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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 computationFri, 16 Jan 2015 10:41:07 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Jan/16/t14214048723t1vuk38yox2x2z.htm/, Retrieved Wed, 15 May 2024 23:02:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=273957, Retrieved Wed, 15 May 2024 23:02:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact46
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Kendall tau Correlation Matrix] [] [2015-01-16 10:36:52] [bcd8153d44f369b7624d3c1b4621c4c3]
- R     [Kendall tau Correlation Matrix] [] [2015-01-16 10:37:41] [bcd8153d44f369b7624d3c1b4621c4c3]
- RM D      [Central Tendency] [] [2015-01-16 10:41:07] [6e98989d1e11d52934121e5a163a7817] [Current]
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Dataseries X:
4.2
11.5
7.3
5.8
6.4
10
11.2
11.2
5.2
7
16.5
16.5
15.2
17.3
22.5
17.3
13.6
14.5
18.8
15.5
23.6
18.5
33.9
25.5
26.4
32.5
26.7
21.5
23.3
29.5
15.2
21.5
17.6
9.7
14.5
10
8.2
9.4
16.5
9.7
19.7
23.3
23.6
26.4
20
25.2
25.8
21.2
14.5
27.3
25.5
26.4
22.4
24.5
24.8
30.9
26.4
27.3
29.4
23




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=273957&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=273957&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=273957&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean18.81333333333330.98752234235374919.0510457601313
Geometric Mean16.9307250252311
Harmonic Mean14.6992045414817
Quadratic Mean20.2849287238909
Winsorized Mean ( 1 / 20 )18.80666666666670.977674129928519.2361300058559
Winsorized Mean ( 2 / 20 )18.77333333333330.96098721211344719.5354663378362
Winsorized Mean ( 3 / 20 )18.73333333333330.93992927569817819.9305775633153
Winsorized Mean ( 4 / 20 )18.76666666666670.92989783372562420.1814285247641
Winsorized Mean ( 5 / 20 )18.61666666666670.89310341505402820.8449171203096
Winsorized Mean ( 6 / 20 )18.70666666666670.87426762462800421.3969568810537
Winsorized Mean ( 7 / 20 )18.77666666666670.83520479124254422.4815121555187
Winsorized Mean ( 8 / 20 )18.77666666666670.82128934965508622.8624256171741
Winsorized Mean ( 9 / 20 )18.77666666666670.82128934965508622.8624256171741
Winsorized Mean ( 10 / 20 )18.82666666666670.81199992578367523.1855522012477
Winsorized Mean ( 11 / 20 )18.82666666666670.81199992578367523.1855522012477
Winsorized Mean ( 12 / 20 )18.94666666666670.75005636950751625.2603236728821
Winsorized Mean ( 13 / 20 )18.88166666666670.74009654152152925.5124373745198
Winsorized Mean ( 14 / 20 )18.95166666666670.7278654329697526.0373220216577
Winsorized Mean ( 15 / 20 )19.40166666666670.62941319486341730.8250078406393
Winsorized Mean ( 16 / 20 )19.5350.57626218628731233.899500027684
Winsorized Mean ( 17 / 20 )19.450.56322066201826634.5335342107339
Winsorized Mean ( 18 / 20 )19.180.52333567238312836.6495177228403
Winsorized Mean ( 19 / 20 )19.40166666666670.49041946571689939.561371484929
Winsorized Mean ( 20 / 20 )19.30166666666670.47604474263121340.5459086891324
Trimmed Mean ( 1 / 20 )18.80517241379310.95434949295915319.7047020536301
Trimmed Mean ( 2 / 20 )18.80357142857140.92553938042226520.3163385873355
Trimmed Mean ( 3 / 20 )18.82037037037040.90092110497193620.8901426179339
Trimmed Mean ( 4 / 20 )18.85384615384620.88018860903191921.4202342093278
Trimmed Mean ( 5 / 20 )18.880.85781402294389222.0094326917233
Trimmed Mean ( 6 / 20 )18.94583333333330.84152511800401922.5136872661273
Trimmed Mean ( 7 / 20 )18.99782608695650.82597615580347823.0004534071279
Trimmed Mean ( 8 / 20 )19.04090909090910.81629362813526323.3260538054255
Trimmed Mean ( 9 / 20 )19.08809523809520.80619121709704723.6768831429696
Trimmed Mean ( 10 / 20 )19.140.79158069708653224.1794678299333
Trimmed Mean ( 11 / 20 )19.18947368421050.77347371363570524.8094710213365
Trimmed Mean ( 12 / 20 )19.24444444444440.7478057260278725.7345507992636
Trimmed Mean ( 13 / 20 )19.28823529411760.72935354261337526.445659295772
Trimmed Mean ( 14 / 20 )19.3468750.70477896865418627.4509823086008
Trimmed Mean ( 15 / 20 )19.40333333333330.67228352210924928.8618309020226
Trimmed Mean ( 16 / 20 )19.40357142857140.65660023318085429.5515755980959
Trimmed Mean ( 17 / 20 )19.38461538461540.64778183192734629.9246049043091
Trimmed Mean ( 18 / 20 )19.3750.63520651668617230.5018911031928
Trimmed Mean ( 19 / 20 )19.40454545454550.62607404762142730.9940102584782
Trimmed Mean ( 20 / 20 )19.4050.61944266120950731.3265475808694
Median19.25
Midrange19.05
Midmean - Weighted Average at Xnp19.1483870967742
Midmean - Weighted Average at X(n+1)p19.4033333333333
Midmean - Empirical Distribution Function19.1483870967742
Midmean - Empirical Distribution Function - Averaging19.4033333333333
Midmean - Empirical Distribution Function - Interpolation19.4033333333333
Midmean - Closest Observation19.1483870967742
Midmean - True Basic - Statistics Graphics Toolkit19.4033333333333
