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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 19 Oct 2009 01:37:21 -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/19/t1255937886a9t2sn1nhsznl65.htm/, Retrieved Mon, 29 Apr 2024 22:07:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47560, Retrieved Mon, 29 Apr 2024 22:07:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsGemiddelden task 2.1
Estimated Impact151
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS3] [2009-10-19 07:37:21] [eeda0e496238f8886c14dbbeff6ff613] [Current]
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Dataseries X:
7.5
6.8
6.5
6.6
7.6
8
8.1
7.7
7.5
7.6
7.8
7.8
7.8
7.5
7.5
7.1
7.5
7.5
7.6
7.7
7.7
7.9
8.1
8.2
8.2
8.2
7.9
7.3
6.9
6.6
6.7
6.9
7
7.1
7.2
7.1
6.9
7
6.8
6.4
6.7
6.6
6.4
6.3
6.2
6.5
6.8
6.8
6.4
6.1
5.8
6.1
7.2
7.3
6.9
6.1
5.8
6.2
7.1
7.7
7.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47560&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47560&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47560&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.126229508196720.083433872881208885.4117070454452
Geometric Mean7.09645471824593
Harmonic Mean7.06625848623583
Quadratic Mean7.15547480410148
Winsorized Mean ( 1 / 20 )7.126229508196720.083433872881208885.4117070454452
Winsorized Mean ( 2 / 20 )7.13606557377050.081079896738406388.0127610028177
Winsorized Mean ( 3 / 20 )7.13114754098360.08004578551848289.0883573044215
Winsorized Mean ( 4 / 20 )7.13114754098360.08004578551848289.0883573044215
Winsorized Mean ( 5 / 20 )7.13114754098360.076734621235858792.9325958235285
Winsorized Mean ( 6 / 20 )7.121311475409840.074954075341995695.0089964143667
Winsorized Mean ( 7 / 20 )7.13278688524590.07268170414452398.1373093710462
Winsorized Mean ( 8 / 20 )7.145901639344260.0702677848475879101.695274083904
Winsorized Mean ( 9 / 20 )7.13114754098360.0677322349263869105.284397432536
Winsorized Mean ( 10 / 20 )7.13114754098360.0677322349263869105.284397432536
Winsorized Mean ( 11 / 20 )7.149180327868850.0645972368599738110.673159958312
Winsorized Mean ( 12 / 20 )7.129508196721310.0614196468404526116.078625708177
Winsorized Mean ( 13 / 20 )7.150819672131150.0579062248708723123.48965397204
Winsorized Mean ( 14 / 20 )7.150819672131150.0579062248708723123.48965397204
Winsorized Mean ( 15 / 20 )7.150819672131150.0579062248708723123.48965397204
Winsorized Mean ( 16 / 20 )7.150819672131150.0497876886278657143.626263223011
Winsorized Mean ( 17 / 20 )7.150819672131150.0497876886278657143.626263223011
Winsorized Mean ( 18 / 20 )7.180327868852460.0454978334998016157.816918224991
Winsorized Mean ( 19 / 20 )7.149180327868850.0408664993546842174.939875956109
Winsorized Mean ( 20 / 20 )7.149180327868850.0408664993546842174.939875956109
Trimmed Mean ( 1 / 20 )7.130508474576270.08120419807046587.809603986099
Trimmed Mean ( 2 / 20 )7.135087719298250.07845992655889890.939260744045
Trimmed Mean ( 3 / 20 )7.134545454545450.076638913809413793.0929876209846
Trimmed Mean ( 4 / 20 )7.135849056603770.07485323519222195.3312042997088
Trimmed Mean ( 5 / 20 )7.137254901960780.07259669869411598.3137667462468
Trimmed Mean ( 6 / 20 )7.138775510204080.0708798162727031100.716619844757
Trimmed Mean ( 7 / 20 )7.142553191489360.0692061956054919103.206846280141
Trimmed Mean ( 8 / 20 )7.144444444444440.0676858127530128105.553056894134
Trimmed Mean ( 9 / 20 )7.144186046511630.0663310204203462107.705052647136
Trimmed Mean ( 10 / 20 )7.146341463414630.0651543721251278109.683222020622
Trimmed Mean ( 11 / 20 )7.148717948717950.0635087203116608112.562777420747
Trimmed Mean ( 12 / 20 )7.148648648648650.06207396798841115.163391036697
Trimmed Mean ( 13 / 20 )7.151428571428570.0608582080626388117.509680273003
Trimmed Mean ( 14 / 20 )7.151515151515150.0600065040857965119.179000017898
Trimmed Mean ( 15 / 20 )7.15161290322580.0586351884774285121.967935789595
Trimmed Mean ( 16 / 20 )7.151724137931030.0565033434764618126.571698202431
Trimmed Mean ( 17 / 20 )7.151851851851850.0558208291573747128.121562502928
Trimmed Mean ( 18 / 20 )7.1520.0545038224959192131.220154339367
Trimmed Mean ( 19 / 20 )7.147826086956520.0536676808616401133.186788998471
Trimmed Mean ( 20 / 20 )7.147619047619050.0537272865050222133.035176584824
Median7.1
Midrange7
Midmean - Weighted Average at Xnp7.1
Midmean - Weighted Average at X(n+1)p7.16666666666667
Midmean - Empirical Distribution Function7.16666666666667
Midmean - Empirical Distribution Function - Averaging7.16666666666667
Midmean - Empirical Distribution Function - Interpolation7.16666666666667
Midmean - Closest Observation7.16666666666667
Midmean - True Basic - Statistics Graphics Toolkit7.16666666666667
Midmean - MS Excel (old versions)7.16666666666667
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.12622950819672 & 0.0834338728812088 & 85.4117070454452 \tabularnewline
