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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 computationWed, 21 Oct 2009 12:01:33 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/21/t12561484026mvau9j5i6keq5s.htm/, Retrieved Thu, 02 May 2024 06:33:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49553, Retrieved Thu, 02 May 2024 06:33:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2009-10-12 18:01:53] [74be16979710d4c4e7c6647856088456]
- RMPD    [Central Tendency] [cs.shw.ws3.v2.2] [2009-10-21 18:01:33] [47f146dd9fb230449e079c6cbc92f5f5] [Current]
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Dataseries X:
10.8
11
11.1
11.1
11.1
11.2
11.1
11.2
11
11
10.9
11.2
10.8
10.6
10.7
10.4
10.6
10.4
10.3
10.2
10.3
10.4
10.4
10.2
10.1
10
10.1
10.1
10
10
9.8
9.7
9.6
9.7
9.6
9.5
9.6
9.6
9.5
9.4
9.4
9.4
9.4
9.5
9.4
9.5
9.6
9.6
9.6
9.6
9.9
9.7
9.9
9.9
10
10.2
10.2
10.3
10.2
10.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49553&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49553&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49553&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean10.1650.0741743632139305137.041958428177
Geometric Mean10.1492321563774
Harmonic Mean10.1336779420558
Quadratic Mean10.1809544411776
Winsorized Mean ( 1 / 20 )10.1650.0741743632139305137.041958428177
Winsorized Mean ( 2 / 20 )10.1650.0741743632139305137.041958428177
Winsorized Mean ( 3 / 20 )10.160.0730374101186245139.106794497485
Winsorized Mean ( 4 / 20 )10.160.0730374101186245139.106794497485
Winsorized Mean ( 5 / 20 )10.16833333333330.0716430127828432141.930565708543
Winsorized Mean ( 6 / 20 )10.16833333333330.0716430127828432141.930565708543
Winsorized Mean ( 7 / 20 )10.15666666666670.0691500728852665146.878611155169
Winsorized Mean ( 8 / 20 )10.15666666666670.0691500728852665146.878611155169
Winsorized Mean ( 9 / 20 )10.17166666666670.066853903733772152.147684706231
Winsorized Mean ( 10 / 20 )10.1550.0634428877022476160.065223507161
Winsorized Mean ( 11 / 20 )10.13666666666670.0598947601844418169.241293152381
Winsorized Mean ( 12 / 20 )10.13666666666670.0598947601844418169.241293152381
Winsorized Mean ( 13 / 20 )10.1150.0559370610799306180.828234532134
Winsorized Mean ( 14 / 20 )10.09166666666670.0519284419996618194.337944256683
Winsorized Mean ( 15 / 20 )10.09166666666670.0519284419996618194.337944256683
Winsorized Mean ( 16 / 20 )10.03833333333330.0437049472090534229.684142742859
Winsorized Mean ( 17 / 20 )10.06666666666670.0390325567909942257.904362262769
Winsorized Mean ( 18 / 20 )10.06666666666670.0390325567909942257.904362262769
Winsorized Mean ( 19 / 20 )10.06666666666670.0390325567909942257.904362262769
Winsorized Mean ( 20 / 20 )10.06666666666670.0290787618021688346.186221241232
Trimmed Mean ( 1 / 20 )10.16034482758620.0734154927419666138.395105012736
Trimmed Mean ( 2 / 20 )10.15535714285710.072430873576979140.207575048285
Trimmed Mean ( 3 / 20 )10.150.0711662849375315142.623715835518
Trimmed Mean ( 4 / 20 )10.14615384615380.0700926739727994144.75341388875
Trimmed Mean ( 5 / 20 )10.1420.0686957206878007147.636561614835
Trimmed Mean ( 6 / 20 )10.13541666666670.0673385634072291150.514298996444
Trimmed Mean ( 7 / 20 )10.12826086956520.0655458716445592154.521720673554
Trimmed Mean ( 8 / 20 )10.12272727272730.0639489453770553158.293889180529
Trimmed Mean ( 9 / 20 )10.11666666666670.0618075266012206163.680173321592
Trimmed Mean ( 10 / 20 )10.10750.0595267123834291169.797719297760
Trimmed Mean ( 11 / 20 )10.10.0574468645576995175.814643284066
Trimmed Mean ( 12 / 20 )10.09444444444440.05562693826756181.466835292843
Trimmed Mean ( 13 / 20 )10.08823529411760.0530302281339815190.235562793160
Trimmed Mean ( 14 / 20 )10.0843750.0506230087222873199.205366384323
Trimmed Mean ( 15 / 20 )10.08333333333330.0484431965813483208.147563433410
Trimmed Mean ( 16 / 20 )10.08214285714290.0451492444078207223.307011875407
Trimmed Mean ( 17 / 20 )10.08846153846150.0430837906613553234.159097507420
Trimmed Mean ( 18 / 20 )10.09166666666670.0416666666666667242.2
Trimmed Mean ( 19 / 20 )10.09545454545450.0391894459284169257.606462818965
Trimmed Mean ( 20 / 20 )10.10.0347926186969229290.291457736501
Median10.1
Midrange10.3
Midmean - Weighted Average at Xnp10.0189189189189
Midmean - Weighted Average at X(n+1)p10.0189189189189
Midmean - Empirical Distribution Function10.0189189189189
Midmean - Empirical Distribution Function - Averaging10.0189189189189
Midmean - Empirical Distribution Function - Interpolation10.0189189189189
Midmean - Closest Observation10.0189189189189
Midmean - True Basic - Statistics Graphics Toolkit10.0189189189189
Midmean - MS Excel (old versions)10.0189189189189
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 10.165 & 0.0741743632139305 & 137.041958428177 \tabularnewline
