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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 computationTue, 20 Oct 2009 09:34:23 -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/20/t1256053253fr4xjs9xdkbzph6.htm/, Retrieved Thu, 02 May 2024 14:43:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48741, Retrieved Thu, 02 May 2024 14:43:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordspar 2 vraag 3
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [shw ws 2 3/4] [2009-10-11 14:41:29] [55b7a497389226c9339ee8d75ebc3b97]
- RMPD    [Central Tendency] [shw ws 3 9] [2009-10-20 15:34:23] [84778c3520b84fd5786bccf2e25a5aef] [Current]
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Dataseries X:
4.04
3.91
3.78
3.59
3.53
3.49
3.67
3.54
3.36
3.19
3.22
3.24
3.08
3.25
3.45
3.36
3.33
3.49
3.67
3.95
4.01
4.01
4.04
3.92
3.80
3.84
3.77
3.83
4.06
4.10
4.01
4.24
4.36
4.64
4.62
4.44
4.40
4.42
4.29
4.42
4.25
4.15
4.14
4.39
4.53
4.84
4.86
4.57
4.57
4.44
4.20
3.84
4.04
4.06
4.01
3.90
3.93
4.03
3.78
3.62
3.60




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48741&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48741&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48741&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.952622950819670.055541498116983971.1652203275916
Geometric Mean3.92895191871496
Harmonic Mean3.90504852272863
Quadratic Mean3.97596776547939
Winsorized Mean ( 1 / 20 )3.954098360655740.055007886691963271.8823899343408
Winsorized Mean ( 2 / 20 )3.948524590163930.053188414483581474.2365537401532
Winsorized Mean ( 3 / 20 )3.948524590163930.052755149473136774.8462402172617
Winsorized Mean ( 4 / 20 )3.945901639344260.05193226833569675.9816924197787
Winsorized Mean ( 5 / 20 )3.952459016393440.050526006795670378.2262297588129
Winsorized Mean ( 6 / 20 )3.951475409836070.049140056371511180.4125127566384
Winsorized Mean ( 7 / 20 )3.941147540983610.047215410539203883.4716355523627
Winsorized Mean ( 8 / 20 )3.952950819672130.04490021983363888.0385627134655
Winsorized Mean ( 9 / 20 )3.955901639344260.043289202233465391.3831032969719
Winsorized Mean ( 10 / 20 )3.955901639344260.043289202233465391.3831032969719
Winsorized Mean ( 11 / 20 )3.959508196721310.04137554663730795.6968189793328
Winsorized Mean ( 12 / 20 )3.959508196721310.040688357264861697.3130512727959
Winsorized Mean ( 13 / 20 )3.963770491803280.0377699130951416104.945184327500
Winsorized Mean ( 14 / 20 )3.950.0346662463194356113.943689305220
Winsorized Mean ( 15 / 20 )3.945081967213110.0322597237857567122.291250644711
Winsorized Mean ( 16 / 20 )3.95557377049180.0296892140542066133.232687240212
Winsorized Mean ( 17 / 20 )3.94442622950820.0279485520609573141.131684421618
Winsorized Mean ( 18 / 20 )3.959180327868850.0210558651693773188.032184667810
Winsorized Mean ( 19 / 20 )3.959180327868850.0201229758605567196.749246001398
Winsorized Mean ( 20 / 20 )3.946065573770490.0182143861483418216.64554279419
Trimmed Mean ( 1 / 20 )3.952033898305080.053256752499493874.2071890009186
Trimmed Mean ( 2 / 20 )3.949824561403510.051104033670522377.2898786594576
Trimmed Mean ( 3 / 20 )3.950545454545450.049669899007975779.5360073897291
Trimmed Mean ( 4 / 20 )3.951320754716980.048092072537144182.1615818628977
Trimmed Mean ( 5 / 20 )3.952941176470590.046439751496225185.1197745274737
Trimmed Mean ( 6 / 20 )3.95306122448980.044847819096248788.1438898066829
Trimmed Mean ( 7 / 20 )3.953404255319150.043260154220450091.3867351275018
Trimmed Mean ( 8 / 20 )3.955777777777780.041784063571828994.671926079607
Trimmed Mean ( 9 / 20 )3.956279069767440.04052947364954897.614864283133
Trimmed Mean ( 10 / 20 )3.956341463414630.0393092121294633100.646674127799
Trimmed Mean ( 11 / 20 )3.956410256410260.0376583246697837105.060708119732
Trimmed Mean ( 12 / 20 )3.955945945945950.0359668254291419109.988743758871
Trimmed Mean ( 13 / 20 )3.955428571428570.0338269020710069116.931445957588
Trimmed Mean ( 14 / 20 )3.954242424242420.0317483902688755124.549383157828
Trimmed Mean ( 15 / 20 )3.954838709677420.0298053577046391132.688852416016
Trimmed Mean ( 16 / 20 )3.956206896551720.0277853037008707142.384871482537
Trimmed Mean ( 17 / 20 )3.95629629629630.0257212104883902153.814545317844
Trimmed Mean ( 18 / 20 )3.9580.0232020114070598170.588658481380
Trimmed Mean ( 19 / 20 )3.957826086956520.0222628612004319177.777063393799
Trimmed Mean ( 20 / 20 )3.957619047619050.0210430936742490188.072110920748
Median4.01
Midrange3.97
Midmean - Weighted Average at Xnp3.945
Midmean - Weighted Average at X(n+1)p3.95483870967742
Midmean - Empirical Distribution Function3.95483870967742
Midmean - Empirical Distribution Function - Averaging3.95483870967742
Midmean - Empirical Distribution Function - Interpolation3.95483870967742
Midmean - Closest Observation3.94375
Midmean - True Basic - Statistics Graphics Toolkit3.95483870967742
Midmean - MS Excel (old versions)3.95483870967742
