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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 computationWed, 19 Oct 2011 17:42:02 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/19/t131906058790y8t0qzapjdybl.htm/, Retrieved Wed, 15 May 2024 05:02:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132846, Retrieved Wed, 15 May 2024 05:02:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact80
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Gemiddelde consum...] [2011-10-19 21:42:02] [c0f35385ddfb9717cc41b82f2b64d087] [Current]
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Dataseries X:
49,98
50,12
50,37
50,39
50,34
50,32
50,32
50,32
50,67
50,86
50,95
51,02
51,02
51,06
50,9
51,23
51,29
51,3
51,3
51,3
51,46
51,47
51,77
51,82
51,82
51,84
51,9
51,94
52,22
52,27
52,27
52,28
52,53
52,73
52,72
52,67
52,67
52,65
52,69
52,73
52,84
52,83
52,83
52,84
52,82
53,09
53,4
53,43
53,43
53,42
53,6
53,69
54,05
54,04
54,04
54,08
54,05
54,39
54,38
54,46




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132846&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132846&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132846&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'AstonUniversity' @ aston.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean52.1870.162969322266493320.225912915451
Geometric Mean52.1719924515625
Harmonic Mean52.1569928509466
Quadratic Mean52.2020109765898
Winsorized Mean ( 1 / 20 )52.18816666666670.162177187690366321.797210877191
Winsorized Mean ( 2 / 20 )52.19450.160720732809436324.752750237183
Winsorized Mean ( 3 / 20 )52.17950.157455836333494331.391336231468
Winsorized Mean ( 4 / 20 )52.17750.157049170931895332.236710900098
Winsorized Mean ( 5 / 20 )52.17916666666670.156716356767067332.952907680353
Winsorized Mean ( 6 / 20 )52.18116666666670.155920465685508334.665282310766
Winsorized Mean ( 7 / 20 )52.18350.155462645612349335.66584303551
Winsorized Mean ( 8 / 20 )52.17416666666670.139336257842419374.447882227987
Winsorized Mean ( 9 / 20 )52.18916666666670.131819147565077395.914915478435
Winsorized Mean ( 10 / 20 )52.16750.125694370831621415.034497208177
Winsorized Mean ( 11 / 20 )52.17666666666670.124143316729143420.293802690211
Winsorized Mean ( 12 / 20 )52.18866666666670.121486431007832429.584326691614
Winsorized Mean ( 13 / 20 )52.18433333333330.12074448126179432.188144650608
Winsorized Mean ( 14 / 20 )52.12133333333330.107467106166126484.998016535058
Winsorized Mean ( 15 / 20 )52.10133333333330.0913695132266193570.226670728879
Winsorized Mean ( 16 / 20 )52.11733333333330.0888129077332664586.82160806916
Winsorized Mean ( 17 / 20 )52.11733333333330.0879762637051489592.402213260656
Winsorized Mean ( 18 / 20 )52.11733333333330.0879762637051489592.402213260656
Winsorized Mean ( 19 / 20 )52.11416666666670.0875424970784302595.30134969736
Winsorized Mean ( 20 / 20 )52.13750.0752005322886557693.312911667584
Trimmed Mean ( 1 / 20 )52.18586206896550.159382321507501327.425661612725
Trimmed Mean ( 2 / 20 )52.18339285714290.155896085267302334.731900212045
Trimmed Mean ( 3 / 20 )52.17722222222220.152495756471796342.155240443509
Trimmed Mean ( 4 / 20 )52.17634615384620.149768304930822348.380427874552
Trimmed Mean ( 5 / 20 )52.1760.146425714257839356.330855304035
Trimmed Mean ( 6 / 20 )52.17520833333330.142243918709623366.80097684769
Trimmed Mean ( 7 / 20 )52.17391304347830.137102690192625380.546238517825
Trimmed Mean ( 8 / 20 )52.17204545454550.130548760278686399.636467961645
Trimmed Mean ( 9 / 20 )52.17166666666670.126796001883693411.461449033089
Trimmed Mean ( 10 / 20 )52.168750.123838287594584421.265111245623
Trimmed Mean ( 11 / 20 )52.16894736842110.121405817873819429.707144863865
Trimmed Mean ( 12 / 20 )52.16777777777780.11834648559445440.805466387456
Trimmed Mean ( 13 / 20 )52.1647058823530.114701997283263454.784634251218
Trimmed Mean ( 14 / 20 )52.1618750.109641495614042475.749393127758
Trimmed Mean ( 15 / 20 )52.16766666666670.106396226850968490.315006562585
Trimmed Mean ( 16 / 20 )52.17714285714290.106126929523416491.648473120393
Trimmed Mean ( 17 / 20 )52.18576923076920.105876812420303492.891389888142
Trimmed Mean ( 18 / 20 )52.19583333333330.104987778216701497.161043122543
Trimmed Mean ( 19 / 20 )52.20772727272730.102739387478574508.156886604126
Trimmed Mean ( 20 / 20 )52.22250.098319765641449531.149557358021
Median52.27
Midrange52.22
Midmean - Weighted Average at Xnp52.131935483871
Midmean - Weighted Average at X(n+1)p52.1676666666667
Midmean - Empirical Distribution Function52.131935483871
Midmean - Empirical Distribution Function - Averaging52.1676666666667
Midmean - Empirical Distribution Function - Interpolation52.1676666666667
Midmean - Closest Observation52.131935483871
Midmean - True Basic - Statistics Graphics Toolkit52.1676666666667
