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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 01 Mar 2012 12:28:07 -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/2012/Mar/01/t1330622973vka01rg93hy16hg.htm/, Retrieved Sun, 28 Apr 2024 11:05:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163395, Retrieved Sun, 28 Apr 2024 11:05:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten: Pri...] [2012-03-01 17:28:07] [c7c61aaff161b25e5153c41aabf1c02e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
98,01
99,2
100,7
106,41
107,51
107,1
99,75
98,96
107,26
107,11
107,2
107,65
104,78
105,56
107,95
107,11
107,47
107,06
99,71
99,6
107,19
107,26
113,24
113,52
110,48
111,41
115,5
118,32
118,42
117,5
110,23
109,19
118,41
118,3
116,1
114,11
113,41
114,33
116,61
123,64
123,77
123,39
116,03
114,95
123,4
123,53
114,45
114,26
114,35
112,77
115,31
114,93
116,38
115,07
105
103,43
114,52
115,04
117,16
115

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163395&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163395&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163395&T=0

As an alternative you can also use a QR Code:  
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'Gertrude Mary Cox' @ cox.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.43350.870685320862883127.983666808078
Geometric Mean111.23080096769
Harmonic Mean111.026132291024
Quadratic Mean111.63401096888
Winsorized Mean ( 1 / 20 )111.4471666666670.86616320964578128.667629178389
Winsorized Mean ( 2 / 20 )111.45150.863351563568622129.091675631328
Winsorized Mean ( 3 / 20 )111.4650.857062006208346130.054767557744
Winsorized Mean ( 4 / 20 )111.4716666666670.855189514354212130.347326289242
Winsorized Mean ( 5 / 20 )111.0608333333330.771182132109609144.013753313398
Winsorized Mean ( 6 / 20 )111.1548333333330.747949040971891148.6128429136
Winsorized Mean ( 7 / 20 )111.4628333333330.676102200831995164.860923683091
Winsorized Mean ( 8 / 20 )111.6401666666670.641145051396577174.126223735933
Winsorized Mean ( 9 / 20 )111.5531666666670.614755175726779181.459499767181
Winsorized Mean ( 10 / 20 )111.5898333333330.589030635811644189.446569582192
Winsorized Mean ( 11 / 20 )111.6448333333330.546990920697776204.107287906922
Winsorized Mean ( 12 / 20 )111.7288333333330.519499709991962215.070059105639
Winsorized Mean ( 13 / 20 )111.6768333333330.509108198442414219.357758674879
Winsorized Mean ( 14 / 20 )111.6628333333330.506356213893341220.522292942284
Winsorized Mean ( 15 / 20 )111.5303333333330.487518272389221228.771596163457
Winsorized Mean ( 16 / 20 )111.5010.477322730131894233.596669425715
Winsorized Mean ( 17 / 20 )111.4358333333330.467811909403809238.206490885087
Winsorized Mean ( 18 / 20 )111.4448333333330.463870872086045240.249690247119
Winsorized Mean ( 19 / 20 )111.4321666666670.462210305770899241.085422101989
Winsorized Mean ( 20 / 20 )111.48550.449374733524198248.090272289412
Trimmed Mean ( 1 / 20 )111.452241379310.843330656788293132.157227396144
Trimmed Mean ( 2 / 20 )111.4576785714290.81516666254939136.729927378103
Trimmed Mean ( 3 / 20 )111.4611111111110.78210629918138142.514017887052
Trimmed Mean ( 4 / 20 )111.4596153846150.743862365507819149.839030112142
Trimmed Mean ( 5 / 20 )111.4560.696066557924761160.122618636202
Trimmed Mean ( 6 / 20 )111.5547916666670.666128993480969167.467251475902
Trimmed Mean ( 7 / 20 )111.6417391304350.635458623559259175.68687400152
Trimmed Mean ( 8 / 20 )111.6765909090910.618511387517291180.557049009819
Trimmed Mean ( 9 / 20 )111.6830952380950.605991330160269184.298173388979
Trimmed Mean ( 10 / 20 )111.704750.595842109044213187.473742295899
Trimmed Mean ( 11 / 20 )111.7228947368420.588119203414215189.966411721052
Trimmed Mean ( 12 / 20 )111.7347222222220.587027416967559190.339869983274
Trimmed Mean ( 13 / 20 )111.7355882352940.590149259221596189.334454782969
Trimmed Mean ( 14 / 20 )111.74406250.594181101454434188.06397952825
Trimmed Mean ( 15 / 20 )111.7556666666670.597291719737879187.103994536724
Trimmed Mean ( 16 / 20 )111.7878571428570.602845623526445185.433638033126
Trimmed Mean ( 17 / 20 )111.8292307692310.609107019288684183.595373600891
Trimmed Mean ( 18 / 20 )111.8870833333330.615536610234231181.771614349237
Trimmed Mean ( 19 / 20 )111.9540909090910.620178601244796180.51911285617
Trimmed Mean ( 20 / 20 )112.03650.620371821868483180.595726708799
Median113.325
Midrange110.89
Midmean - Weighted Average at Xnp111.605806451613
Midmean - Weighted Average at X(n+1)p111.605806451613
Midmean - Empirical Distribution Function111.605806451613
Midmean - Empirical Distribution Function - Averaging111.605806451613
Midmean - Empirical Distribution Function - Interpolation111.605806451613
Midmean - Closest Observation111.605806451613
Midmean - True Basic - Statistics Graphics Toolkit111.605806451613