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.95262295081967 & 0.0555414981169839 & 71.1652203275916 \tabularnewline
Geometric Mean & 3.92895191871496 &  &  \tabularnewline
Harmonic Mean & 3.90504852272863 &  &  \tabularnewline
Quadratic Mean & 3.97596776547939 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3.95409836065574 & 0.0550078866919632 & 71.8823899343408 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3.94852459016393 & 0.0531884144835814 & 74.2365537401532 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3.94852459016393 & 0.0527551494731367 & 74.8462402172617 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3.94590163934426 & 0.051932268335696 & 75.9816924197787 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3.95245901639344 & 0.0505260067956703 & 78.2262297588129 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3.95147540983607 & 0.0491400563715111 & 80.4125127566384 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3.94114754098361 & 0.0472154105392038 & 83.4716355523627 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3.95295081967213 & 0.044900219833638 & 88.0385627134655 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3.95590163934426 & 0.0432892022334653 & 91.3831032969719 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3.95590163934426 & 0.0432892022334653 & 91.3831032969719 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3.95950819672131 & 0.041375546637307 & 95.6968189793328 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3.95950819672131 & 0.0406883572648616 & 97.3130512727959 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3.96377049180328 & 0.0377699130951416 & 104.945184327500 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3.95 & 0.0346662463194356 & 113.943689305220 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3.94508196721311 & 0.0322597237857567 & 122.291250644711 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3.9555737704918 & 0.0296892140542066 & 133.232687240212 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3.9444262295082 & 0.0279485520609573 & 141.131684421618 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3.95918032786885 & 0.0210558651693773 & 188.032184667810 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3.95918032786885 & 0.0201229758605567 & 196.749246001398 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3.94606557377049 & 0.0182143861483418 & 216.64554279419 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3.95203389830508 & 0.0532567524994938 & 74.2071890009186 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3.94982456140351 & 0.0511040336705223 & 77.2898786594576 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3.95054545454545 & 0.0496698990079757 & 79.5360073897291 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3.95132075471698 & 0.0480920725371441 & 82.1615818628977 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3.95294117647059 & 0.0464397514962251 & 85.1197745274737 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3.9530612244898 & 0.0448478190962487 & 88.1438898066829 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3.95340425531915 & 0.0432601542204500 & 91.3867351275018 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3.95577777777778 & 0.0417840635718289 & 94.671926079607 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3.95627906976744 & 0.040529473649548 & 97.614864283133 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3.95634146341463 & 0.0393092121294633 & 100.646674127799 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3.95641025641026 & 0.0376583246697837 & 105.060708119732 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3.95594594594595 & 0.0359668254291419 & 109.988743758871 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3.95542857142857 & 0.0338269020710069 & 116.931445957588 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3.95424242424242 & 0.0317483902688755 & 124.549383157828 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3.95483870967742 & 0.0298053577046391 & 132.688852416016 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3.95620689655172 & 0.0277853037008707 & 142.384871482537 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3.9562962962963 & 0.0257212104883902 & 153.814545317844 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3.958 & 0.0232020114070598 & 170.588658481380 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3.95782608695652 & 0.0222628612004319 & 177.777063393799 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3.95761904761905 & 0.0210430936742490 & 188.072110920748 \tabularnewline
Median & 4.01 &  &  \tabularnewline
Midrange & 3.97 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.945 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.95483870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.95483870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.95483870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.95483870967742 &  &  \tabularnewline