Midmean - MS Excel (old versions)52.161875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 52.187 & 0.162969322266493 & 320.225912915451 \tabularnewline
Geometric Mean & 52.1719924515625 &  &  \tabularnewline
Harmonic Mean & 52.1569928509466 &  &  \tabularnewline
Quadratic Mean & 52.2020109765898 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 52.1881666666667 & 0.162177187690366 & 321.797210877191 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 52.1945 & 0.160720732809436 & 324.752750237183 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 52.1795 & 0.157455836333494 & 331.391336231468 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 52.1775 & 0.157049170931895 & 332.236710900098 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 52.1791666666667 & 0.156716356767067 & 332.952907680353 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 52.1811666666667 & 0.155920465685508 & 334.665282310766 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 52.1835 & 0.155462645612349 & 335.66584303551 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 52.1741666666667 & 0.139336257842419 & 374.447882227987 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 52.1891666666667 & 0.131819147565077 & 395.914915478435 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 52.1675 & 0.125694370831621 & 415.034497208177 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 52.1766666666667 & 0.124143316729143 & 420.293802690211 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 52.1886666666667 & 0.121486431007832 & 429.584326691614 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 52.1843333333333 & 0.12074448126179 & 432.188144650608 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 52.1213333333333 & 0.107467106166126 & 484.998016535058 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 52.1013333333333 & 0.0913695132266193 & 570.226670728879 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 52.1173333333333 & 0.0888129077332664 & 586.82160806916 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 52.1173333333333 & 0.0879762637051489 & 592.402213260656 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 52.1173333333333 & 0.0879762637051489 & 592.402213260656 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 52.1141666666667 & 0.0875424970784302 & 595.30134969736 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 52.1375 & 0.0752005322886557 & 693.312911667584 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 52.1858620689655 & 0.159382321507501 & 327.425661612725 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 52.1833928571429 & 0.155896085267302 & 334.731900212045 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 52.1772222222222 & 0.152495756471796 & 342.155240443509 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 52.1763461538462 & 0.149768304930822 & 348.380427874552 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 52.176 & 0.146425714257839 & 356.330855304035 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 52.1752083333333 & 0.142243918709623 & 366.80097684769 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 52.1739130434783 & 0.137102690192625 & 380.546238517825 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 52.1720454545455 & 0.130548760278686 & 399.636467961645 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 52.1716666666667 & 0.126796001883693 & 411.461449033089 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 52.16875 & 0.123838287594584 & 421.265111245623 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 52.1689473684211 & 0.121405817873819 & 429.707144863865 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 52.1677777777778 & 0.11834648559445 & 440.805466387456 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 52.164705882353 & 0.114701997283263 & 454.784634251218 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 52.161875 & 0.109641495614042 & 475.749393127758 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 52.1676666666667 & 0.106396226850968 & 490.315006562585 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 52.1771428571429 & 0.106126929523416 & 491.648473120393 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 52.1857692307692 & 0.105876812420303 & 492.891389888142 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 52.1958333333333 & 0.104987778216701 & 497.161043122543 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 52.2077272727273 & 0.102739387478574 & 508.156886604126 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 52.2225 & 0.098319765641449 & 531.149557358021 \tabularnewline
Median & 52.27 &  &  \tabularnewline
Midrange & 52.22 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 52.131935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 52.1676666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 52.131935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 52.1676666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 52.1676666666667 &  &  \tabularnewline
