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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Oct 2007 10:43:33 -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/2007/Oct/22/jt1ml2g6msv4uvn1193074777.htm/, Retrieved Thu, 31 Oct 2024 23:09:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1503, Retrieved Thu, 31 Oct 2024 23:09:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWerkloosheid, vrouwen, central tendency
Estimated Impact219
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-10-22 17:43:33] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
7,7
7,8
7,7
7,7
7,7
7,7
7,6
7,5
7,4
7,4
7,5
7,6
7,6
8,1
7,8
8
7,9
7,9
7,8
6,7
6,6
6,6
7,7
7,9
8
7,7
7,5
7,6
7,8
7,8
7,7
7,4
7,5
7,2
7,5
7,6
7,6
7,8
7,7
7,7
8,2
8,2
8,1
7,8
7,8
7,7
6,7
6,7
6,7
7,2
6,9
6,8
7,2
7,1
6,9
6,9
6,7
6,5
6,6
6,6
6,5




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1503&T=0

[TABLE]
[ROW][C]Summary of compuational 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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1503&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1503&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.439344262295080.0621684073002887119.664385583520
Geometric Mean7.42329091216426
Harmonic Mean7.40678158158999
Quadratic Mean7.45491366180173
Winsorized Mean ( 1 / 20 )7.439344262295080.0621684073002887119.664385583520
Winsorized Mean ( 2 / 20 )7.439344262295080.0607457609901831122.466887253208
Winsorized Mean ( 3 / 20 )7.439344262295080.0607457609901831122.466887253208
Winsorized Mean ( 4 / 20 )7.43278688524590.0596309832307653124.646391565972
Winsorized Mean ( 5 / 20 )7.43278688524590.0596309832307653124.646391565972
Winsorized Mean ( 6 / 20 )7.43278688524590.0559430482979887132.863458667002
Winsorized Mean ( 7 / 20 )7.43278688524590.0559430482979887132.863458667002
Winsorized Mean ( 8 / 20 )7.43278688524590.0559430482979887132.863458667002
Winsorized Mean ( 9 / 20 )7.418032786885250.0540445170035707137.257823701064
Winsorized Mean ( 10 / 20 )7.418032786885250.0540445170035707137.257823701064
Winsorized Mean ( 11 / 20 )7.43606557377050.0501382126276271148.311341471177
Winsorized Mean ( 12 / 20 )7.455737704918030.0460769485985416161.8105784278
Winsorized Mean ( 13 / 20 )7.455737704918030.0460769485985416161.8105784278
Winsorized Mean ( 14 / 20 )7.455737704918030.0460769485985416161.810578427800
Winsorized Mean ( 15 / 20 )7.504918032786890.0365467160813245205.351364978642
Winsorized Mean ( 16 / 20 )7.53114754098360.0318415633460417236.519402616575
Winsorized Mean ( 17 / 20 )7.503278688524590.0282424333998138265.673944674118
Winsorized Mean ( 18 / 20 )7.503278688524590.0282424333998138265.673944674118
Winsorized Mean ( 19 / 20 )7.56557377049180.0176308915900565429.108972274474
Winsorized Mean ( 20 / 20 )7.56557377049180.0176308915900565429.108972274474
Trimmed Mean ( 1 / 20 )7.442372881355930.0608820510244229122.242479616372
Trimmed Mean ( 2 / 20 )7.445614035087720.0592914605125858125.576499056002
Trimmed Mean ( 3 / 20 )7.449090909090910.0582501702876213127.881015150850
Trimmed Mean ( 4 / 20 )7.452830188679250.0569293972121975130.913562300681
Trimmed Mean ( 5 / 20 )7.458823529411760.0556724644571377133.976887894990
Trimmed Mean ( 6 / 20 )7.465306122448980.0540495348208949138.119710876087
Trimmed Mean ( 7 / 20 )7.472340425531910.0530914878658279140.74460381325
Trimmed Mean ( 8 / 20 )7.480.0517960257435673144.412624185341
Trimmed Mean ( 9 / 20 )7.488372093023260.0500508381996894149.615318391805
Trimmed Mean ( 10 / 20 )7.50.0481359862341233155.808587020978
Trimmed Mean ( 11 / 20 )7.512820512820510.0454664662919618165.238716036939
Trimmed Mean ( 12 / 20 )7.524324324324320.0430457200554965174.798430938630
Trimmed Mean ( 13 / 20 )7.534285714285710.0409842882670164183.833513594262
Trimmed Mean ( 14 / 20 )7.545454545454550.0379620297465683198.763200909631
Trimmed Mean ( 15 / 20 )7.558064516129030.0333680013960923226.506359383399
Trimmed Mean ( 16 / 20 )7.565517241379310.0307043192950688246.399119572547
Trimmed Mean ( 17 / 20 )7.570370370370370.0286519614513382264.218224055191
Trimmed Mean ( 18 / 20 )7.580.0264575131106459286.497070540994
Trimmed Mean ( 19 / 20 )7.591304347826090.0225919670552462336.017856668362
Trimmed Mean ( 20 / 20 )7.59523809523810.0223353131420163340.055142587199
Median7.6
Midrange7.35
Midmean - Weighted Average at Xnp7.5972972972973
Midmean - Weighted Average at X(n+1)p7.5972972972973
Midmean - Empirical Distribution Function7.5972972972973
Midmean - Empirical Distribution Function - Averaging7.5972972972973
Midmean - Empirical Distribution Function - Interpolation7.5972972972973
Midmean - Closest Observation7.545
Midmean - True Basic - Statistics Graphics Toolkit7.5972972972973
Midmean - MS Excel (old versions)7.5972972972973
