov/05/t1257414857et610sx37mc62kr.htm/, Retrieved Thu, 02 May 2024 17:30:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=53910, Retrieved Thu, 02 May 2024 17:30:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws3-part2-ct
Estimated Impact153
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      [Percentiles] [Part 1: Percentiles] [2009-10-15 15:30:33] [f924a0adda9c1905a1ba8f1c751261ff]
- RM D          [Central Tendency] [ws3: part2: ct] [2009-11-05 09:49:33] [a315839f8c359622c3a1e6ed387dd5cd] [Current]
- RM              [Univariate Data Series] [ws3:part2: univ t...] [2009-11-05 10:19:05] [bd8e774728cf1f2f4e6868fd314defe3]
- RM D            [Univariate Data Series] [ws3:part2: univ t...] [2009-11-05 10:22:12] [bd8e774728cf1f2f4e6868fd314defe3]
- RM D            [Univariate Data Series] [ws3:part2: yt-xt] [2009-11-05 10:29:29] [bd8e774728cf1f2f4e6868fd314defe3]
- RM D            [Univariate Data Series] [ws3:part2: yt/xt] [2009-11-05 10:33:10] [bd8e774728cf1f2f4e6868fd314defe3]
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Dataseries X:
3843
3905
3999
4070
4084
4042
3951
3933
3958
4147
4221
4058
4057
4089
4268
4309
4303
4177
4117
4065
3983
4091
4067
4024
3868
3800
3804
3862
3792
3674
3560
3489
3412
3674
3672
3463
3429
3400
3533
3578
3544
3435
3352
3213
3235
3460
3385
3283
3295
3331
3520
3668
3714
3691
3604
3581
3675
3833
3810
3663




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=53910&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=53910&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=53910&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 Mean3767.7166666666738.651872961442697.478243044656
Geometric Mean3755.94089219125
Harmonic Mean3744.10781742241
Quadratic Mean3779.39584457622
Winsorized Mean ( 1 / 20 )3767.9833333333338.540671097234997.7664172953042
Winsorized Mean ( 2 / 20 )3768.4166666666737.911838644626599.399469964794
Winsorized Mean ( 3 / 20 )3766.6666666666737.2770636275583101.045154851790
Winsorized Mean ( 4 / 20 )3766.1333333333336.1894611705076104.067129255921
Winsorized Mean ( 5 / 20 )3765.3833333333335.3684807465652106.461551467658
Winsorized Mean ( 6 / 20 )3765.6833333333334.1942646565897110.126167974419
Winsorized Mean ( 7 / 20 )3764.433.3510788922463112.871910745747
Winsorized Mean ( 8 / 20 )3765.7333333333333.0133671494766114.066926777962
Winsorized Mean ( 9 / 20 )3767.5333333333332.4319319060137116.167403910796
Winsorized Mean ( 10 / 20 )3766.231.8739466426150118.159198866344
Winsorized Mean ( 11 / 20 )3770.2333333333330.9922750231588121.650744597357
Winsorized Mean ( 12 / 20 )3770.4333333333330.8258124893876122.314159103880
Winsorized Mean ( 13 / 20 )3774.5529.6437837063587127.330236834455
Winsorized Mean ( 14 / 20 )3781.5528.4511815508323132.913636407110
Winsorized Mean ( 15 / 20 )3781.0527.3368857929859138.313121276240
Winsorized Mean ( 16 / 20 )3779.1833333333326.1176768901708144.698295687838
Winsorized Mean ( 17 / 20 )3776.6333333333324.3172530259265155.306741649921
Winsorized Mean ( 18 / 20 )3777.2333333333322.7691729187710165.89242599231
Winsorized Mean ( 19 / 20 )3770.2666666666721.4331422261735175.908255862854
Winsorized Mean ( 20 / 20 )3775.619.9530975463690189.223752914849
Trimmed Mean ( 1 / 20 )3767.9482758620737.6564807154791100.061083889690
Trimmed Mean ( 2 / 20 )3767.9107142857136.5635390453822103.051039714975
Trimmed Mean ( 3 / 20 )3767.6296296296335.6255694602694105.756334192255
Trimmed Mean ( 4 / 20 )376834.7554807032506108.414555740775
Trimmed Mean ( 5 / 20 )3768.5634.0779437915674110.586484414959
Trimmed Mean ( 6 / 20 )3769.3541666666733.4777301015344112.592883544811
Trimmed Mean ( 7 / 20 )3770.1521739130433.0408613570931114.105747219077
Trimmed Mean ( 8 / 20 )3771.2727272727332.6733846925733115.423387039848
Trimmed Mean ( 9 / 20 )3772.261904761932.2387302068033117.010250731459
Trimmed Mean ( 10 / 20 )3773.0531.7714383506916118.756033590713
Trimmed Mean ( 11 / 20 )3774.1315789473731.2403651389532120.809457961215
Trimmed Mean ( 12 / 20 )3774.7222222222230.7025827751552122.944777964307
Trimmed Mean ( 13 / 20 )3775.3529411764729.9478418350247126.06427407938
Trimmed Mean ( 14 / 20 )3775.4687529.1755664585180129.405156721395
Trimmed Mean ( 15 / 20 )3774.628.3625380249792133.083999629218
Trimmed Mean ( 16 / 20 )3773.6785714285727.4575214766137137.43697058173
Trimmed Mean ( 17 / 20 )3772.8846153846226.4438637304401142.675240420392
Trimmed Mean ( 18 / 20 )3772.3333333333325.4693383908501148.112733650299
Trimmed Mean ( 19 / 20 )3771.5909090909124.4381593502493154.332036837808
Trimmed Mean ( 20 / 20 )3771.823.2176883567589162.453726746745
Median3796
Midrange3761
Midmean - Weighted Average at Xnp3766.38709677419
Midmean - Weighted Average at X(n+1)p3774.6
Midmean - Empirical Distribution Function3766.38709677419
Midmean - Empirical Distribution Function - Averaging3774.6
