Free Statistics

of Irreproducible Research!

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, 20 Oct 2008 10:36:05 -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/2008/Oct/20/t1224520627o70bhrqizrafuqa.htm/, Retrieved Sun, 19 May 2024 16:13:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17618, Retrieved Sun, 19 May 2024 16:13:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
F R  D    [Central Tendency] [Central Tendency ...] [2008-10-20 16:36:05] [270782e2502ae87124d0ebdcd1862d6a] [Current]
Feedback Forum
2008-10-24 10:38:53 [Nathalie Koulouris] [reply
Het antwoord van de student is niet correct. Een tijdreeks kan niet geordend worden omdat we de tijd moeten respecteren. Het is dus niet mogelijk dat de computer de gemiddelden van laag naar hoog heeft geplaatst.

Post a new message
Dataseries X:
8,3
8,3
8,4
8,4
8,4
8,3
8
8
8,2
8,6
8,7
8,7
8,5
8,4
8,4
8,4
8,5
8,5
8,5
8,5
8,5
8,4
8,4
8,4
8,5
8,6
8,6
8,6
8,6
8,5
8,4
8,4
8,3
8,2
8,1
8,2
8,1
8
7,9
7,8
7,7
7,7
7,9
7,8
7,6
7,4
7,3
7,1
7,1
7
7
7
6,9
6,8
6,7
6,6
6,6
6,6
6,6
6,6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17618&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17618&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17618&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.941666666666670.087148540855587591.1279361501494
Geometric Mean7.91185663604885
Harmonic Mean7.88046023625344
Quadratic Mean7.96982852178556
Winsorized Mean ( 1 / 20 )7.941666666666670.087148540855587591.1279361501494
Winsorized Mean ( 2 / 20 )7.938333333333330.086687035850566791.5746311480488
Winsorized Mean ( 3 / 20 )7.938333333333330.086687035850566791.5746311480488
Winsorized Mean ( 4 / 20 )7.938333333333330.086687035850566791.5746311480488
Winsorized Mean ( 5 / 20 )7.946666666666670.084554888623941593.9823444391196
Winsorized Mean ( 6 / 20 )7.956666666666670.082110806581343596.9015772459178
Winsorized Mean ( 7 / 20 )7.956666666666670.0779093587013653102.127225782533
Winsorized Mean ( 8 / 20 )7.970.0749123781946593106.390962242448
Winsorized Mean ( 9 / 20 )7.970.0749123781946593106.390962242448
Winsorized Mean ( 10 / 20 )7.970.0749123781946593106.390962242448
Winsorized Mean ( 11 / 20 )7.988333333333330.07095362003349112.585282182401
Winsorized Mean ( 12 / 20 )7.988333333333330.07095362003349112.585282182401
Winsorized Mean ( 13 / 20 )8.031666666666670.0620047231054401129.533143031841
Winsorized Mean ( 14 / 20 )8.0550.0574124240968622140.300642704272
Winsorized Mean ( 15 / 20 )8.080.0448349137561948180.216695496232
Winsorized Mean ( 16 / 20 )8.106666666666670.0401175297825885202.072926987271
Winsorized Mean ( 17 / 20 )8.106666666666670.0401175297825885202.072926987271
Winsorized Mean ( 18 / 20 )8.136666666666670.0350920232269666231.866558791458
Winsorized Mean ( 19 / 20 )8.136666666666670.0350920232269666231.866558791458
Winsorized Mean ( 20 / 20 )8.170.0298110812445935274.059163871546
Trimmed Mean ( 1 / 20 )7.951724137931030.086094300333830792.360633713245
Trimmed Mean ( 2 / 20 )7.96250.084728845576505393.976259747459
Trimmed Mean ( 3 / 20 )7.975925925925930.08325720569647895.7986261874188
Trimmed Mean ( 4 / 20 )7.990384615384620.081337778451983198.2370648357658
Trimmed Mean ( 5 / 20 )8.0060.0788390248337376101.548693897264
Trimmed Mean ( 6 / 20 )8.020833333333330.0763738433496085105.020684851713
Trimmed Mean ( 7 / 20 )8.034782608695650.073964176686368108.630731371022
Trimmed Mean ( 8 / 20 )8.050.072006870708117111.794887360555
Trimmed Mean ( 9 / 20 )8.064285714285710.0702427703713876114.805917700117
Trimmed Mean ( 10 / 20 )8.080.0677665676591909119.232835291816
Trimmed Mean ( 11 / 20 )8.097368421052630.0642814360227319125.967447556541
Trimmed Mean ( 12 / 20 )8.113888888888890.0607039103075856133.663364481398
Trimmed Mean ( 13 / 20 )8.132352941176470.0554869206594265146.563421514992
Trimmed Mean ( 14 / 20 )8.1468750.0513888510486154158.533900520423
Trimmed Mean ( 15 / 20 )8.160.0471241939471904173.159460491663
Trimmed Mean ( 16 / 20 )8.171428571428570.0453840585888756180.050635079859
Trimmed Mean ( 17 / 20 )8.180769230769230.0443826822669282184.323452592795
Trimmed Mean ( 18 / 20 )8.191666666666670.0425273427247348192.621173622076
Trimmed Mean ( 19 / 20 )8.20.041612518928824197.056083387446
Trimmed Mean ( 20 / 20 )8.210.0396696888130764206.959022005076
Median8.25
Midrange7.65
Midmean - Weighted Average at Xnp8.13548387096774
Midmean - Weighted Average at X(n+1)p8.16
Midmean - Empirical Distribution Function8.13548387096774
Midmean - Empirical Distribution Function - Averaging8.16
Midmean - Empirical Distribution Function - Interpolation8.16
Midmean - Closest Observation8.13548387096774