Midmean - Closest Observation & 52.131935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 52.1676666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 52.161875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132846&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]52.187[/C][C]0.162969322266493[/C][C]320.225912915451[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]52.1719924515625[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]52.1569928509466[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]52.2020109765898[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]52.1881666666667[/C][C]0.162177187690366[/C][C]321.797210877191[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]52.1945[/C][C]0.160720732809436[/C][C]324.752750237183[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]52.1795[/C][C]0.157455836333494[/C][C]331.391336231468[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]52.1775[/C][C]0.157049170931895[/C][C]332.236710900098[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]52.1791666666667[/C][C]0.156716356767067[/C][C]332.952907680353[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]52.1811666666667[/C][C]0.155920465685508[/C][C]334.665282310766[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]52.1835[/C][C]0.155462645612349[/C][C]335.66584303551[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]52.1741666666667[/C][C]0.139336257842419[/C][C]374.447882227987[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]52.1891666666667[/C][C]0.131819147565077[/C][C]395.914915478435[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]52.1675[/C][C]0.125694370831621[/C][C]415.034497208177[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]52.1766666666667[/C][C]0.124143316729143[/C][C]420.293802690211[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]52.1886666666667[/C][C]0.121486431007832[/C][C]429.584326691614[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]52.1843333333333[/C][C]0.12074448126179[/C][C]432.188144650608[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]52.1213333333333[/C][C]0.107467106166126[/C][C]484.998016535058[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]52.1013333333333[/C][C]0.0913695132266193[/C][C]570.226670728879[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]52.1173333333333[/C][C]0.0888129077332664[/C][C]586.82160806916[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]52.1173333333333[/C][C]0.0879762637051489[/C][C]592.402213260656[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]52.1173333333333[/C][C]0.0879762637051489[/C][C]592.402213260656[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]52.1141666666667[/C][C]0.0875424970784302[/C][C]595.30134969736[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]52.1375[/C][C]0.0752005322886557[/C][C]693.312911667584[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]52.1858620689655[/C][C]0.159382321507501[/C][C]327.425661612725[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]52.1833928571429[/C][C]0.155896085267302[/C][C]334.731900212045[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]52.1772222222222[/C][C]0.152495756471796[/C][C]342.155240443509[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]52.1763461538462[/C][C]0.149768304930822[/C][C]348.380427874552[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]52.176[/C][C]0.146425714257839[/C][C]356.330855304035[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]52.1752083333333[/C][C]0.142243918709623[/C][C]366.80097684769[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]52.1739130434783[/C][C]0.137102690192625[/C][C]380.546238517825[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]52.1720454545455[/C][C]0.130548760278686[/C][C]399.636467961645[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]52.1716666666667[/C][C]0.126796001883693[/C][C]411.461449033089[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]52.16875[/C][C]0.123838287594584[/C][C]421.265111245623[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]52.1689473684211[/C][C]0.121405817873819[/C][C]429.707144863865[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]52.1677777777778[/C][C]0.11834648559445[/C][C]440.805466387456[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]52.164705882353[/C][C]0.114701997283263[/C][C]454.784634251218[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]52.161875[/C][C]0.109641495614042[/C][C]475.749393127758[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]52.1676666666667[/C][C]0.106396226850968[/C][C]490.315006562585[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]52.1771428571429[/C][C]0.106126929523416[/C][C]491.648473120393[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]52.1857692307692[/C][C]0.105876812420303[/C][C]492.891389888142[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]52.1958333333333[/C][C]0.104987778216701[/C][C]497.161043122543[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]52.2077272727273[/C][C]0.102739387478574[/C][C]508.156886604126[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]52.2225[/C][C]0.098319765641449[/C][C]531.149557358021[/C][/ROW]
