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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 computationSun, 18 Dec 2011 07:40:51 -0500
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/Dec/18/t1324212294l9gpmbh5xpnxfqn.htm/, Retrieved Sun, 05 May 2024 20:06:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156784, Retrieved Sun, 05 May 2024 20:06:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [SHW_WS3_Yt=c+Xt] [2009-10-16 08:10:06] [8b1aef4e7013bd33fbc2a5833375c5f5]
-  M D  [Central Tendency] [paper univariate] [2010-12-04 09:51:15] [814f53995537cd15c528d8efbf1cf544]
-    D      [Central Tendency] [Central Tendancy] [2011-12-18 12:40:51] [274a40ad31da88f12aea425a159a1f93] [Current]
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Dataseries X:
2.30
2.80
8.80
10.70
13.90
19.30
19.50
20.40
15.30
7.90
8.30
4.50
3.20
5.00
6.60
11.10
12.80
16.30
17.40
18.90
15.80
11.70
6.40
2.90
4.70
2.40
7.20
10.70
13.40
18.30
18.40
16.80
16.60
14.10
6.10
3.50
1.70
2.30
4.50
9.30
14.20
17.30
23.00
16.30
18.40
14.20
9.10
5.90
7.20
6.80
8.00
14.30
14.60
17.50
17.20
17.20
14.10
10.40
6.80
4.10




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=156784&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=156784&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156784&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 Mean11.140.75231169162517514.8076922424732
Geometric Mean9.25664991888288
Harmonic Mean7.17012010538216
Quadratic Mean12.5495816663345
Winsorized Mean ( 1 / 20 )11.10666666666670.73982692534990415.0125202072278
Winsorized Mean ( 2 / 20 )11.07666666666670.73371343513419615.0967205127445
Winsorized Mean ( 3 / 20 )11.07166666666670.7307765843237315.1505492980629
Winsorized Mean ( 4 / 20 )11.07166666666670.72049924493962415.3666596383379
Winsorized Mean ( 5 / 20 )11.03833333333330.71138875744451815.5165979470715
Winsorized Mean ( 6 / 20 )11.06833333333330.70564508158677615.6854112954973
Winsorized Mean ( 7 / 20 )11.09166666666670.69705713789042615.9121341189253
Winsorized Mean ( 8 / 20 )11.0650.66444329103818216.6530389413837
Winsorized Mean ( 9 / 20 )11.110.651494154055417.0531077383317
Winsorized Mean ( 10 / 20 )11.09333333333330.64877923898782417.0987797800687
Winsorized Mean ( 11 / 20 )11.11166666666670.63954031720119117.3744584474275
Winsorized Mean ( 12 / 20 )11.17166666666670.62945627898711817.7481217355452
Winsorized Mean ( 13 / 20 )11.280.5840139693399319.3146064857815
Winsorized Mean ( 14 / 20 )11.280.56933800392373619.8124838360711
Winsorized Mean ( 15 / 20 )11.280.54608933273049220.6559610743522
Winsorized Mean ( 16 / 20 )11.33333333333330.53807391731029121.0627814668774
Winsorized Mean ( 17 / 20 )11.24833333333330.5077895581881322.1515648597996
Winsorized Mean ( 18 / 20 )11.09833333333330.48538232159480322.8651371085538
Winsorized Mean ( 19 / 20 )11.00333333333330.43463060922850625.3165172900842
Winsorized Mean ( 20 / 20 )10.90333333333330.42077388123992425.9125716197111
Trimmed Mean ( 1 / 20 )11.0982758620690.73246177397087215.1520205647077
Trimmed Mean ( 2 / 20 )11.08928571428570.72293898078907115.3391724737017
Trimmed Mean ( 3 / 20 )11.09629629629630.71466109584996615.5266550267427
Trimmed Mean ( 4 / 20 )11.10576923076920.70518663202336215.7486950637506
Trimmed Mean ( 5 / 20 )11.1160.6966588483758815.9561599280835
Trimmed Mean ( 6 / 20 )11.13541666666670.68820154137750516.1804587713913
Trimmed Mean ( 7 / 20 )11.150.67842350645174416.4351616563467
Trimmed Mean ( 8 / 20 )11.16136363636360.66753638053292616.7202327271706
Trimmed Mean ( 9 / 20 )11.17857142857140.66128667487558716.9042744293533
Trimmed Mean ( 10 / 20 )11.190.6552138034299417.0783947795699
Trimmed Mean ( 11 / 20 )11.20526315789470.64648021038868417.3327241543214
Trimmed Mean ( 12 / 20 )11.21944444444440.6358074412058817.6459785106722
Trimmed Mean ( 13 / 20 )11.22647058823530.62258887965927418.0319163335831
Trimmed Mean ( 14 / 20 )11.218750.61522087398780818.2353207999609
Trimmed Mean ( 15 / 20 )11.210.60676928524542318.4748969214317
Trimmed Mean ( 16 / 20 )11.20.59900711499073518.6976076238648
Trimmed Mean ( 17 / 20 )11.18076923076920.58714483158283719.0426086194575
Trimmed Mean ( 18 / 20 )11.17083333333330.57664318352956519.3721761609285
Trimmed Mean ( 19 / 20 )11.18181818181820.56482906902327119.7968178251773
Trimmed Mean ( 20 / 20 )11.210.56157204158926619.9618199799893
Median10.9
Midrange12.35
Midmean - Weighted Average at Xnp11.0451612903226
Midmean - Weighted Average at X(n+1)p11.21
Midmean - Empirical Distribution Function11.0451612903226
Midmean - Empirical Distribution Function - Averaging11.21
Midmean - Empirical Distribution Function - Interpolation11.21
Midmean - Closest Observation11.0451612903226
Midmean - True Basic - Statistics Graphics Toolkit11.21