Midmean - Closest Observation & 3.94375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.95483870967742 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.95483870967742 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48741&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]3.95262295081967[/C][C]0.0555414981169839[/C][C]71.1652203275916[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.92895191871496[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.90504852272863[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.97596776547939[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3.95409836065574[/C][C]0.0550078866919632[/C][C]71.8823899343408[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3.94852459016393[/C][C]0.0531884144835814[/C][C]74.2365537401532[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3.94852459016393[/C][C]0.0527551494731367[/C][C]74.8462402172617[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3.94590163934426[/C][C]0.051932268335696[/C][C]75.9816924197787[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3.95245901639344[/C][C]0.0505260067956703[/C][C]78.2262297588129[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3.95147540983607[/C][C]0.0491400563715111[/C][C]80.4125127566384[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3.94114754098361[/C][C]0.0472154105392038[/C][C]83.4716355523627[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3.95295081967213[/C][C]0.044900219833638[/C][C]88.0385627134655[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3.95590163934426[/C][C]0.0432892022334653[/C][C]91.3831032969719[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3.95590163934426[/C][C]0.0432892022334653[/C][C]91.3831032969719[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3.95950819672131[/C][C]0.041375546637307[/C][C]95.6968189793328[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3.95950819672131[/C][C]0.0406883572648616[/C][C]97.3130512727959[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3.96377049180328[/C][C]0.0377699130951416[/C][C]104.945184327500[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3.95[/C][C]0.0346662463194356[/C][C]113.943689305220[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3.94508196721311[/C][C]0.0322597237857567[/C][C]122.291250644711[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3.9555737704918[/C][C]0.0296892140542066[/C][C]133.232687240212[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3.9444262295082[/C][C]0.0279485520609573[/C][C]141.131684421618[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3.95918032786885[/C][C]0.0210558651693773[/C][C]188.032184667810[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3.95918032786885[/C][C]0.0201229758605567[/C][C]196.749246001398[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3.94606557377049[/C][C]0.0182143861483418[/C][C]216.64554279419[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3.95203389830508[/C][C]0.0532567524994938[/C][C]74.2071890009186[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3.94982456140351[/C][C]0.0511040336705223[/C][C]77.2898786594576[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3.95054545454545[/C][C]0.0496698990079757[/C][C]79.5360073897291[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3.95132075471698[/C][C]0.0480920725371441[/C][C]82.1615818628977[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3.95294117647059[/C][C]0.0464397514962251[/C][C]85.1197745274737[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3.9530612244898[/C][C]0.0448478190962487[/C][C]88.1438898066829[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3.95340425531915[/C][C]0.0432601542204500[/C][C]91.3867351275018[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3.95577777777778[/C][C]0.0417840635718289[/C][C]94.671926079607[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3.95627906976744[/C][C]0.040529473649548[/C][C]97.614864283133[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3.95634146341463[/C][C]0.0393092121294633[/C][C]100.646674127799[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3.95641025641026[/C][C]0.0376583246697837[/C][C]105.060708119732[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3.95594594594595[/C][C]0.0359668254291419[/C][C]109.988743758871[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3.95542857142857[/C][C]0.0338269020710069[/C][C]116.931445957588[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3.95424242424242[/C][C]0.0317483902688755[/C][C]124.549383157828[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3.95483870967742[/C][C]0.0298053577046391[/C][C]132.688852416016[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3.95620689655172[/C][C]0.0277853037008707[/C][C]142.384871482537[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3.9562962962963[/C][C]0.0257212104883902[/C][C]153.814545317844[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3.958[/C][C]0.0232020114070598[/C][C]170.588658481380[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3.95782608695652[/C][C]0.0222628612004319[/C][C]177.777063393799[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3.95761904761905[/C][C]0.0210430936742490[/C][C]188.072110920748[/C][/ROW]