Geometric Mean & 7.09645471824593 &  &  \tabularnewline
Harmonic Mean & 7.06625848623583 &  &  \tabularnewline
Quadratic Mean & 7.15547480410148 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.12622950819672 & 0.0834338728812088 & 85.4117070454452 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.1360655737705 & 0.0810798967384063 & 88.0127610028177 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.1311475409836 & 0.080045785518482 & 89.0883573044215 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.1311475409836 & 0.080045785518482 & 89.0883573044215 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.1311475409836 & 0.0767346212358587 & 92.9325958235285 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.12131147540984 & 0.0749540753419956 & 95.0089964143667 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.1327868852459 & 0.072681704144523 & 98.1373093710462 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.14590163934426 & 0.0702677848475879 & 101.695274083904 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.1311475409836 & 0.0677322349263869 & 105.284397432536 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.1311475409836 & 0.0677322349263869 & 105.284397432536 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.14918032786885 & 0.0645972368599738 & 110.673159958312 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.12950819672131 & 0.0614196468404526 & 116.078625708177 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.15081967213115 & 0.0579062248708723 & 123.48965397204 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.15081967213115 & 0.0579062248708723 & 123.48965397204 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.15081967213115 & 0.0579062248708723 & 123.48965397204 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.15081967213115 & 0.0497876886278657 & 143.626263223011 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.15081967213115 & 0.0497876886278657 & 143.626263223011 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.18032786885246 & 0.0454978334998016 & 157.816918224991 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.14918032786885 & 0.0408664993546842 & 174.939875956109 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.14918032786885 & 0.0408664993546842 & 174.939875956109 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.13050847457627 & 0.081204198070465 & 87.809603986099 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.13508771929825 & 0.078459926558898 & 90.939260744045 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.13454545454545 & 0.0766389138094137 & 93.0929876209846 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.13584905660377 & 0.074853235192221 & 95.3312042997088 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.13725490196078 & 0.072596698694115 & 98.3137667462468 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.13877551020408 & 0.0708798162727031 & 100.716619844757 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.14255319148936 & 0.0692061956054919 & 103.206846280141 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.14444444444444 & 0.0676858127530128 & 105.553056894134 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.14418604651163 & 0.0663310204203462 & 107.705052647136 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.14634146341463 & 0.0651543721251278 & 109.683222020622 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.14871794871795 & 0.0635087203116608 & 112.562777420747 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.14864864864865 & 0.06207396798841 & 115.163391036697 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.15142857142857 & 0.0608582080626388 & 117.509680273003 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.15151515151515 & 0.0600065040857965 & 119.179000017898 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.1516129032258 & 0.0586351884774285 & 121.967935789595 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.15172413793103 & 0.0565033434764618 & 126.571698202431 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.15185185185185 & 0.0558208291573747 & 128.121562502928 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.152 & 0.0545038224959192 & 131.220154339367 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.14782608695652 & 0.0536676808616401 & 133.186788998471 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.14761904761905 & 0.0537272865050222 & 133.035176584824 \tabularnewline
Median & 7.1 &  &  \tabularnewline
Midrange & 7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.1 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.16666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.16666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.16666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.16666666666667 &  &  \tabularnewline