Midmean - True Basic - Statistics Graphics Toolkit8.16
Midmean - MS Excel (old versions)8.21025641025641
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.94166666666667 & 0.0871485408555875 & 91.1279361501494 \tabularnewline
Geometric Mean & 7.91185663604885 &  &  \tabularnewline
Harmonic Mean & 7.88046023625344 &  &  \tabularnewline
Quadratic Mean & 7.96982852178556 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.94166666666667 & 0.0871485408555875 & 91.1279361501494 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.93833333333333 & 0.0866870358505667 & 91.5746311480488 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.93833333333333 & 0.0866870358505667 & 91.5746311480488 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.93833333333333 & 0.0866870358505667 & 91.5746311480488 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.94666666666667 & 0.0845548886239415 & 93.9823444391196 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.95666666666667 & 0.0821108065813435 & 96.9015772459178 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.95666666666667 & 0.0779093587013653 & 102.127225782533 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.97 & 0.0749123781946593 & 106.390962242448 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.97 & 0.0749123781946593 & 106.390962242448 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.97 & 0.0749123781946593 & 106.390962242448 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.98833333333333 & 0.07095362003349 & 112.585282182401 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.98833333333333 & 0.07095362003349 & 112.585282182401 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.03166666666667 & 0.0620047231054401 & 129.533143031841 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.055 & 0.0574124240968622 & 140.300642704272 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8.08 & 0.0448349137561948 & 180.216695496232 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8.10666666666667 & 0.0401175297825885 & 202.072926987271 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8.10666666666667 & 0.0401175297825885 & 202.072926987271 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8.13666666666667 & 0.0350920232269666 & 231.866558791458 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8.13666666666667 & 0.0350920232269666 & 231.866558791458 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8.17 & 0.0298110812445935 & 274.059163871546 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.95172413793103 & 0.0860943003338307 & 92.360633713245 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.9625 & 0.0847288455765053 & 93.976259747459 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.97592592592593 & 0.083257205696478 & 95.7986261874188 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.99038461538462 & 0.0813377784519831 & 98.2370648357658 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8.006 & 0.0788390248337376 & 101.548693897264 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8.02083333333333 & 0.0763738433496085 & 105.020684851713 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8.03478260869565 & 0.073964176686368 & 108.630731371022 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8.05 & 0.072006870708117 & 111.794887360555 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8.06428571428571 & 0.0702427703713876 & 114.805917700117 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8.08 & 0.0677665676591909 & 119.232835291816 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8.09736842105263 & 0.0642814360227319 & 125.967447556541 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8.11388888888889 & 0.0607039103075856 & 133.663364481398 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.13235294117647 & 0.0554869206594265 & 146.563421514992 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8.146875 & 0.0513888510486154 & 158.533900520423 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8.16 & 0.0471241939471904 & 173.159460491663 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8.17142857142857 & 0.0453840585888756 & 180.050635079859 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8.18076923076923 & 0.0443826822669282 & 184.323452592795 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8.19166666666667 & 0.0425273427247348 & 192.621173622076 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8.2 & 0.041612518928824 & 197.056083387446 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8.21 & 0.0396696888130764 & 206.959022005076 \tabularnewline
Median & 8.25 &  &  \tabularnewline