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.43934426229508 & 0.0621684073002887 & 119.664385583520 \tabularnewline
Geometric Mean & 7.42329091216426 &  &  \tabularnewline
Harmonic Mean & 7.40678158158999 &  &  \tabularnewline
Quadratic Mean & 7.45491366180173 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.43934426229508 & 0.0621684073002887 & 119.664385583520 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.43934426229508 & 0.0607457609901831 & 122.466887253208 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.43934426229508 & 0.0607457609901831 & 122.466887253208 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.4327868852459 & 0.0596309832307653 & 124.646391565972 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.4327868852459 & 0.0596309832307653 & 124.646391565972 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.4327868852459 & 0.0559430482979887 & 132.863458667002 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.4327868852459 & 0.0559430482979887 & 132.863458667002 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.4327868852459 & 0.0559430482979887 & 132.863458667002 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.41803278688525 & 0.0540445170035707 & 137.257823701064 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.41803278688525 & 0.0540445170035707 & 137.257823701064 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.4360655737705 & 0.0501382126276271 & 148.311341471177 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.45573770491803 & 0.0460769485985416 & 161.8105784278 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.45573770491803 & 0.0460769485985416 & 161.8105784278 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.45573770491803 & 0.0460769485985416 & 161.810578427800 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.50491803278689 & 0.0365467160813245 & 205.351364978642 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.5311475409836 & 0.0318415633460417 & 236.519402616575 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.50327868852459 & 0.0282424333998138 & 265.673944674118 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.50327868852459 & 0.0282424333998138 & 265.673944674118 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.5655737704918 & 0.0176308915900565 & 429.108972274474 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.5655737704918 & 0.0176308915900565 & 429.108972274474 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.44237288135593 & 0.0608820510244229 & 122.242479616372 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.44561403508772 & 0.0592914605125858 & 125.576499056002 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.44909090909091 & 0.0582501702876213 & 127.881015150850 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.45283018867925 & 0.0569293972121975 & 130.913562300681 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.45882352941176 & 0.0556724644571377 & 133.976887894990 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.46530612244898 & 0.0540495348208949 & 138.119710876087 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.47234042553191 & 0.0530914878658279 & 140.74460381325 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.48 & 0.0517960257435673 & 144.412624185341 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.48837209302326 & 0.0500508381996894 & 149.615318391805 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.5 & 0.0481359862341233 & 155.808587020978 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.51282051282051 & 0.0454664662919618 & 165.238716036939 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.52432432432432 & 0.0430457200554965 & 174.798430938630 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.53428571428571 & 0.0409842882670164 & 183.833513594262 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.54545454545455 & 0.0379620297465683 & 198.763200909631 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.55806451612903 & 0.0333680013960923 & 226.506359383399 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.56551724137931 & 0.0307043192950688 & 246.399119572547 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.57037037037037 & 0.0286519614513382 & 264.218224055191 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.58 & 0.0264575131106459 & 286.497070540994 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.59130434782609 & 0.0225919670552462 & 336.017856668362 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.5952380952381 & 0.0223353131420163 & 340.055142587199 \tabularnewline
Median & 7.6 &  &  \tabularnewline
Midrange & 7.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.5972972972973 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.5972972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.5972972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.5972972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.5972972972973 &  &  \tabularnewline