Geometric Mean & 10.1492321563774 &  &  \tabularnewline
Harmonic Mean & 10.1336779420558 &  &  \tabularnewline
Quadratic Mean & 10.1809544411776 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 10.165 & 0.0741743632139305 & 137.041958428177 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 10.165 & 0.0741743632139305 & 137.041958428177 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 10.16 & 0.0730374101186245 & 139.106794497485 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 10.16 & 0.0730374101186245 & 139.106794497485 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 10.1683333333333 & 0.0716430127828432 & 141.930565708543 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 10.1683333333333 & 0.0716430127828432 & 141.930565708543 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 10.1566666666667 & 0.0691500728852665 & 146.878611155169 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 10.1566666666667 & 0.0691500728852665 & 146.878611155169 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 10.1716666666667 & 0.066853903733772 & 152.147684706231 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 10.155 & 0.0634428877022476 & 160.065223507161 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 10.1366666666667 & 0.0598947601844418 & 169.241293152381 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 10.1366666666667 & 0.0598947601844418 & 169.241293152381 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 10.115 & 0.0559370610799306 & 180.828234532134 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 10.0916666666667 & 0.0519284419996618 & 194.337944256683 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 10.0916666666667 & 0.0519284419996618 & 194.337944256683 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 10.0383333333333 & 0.0437049472090534 & 229.684142742859 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 10.0666666666667 & 0.0390325567909942 & 257.904362262769 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 10.0666666666667 & 0.0390325567909942 & 257.904362262769 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 10.0666666666667 & 0.0390325567909942 & 257.904362262769 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 10.0666666666667 & 0.0290787618021688 & 346.186221241232 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 10.1603448275862 & 0.0734154927419666 & 138.395105012736 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 10.1553571428571 & 0.072430873576979 & 140.207575048285 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 10.15 & 0.0711662849375315 & 142.623715835518 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 10.1461538461538 & 0.0700926739727994 & 144.75341388875 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 10.142 & 0.0686957206878007 & 147.636561614835 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 10.1354166666667 & 0.0673385634072291 & 150.514298996444 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 10.1282608695652 & 0.0655458716445592 & 154.521720673554 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 10.1227272727273 & 0.0639489453770553 & 158.293889180529 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 10.1166666666667 & 0.0618075266012206 & 163.680173321592 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 10.1075 & 0.0595267123834291 & 169.797719297760 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 10.1 & 0.0574468645576995 & 175.814643284066 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 10.0944444444444 & 0.05562693826756 & 181.466835292843 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 10.0882352941176 & 0.0530302281339815 & 190.235562793160 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 10.084375 & 0.0506230087222873 & 199.205366384323 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 10.0833333333333 & 0.0484431965813483 & 208.147563433410 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 10.0821428571429 & 0.0451492444078207 & 223.307011875407 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 10.0884615384615 & 0.0430837906613553 & 234.159097507420 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 10.0916666666667 & 0.0416666666666667 & 242.2 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 10.0954545454545 & 0.0391894459284169 & 257.606462818965 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 10.1 & 0.0347926186969229 & 290.291457736501 \tabularnewline
Median & 10.1 &  &  \tabularnewline
Midrange & 10.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 10.0189189189189 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 10.0189189189189 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 10.0189189189189 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 10.0189189189189 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 10.0189189189189 &  &  \tabularnewline