Midmean - Empirical Distribution Function - Interpolation3774.6
Midmean - Closest Observation3766.38709677419
Midmean - True Basic - Statistics Graphics Toolkit3774.6
Midmean - MS Excel (old versions)3775.46875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3767.71666666667 & 38.6518729614426 & 97.478243044656 \tabularnewline
Geometric Mean & 3755.94089219125 &  &  \tabularnewline
Harmonic Mean & 3744.10781742241 &  &  \tabularnewline
Quadratic Mean & 3779.39584457622 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3767.98333333333 & 38.5406710972349 & 97.7664172953042 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3768.41666666667 & 37.9118386446265 & 99.399469964794 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3766.66666666667 & 37.2770636275583 & 101.045154851790 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3766.13333333333 & 36.1894611705076 & 104.067129255921 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3765.38333333333 & 35.3684807465652 & 106.461551467658 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3765.68333333333 & 34.1942646565897 & 110.126167974419 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3764.4 & 33.3510788922463 & 112.871910745747 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3765.73333333333 & 33.0133671494766 & 114.066926777962 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3767.53333333333 & 32.4319319060137 & 116.167403910796 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3766.2 & 31.8739466426150 & 118.159198866344 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3770.23333333333 & 30.9922750231588 & 121.650744597357 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3770.43333333333 & 30.8258124893876 & 122.314159103880 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3774.55 & 29.6437837063587 & 127.330236834455 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3781.55 & 28.4511815508323 & 132.913636407110 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3781.05 & 27.3368857929859 & 138.313121276240 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3779.18333333333 & 26.1176768901708 & 144.698295687838 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3776.63333333333 & 24.3172530259265 & 155.306741649921 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3777.23333333333 & 22.7691729187710 & 165.89242599231 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3770.26666666667 & 21.4331422261735 & 175.908255862854 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3775.6 & 19.9530975463690 & 189.223752914849 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3767.94827586207 & 37.6564807154791 & 100.061083889690 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3767.91071428571 & 36.5635390453822 & 103.051039714975 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3767.62962962963 & 35.6255694602694 & 105.756334192255 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3768 & 34.7554807032506 & 108.414555740775 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3768.56 & 34.0779437915674 & 110.586484414959 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3769.35416666667 & 33.4777301015344 & 112.592883544811 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3770.15217391304 & 33.0408613570931 & 114.105747219077 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3771.27272727273 & 32.6733846925733 & 115.423387039848 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3772.2619047619 & 32.2387302068033 & 117.010250731459 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3773.05 & 31.7714383506916 & 118.756033590713 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3774.13157894737 & 31.2403651389532 & 120.809457961215 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3774.72222222222 & 30.7025827751552 & 122.944777964307 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3775.35294117647 & 29.9478418350247 & 126.06427407938 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3775.46875 & 29.1755664585180 & 129.405156721395 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3774.6 & 28.3625380249792 & 133.083999629218 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3773.67857142857 & 27.4575214766137 & 137.43697058173 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3772.88461538462 & 26.4438637304401 & 142.675240420392 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3772.33333333333 & 25.4693383908501 & 148.112733650299 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3771.59090909091 & 24.4381593502493 & 154.332036837808 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3771.8 & 23.2176883567589 & 162.453726746745 \tabularnewline
Median & 3796 &  &  \tabularnewline
