FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 01 Mar 2016 12:24:53 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/01/t145683511263tz4uf5hwm9960.htm/, Retrieved Tue, 07 May 2024 21:08:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293130, Retrieved Tue, 07 May 2024 21:08:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-01 12:24:53] [3fd8a2781b4a66a294f894c9e659cf7e] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
97,78
97,73
97,61
97,69
97,68
97,67
97,67
97,96
98,27
99,52
99,59
99,75
99,75
99,8
99,99
100,25
100,08
100,08
100,08
100,06
101
101,81
101,82
101,96
101,96
101,93
102,03
102,11
102,07
102,34
102,34
102,33
102,77
103,08
103,38
103,44
99,1
99,15
99,21
99,01
99,08
99,11
100,11
100,31
100,55
101,38
101,49
101,5
100,69
100,8
100,58
100,34
100,38
100,33
101,06
101,15
101,36
101,98
102,24
102,34

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'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293130&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293130&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293130&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'Gwilym Jenkins' @ jenkins.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean100.4771666666670.20738812812546484.488517133838
Geometric Mean100.46450806089
Harmonic Mean100.451819012573
Quadratic Mean100.489793519873
Winsorized Mean ( 1 / 20 )100.4771666666670.206916027574094485.593928342197
Winsorized Mean ( 2 / 20 )100.4671666666670.204644530124753490.935020864818
Winsorized Mean ( 3 / 20 )100.4521666666670.201337630206327498.923954571856
Winsorized Mean ( 4 / 20 )100.4241666666670.196004048682194512.357613742445
Winsorized Mean ( 5 / 20 )100.42750.195219653920491514.433347171603
Winsorized Mean ( 6 / 20 )100.43250.1940549495538517.546706388729
Winsorized Mean ( 7 / 20 )100.4523333333330.18908004562482531.268823219213
Winsorized Mean ( 8 / 20 )100.4816666666670.178090652766046564.216398255708
Winsorized Mean ( 9 / 20 )100.5731666666670.153379904190269655.71280147564
Winsorized Mean ( 10 / 20 )100.5781666666670.150259190693772669.364490799402
Winsorized Mean ( 11 / 20 )100.57450.14841410706244677.661322031113
Winsorized Mean ( 12 / 20 )100.56650.146427866393311686.798916606998
Winsorized Mean ( 13 / 20 )100.5708333333330.144265780240496697.121889651713
Winsorized Mean ( 14 / 20 )100.5848333333330.141948007444014708.603348116777
Winsorized Mean ( 15 / 20 )100.6548333333330.128513555675918783.22347244957
Winsorized Mean ( 16 / 20 )100.6441666666670.120849463174352832.806071479732
Winsorized Mean ( 17 / 20 )100.6866666666670.113861762421015884.288671857793
Winsorized Mean ( 18 / 20 )100.5936666666670.09881900554485371017.95870249886
Winsorized Mean ( 19 / 20 )100.6063333333330.09605376515460821047.39604086729
Winsorized Mean ( 20 / 20 )100.6330.08159127155045651233.37947905087
Trimmed Mean ( 1 / 20 )100.4755172413790.202267570658213496.745557947894
Trimmed Mean ( 2 / 20 )100.473750.196518820766827511.267824669138
Trimmed Mean ( 3 / 20 )100.4774074074070.190895346214914526.348124245459
Trimmed Mean ( 4 / 20 )100.4871153846150.185451090123348541.852384463088
Trimmed Mean ( 5 / 20 )100.5060.180625895944392556.431842037435
Trimmed Mean ( 6 / 20 )100.5256250.17468916321732575.454270594578
Trimmed Mean ( 7 / 20 )100.5458695652170.167383264127125600.692489117994
Trimmed Mean ( 8 / 20 )100.5640909090910.159463728066613630.639281599402
Trimmed Mean ( 9 / 20 )100.578809523810.152467967497341659.671740725234
Trimmed Mean ( 10 / 20 )100.579750.15026621142117669.343753653923
Trimmed Mean ( 11 / 20 )100.580.147898027228347680.063161658738
Trimmed Mean ( 12 / 20 )100.5808333333330.144918354134593694.051722668053
Trimmed Mean ( 13 / 20 )100.5829411764710.141107492061274712.810777848661
Trimmed Mean ( 14 / 20 )100.58468750.136158399494942738.732886646017
Trimmed Mean ( 15 / 20 )100.5846666666670.129586196701188776.198925712778
Trimmed Mean ( 16 / 20 )100.5746428571430.124208054402819809.727222124979
Trimmed Mean ( 17 / 20 )100.5646153846150.118582954760637848.052872249707
Trimmed Mean ( 18 / 20 )100.5466666666670.111948595001033898.150322170089
Trimmed Mean ( 19 / 20 )100.5395454545450.107844840589957932.261060469387
Trimmed Mean ( 20 / 20 )100.5290.101576779360556989.684853495529
Median100.36
Midrange100.525
Midmean - Weighted Average at Xnp100.540322580645
Midmean - Weighted Average at X(n+1)p100.584666666667
Midmean - Empirical Distribution Function100.540322580645
Midmean - Empirical Distribution Function - Averaging100.584666666667
Midmean - Empirical Distribution Function - Interpolation100.584666666667
Midmean - Closest Observation100.540322580645
Midmean - True Basic - Statistics Graphics Toolkit100.584666666667
Midmean - MS Excel (old versions)100.626363636364
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 100.477166666667 & 0.20738812812546 & 484.488517133838 \tabularnewline