Midmean - MS Excel (old versions)19.5333333333333
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 18.8133333333333 & 0.987522342353749 & 19.0510457601313 \tabularnewline
Geometric Mean & 16.9307250252311 &  &  \tabularnewline
Harmonic Mean & 14.6992045414817 &  &  \tabularnewline
Quadratic Mean & 20.2849287238909 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 18.8066666666667 & 0.9776741299285 & 19.2361300058559 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 18.7733333333333 & 0.960987212113447 & 19.5354663378362 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 18.7333333333333 & 0.939929275698178 & 19.9305775633153 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 18.7666666666667 & 0.929897833725624 & 20.1814285247641 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 18.6166666666667 & 0.893103415054028 & 20.8449171203096 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 18.7066666666667 & 0.874267624628004 & 21.3969568810537 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 18.7766666666667 & 0.835204791242544 & 22.4815121555187 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 18.7766666666667 & 0.821289349655086 & 22.8624256171741 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 18.7766666666667 & 0.821289349655086 & 22.8624256171741 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 18.8266666666667 & 0.811999925783675 & 23.1855522012477 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 18.8266666666667 & 0.811999925783675 & 23.1855522012477 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 18.9466666666667 & 0.750056369507516 & 25.2603236728821 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 18.8816666666667 & 0.740096541521529 & 25.5124373745198 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 18.9516666666667 & 0.72786543296975 & 26.0373220216577 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 19.4016666666667 & 0.629413194863417 & 30.8250078406393 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 19.535 & 0.576262186287312 & 33.899500027684 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 19.45 & 0.563220662018266 & 34.5335342107339 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 19.18 & 0.523335672383128 & 36.6495177228403 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 19.4016666666667 & 0.490419465716899 & 39.561371484929 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 19.3016666666667 & 0.476044742631213 & 40.5459086891324 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 18.8051724137931 & 0.954349492959153 & 19.7047020536301 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 18.8035714285714 & 0.925539380422265 & 20.3163385873355 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 18.8203703703704 & 0.900921104971936 & 20.8901426179339 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 18.8538461538462 & 0.880188609031919 & 21.4202342093278 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 18.88 & 0.857814022943892 & 22.0094326917233 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 18.9458333333333 & 0.841525118004019 & 22.5136872661273 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 18.9978260869565 & 0.825976155803478 & 23.0004534071279 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 19.0409090909091 & 0.816293628135263 & 23.3260538054255 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 19.0880952380952 & 0.806191217097047 & 23.6768831429696 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 19.14 & 0.791580697086532 & 24.1794678299333 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 19.1894736842105 & 0.773473713635705 & 24.8094710213365 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 19.2444444444444 & 0.74780572602787 & 25.7345507992636 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 19.2882352941176 & 0.729353542613375 & 26.445659295772 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 19.346875 & 0.704778968654186 & 27.4509823086008 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 19.4033333333333 & 0.672283522109249 & 28.8618309020226 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 19.4035714285714 & 0.656600233180854 & 29.5515755980959 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 19.3846153846154 & 0.647781831927346 & 29.9246049043091 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 19.375 & 0.635206516686172 & 30.5018911031928 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 19.4045454545455 & 0.626074047621427 & 30.9940102584782 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 19.405 & 0.619442661209507 & 31.3265475808694 \tabularnewline
Median & 19.25 &  &  \tabularnewline
Midrange & 19.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 19.1483870967742 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 19.4033333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 19.1483870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 19.4033333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 19.4033333333333 &  &  \tabularnewline