Midrange & 3761 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3766.38709677419 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3774.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3766.38709677419 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3774.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3774.6 &  &  \tabularnewline
Midmean - Closest Observation & 3766.38709677419 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3774.6 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3775.46875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=53910&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]3767.71666666667[/C][C]38.6518729614426[/C][C]97.478243044656[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3755.94089219125[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3744.10781742241[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3779.39584457622[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3767.98333333333[/C][C]38.5406710972349[/C][C]97.7664172953042[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3768.41666666667[/C][C]37.9118386446265[/C][C]99.399469964794[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3766.66666666667[/C][C]37.2770636275583[/C][C]101.045154851790[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3766.13333333333[/C][C]36.1894611705076[/C][C]104.067129255921[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3765.38333333333[/C][C]35.3684807465652[/C][C]106.461551467658[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3765.68333333333[/C][C]34.1942646565897[/C][C]110.126167974419[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3764.4[/C][C]33.3510788922463[/C][C]112.871910745747[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3765.73333333333[/C][C]33.0133671494766[/C][C]114.066926777962[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3767.53333333333[/C][C]32.4319319060137[/C][C]116.167403910796[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3766.2[/C][C]31.8739466426150[/C][C]118.159198866344[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3770.23333333333[/C][C]30.9922750231588[/C][C]121.650744597357[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3770.43333333333[/C][C]30.8258124893876[/C][C]122.314159103880[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3774.55[/C][C]29.6437837063587[/C][C]127.330236834455[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3781.55[/C][C]28.4511815508323[/C][C]132.913636407110[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3781.05[/C][C]27.3368857929859[/C][C]138.313121276240[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3779.18333333333[/C][C]26.1176768901708[/C][C]144.698295687838[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3776.63333333333[/C][C]24.3172530259265[/C][C]155.306741649921[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3777.23333333333[/C][C]22.7691729187710[/C][C]165.89242599231[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3770.26666666667[/C][C]21.4331422261735[/C][C]175.908255862854[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3775.6[/C][C]19.9530975463690[/C][C]189.223752914849[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3767.94827586207[/C][C]37.6564807154791[/C][C]100.061083889690[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3767.91071428571[/C][C]36.5635390453822[/C][C]103.051039714975[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3767.62962962963[/C][C]35.6255694602694[/C][C]105.756334192255[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3768[/C][C]34.7554807032506[/C][C]108.414555740775[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3768.56[/C][C]34.0779437915674[/C][C]110.586484414959[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3769.35416666667[/C][C]33.4777301015344[/C][C]112.592883544811[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3770.15217391304[/C][C]33.0408613570931[/C][C]114.105747219077[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3771.27272727273[/C][C]32.6733846925733[/C][C]115.423387039848[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3772.2619047619[/C][C]32.2387302068033[/C][C]117.010250731459[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3773.05[/C][C]31.7714383506916[/C][C]118.756033590713[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3774.13157894737[/C][C]31.2403651389532[/C][C]120.809457961215[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3774.72222222222[/C][C]30.7025827751552[/C][C]122.944777964307[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3775.35294117647[/C][C]29.9478418350247[/C][C]126.06427407938[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3775.46875[/C][C]29.1755664585180[/C][C]129.405156721395[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3774.6[/C][C]28.3625380249792[/C][C]133.083999629218[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3773.67857142857[/C][C]27.4575214766137[/C][C]137.43697058173[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3772.88461538462[/C][C]26.4438637304401[/C][C]142.675240420392[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3772.33333333333[/C][C]25.4693383908501[/C][C]148.112733650299[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3771.59090909091[/C][C]24.4381593502493[/C][C]154.332036837808[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3771.8[/C][C]23.2176883567589[/C][C]162.453726746745[/C][/ROW]