Midmean - Closest Observation & 7.16666666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.16666666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.16666666666667 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47560&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]7.12622950819672[/C][C]0.0834338728812088[/C][C]85.4117070454452[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.09645471824593[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.06625848623583[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.15547480410148[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.12622950819672[/C][C]0.0834338728812088[/C][C]85.4117070454452[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.1360655737705[/C][C]0.0810798967384063[/C][C]88.0127610028177[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.1311475409836[/C][C]0.080045785518482[/C][C]89.0883573044215[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.1311475409836[/C][C]0.080045785518482[/C][C]89.0883573044215[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.1311475409836[/C][C]0.0767346212358587[/C][C]92.9325958235285[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.12131147540984[/C][C]0.0749540753419956[/C][C]95.0089964143667[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.1327868852459[/C][C]0.072681704144523[/C][C]98.1373093710462[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.14590163934426[/C][C]0.0702677848475879[/C][C]101.695274083904[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.1311475409836[/C][C]0.0677322349263869[/C][C]105.284397432536[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.1311475409836[/C][C]0.0677322349263869[/C][C]105.284397432536[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.14918032786885[/C][C]0.0645972368599738[/C][C]110.673159958312[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.12950819672131[/C][C]0.0614196468404526[/C][C]116.078625708177[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.15081967213115[/C][C]0.0579062248708723[/C][C]123.48965397204[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.15081967213115[/C][C]0.0579062248708723[/C][C]123.48965397204[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.15081967213115[/C][C]0.0579062248708723[/C][C]123.48965397204[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.15081967213115[/C][C]0.0497876886278657[/C][C]143.626263223011[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.15081967213115[/C][C]0.0497876886278657[/C][C]143.626263223011[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.18032786885246[/C][C]0.0454978334998016[/C][C]157.816918224991[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.14918032786885[/C][C]0.0408664993546842[/C][C]174.939875956109[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.14918032786885[/C][C]0.0408664993546842[/C][C]174.939875956109[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.13050847457627[/C][C]0.081204198070465[/C][C]87.809603986099[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.13508771929825[/C][C]0.078459926558898[/C][C]90.939260744045[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.13454545454545[/C][C]0.0766389138094137[/C][C]93.0929876209846[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.13584905660377[/C][C]0.074853235192221[/C][C]95.3312042997088[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.13725490196078[/C][C]0.072596698694115[/C][C]98.3137667462468[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.13877551020408[/C][C]0.0708798162727031[/C][C]100.716619844757[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.14255319148936[/C][C]0.0692061956054919[/C][C]103.206846280141[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.14444444444444[/C][C]0.0676858127530128[/C][C]105.553056894134[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.14418604651163[/C][C]0.0663310204203462[/C][C]107.705052647136[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.14634146341463[/C][C]0.0651543721251278[/C][C]109.683222020622[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.14871794871795[/C][C]0.0635087203116608[/C][C]112.562777420747[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.14864864864865[/C][C]0.06207396798841[/C][C]115.163391036697[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.15142857142857[/C][C]0.0608582080626388[/C][C]117.509680273003[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.15151515151515[/C][C]0.0600065040857965[/C][C]119.179000017898[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.1516129032258[/C][C]0.0586351884774285[/C][C]121.967935789595[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.15172413793103[/C][C]0.0565033434764618[/C][C]126.571698202431[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.15185185185185[/C][C]0.0558208291573747[/C][C]128.121562502928[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.152[/C][C]0.0545038224959192[/C][C]131.220154339367[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.14782608695652[/C][C]0.0536676808616401[/C][C]133.186788998471[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.14761904761905[/C][C]0.0537272865050222[/C][C]133.035176584824[/C][/ROW]