Midmean - Closest Observation & 19.1483870967742 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 19.4033333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 19.5333333333333 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=273957&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]18.8133333333333[/C][C]0.987522342353749[/C][C]19.0510457601313[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]16.9307250252311[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]14.6992045414817[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]20.2849287238909[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]18.8066666666667[/C][C]0.9776741299285[/C][C]19.2361300058559[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]18.7733333333333[/C][C]0.960987212113447[/C][C]19.5354663378362[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]18.7333333333333[/C][C]0.939929275698178[/C][C]19.9305775633153[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]18.7666666666667[/C][C]0.929897833725624[/C][C]20.1814285247641[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]18.6166666666667[/C][C]0.893103415054028[/C][C]20.8449171203096[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]18.7066666666667[/C][C]0.874267624628004[/C][C]21.3969568810537[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]18.7766666666667[/C][C]0.835204791242544[/C][C]22.4815121555187[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]18.7766666666667[/C][C]0.821289349655086[/C][C]22.8624256171741[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]18.7766666666667[/C][C]0.821289349655086[/C][C]22.8624256171741[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]18.8266666666667[/C][C]0.811999925783675[/C][C]23.1855522012477[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]18.8266666666667[/C][C]0.811999925783675[/C][C]23.1855522012477[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]18.9466666666667[/C][C]0.750056369507516[/C][C]25.2603236728821[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]18.8816666666667[/C][C]0.740096541521529[/C][C]25.5124373745198[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]18.9516666666667[/C][C]0.72786543296975[/C][C]26.0373220216577[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]19.4016666666667[/C][C]0.629413194863417[/C][C]30.8250078406393[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]19.535[/C][C]0.576262186287312[/C][C]33.899500027684[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]19.45[/C][C]0.563220662018266[/C][C]34.5335342107339[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]19.18[/C][C]0.523335672383128[/C][C]36.6495177228403[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]19.4016666666667[/C][C]0.490419465716899[/C][C]39.561371484929[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]19.3016666666667[/C][C]0.476044742631213[/C][C]40.5459086891324[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]18.8051724137931[/C][C]0.954349492959153[/C][C]19.7047020536301[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]18.8035714285714[/C][C]0.925539380422265[/C][C]20.3163385873355[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]18.8203703703704[/C][C]0.900921104971936[/C][C]20.8901426179339[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]18.8538461538462[/C][C]0.880188609031919[/C][C]21.4202342093278[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]18.88[/C][C]0.857814022943892[/C][C]22.0094326917233[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]18.9458333333333[/C][C]0.841525118004019[/C][C]22.5136872661273[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]18.9978260869565[/C][C]0.825976155803478[/C][C]23.0004534071279[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]19.0409090909091[/C][C]0.816293628135263[/C][C]23.3260538054255[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]19.0880952380952[/C][C]0.806191217097047[/C][C]23.6768831429696[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]19.14[/C][C]0.791580697086532[/C][C]24.1794678299333[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]19.1894736842105[/C][C]0.773473713635705[/C][C]24.8094710213365[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]19.2444444444444[/C][C]0.74780572602787[/C][C]25.7345507992636[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]19.2882352941176[/C][C]0.729353542613375[/C][C]26.445659295772[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]19.346875[/C][C]0.704778968654186[/C][C]27.4509823086008[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]19.4033333333333[/C][C]0.672283522109249[/C][C]28.8618309020226[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]19.4035714285714[/C][C]0.656600233180854[/C][C]29.5515755980959[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]19.3846153846154[/C][C]0.647781831927346[/C][C]29.9246049043091[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]19.375[/C][C]0.635206516686172[/C][C]30.5018911031928[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]19.4045454545455[/C][C]0.626074047621427[/C][C]30.9940102584782[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]19.405[/C][C]0.619442661209507[/C][C]31.3265475808694[/C][/ROW]