Midmean - MS Excel (old versions)11.21875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 11.14 & 0.752311691625175 & 14.8076922424732 \tabularnewline
Geometric Mean & 9.25664991888288 &  &  \tabularnewline
Harmonic Mean & 7.17012010538216 &  &  \tabularnewline
Quadratic Mean & 12.5495816663345 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 11.1066666666667 & 0.739826925349904 & 15.0125202072278 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 11.0766666666667 & 0.733713435134196 & 15.0967205127445 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 11.0716666666667 & 0.73077658432373 & 15.1505492980629 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 11.0716666666667 & 0.720499244939624 & 15.3666596383379 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 11.0383333333333 & 0.711388757444518 & 15.5165979470715 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 11.0683333333333 & 0.705645081586776 & 15.6854112954973 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 11.0916666666667 & 0.697057137890426 & 15.9121341189253 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 11.065 & 0.664443291038182 & 16.6530389413837 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 11.11 & 0.6514941540554 & 17.0531077383317 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 11.0933333333333 & 0.648779238987824 & 17.0987797800687 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 11.1116666666667 & 0.639540317201191 & 17.3744584474275 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 11.1716666666667 & 0.629456278987118 & 17.7481217355452 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 11.28 & 0.58401396933993 & 19.3146064857815 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 11.28 & 0.569338003923736 & 19.8124838360711 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 11.28 & 0.546089332730492 & 20.6559610743522 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 11.3333333333333 & 0.538073917310291 & 21.0627814668774 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 11.2483333333333 & 0.50778955818813 & 22.1515648597996 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 11.0983333333333 & 0.485382321594803 & 22.8651371085538 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 11.0033333333333 & 0.434630609228506 & 25.3165172900842 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 10.9033333333333 & 0.420773881239924 & 25.9125716197111 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 11.098275862069 & 0.732461773970872 & 15.1520205647077 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 11.0892857142857 & 0.722938980789071 & 15.3391724737017 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 11.0962962962963 & 0.714661095849966 & 15.5266550267427 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 11.1057692307692 & 0.705186632023362 & 15.7486950637506 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 11.116 & 0.69665884837588 & 15.9561599280835 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 11.1354166666667 & 0.688201541377505 & 16.1804587713913 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 11.15 & 0.678423506451744 & 16.4351616563467 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 11.1613636363636 & 0.667536380532926 & 16.7202327271706 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 11.1785714285714 & 0.661286674875587 & 16.9042744293533 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 11.19 & 0.65521380342994 & 17.0783947795699 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 11.2052631578947 & 0.646480210388684 & 17.3327241543214 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 11.2194444444444 & 0.63580744120588 & 17.6459785106722 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 11.2264705882353 & 0.622588879659274 & 18.0319163335831 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 11.21875 & 0.615220873987808 & 18.2353207999609 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 11.21 & 0.606769285245423 & 18.4748969214317 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 11.2 & 0.599007114990735 & 18.6976076238648 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 11.1807692307692 & 0.587144831582837 & 19.0426086194575 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 11.1708333333333 & 0.576643183529565 & 19.3721761609285 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 11.1818181818182 & 0.564829069023271 & 19.7968178251773 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 11.21 & 0.561572041589266 & 19.9618199799893 \tabularnewline
Median & 10.9 &  &  \tabularnewline
Midrange & 12.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 11.0451612903226 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 11.21 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 11.0451612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 11.21 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 11.21 &  &  \tabularnewline