[ROW][C]Median[/C][C]7.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.16666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.16666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.16666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.16666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.16666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.16666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.16666666666667[/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=47560&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47560&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 Mean7.126229508196720.083433872881208885.4117070454452
Geometric Mean7.09645471824593
Harmonic Mean7.06625848623583
Quadratic Mean7.15547480410148
Winsorized Mean ( 1 / 20 )7.126229508196720.083433872881208885.4117070454452
Winsorized Mean ( 2 / 20 )7.13606557377050.081079896738406388.0127610028177
Winsorized Mean ( 3 / 20 )7.13114754098360.08004578551848289.0883573044215
Winsorized Mean ( 4 / 20 )7.13114754098360.08004578551848289.0883573044215
Winsorized Mean ( 5 / 20 )7.13114754098360.076734621235858792.9325958235285
Winsorized Mean ( 6 / 20 )7.121311475409840.074954075341995695.0089964143667
Winsorized Mean ( 7 / 20 )7.13278688524590.07268170414452398.1373093710462
Winsorized Mean ( 8 / 20 )7.145901639344260.0702677848475879101.695274083904
Winsorized Mean ( 9 / 20 )7.13114754098360.0677322349263869105.284397432536
Winsorized Mean ( 10 / 20 )7.13114754098360.0677322349263869105.284397432536
Winsorized Mean ( 11 / 20 )7.149180327868850.0645972368599738110.673159958312
Winsorized Mean ( 12 / 20 )7.129508196721310.0614196468404526116.078625708177
Winsorized Mean ( 13 / 20 )7.150819672131150.0579062248708723123.48965397204
Winsorized Mean ( 14 / 20 )7.150819672131150.0579062248708723123.48965397204
Winsorized Mean ( 15 / 20 )7.150819672131150.0579062248708723123.48965397204
Winsorized Mean ( 16 / 20 )7.150819672131150.0497876886278657143.626263223011
Winsorized Mean ( 17 / 20 )7.150819672131150.0497876886278657143.626263223011
Winsorized Mean ( 18 / 20 )7.180327868852460.0454978334998016157.816918224991
Winsorized Mean ( 19 / 20 )7.149180327868850.0408664993546842174.939875956109
Winsorized Mean ( 20 / 20 )7.149180327868850.0408664993546842174.939875956109
Trimmed Mean ( 1 / 20 )7.130508474576270.08120419807046587.809603986099
Trimmed Mean ( 2 / 20 )7.135087719298250.07845992655889890.939260744045
Trimmed Mean ( 3 / 20 )7.134545454545450.076638913809413793.0929876209846
Trimmed Mean ( 4 / 20 )7.135849056603770.07485323519222195.3312042997088
Trimmed Mean ( 5 / 20 )7.137254901960780.07259669869411598.3137667462468
Trimmed Mean ( 6 / 20 )7.138775510204080.0708798162727031100.716619844757
Trimmed Mean ( 7 / 20 )7.142553191489360.0692061956054919103.206846280141
Trimmed Mean ( 8 / 20 )7.144444444444440.0676858127530128105.553056894134
Trimmed Mean ( 9 / 20 )7.144186046511630.0663310204203462107.705052647136
Trimmed Mean ( 10 / 20 )7.146341463414630.0651543721251278109.683222020622
Trimmed Mean ( 11 / 20 )7.148717948717950.0635087203116608112.562777420747
Trimmed Mean ( 12 / 20 )7.148648648648650.06207396798841115.163391036697
Trimmed Mean ( 13 / 20 )7.151428571428570.0608582080626388117.509680273003
Trimmed Mean ( 14 / 20 )7.151515151515150.0600065040857965119.179000017898
Trimmed Mean ( 15 / 20 )7.15161290322580.0586351884774285121.967935789595
Trimmed Mean ( 16 / 20 )7.151724137931030.0565033434764618126.571698202431
Trimmed Mean ( 17 / 20 )7.151851851851850.0558208291573747128.121562502928
Trimmed Mean ( 18 / 20 )7.1520.0545038224959192131.220154339367
Trimmed Mean ( 19 / 20 )7.147826086956520.0536676808616401133.186788998471
Trimmed Mean ( 20 / 20 )7.147619047619050.0537272865050222133.035176584824
Median7.1
Midrange7
Midmean - Weighted Average at Xnp7.1
Midmean - Weighted Average at X(n+1)p7.16666666666667
Midmean - Empirical Distribution Function7.16666666666667
Midmean - Empirical Distribution Function - Averaging7.16666666666667
Midmean - Empirical Distribution Function - Interpolation7.16666666666667
Midmean - Closest Observation7.16666666666667
Midmean - True Basic - Statistics Graphics Toolkit7.16666666666667
Midmean - MS Excel (old versions)7.16666666666667
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')