Midrange & 7.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.13548387096774 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.16 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.13548387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.16 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.16 &  &  \tabularnewline
Midmean - Closest Observation & 8.13548387096774 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.16 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.21025641025641 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17618&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]7.94166666666667[/C][C]0.0871485408555875[/C][C]91.1279361501494[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.91185663604885[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.88046023625344[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.96982852178556[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.94166666666667[/C][C]0.0871485408555875[/C][C]91.1279361501494[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.93833333333333[/C][C]0.0866870358505667[/C][C]91.5746311480488[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.93833333333333[/C][C]0.0866870358505667[/C][C]91.5746311480488[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.93833333333333[/C][C]0.0866870358505667[/C][C]91.5746311480488[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.94666666666667[/C][C]0.0845548886239415[/C][C]93.9823444391196[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.95666666666667[/C][C]0.0821108065813435[/C][C]96.9015772459178[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.95666666666667[/C][C]0.0779093587013653[/C][C]102.127225782533[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.97[/C][C]0.0749123781946593[/C][C]106.390962242448[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.97[/C][C]0.0749123781946593[/C][C]106.390962242448[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.97[/C][C]0.0749123781946593[/C][C]106.390962242448[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.98833333333333[/C][C]0.07095362003349[/C][C]112.585282182401[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.98833333333333[/C][C]0.07095362003349[/C][C]112.585282182401[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.03166666666667[/C][C]0.0620047231054401[/C][C]129.533143031841[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.055[/C][C]0.0574124240968622[/C][C]140.300642704272[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8.08[/C][C]0.0448349137561948[/C][C]180.216695496232[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8.10666666666667[/C][C]0.0401175297825885[/C][C]202.072926987271[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8.10666666666667[/C][C]0.0401175297825885[/C][C]202.072926987271[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8.13666666666667[/C][C]0.0350920232269666[/C][C]231.866558791458[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8.13666666666667[/C][C]0.0350920232269666[/C][C]231.866558791458[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8.17[/C][C]0.0298110812445935[/C][C]274.059163871546[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.95172413793103[/C][C]0.0860943003338307[/C][C]92.360633713245[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.9625[/C][C]0.0847288455765053[/C][C]93.976259747459[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.97592592592593[/C][C]0.083257205696478[/C][C]95.7986261874188[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.99038461538462[/C][C]0.0813377784519831[/C][C]98.2370648357658[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8.006[/C][C]0.0788390248337376[/C][C]101.548693897264[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8.02083333333333[/C][C]0.0763738433496085[/C][C]105.020684851713[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8.03478260869565[/C][C]0.073964176686368[/C][C]108.630731371022[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8.05[/C][C]0.072006870708117[/C][C]111.794887360555[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8.06428571428571[/C][C]0.0702427703713876[/C][C]114.805917700117[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8.08[/C][C]0.0677665676591909[/C][C]119.232835291816[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8.09736842105263[/C][C]0.0642814360227319[/C][C]125.967447556541[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8.11388888888889[/C][C]0.0607039103075856[/C][C]133.663364481398[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.13235294117647[/C][C]0.0554869206594265[/C][C]146.563421514992[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8.146875[/C][C]0.0513888