[ROW][C]Median[/C][C]52.27[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]52.22[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]52.131935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]52.1676666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]52.131935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]52.1676666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]52.1676666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]52.131935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]52.1676666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]52.161875[/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=132846&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132846&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 Mean52.1870.162969322266493320.225912915451
Geometric Mean52.1719924515625
Harmonic Mean52.1569928509466
Quadratic Mean52.2020109765898
Winsorized Mean ( 1 / 20 )52.18816666666670.162177187690366321.797210877191
Winsorized Mean ( 2 / 20 )52.19450.160720732809436324.752750237183
Winsorized Mean ( 3 / 20 )52.17950.157455836333494331.391336231468
Winsorized Mean ( 4 / 20 )52.17750.157049170931895332.236710900098
Winsorized Mean ( 5 / 20 )52.17916666666670.156716356767067332.952907680353
Winsorized Mean ( 6 / 20 )52.18116666666670.155920465685508334.665282310766
Winsorized Mean ( 7 / 20 )52.18350.155462645612349335.66584303551
Winsorized Mean ( 8 / 20 )52.17416666666670.139336257842419374.447882227987
Winsorized Mean ( 9 / 20 )52.18916666666670.131819147565077395.914915478435
Winsorized Mean ( 10 / 20 )52.16750.125694370831621415.034497208177
Winsorized Mean ( 11 / 20 )52.17666666666670.124143316729143420.293802690211
Winsorized Mean ( 12 / 20 )52.18866666666670.121486431007832429.584326691614
Winsorized Mean ( 13 / 20 )52.18433333333330.12074448126179432.188144650608
Winsorized Mean ( 14 / 20 )52.12133333333330.107467106166126484.998016535058
Winsorized Mean ( 15 / 20 )52.10133333333330.0913695132266193570.226670728879
Winsorized Mean ( 16 / 20 )52.11733333333330.0888129077332664586.82160806916
Winsorized Mean ( 17 / 20 )52.11733333333330.0879762637051489592.402213260656
Winsorized Mean ( 18 / 20 )52.11733333333330.0879762637051489592.402213260656
Winsorized Mean ( 19 / 20 )52.11416666666670.0875424970784302595.30134969736
Winsorized Mean ( 20 / 20 )52.13750.0752005322886557693.312911667584
Trimmed Mean ( 1 / 20 )52.18586206896550.159382321507501327.425661612725
Trimmed Mean ( 2 / 20 )52.18339285714290.155896085267302334.731900212045
Trimmed Mean ( 3 / 20 )52.17722222222220.152495756471796342.155240443509
Trimmed Mean ( 4 / 20 )52.17634615384620.149768304930822348.380427874552
Trimmed Mean ( 5 / 20 )52.1760.146425714257839356.330855304035
Trimmed Mean ( 6 / 20 )52.17520833333330.142243918709623366.80097684769
Trimmed Mean ( 7 / 20 )52.17391304347830.137102690192625380.546238517825
Trimmed Mean ( 8 / 20 )52.17204545454550.130548760278686399.636467961645
Trimmed Mean ( 9 / 20 )52.17166666666670.126796001883693411.461449033089
Trimmed Mean ( 10 / 20 )52.168750.123838287594584421.265111245623
Trimmed Mean ( 11 / 20 )52.16894736842110.121405817873819429.707144863865
Trimmed Mean ( 12 / 20 )52.16777777777780.11834648559445440.805466387456
Trimmed Mean ( 13 / 20 )52.1647058823530.114701997283263454.784634251218
Trimmed Mean ( 14 / 20 )52.1618750.109641495614042475.749393127758
Trimmed Mean ( 15 / 20 )52.16766666666670.106396226850968490.315006562585
Trimmed Mean ( 16 / 20 )52.17714285714290.106126929523416491.648473120393
Trimmed Mean ( 17 / 20 )52.18576923076920.105876812420303492.891389888142
Trimmed Mean ( 18 / 20 )52.19583333333330.104987778216701497.161043122543
Trimmed Mean ( 19 / 20 )52.20772727272730.102739387478574508.156886604126
Trimmed Mean ( 20 / 20 )52.22250.098319765641449531.149557358021
Median52.27
Midrange52.22
Midmean - Weighted Average at Xnp52.131935483871
Midmean - Weighted Average at X(n+1)p52.1676666666667
Midmean - Empirical Distribution Function52.131935483871
Midmean - Empirical Distribution Function - Averaging52.1676666666667
Midmean - Empirical Distribution Function - Interpolation52.1676666666667
Midmean - Closest Observation52.131935483871
Midmean - True Basic - Statistics Graphics Toolkit52.1676666666667
Midmean - MS Excel (old versions)52.161875
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')