Midmean - MS Excel (old versions)111.7440625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 111.4335 & 0.870685320862883 & 127.983666808078 \tabularnewline
Geometric Mean & 111.23080096769 &  &  \tabularnewline
Harmonic Mean & 111.026132291024 &  &  \tabularnewline
Quadratic Mean & 111.63401096888 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 111.447166666667 & 0.86616320964578 & 128.667629178389 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 111.4515 & 0.863351563568622 & 129.091675631328 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 111.465 & 0.857062006208346 & 130.054767557744 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 111.471666666667 & 0.855189514354212 & 130.347326289242 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 111.060833333333 & 0.771182132109609 & 144.013753313398 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 111.154833333333 & 0.747949040971891 & 148.6128429136 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 111.462833333333 & 0.676102200831995 & 164.860923683091 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 111.640166666667 & 0.641145051396577 & 174.126223735933 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 111.553166666667 & 0.614755175726779 & 181.459499767181 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 111.589833333333 & 0.589030635811644 & 189.446569582192 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 111.644833333333 & 0.546990920697776 & 204.107287906922 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 111.728833333333 & 0.519499709991962 & 215.070059105639 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 111.676833333333 & 0.509108198442414 & 219.357758674879 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 111.662833333333 & 0.506356213893341 & 220.522292942284 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 111.530333333333 & 0.487518272389221 & 228.771596163457 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 111.501 & 0.477322730131894 & 233.596669425715 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 111.435833333333 & 0.467811909403809 & 238.206490885087 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 111.444833333333 & 0.463870872086045 & 240.249690247119 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 111.432166666667 & 0.462210305770899 & 241.085422101989 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 111.4855 & 0.449374733524198 & 248.090272289412 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 111.45224137931 & 0.843330656788293 & 132.157227396144 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 111.457678571429 & 0.81516666254939 & 136.729927378103 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 111.461111111111 & 0.78210629918138 & 142.514017887052 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 111.459615384615 & 0.743862365507819 & 149.839030112142 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 111.456 & 0.696066557924761 & 160.122618636202 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 111.554791666667 & 0.666128993480969 & 167.467251475902 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 111.641739130435 & 0.635458623559259 & 175.68687400152 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 111.676590909091 & 0.618511387517291 & 180.557049009819 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 111.683095238095 & 0.605991330160269 & 184.298173388979 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 111.70475 & 0.595842109044213 & 187.473742295899 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 111.722894736842 & 0.588119203414215 & 189.966411721052 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 111.734722222222 & 0.587027416967559 & 190.339869983274 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 111.735588235294 & 0.590149259221596 & 189.334454782969 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 111.7440625 & 0.594181101454434 & 188.06397952825 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 111.755666666667 & 0.597291719737879 & 187.103994536724 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 111.787857142857 & 0.602845623526445 & 185.433638033126 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 111.829230769231 & 0.609107019288684 & 183.595373600891 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 111.887083333333 & 0.615536610234231 & 181.771614349237 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 111.954090909091 & 0.620178601244796 & 180.51911285617 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 112.0365 & 0.620371821868483 & 180.595726708799 \tabularnewline
Median & 113.325 &  &  \tabularnewline
Midrange & 110.89 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.605806451613 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111.605806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.605806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111.605806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111.605806451613 &  &  \tabularnewline