Midmean - Closest Observation & 11.0451612903226 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 11.21 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 11.21875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156784&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]11.14[/C][C]0.752311691625175[/C][C]14.8076922424732[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]9.25664991888288[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.17012010538216[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]12.5495816663345[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]11.1066666666667[/C][C]0.739826925349904[/C][C]15.0125202072278[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]11.0766666666667[/C][C]0.733713435134196[/C][C]15.0967205127445[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]11.0716666666667[/C][C]0.73077658432373[/C][C]15.1505492980629[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]11.0716666666667[/C][C]0.720499244939624[/C][C]15.3666596383379[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]11.0383333333333[/C][C]0.711388757444518[/C][C]15.5165979470715[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]11.0683333333333[/C][C]0.705645081586776[/C][C]15.6854112954973[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]11.0916666666667[/C][C]0.697057137890426[/C][C]15.9121341189253[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]11.065[/C][C]0.664443291038182[/C][C]16.6530389413837[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]11.11[/C][C]0.6514941540554[/C][C]17.0531077383317[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]11.0933333333333[/C][C]0.648779238987824[/C][C]17.0987797800687[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]11.1116666666667[/C][C]0.639540317201191[/C][C]17.3744584474275[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]11.1716666666667[/C][C]0.629456278987118[/C][C]17.7481217355452[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]11.28[/C][C]0.58401396933993[/C][C]19.3146064857815[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]11.28[/C][C]0.569338003923736[/C][C]19.8124838360711[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]11.28[/C][C]0.546089332730492[/C][C]20.6559610743522[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]11.3333333333333[/C][C]0.538073917310291[/C][C]21.0627814668774[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]11.2483333333333[/C][C]0.50778955818813[/C][C]22.1515648597996[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]11.0983333333333[/C][C]0.485382321594803[/C][C]22.8651371085538[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]11.0033333333333[/C][C]0.434630609228506[/C][C]25.3165172900842[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]10.9033333333333[/C][C]0.420773881239924[/C][C]25.9125716197111[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]11.098275862069[/C][C]0.732461773970872[/C][C]15.1520205647077[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]11.0892857142857[/C][C]0.722938980789071[/C][C]15.3391724737017[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]11.0962962962963[/C][C]0.714661095849966[/C][C]15.5266550267427[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]11.1057692307692[/C][C]0.705186632023362[/C][C]15.7486950637506[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]11.116[/C][C]0.69665884837588[/C][C]15.9561599280835[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]11.1354166666667[/C][C]0.688201541377505[/C][C]16.1804587713913[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]11.15[/C][C]0.678423506451744[/C][C]16.4351616563467[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]11.1613636363636[/C][C]0.667536380532926[/C][C]16.7202327271706[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]11.1785714285714[/C][C]0.661286674875587[/C][C]16.9042744293533[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]11.19[/C][C]0.65521380342994[/C][C]17.0783947795699[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]11.2052631578947[/C][C]0.646480210388684[/C][C]17.3327241543214[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]11.2194444444444[/C][C]0.63580744120588[/C][C]17.6459785106722[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]11.2264705882353[/C][C]0.622588879659274[/C][C]18.0319163335831[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]11.21875[/C][C]0.615220873987808[/C][C]18.2353207999609[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]11.21[/C][C]0.606769285245423[/C][C]18.4748969214317[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]11.2[/C][C]0.599007114990735[/C][C]18.6976076238648[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]11.1807692307692[/C][C]0.587144831582837[/C][C]19.0426086194575[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]11.1708333333333[/C][C]0.576643183529565[/C][C]19.3721761609285[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]11.1818181818182[/C][C]0.564829069023271[/C][C]19.7968178251773[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]11.21[/C][C]0.561572041589266[/C][C]19.9618199799893[/C][/ROW]