[ROW][C]Median[/C][C]4.01[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.97[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.945[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.95483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.95483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.95483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.95483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.94375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.95483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.95483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48741&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48741&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 Mean3.952622950819670.055541498116983971.1652203275916
Geometric Mean3.92895191871496
Harmonic Mean3.90504852272863
Quadratic Mean3.97596776547939
Winsorized Mean ( 1 / 20 )3.954098360655740.055007886691963271.8823899343408
Winsorized Mean ( 2 / 20 )3.948524590163930.053188414483581474.2365537401532
Winsorized Mean ( 3 / 20 )3.948524590163930.052755149473136774.8462402172617
Winsorized Mean ( 4 / 20 )3.945901639344260.05193226833569675.9816924197787
Winsorized Mean ( 5 / 20 )3.952459016393440.050526006795670378.2262297588129
Winsorized Mean ( 6 / 20 )3.951475409836070.049140056371511180.4125127566384
Winsorized Mean ( 7 / 20 )3.941147540983610.047215410539203883.4716355523627
Winsorized Mean ( 8 / 20 )3.952950819672130.04490021983363888.0385627134655
Winsorized Mean ( 9 / 20 )3.955901639344260.043289202233465391.3831032969719
Winsorized Mean ( 10 / 20 )3.955901639344260.043289202233465391.3831032969719
Winsorized Mean ( 11 / 20 )3.959508196721310.04137554663730795.6968189793328
Winsorized Mean ( 12 / 20 )3.959508196721310.040688357264861697.3130512727959
Winsorized Mean ( 13 / 20 )3.963770491803280.0377699130951416104.945184327500
Winsorized Mean ( 14 / 20 )3.950.0346662463194356113.943689305220
Winsorized Mean ( 15 / 20 )3.945081967213110.0322597237857567122.291250644711
Winsorized Mean ( 16 / 20 )3.95557377049180.0296892140542066133.232687240212
Winsorized Mean ( 17 / 20 )3.94442622950820.0279485520609573141.131684421618
Winsorized Mean ( 18 / 20 )3.959180327868850.0210558651693773188.032184667810
Winsorized Mean ( 19 / 20 )3.959180327868850.0201229758605567196.749246001398
Winsorized Mean ( 20 / 20 )3.946065573770490.0182143861483418216.64554279419
Trimmed Mean ( 1 / 20 )3.952033898305080.053256752499493874.2071890009186
Trimmed Mean ( 2 / 20 )3.949824561403510.051104033670522377.2898786594576
Trimmed Mean ( 3 / 20 )3.950545454545450.049669899007975779.5360073897291
Trimmed Mean ( 4 / 20 )3.951320754716980.048092072537144182.1615818628977
Trimmed Mean ( 5 / 20 )3.952941176470590.046439751496225185.1197745274737
Trimmed Mean ( 6 / 20 )3.95306122448980.044847819096248788.1438898066829
Trimmed Mean ( 7 / 20 )3.953404255319150.043260154220450091.3867351275018
Trimmed Mean ( 8 / 20 )3.955777777777780.041784063571828994.671926079607
Trimmed Mean ( 9 / 20 )3.956279069767440.04052947364954897.614864283133
Trimmed Mean ( 10 / 20 )3.956341463414630.0393092121294633100.646674127799
Trimmed Mean ( 11 / 20 )3.956410256410260.0376583246697837105.060708119732
Trimmed Mean ( 12 / 20 )3.955945945945950.0359668254291419109.988743758871
Trimmed Mean ( 13 / 20 )3.955428571428570.0338269020710069116.931445957588
Trimmed Mean ( 14 / 20 )3.954242424242420.0317483902688755124.549383157828
Trimmed Mean ( 15 / 20 )3.954838709677420.0298053577046391132.688852416016
Trimmed Mean ( 16 / 20 )3.956206896551720.0277853037008707142.384871482537
Trimmed Mean ( 17 / 20 )3.95629629629630.0257212104883902153.814545317844
Trimmed Mean ( 18 / 20 )3.9580.0232020114070598170.588658481380
Trimmed Mean ( 19 / 20 )3.957826086956520.0222628612004319177.777063393799
Trimmed Mean ( 20 / 20 )3.957619047619050.0210430936742490188.072110920748
Median4.01
Midrange3.97
Midmean - Weighted Average at Xnp3.945
Midmean - Weighted Average at X(n+1)p3.95483870967742
Midmean - Empirical Distribution Function3.95483870967742
Midmean - Empirical Distribution Function - Averaging3.95483870967742
Midmean - Empirical Distribution Function - Interpolation3.95483870967742
Midmean - Closest Observation3.94375
Midmean - True Basic - Statistics Graphics Toolkit3.95483870967742
Midmean - MS Excel (old versions)3.95483870967742
Number of observations61



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')