Midmean - Closest Observation & 111.605806451613 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111.605806451613 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111.7440625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163395&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]111.4335[/C][C]0.870685320862883[/C][C]127.983666808078[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111.23080096769[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.026132291024[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]111.63401096888[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]111.447166666667[/C][C]0.86616320964578[/C][C]128.667629178389[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]111.4515[/C][C]0.863351563568622[/C][C]129.091675631328[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]111.465[/C][C]0.857062006208346[/C][C]130.054767557744[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]111.471666666667[/C][C]0.855189514354212[/C][C]130.347326289242[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]111.060833333333[/C][C]0.771182132109609[/C][C]144.013753313398[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]111.154833333333[/C][C]0.747949040971891[/C][C]148.6128429136[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]111.462833333333[/C][C]0.676102200831995[/C][C]164.860923683091[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]111.640166666667[/C][C]0.641145051396577[/C][C]174.126223735933[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]111.553166666667[/C][C]0.614755175726779[/C][C]181.459499767181[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]111.589833333333[/C][C]0.589030635811644[/C][C]189.446569582192[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]111.644833333333[/C][C]0.546990920697776[/C][C]204.107287906922[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]111.728833333333[/C][C]0.519499709991962[/C][C]215.070059105639[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]111.676833333333[/C][C]0.509108198442414[/C][C]219.357758674879[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]111.662833333333[/C][C]0.506356213893341[/C][C]220.522292942284[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]111.530333333333[/C][C]0.487518272389221[/C][C]228.771596163457[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]111.501[/C][C]0.477322730131894[/C][C]233.596669425715[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]111.435833333333[/C][C]0.467811909403809[/C][C]238.206490885087[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]111.444833333333[/C][C]0.463870872086045[/C][C]240.249690247119[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]111.432166666667[/C][C]0.462210305770899[/C][C]241.085422101989[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]111.4855[/C][C]0.449374733524198[/C][C]248.090272289412[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]111.45224137931[/C][C]0.843330656788293[/C][C]132.157227396144[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]111.457678571429[/C][C]0.81516666254939[/C][C]136.729927378103[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]111.461111111111[/C][C]0.78210629918138[/C][C]142.514017887052[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]111.459615384615[/C][C]0.743862365507819[/C][C]149.839030112142[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]111.456[/C][C]0.696066557924761[/C][C]160.122618636202[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]111.554791666667[/C][C]0.666128993480969[/C][C]167.467251475902[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]111.641739130435[/C][C]0.635458623559259[/C][C]175.68687400152[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]111.676590909091[/C][C]0.618511387517291[/C][C]180.557049009819[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]111.683095238095[/C][C]0.605991330160269[/C][C]184.298173388979[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]111.70475[/C][C]0.595842109044213[/C][C]187.473742295899[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]111.722894736842[/C][C]0.588119203414215[/C][C]189.966411721052[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]111.734722222222[/C][C]0.587027416967559[/C][C]190.339869983274[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]111.735588235294[/C][C]0.590149259221596[/C][C]189.334454782969[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]111.7440625[/C][C]0.594181101454434[/C][C]188.06397952825[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]111.755666666667[/C][C]0.597291719737879[/C][C]187.103994536724[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]111.787857142857[/C][C]0.602845623526445[/C][C]185.433638033126[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]111.829230769231[/C][C]0.609107019288684[/C][C]183.595373600891[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]111.887083333333[/C][C]0.615536610234231[/C][C]181.771614349237[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]111.954090909091[/C][C]0.620178601244796[/C][C]180.51911285617[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]112.0365[/C][C]0.620371821868483[/C][C]180.595726708799[/C][/ROW]