[ROW][C]Median[/C][C]10.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]12.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]11.0451612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]11.21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]11.0451612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]11.21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]11.21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]11.0451612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]11.21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]11.21875[/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=156784&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156784&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 Mean11.140.75231169162517514.8076922424732
Geometric Mean9.25664991888288
Harmonic Mean7.17012010538216
Quadratic Mean12.5495816663345
Winsorized Mean ( 1 / 20 )11.10666666666670.73982692534990415.0125202072278
Winsorized Mean ( 2 / 20 )11.07666666666670.73371343513419615.0967205127445
Winsorized Mean ( 3 / 20 )11.07166666666670.7307765843237315.1505492980629
Winsorized Mean ( 4 / 20 )11.07166666666670.72049924493962415.3666596383379
Winsorized Mean ( 5 / 20 )11.03833333333330.71138875744451815.5165979470715
Winsorized Mean ( 6 / 20 )11.06833333333330.70564508158677615.6854112954973
Winsorized Mean ( 7 / 20 )11.09166666666670.69705713789042615.9121341189253
Winsorized Mean ( 8 / 20 )11.0650.66444329103818216.6530389413837
Winsorized Mean ( 9 / 20 )11.110.651494154055417.0531077383317
Winsorized Mean ( 10 / 20 )11.09333333333330.64877923898782417.0987797800687
Winsorized Mean ( 11 / 20 )11.11166666666670.63954031720119117.3744584474275
Winsorized Mean ( 12 / 20 )11.17166666666670.62945627898711817.7481217355452
Winsorized Mean ( 13 / 20 )11.280.5840139693399319.3146064857815
Winsorized Mean ( 14 / 20 )11.280.56933800392373619.8124838360711
Winsorized Mean ( 15 / 20 )11.280.54608933273049220.6559610743522
Winsorized Mean ( 16 / 20 )11.33333333333330.53807391731029121.0627814668774
Winsorized Mean ( 17 / 20 )11.24833333333330.5077895581881322.1515648597996
Winsorized Mean ( 18 / 20 )11.09833333333330.48538232159480322.8651371085538
Winsorized Mean ( 19 / 20 )11.00333333333330.43463060922850625.3165172900842
Winsorized Mean ( 20 / 20 )10.90333333333330.42077388123992425.9125716197111
Trimmed Mean ( 1 / 20 )11.0982758620690.73246177397087215.1520205647077
Trimmed Mean ( 2 / 20 )11.08928571428570.72293898078907115.3391724737017
Trimmed Mean ( 3 / 20 )11.09629629629630.71466109584996615.5266550267427
Trimmed Mean ( 4 / 20 )11.10576923076920.70518663202336215.7486950637506
Trimmed Mean ( 5 / 20 )11.1160.6966588483758815.9561599280835
Trimmed Mean ( 6 / 20 )11.13541666666670.68820154137750516.1804587713913
Trimmed Mean ( 7 / 20 )11.150.67842350645174416.4351616563467
Trimmed Mean ( 8 / 20 )11.16136363636360.66753638053292616.7202327271706
Trimmed Mean ( 9 / 20 )11.17857142857140.66128667487558716.9042744293533
Trimmed Mean ( 10 / 20 )11.190.6552138034299417.0783947795699
Trimmed Mean ( 11 / 20 )11.20526315789470.64648021038868417.3327241543214
Trimmed Mean ( 12 / 20 )11.21944444444440.6358074412058817.6459785106722
Trimmed Mean ( 13 / 20 )11.22647058823530.62258887965927418.0319163335831
Trimmed Mean ( 14 / 20 )11.218750.61522087398780818.2353207999609
Trimmed Mean ( 15 / 20 )11.210.60676928524542318.4748969214317
Trimmed Mean ( 16 / 20 )11.20.59900711499073518.6976076238648
Trimmed Mean ( 17 / 20 )11.18076923076920.58714483158283719.0426086194575
Trimmed Mean ( 18 / 20 )11.17083333333330.57664318352956519.3721761609285
Trimmed Mean ( 19 / 20 )11.18181818181820.56482906902327119.7968178251773
Trimmed Mean ( 20 / 20 )11.210.56157204158926619.9618199799893
Median10.9
Midrange12.35
Midmean - Weighted Average at Xnp11.0451612903226
Midmean - Weighted Average at X(n+1)p11.21
Midmean - Empirical Distribution Function11.0451612903226
Midmean - Empirical Distribution Function - Averaging11.21
Midmean - Empirical Distribution Function - Interpolation11.21
Midmean - Closest Observation11.0451612903226
Midmean - True Basic - Statistics Graphics Toolkit11.21
Midmean - MS Excel (old versions)11.21875
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')