[ROW][C]Median[/C][C]19.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]19.1483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]19.4033333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]19.1483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]19.4033333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]19.4033333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]19.1483870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]19.4033333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]19.5333333333333[/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=273957&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=273957&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 Mean18.81333333333330.98752234235374919.0510457601313
Geometric Mean16.9307250252311
Harmonic Mean14.6992045414817
Quadratic Mean20.2849287238909
Winsorized Mean ( 1 / 20 )18.80666666666670.977674129928519.2361300058559
Winsorized Mean ( 2 / 20 )18.77333333333330.96098721211344719.5354663378362
Winsorized Mean ( 3 / 20 )18.73333333333330.93992927569817819.9305775633153
Winsorized Mean ( 4 / 20 )18.76666666666670.92989783372562420.1814285247641
Winsorized Mean ( 5 / 20 )18.61666666666670.89310341505402820.8449171203096
Winsorized Mean ( 6 / 20 )18.70666666666670.87426762462800421.3969568810537
Winsorized Mean ( 7 / 20 )18.77666666666670.83520479124254422.4815121555187
Winsorized Mean ( 8 / 20 )18.77666666666670.82128934965508622.8624256171741
Winsorized Mean ( 9 / 20 )18.77666666666670.82128934965508622.8624256171741
Winsorized Mean ( 10 / 20 )18.82666666666670.81199992578367523.1855522012477
Winsorized Mean ( 11 / 20 )18.82666666666670.81199992578367523.1855522012477
Winsorized Mean ( 12 / 20 )18.94666666666670.75005636950751625.2603236728821
Winsorized Mean ( 13 / 20 )18.88166666666670.74009654152152925.5124373745198
Winsorized Mean ( 14 / 20 )18.95166666666670.7278654329697526.0373220216577
Winsorized Mean ( 15 / 20 )19.40166666666670.62941319486341730.8250078406393
Winsorized Mean ( 16 / 20 )19.5350.57626218628731233.899500027684
Winsorized Mean ( 17 / 20 )19.450.56322066201826634.5335342107339
Winsorized Mean ( 18 / 20 )19.180.52333567238312836.6495177228403
Winsorized Mean ( 19 / 20 )19.40166666666670.49041946571689939.561371484929
Winsorized Mean ( 20 / 20 )19.30166666666670.47604474263121340.5459086891324
Trimmed Mean ( 1 / 20 )18.80517241379310.95434949295915319.7047020536301
Trimmed Mean ( 2 / 20 )18.80357142857140.92553938042226520.3163385873355
Trimmed Mean ( 3 / 20 )18.82037037037040.90092110497193620.8901426179339
Trimmed Mean ( 4 / 20 )18.85384615384620.88018860903191921.4202342093278
Trimmed Mean ( 5 / 20 )18.880.85781402294389222.0094326917233
Trimmed Mean ( 6 / 20 )18.94583333333330.84152511800401922.5136872661273
Trimmed Mean ( 7 / 20 )18.99782608695650.82597615580347823.0004534071279
Trimmed Mean ( 8 / 20 )19.04090909090910.81629362813526323.3260538054255
Trimmed Mean ( 9 / 20 )19.08809523809520.80619121709704723.6768831429696
Trimmed Mean ( 10 / 20 )19.140.79158069708653224.1794678299333
Trimmed Mean ( 11 / 20 )19.18947368421050.77347371363570524.8094710213365
Trimmed Mean ( 12 / 20 )19.24444444444440.7478057260278725.7345507992636
Trimmed Mean ( 13 / 20 )19.28823529411760.72935354261337526.445659295772
Trimmed Mean ( 14 / 20 )19.3468750.70477896865418627.4509823086008
Trimmed Mean ( 15 / 20 )19.40333333333330.67228352210924928.8618309020226
Trimmed Mean ( 16 / 20 )19.40357142857140.65660023318085429.5515755980959
Trimmed Mean ( 17 / 20 )19.38461538461540.64778183192734629.9246049043091
Trimmed Mean ( 18 / 20 )19.3750.63520651668617230.5018911031928
Trimmed Mean ( 19 / 20 )19.40454545454550.62607404762142730.9940102584782
Trimmed Mean ( 20 / 20 )19.4050.61944266120950731.3265475808694
Median19.25
Midrange19.05
Midmean - Weighted Average at Xnp19.1483870967742
Midmean - Weighted Average at X(n+1)p19.4033333333333
Midmean - Empirical Distribution Function19.1483870967742
Midmean - Empirical Distribution Function - Averaging19.4033333333333
Midmean - Empirical Distribution Function - Interpolation19.4033333333333
Midmean - Closest Observation19.1483870967742
Midmean - True Basic - Statistics Graphics Toolkit19.4033333333333
Midmean - MS Excel (old versions)19.5333333333333
Number of observations60



Parameters (Session):
par1 = 0 ; par2 = no ; par3 = 512 ;
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')