Geometric Mean & 100.46450806089 &  &  \tabularnewline
Harmonic Mean & 100.451819012573 &  &  \tabularnewline
Quadratic Mean & 100.489793519873 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 100.477166666667 & 0.206916027574094 & 485.593928342197 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 100.467166666667 & 0.204644530124753 & 490.935020864818 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 100.452166666667 & 0.201337630206327 & 498.923954571856 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 100.424166666667 & 0.196004048682194 & 512.357613742445 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 100.4275 & 0.195219653920491 & 514.433347171603 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 100.4325 & 0.1940549495538 & 517.546706388729 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 100.452333333333 & 0.18908004562482 & 531.268823219213 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 100.481666666667 & 0.178090652766046 & 564.216398255708 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 100.573166666667 & 0.153379904190269 & 655.71280147564 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 100.578166666667 & 0.150259190693772 & 669.364490799402 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 100.5745 & 0.14841410706244 & 677.661322031113 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 100.5665 & 0.146427866393311 & 686.798916606998 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 100.570833333333 & 0.144265780240496 & 697.121889651713 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 100.584833333333 & 0.141948007444014 & 708.603348116777 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 100.654833333333 & 0.128513555675918 & 783.22347244957 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 100.644166666667 & 0.120849463174352 & 832.806071479732 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 100.686666666667 & 0.113861762421015 & 884.288671857793 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 100.593666666667 & 0.0988190055448537 & 1017.95870249886 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 100.606333333333 & 0.0960537651546082 & 1047.39604086729 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 100.633 & 0.0815912715504565 & 1233.37947905087 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 100.475517241379 & 0.202267570658213 & 496.745557947894 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 100.47375 & 0.196518820766827 & 511.267824669138 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 100.477407407407 & 0.190895346214914 & 526.348124245459 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 100.487115384615 & 0.185451090123348 & 541.852384463088 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 100.506 & 0.180625895944392 & 556.431842037435 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 100.525625 & 0.17468916321732 & 575.454270594578 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 100.545869565217 & 0.167383264127125 & 600.692489117994 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 100.564090909091 & 0.159463728066613 & 630.639281599402 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 100.57880952381 & 0.152467967497341 & 659.671740725234 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 100.57975 & 0.15026621142117 & 669.343753653923 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 100.58 & 0.147898027228347 & 680.063161658738 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 100.580833333333 & 0.144918354134593 & 694.051722668053 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 100.582941176471 & 0.141107492061274 & 712.810777848661 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 100.5846875 & 0.136158399494942 & 738.732886646017 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 100.584666666667 & 0.129586196701188 & 776.198925712778 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 100.574642857143 & 0.124208054402819 & 809.727222124979 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 100.564615384615 & 0.118582954760637 & 848.052872249707 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 100.546666666667 & 0.111948595001033 & 898.150322170089 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 100.539545454545 & 0.107844840589957 & 932.261060469387 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 100.529 & 0.101576779360556 & 989.684853495529 \tabularnewline
Median & 100.36 &  &  \tabularnewline
Midrange & 100.525 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 100.540322580645 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 100.584666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 100.540322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 100.584666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 100.584666666667 &  &  \tabularnewline