Midmean - Closest Observation & 7.545 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.5972972972973 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.5972972972973 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1503&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]7.43934426229508[/C][C]0.0621684073002887[/C][C]119.664385583520[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.42329091216426[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.40678158158999[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.45491366180173[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.43934426229508[/C][C]0.0621684073002887[/C][C]119.664385583520[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.43934426229508[/C][C]0.0607457609901831[/C][C]122.466887253208[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.43934426229508[/C][C]0.0607457609901831[/C][C]122.466887253208[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.4327868852459[/C][C]0.0596309832307653[/C][C]124.646391565972[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.4327868852459[/C][C]0.0596309832307653[/C][C]124.646391565972[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.4327868852459[/C][C]0.0559430482979887[/C][C]132.863458667002[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.4327868852459[/C][C]0.0559430482979887[/C][C]132.863458667002[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.4327868852459[/C][C]0.0559430482979887[/C][C]132.863458667002[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.41803278688525[/C][C]0.0540445170035707[/C][C]137.257823701064[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.41803278688525[/C][C]0.0540445170035707[/C][C]137.257823701064[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.4360655737705[/C][C]0.0501382126276271[/C][C]148.311341471177[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.45573770491803[/C][C]0.0460769485985416[/C][C]161.8105784278[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.45573770491803[/C][C]0.0460769485985416[/C][C]161.8105784278[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.45573770491803[/C][C]0.0460769485985416[/C][C]161.810578427800[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.50491803278689[/C][C]0.0365467160813245[/C][C]205.351364978642[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.5311475409836[/C][C]0.0318415633460417[/C][C]236.519402616575[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.50327868852459[/C][C]0.0282424333998138[/C][C]265.673944674118[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.50327868852459[/C][C]0.0282424333998138[/C][C]265.673944674118[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.5655737704918[/C][C]0.0176308915900565[/C][C]429.108972274474[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.5655737704918[/C][C]0.0176308915900565[/C][C]429.108972274474[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.44237288135593[/C][C]0.0608820510244229[/C][C]122.242479616372[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.44561403508772[/C][C]0.0592914605125858[/C][C]125.576499056002[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.44909090909091[/C][C]0.0582501702876213[/C][C]127.881015150850[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.45283018867925[/C][C]0.0569293972121975[/C][C]130.913562300681[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.45882352941176[/C][C]0.0556724644571377[/C][C]133.976887894990[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.46530612244898[/C][C]0.0540495348208949[/C][C]138.119710876087[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.47234042553191[/C][C]0.0530914878658279[/C][C]140.74460381325[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.48[/C][C]0.0517960257435673[/C][C]144.412624185341[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.48837209302326[/C][C]0.0500508381996894[/C][C]149.615318391805[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.5[/C][C]0.0481359862341233[/C][C]155.808587020978[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.51282051282051[/C][C]0.0454664662919618[/C][C]165.238716036939[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.52432432432432[/C][C]0.0430457200554965[/C][C]174.798430938630[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.53428571428571[/C][C]0.0409842882670164[/C][C]183.833513594262[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.54545454545455[/C][C]0.0379620297465683[/C][C]198.763200909631[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.55806451612903[/C][C]0.0333680013960923[/C][C]226.506359383399[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.56551724137931[/C][C]0.0307043192950688[/C][C]246.399119572547[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.57037037037037[/C][C]0.0286519614513382[/C][C]264.218224055191[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.58[/C][C]0.0264575131106459[/C][C]286.497070540994[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.59130434782609[/C][C]0.0225919670552462[/C][C]336.017856668362[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.5952380952381[/C][C]0.0223353131420163[/C][C]340.055142587199[/C][/ROW]