Midmean - Closest Observation & 10.0189189189189 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 10.0189189189189 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 10.0189189189189 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49553&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]10.165[/C][C]0.0741743632139305[/C][C]137.041958428177[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]10.1492321563774[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]10.1336779420558[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10.1809544411776[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]10.165[/C][C]0.0741743632139305[/C][C]137.041958428177[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]10.165[/C][C]0.0741743632139305[/C][C]137.041958428177[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]10.16[/C][C]0.0730374101186245[/C][C]139.106794497485[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]10.16[/C][C]0.0730374101186245[/C][C]139.106794497485[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]10.1683333333333[/C][C]0.0716430127828432[/C][C]141.930565708543[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]10.1683333333333[/C][C]0.0716430127828432[/C][C]141.930565708543[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]10.1566666666667[/C][C]0.0691500728852665[/C][C]146.878611155169[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]10.1566666666667[/C][C]0.0691500728852665[/C][C]146.878611155169[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]10.1716666666667[/C][C]0.066853903733772[/C][C]152.147684706231[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]10.155[/C][C]0.0634428877022476[/C][C]160.065223507161[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]10.1366666666667[/C][C]0.0598947601844418[/C][C]169.241293152381[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]10.1366666666667[/C][C]0.0598947601844418[/C][C]169.241293152381[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]10.115[/C][C]0.0559370610799306[/C][C]180.828234532134[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]10.0916666666667[/C][C]0.0519284419996618[/C][C]194.337944256683[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]10.0916666666667[/C][C]0.0519284419996618[/C][C]194.337944256683[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]10.0383333333333[/C][C]0.0437049472090534[/C][C]229.684142742859[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]10.0666666666667[/C][C]0.0390325567909942[/C][C]257.904362262769[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]10.0666666666667[/C][C]0.0390325567909942[/C][C]257.904362262769[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]10.0666666666667[/C][C]0.0390325567909942[/C][C]257.904362262769[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]10.0666666666667[/C][C]0.0290787618021688[/C][C]346.186221241232[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]10.1603448275862[/C][C]0.0734154927419666[/C][C]138.395105012736[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]10.1553571428571[/C][C]0.072430873576979[/C][C]140.207575048285[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]10.15[/C][C]0.0711662849375315[/C][C]142.623715835518[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]10.1461538461538[/C][C]0.0700926739727994[/C][C]144.75341388875[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]10.142[/C][C]0.0686957206878007[/C][C]147.636561614835[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]10.1354166666667[/C][C]0.0673385634072291[/C][C]150.514298996444[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]10.1282608695652[/C][C]0.0655458716445592[/C][C]154.521720673554[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]10.1227272727273[/C][C]0.0639489453770553[/C][C]158.293889180529[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]10.1166666666667[/C][C]0.0618075266012206[/C][C]163.680173321592[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]10.1075[/C][C]0.0595267123834291[/C][C]169.797719297760[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]10.1[/C][C]0.0574468645576995[/C][C]175.814643284066[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]10.0944444444444[/C][C]0.05562693826756[/C][C]181.466835292843[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]10.0882352941176[/C][C]0.0530302281339815[/C][C]190.235562793160[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]10.084375[/C][C]0.0506230087222873[/C][C]199.205366384323[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]10.0833333333333[/C][C]0.0484431965813483[/C][C]208.147563433410[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]10.0821428571429[/C][C]0.0451492444078207[/C][C]223.307011875407[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]10.0884615384615[/C][C]0.0430837906613553[/C][C]234.159097507420[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]10.0916666666667[/C][C]0.0416666666666667[/C][C]242.2[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]10.0954545454545[/C][C]0.0391894459284169[/C][C]257.606462818965[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]10.1[/C][C]0.0347926186969229[/C][C]290.291457736501[/C][/ROW]