Midmean - Closest Observation & 100.540322580645 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 100.584666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 100.626363636364 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293130&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]100.477166666667[/C][C]0.20738812812546[/C][C]484.488517133838[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]100.46450806089[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]100.451819012573[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]100.489793519873[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]100.477166666667[/C][C]0.206916027574094[/C][C]485.593928342197[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]100.467166666667[/C][C]0.204644530124753[/C][C]490.935020864818[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]100.452166666667[/C][C]0.201337630206327[/C][C]498.923954571856[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]100.424166666667[/C][C]0.196004048682194[/C][C]512.357613742445[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]100.4275[/C][C]0.195219653920491[/C][C]514.433347171603[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]100.4325[/C][C]0.1940549495538[/C][C]517.546706388729[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]100.452333333333[/C][C]0.18908004562482[/C][C]531.268823219213[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]100.481666666667[/C][C]0.178090652766046[/C][C]564.216398255708[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]100.573166666667[/C][C]0.153379904190269[/C][C]655.71280147564[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]100.578166666667[/C][C]0.150259190693772[/C][C]669.364490799402[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]100.5745[/C][C]0.14841410706244[/C][C]677.661322031113[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]100.5665[/C][C]0.146427866393311[/C][C]686.798916606998[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]100.570833333333[/C][C]0.144265780240496[/C][C]697.121889651713[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]100.584833333333[/C][C]0.141948007444014[/C][C]708.603348116777[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]100.654833333333[/C][C]0.128513555675918[/C][C]783.22347244957[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]100.644166666667[/C][C]0.120849463174352[/C][C]832.806071479732[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]100.686666666667[/C][C]0.113861762421015[/C][C]884.288671857793[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]100.593666666667[/C][C]0.0988190055448537[/C][C]1017.95870249886[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]100.606333333333[/C][C]0.0960537651546082[/C][C]1047.39604086729[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]100.633[/C][C]0.0815912715504565[/C][C]1233.37947905087[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]100.475517241379[/C][C]0.202267570658213[/C][C]496.745557947894[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]100.47375[/C][C]0.196518820766827[/C][C]511.267824669138[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]100.477407407407[/C][C]0.190895346214914[/C][C]526.348124245459[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]100.487115384615[/C][C]0.185451090123348[/C][C]541.852384463088[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]100.506[/C][C]0.180625895944392[/C][C]556.431842037435[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]100.525625[/C][C]0.17468916321732[/C][C]575.454270594578[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]100.545869565217[/C][C]0.167383264127125[/C][C]600.692489117994[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]100.564090909091[/C][C]0.159463728066613[/C][C]630.639281599402[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]100.57880952381[/C][C]0.152467967497341[/C][C]659.671740725234[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]100.57975[/C][C]0.15026621142117[/C][C]669.343753653923[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]100.58[/C][C]0.147898027228347[/C][C]680.063161658738[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]100.580833333333[/C][C]0.144918354134593[/C][C]694.051722668053[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]100.582941176471[/C][C]0.141107492061274[/C][C]712.810777848661[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]100.5846875[/C][C]0.136158399494942[/C][C]738.732886646017[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]100.584666666667[/C][C]0.129586196701188[/C][C]776.198925712778[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]100.574642857143[/C][C]0.124208054402819[/C][C]809.727222124979[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]100.564615384615[/C][C]0.118582954760637[/C][C]848.052872249707[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]100.546666666667[/C][C]0.111948595001033[/C][C]898.150322170089[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]100.539545454545[/C][C]0.107844840589957[/C][C]932.261060469387[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]100.529[/C][C]0.101576779360556[/C][C]989.684853495529[/C][/ROW]