[ROW][C]Median[/C][C]7.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.5972972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.5972972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.5972972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.5972972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.5972972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.5972972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.5972972972973[/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=1503&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1503&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 Mean7.439344262295080.0621684073002887119.664385583520
Geometric Mean7.42329091216426
Harmonic Mean7.40678158158999
Quadratic Mean7.45491366180173
Winsorized Mean ( 1 / 20 )7.439344262295080.0621684073002887119.664385583520
Winsorized Mean ( 2 / 20 )7.439344262295080.0607457609901831122.466887253208
Winsorized Mean ( 3 / 20 )7.439344262295080.0607457609901831122.466887253208
Winsorized Mean ( 4 / 20 )7.43278688524590.0596309832307653124.646391565972
Winsorized Mean ( 5 / 20 )7.43278688524590.0596309832307653124.646391565972
Winsorized Mean ( 6 / 20 )7.43278688524590.0559430482979887132.863458667002
Winsorized Mean ( 7 / 20 )7.43278688524590.0559430482979887132.863458667002
Winsorized Mean ( 8 / 20 )7.43278688524590.0559430482979887132.863458667002
Winsorized Mean ( 9 / 20 )7.418032786885250.0540445170035707137.257823701064
Winsorized Mean ( 10 / 20 )7.418032786885250.0540445170035707137.257823701064
Winsorized Mean ( 11 / 20 )7.43606557377050.0501382126276271148.311341471177
Winsorized Mean ( 12 / 20 )7.455737704918030.0460769485985416161.8105784278
Winsorized Mean ( 13 / 20 )7.455737704918030.0460769485985416161.8105784278
Winsorized Mean ( 14 / 20 )7.455737704918030.0460769485985416161.810578427800
Winsorized Mean ( 15 / 20 )7.504918032786890.0365467160813245205.351364978642
Winsorized Mean ( 16 / 20 )7.53114754098360.0318415633460417236.519402616575
Winsorized Mean ( 17 / 20 )7.503278688524590.0282424333998138265.673944674118
Winsorized Mean ( 18 / 20 )7.503278688524590.0282424333998138265.673944674118
Winsorized Mean ( 19 / 20 )7.56557377049180.0176308915900565429.108972274474
Winsorized Mean ( 20 / 20 )7.56557377049180.0176308915900565429.108972274474
Trimmed Mean ( 1 / 20 )7.442372881355930.0608820510244229122.242479616372
Trimmed Mean ( 2 / 20 )7.445614035087720.0592914605125858125.576499056002
Trimmed Mean ( 3 / 20 )7.449090909090910.0582501702876213127.881015150850
Trimmed Mean ( 4 / 20 )7.452830188679250.0569293972121975130.913562300681
Trimmed Mean ( 5 / 20 )7.458823529411760.0556724644571377133.976887894990
Trimmed Mean ( 6 / 20 )7.465306122448980.0540495348208949138.119710876087
Trimmed Mean ( 7 / 20 )7.472340425531910.0530914878658279140.74460381325
Trimmed Mean ( 8 / 20 )7.480.0517960257435673144.412624185341
Trimmed Mean ( 9 / 20 )7.488372093023260.0500508381996894149.615318391805
Trimmed Mean ( 10 / 20 )7.50.0481359862341233155.808587020978
Trimmed Mean ( 11 / 20 )7.512820512820510.0454664662919618165.238716036939
Trimmed Mean ( 12 / 20 )7.524324324324320.0430457200554965174.798430938630
Trimmed Mean ( 13 / 20 )7.534285714285710.0409842882670164183.833513594262
Trimmed Mean ( 14 / 20 )7.545454545454550.0379620297465683198.763200909631
Trimmed Mean ( 15 / 20 )7.558064516129030.0333680013960923226.506359383399
Trimmed Mean ( 16 / 20 )7.565517241379310.0307043192950688246.399119572547
Trimmed Mean ( 17 / 20 )7.570370370370370.0286519614513382264.218224055191
Trimmed Mean ( 18 / 20 )7.580.0264575131106459286.497070540994
Trimmed Mean ( 19 / 20 )7.591304347826090.0225919670552462336.017856668362
Trimmed Mean ( 20 / 20 )7.59523809523810.0223353131420163340.055142587199
Median7.6
Midrange7.35
Midmean - Weighted Average at Xnp7.5972972972973
Midmean - Weighted Average at X(n+1)p7.5972972972973
Midmean - Empirical Distribution Function7.5972972972973
Midmean - Empirical Distribution Function - Averaging7.5972972972973
Midmean - Empirical Distribution Function - Interpolation7.5972972972973
Midmean - Closest Observation7.545
Midmean - True Basic - Statistics Graphics Toolkit7.5972972972973
Midmean - MS Excel (old versions)7.5972972972973
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')