510486154[/C][C]158.533900520423[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8.16[/C][C]0.0471241939471904[/C][C]173.159460491663[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8.17142857142857[/C][C]0.0453840585888756[/C][C]180.050635079859[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8.18076923076923[/C][C]0.0443826822669282[/C][C]184.323452592795[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8.19166666666667[/C][C]0.0425273427247348[/C][C]192.621173622076[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8.2[/C][C]0.041612518928824[/C][C]197.056083387446[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8.21[/C][C]0.0396696888130764[/C][C]206.959022005076[/C][/ROW]
[ROW][C]Median[/C][C]8.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.13548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.13548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.13548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.21025641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17618&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17618&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 Mean7.941666666666670.087148540855587591.1279361501494
Geometric Mean7.91185663604885
Harmonic Mean7.88046023625344
Quadratic Mean7.96982852178556
Winsorized Mean ( 1 / 20 )7.941666666666670.087148540855587591.1279361501494
Winsorized Mean ( 2 / 20 )7.938333333333330.086687035850566791.5746311480488
Winsorized Mean ( 3 / 20 )7.938333333333330.086687035850566791.5746311480488
Winsorized Mean ( 4 / 20 )7.938333333333330.086687035850566791.5746311480488
Winsorized Mean ( 5 / 20 )7.946666666666670.084554888623941593.9823444391196
Winsorized Mean ( 6 / 20 )7.956666666666670.082110806581343596.9015772459178
Winsorized Mean ( 7 / 20 )7.956666666666670.0779093587013653102.127225782533
Winsorized Mean ( 8 / 20 )7.970.0749123781946593106.390962242448
Winsorized Mean ( 9 / 20 )7.970.0749123781946593106.390962242448
Winsorized Mean ( 10 / 20 )7.970.0749123781946593106.390962242448
Winsorized Mean ( 11 / 20 )7.988333333333330.07095362003349112.585282182401
Winsorized Mean ( 12 / 20 )7.988333333333330.07095362003349112.585282182401
Winsorized Mean ( 13 / 20 )8.031666666666670.0620047231054401129.533143031841
Winsorized Mean ( 14 / 20 )8.0550.0574124240968622140.300642704272
Winsorized Mean ( 15 / 20 )8.080.0448349137561948180.216695496232
Winsorized Mean ( 16 / 20 )8.106666666666670.0401175297825885202.072926987271
Winsorized Mean ( 17 / 20 )8.106666666666670.0401175297825885202.072926987271
Winsorized Mean ( 18 / 20 )8.136666666666670.0350920232269666231.866558791458
Winsorized Mean ( 19 / 20 )8.136666666666670.0350920232269666231.866558791458
Winsorized Mean ( 20 / 20 )8.170.0298110812445935274.059163871546
Trimmed Mean ( 1 / 20 )7.951724137931030.086094300333830792.360633713245
Trimmed Mean ( 2 / 20 )7.96250.084728845576505393.976259747459
Trimmed Mean ( 3 / 20 )7.975925925925930.08325720569647895.7986261874188
Trimmed Mean ( 4 / 20 )7.990384615384620.081337778451983198.2370648357658
Trimmed Mean ( 5 / 20 )8.0060.0788390248337376101.548693897264
Trimmed Mean ( 6 / 20 )8.020833333333330.0763738433496085105.020684851713
Trimmed Mean ( 7 / 20 )8.034782608695650.073964176686368108.630731371022
Trimmed Mean ( 8 / 20 )8.050.072006870708117111.794887360555
Trimmed Mean ( 9 / 20 )8.064285714285710.0702427703713876114.805917700117
Trimmed Mean ( 10 / 20 )8.080.0677665676591909119.232835291816
Trimmed Mean ( 11 / 20 )8.097368421052630.0642814360227319125.967447556541
Trimmed Mean ( 12 / 20 )8.113888888888890.0607039103075856133.663364481398
Trimmed Mean ( 13 / 20 )8.132352941176470.0554869206594265146.563421514992
Trimmed Mean ( 14 / 20 )8.1468750.0513888510486154158.533900520423
Trimmed Mean ( 15 / 20 )8.160.0471241939471904173.159460491663
Trimmed Mean ( 16 / 20 )8.171428571428570.0453840585888756180.050635079859
Trimmed Mean ( 17 / 20 )8.180769230769230.0443826822669282184.323452592795
Trimmed Mean ( 18 / 20 )8.191666666666670.0425273427247348192.621173622076
Trimmed Mean ( 19 / 20 )8.20.041612518928824197.056083387446
Trimmed Mean ( 20 / 20 )8.210.0396696888130764206.959022005076
Median8.25
Midrange7.65
Midmean - Weighted Average at Xnp8.13548387096774
Midmean - Weighted Average at X(n+1)p8.16
Midmean - Empirical Distribution Function8.13548387096774
Midmean - Empirical Distribution Function - Averaging8.16
Midmean - Empirical Distribution Function - Interpolation8.16
Midmean - Closest Observation8.13548387096774
Midmean - True Basic - Statistics Graphics Toolkit8.16
Midmean - MS Excel (old versions)8.21025641025641
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')