[ROW][C]Median[/C][C]10.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]10.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]10.0189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]10.0189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]10.0189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]10.0189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]10.0189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]10.0189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]10.0189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]10.0189189189189[/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=49553&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49553&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 Mean10.1650.0741743632139305137.041958428177
Geometric Mean10.1492321563774
Harmonic Mean10.1336779420558
Quadratic Mean10.1809544411776
Winsorized Mean ( 1 / 20 )10.1650.0741743632139305137.041958428177
Winsorized Mean ( 2 / 20 )10.1650.0741743632139305137.041958428177
Winsorized Mean ( 3 / 20 )10.160.0730374101186245139.106794497485
Winsorized Mean ( 4 / 20 )10.160.0730374101186245139.106794497485
Winsorized Mean ( 5 / 20 )10.16833333333330.0716430127828432141.930565708543
Winsorized Mean ( 6 / 20 )10.16833333333330.0716430127828432141.930565708543
Winsorized Mean ( 7 / 20 )10.15666666666670.0691500728852665146.878611155169
Winsorized Mean ( 8 / 20 )10.15666666666670.0691500728852665146.878611155169
Winsorized Mean ( 9 / 20 )10.17166666666670.066853903733772152.147684706231
Winsorized Mean ( 10 / 20 )10.1550.0634428877022476160.065223507161
Winsorized Mean ( 11 / 20 )10.13666666666670.0598947601844418169.241293152381
Winsorized Mean ( 12 / 20 )10.13666666666670.0598947601844418169.241293152381
Winsorized Mean ( 13 / 20 )10.1150.0559370610799306180.828234532134
Winsorized Mean ( 14 / 20 )10.09166666666670.0519284419996618194.337944256683
Winsorized Mean ( 15 / 20 )10.09166666666670.0519284419996618194.337944256683
Winsorized Mean ( 16 / 20 )10.03833333333330.0437049472090534229.684142742859
Winsorized Mean ( 17 / 20 )10.06666666666670.0390325567909942257.904362262769
Winsorized Mean ( 18 / 20 )10.06666666666670.0390325567909942257.904362262769
Winsorized Mean ( 19 / 20 )10.06666666666670.0390325567909942257.904362262769
Winsorized Mean ( 20 / 20 )10.06666666666670.0290787618021688346.186221241232
Trimmed Mean ( 1 / 20 )10.16034482758620.0734154927419666138.395105012736
Trimmed Mean ( 2 / 20 )10.15535714285710.072430873576979140.207575048285
Trimmed Mean ( 3 / 20 )10.150.0711662849375315142.623715835518
Trimmed Mean ( 4 / 20 )10.14615384615380.0700926739727994144.75341388875
Trimmed Mean ( 5 / 20 )10.1420.0686957206878007147.636561614835
Trimmed Mean ( 6 / 20 )10.13541666666670.0673385634072291150.514298996444
Trimmed Mean ( 7 / 20 )10.12826086956520.0655458716445592154.521720673554
Trimmed Mean ( 8 / 20 )10.12272727272730.0639489453770553158.293889180529
Trimmed Mean ( 9 / 20 )10.11666666666670.0618075266012206163.680173321592
Trimmed Mean ( 10 / 20 )10.10750.0595267123834291169.797719297760
Trimmed Mean ( 11 / 20 )10.10.0574468645576995175.814643284066
Trimmed Mean ( 12 / 20 )10.09444444444440.05562693826756181.466835292843
Trimmed Mean ( 13 / 20 )10.08823529411760.0530302281339815190.235562793160
Trimmed Mean ( 14 / 20 )10.0843750.0506230087222873199.205366384323
Trimmed Mean ( 15 / 20 )10.08333333333330.0484431965813483208.147563433410
Trimmed Mean ( 16 / 20 )10.08214285714290.0451492444078207223.307011875407
Trimmed Mean ( 17 / 20 )10.08846153846150.0430837906613553234.159097507420
Trimmed Mean ( 18 / 20 )10.09166666666670.0416666666666667242.2
Trimmed Mean ( 19 / 20 )10.09545454545450.0391894459284169257.606462818965
Trimmed Mean ( 20 / 20 )10.10.0347926186969229290.291457736501
Median10.1
Midrange10.3
Midmean - Weighted Average at Xnp10.0189189189189
Midmean - Weighted Average at X(n+1)p10.0189189189189
Midmean - Empirical Distribution Function10.0189189189189
Midmean - Empirical Distribution Function - Averaging10.0189189189189
Midmean - Empirical Distribution Function - Interpolation10.0189189189189
Midmean - Closest Observation10.0189189189189
Midmean - True Basic - Statistics Graphics Toolkit10.0189189189189
Midmean - MS Excel (old versions)10.0189189189189
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')