[ROW][C]Median[/C][C]113.325[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]110.89[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.605806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111.605806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.605806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111.605806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111.605806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.605806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111.605806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111.7440625[/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=163395&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163395&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.43350.870685320862883127.983666808078
Geometric Mean111.23080096769
Harmonic Mean111.026132291024
Quadratic Mean111.63401096888
Winsorized Mean ( 1 / 20 )111.4471666666670.86616320964578128.667629178389
Winsorized Mean ( 2 / 20 )111.45150.863351563568622129.091675631328
Winsorized Mean ( 3 / 20 )111.4650.857062006208346130.054767557744
Winsorized Mean ( 4 / 20 )111.4716666666670.855189514354212130.347326289242
Winsorized Mean ( 5 / 20 )111.0608333333330.771182132109609144.013753313398
Winsorized Mean ( 6 / 20 )111.1548333333330.747949040971891148.6128429136
Winsorized Mean ( 7 / 20 )111.4628333333330.676102200831995164.860923683091
Winsorized Mean ( 8 / 20 )111.6401666666670.641145051396577174.126223735933
Winsorized Mean ( 9 / 20 )111.5531666666670.614755175726779181.459499767181
Winsorized Mean ( 10 / 20 )111.5898333333330.589030635811644189.446569582192
Winsorized Mean ( 11 / 20 )111.6448333333330.546990920697776204.107287906922
Winsorized Mean ( 12 / 20 )111.7288333333330.519499709991962215.070059105639
Winsorized Mean ( 13 / 20 )111.6768333333330.509108198442414219.357758674879
Winsorized Mean ( 14 / 20 )111.6628333333330.506356213893341220.522292942284
Winsorized Mean ( 15 / 20 )111.5303333333330.487518272389221228.771596163457
Winsorized Mean ( 16 / 20 )111.5010.477322730131894233.596669425715
Winsorized Mean ( 17 / 20 )111.4358333333330.467811909403809238.206490885087
Winsorized Mean ( 18 / 20 )111.4448333333330.463870872086045240.249690247119
Winsorized Mean ( 19 / 20 )111.4321666666670.462210305770899241.085422101989
Winsorized Mean ( 20 / 20 )111.48550.449374733524198248.090272289412
Trimmed Mean ( 1 / 20 )111.452241379310.843330656788293132.157227396144
Trimmed Mean ( 2 / 20 )111.4576785714290.81516666254939136.729927378103
Trimmed Mean ( 3 / 20 )111.4611111111110.78210629918138142.514017887052
Trimmed Mean ( 4 / 20 )111.4596153846150.743862365507819149.839030112142
Trimmed Mean ( 5 / 20 )111.4560.696066557924761160.122618636202
Trimmed Mean ( 6 / 20 )111.5547916666670.666128993480969167.467251475902
Trimmed Mean ( 7 / 20 )111.6417391304350.635458623559259175.68687400152
Trimmed Mean ( 8 / 20 )111.6765909090910.618511387517291180.557049009819
Trimmed Mean ( 9 / 20 )111.6830952380950.605991330160269184.298173388979
Trimmed Mean ( 10 / 20 )111.704750.595842109044213187.473742295899
Trimmed Mean ( 11 / 20 )111.7228947368420.588119203414215189.966411721052
Trimmed Mean ( 12 / 20 )111.7347222222220.587027416967559190.339869983274
Trimmed Mean ( 13 / 20 )111.7355882352940.590149259221596189.334454782969
Trimmed Mean ( 14 / 20 )111.74406250.594181101454434188.06397952825
Trimmed Mean ( 15 / 20 )111.7556666666670.597291719737879187.103994536724
Trimmed Mean ( 16 / 20 )111.7878571428570.602845623526445185.433638033126
Trimmed Mean ( 17 / 20 )111.8292307692310.609107019288684183.595373600891
Trimmed Mean ( 18 / 20 )111.8870833333330.615536610234231181.771614349237
Trimmed Mean ( 19 / 20 )111.9540909090910.620178601244796180.51911285617
Trimmed Mean ( 20 / 20 )112.03650.620371821868483180.595726708799
Median113.325
Midrange110.89
Midmean - Weighted Average at Xnp111.605806451613
Midmean - Weighted Average at X(n+1)p111.605806451613
Midmean - Empirical Distribution Function111.605806451613
Midmean - Empirical Distribution Function - Averaging111.605806451613
Midmean - Empirical Distribution Function - Interpolation111.605806451613
Midmean - Closest Observation111.605806451613
Midmean - True Basic - Statistics Graphics Toolkit111.605806451613
Midmean - MS Excel (old versions)111.7440625
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')