[ROW][C]Median[/C][C]100.36[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]100.525[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]100.540322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]100.584666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]100.540322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]100.584666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]100.584666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]100.540322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]100.584666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]100.626363636364[/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=293130&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293130&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 Mean100.4771666666670.20738812812546484.488517133838
Geometric Mean100.46450806089
Harmonic Mean100.451819012573
Quadratic Mean100.489793519873
Winsorized Mean ( 1 / 20 )100.4771666666670.206916027574094485.593928342197
Winsorized Mean ( 2 / 20 )100.4671666666670.204644530124753490.935020864818
Winsorized Mean ( 3 / 20 )100.4521666666670.201337630206327498.923954571856
Winsorized Mean ( 4 / 20 )100.4241666666670.196004048682194512.357613742445
Winsorized Mean ( 5 / 20 )100.42750.195219653920491514.433347171603
Winsorized Mean ( 6 / 20 )100.43250.1940549495538517.546706388729
Winsorized Mean ( 7 / 20 )100.4523333333330.18908004562482531.268823219213
Winsorized Mean ( 8 / 20 )100.4816666666670.178090652766046564.216398255708
Winsorized Mean ( 9 / 20 )100.5731666666670.153379904190269655.71280147564
Winsorized Mean ( 10 / 20 )100.5781666666670.150259190693772669.364490799402
Winsorized Mean ( 11 / 20 )100.57450.14841410706244677.661322031113
Winsorized Mean ( 12 / 20 )100.56650.146427866393311686.798916606998
Winsorized Mean ( 13 / 20 )100.5708333333330.144265780240496697.121889651713
Winsorized Mean ( 14 / 20 )100.5848333333330.141948007444014708.603348116777
Winsorized Mean ( 15 / 20 )100.6548333333330.128513555675918783.22347244957
Winsorized Mean ( 16 / 20 )100.6441666666670.120849463174352832.806071479732
Winsorized Mean ( 17 / 20 )100.6866666666670.113861762421015884.288671857793
Winsorized Mean ( 18 / 20 )100.5936666666670.09881900554485371017.95870249886
Winsorized Mean ( 19 / 20 )100.6063333333330.09605376515460821047.39604086729
Winsorized Mean ( 20 / 20 )100.6330.08159127155045651233.37947905087
Trimmed Mean ( 1 / 20 )100.4755172413790.202267570658213496.745557947894
Trimmed Mean ( 2 / 20 )100.473750.196518820766827511.267824669138
Trimmed Mean ( 3 / 20 )100.4774074074070.190895346214914526.348124245459
Trimmed Mean ( 4 / 20 )100.4871153846150.185451090123348541.852384463088
Trimmed Mean ( 5 / 20 )100.5060.180625895944392556.431842037435
Trimmed Mean ( 6 / 20 )100.5256250.17468916321732575.454270594578
Trimmed Mean ( 7 / 20 )100.5458695652170.167383264127125600.692489117994
Trimmed Mean ( 8 / 20 )100.5640909090910.159463728066613630.639281599402
Trimmed Mean ( 9 / 20 )100.578809523810.152467967497341659.671740725234
Trimmed Mean ( 10 / 20 )100.579750.15026621142117669.343753653923
Trimmed Mean ( 11 / 20 )100.580.147898027228347680.063161658738
Trimmed Mean ( 12 / 20 )100.5808333333330.144918354134593694.051722668053
Trimmed Mean ( 13 / 20 )100.5829411764710.141107492061274712.810777848661
Trimmed Mean ( 14 / 20 )100.58468750.136158399494942738.732886646017
Trimmed Mean ( 15 / 20 )100.5846666666670.129586196701188776.198925712778
Trimmed Mean ( 16 / 20 )100.5746428571430.124208054402819809.727222124979
Trimmed Mean ( 17 / 20 )100.5646153846150.118582954760637848.052872249707
Trimmed Mean ( 18 / 20 )100.5466666666670.111948595001033898.150322170089
Trimmed Mean ( 19 / 20 )100.5395454545450.107844840589957932.261060469387
Trimmed Mean ( 20 / 20 )100.5290.101576779360556989.684853495529
Median100.36
Midrange100.525
Midmean - Weighted Average at Xnp100.540322580645
Midmean - Weighted Average at X(n+1)p100.584666666667
Midmean - Empirical Distribution Function100.540322580645
Midmean - Empirical Distribution Function - Averaging100.584666666667
Midmean - Empirical Distribution Function - Interpolation100.584666666667
Midmean - Closest Observation100.540322580645
Midmean - True Basic - Statistics Graphics Toolkit100.584666666667
Midmean - MS Excel (old versions)100.626363636364
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')