[ROW][C]Median[/C][C]3796[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3761[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3766.38709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3774.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3766.38709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3774.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3774.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3766.38709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3774.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3775.46875[/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=53910&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=53910&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 Mean3767.7166666666738.651872961442697.478243044656
Geometric Mean3755.94089219125
Harmonic Mean3744.10781742241
Quadratic Mean3779.39584457622
Winsorized Mean ( 1 / 20 )3767.9833333333338.540671097234997.7664172953042
Winsorized Mean ( 2 / 20 )3768.4166666666737.911838644626599.399469964794
Winsorized Mean ( 3 / 20 )3766.6666666666737.2770636275583101.045154851790
Winsorized Mean ( 4 / 20 )3766.1333333333336.1894611705076104.067129255921
Winsorized Mean ( 5 / 20 )3765.3833333333335.3684807465652106.461551467658
Winsorized Mean ( 6 / 20 )3765.6833333333334.1942646565897110.126167974419
Winsorized Mean ( 7 / 20 )3764.433.3510788922463112.871910745747
Winsorized Mean ( 8 / 20 )3765.7333333333333.0133671494766114.066926777962
Winsorized Mean ( 9 / 20 )3767.5333333333332.4319319060137116.167403910796
Winsorized Mean ( 10 / 20 )3766.231.8739466426150118.159198866344
Winsorized Mean ( 11 / 20 )3770.2333333333330.9922750231588121.650744597357
Winsorized Mean ( 12 / 20 )3770.4333333333330.8258124893876122.314159103880
Winsorized Mean ( 13 / 20 )3774.5529.6437837063587127.330236834455
Winsorized Mean ( 14 / 20 )3781.5528.4511815508323132.913636407110
Winsorized Mean ( 15 / 20 )3781.0527.3368857929859138.313121276240
Winsorized Mean ( 16 / 20 )3779.1833333333326.1176768901708144.698295687838
Winsorized Mean ( 17 / 20 )3776.6333333333324.3172530259265155.306741649921
Winsorized Mean ( 18 / 20 )3777.2333333333322.7691729187710165.89242599231
Winsorized Mean ( 19 / 20 )3770.2666666666721.4331422261735175.908255862854
Winsorized Mean ( 20 / 20 )3775.619.9530975463690189.223752914849
Trimmed Mean ( 1 / 20 )3767.9482758620737.6564807154791100.061083889690
Trimmed Mean ( 2 / 20 )3767.9107142857136.5635390453822103.051039714975
Trimmed Mean ( 3 / 20 )3767.6296296296335.6255694602694105.756334192255
Trimmed Mean ( 4 / 20 )376834.7554807032506108.414555740775
Trimmed Mean ( 5 / 20 )3768.5634.0779437915674110.586484414959
Trimmed Mean ( 6 / 20 )3769.3541666666733.4777301015344112.592883544811
Trimmed Mean ( 7 / 20 )3770.1521739130433.0408613570931114.105747219077
Trimmed Mean ( 8 / 20 )3771.2727272727332.6733846925733115.423387039848
Trimmed Mean ( 9 / 20 )3772.261904761932.2387302068033117.010250731459
Trimmed Mean ( 10 / 20 )3773.0531.7714383506916118.756033590713
Trimmed Mean ( 11 / 20 )3774.1315789473731.2403651389532120.809457961215
Trimmed Mean ( 12 / 20 )3774.7222222222230.7025827751552122.944777964307
Trimmed Mean ( 13 / 20 )3775.3529411764729.9478418350247126.06427407938
Trimmed Mean ( 14 / 20 )3775.4687529.1755664585180129.405156721395
Trimmed Mean ( 15 / 20 )3774.628.3625380249792133.083999629218
Trimmed Mean ( 16 / 20 )3773.6785714285727.4575214766137137.43697058173
Trimmed Mean ( 17 / 20 )3772.8846153846226.4438637304401142.675240420392
Trimmed Mean ( 18 / 20 )3772.3333333333325.4693383908501148.112733650299
Trimmed Mean ( 19 / 20 )3771.5909090909124.4381593502493154.332036837808
Trimmed Mean ( 20 / 20 )3771.823.2176883567589162.453726746745
Median3796
Midrange3761
Midmean - Weighted Average at Xnp3766.38709677419
Midmean - Weighted Average at X(n+1)p3774.6
Midmean - Empirical Distribution Function3766.38709677419
Midmean - Empirical Distribution Function - Averaging3774.6
Midmean - Empirical Distribution Function - Interpolation3774.6
Midmean - Closest Observation3766.38709677419
Midmean - True Basic - Statistics Graphics Toolkit3774.6
Midmean - MS Excel (old versions)3775.46875
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')