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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 13 Mar 2017 21:50:35 +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/2017/Mar/13/t1489441996t903w5qjufr2x5e.htm/, Retrieved Wed, 15 May 2024 00:24:47 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 15 May 2024 00:24:47 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
92.76
93.12
93.6
93.24
93.4
93.32
93.13
93.19
93.84
94.01
93.78
93.47
93.6
92.85
92.91
92.29
92.5
93.1
92.86
93.19
93.73
93.88
93.85
93.45
93.43
93.59
95.28
94.95
94.49
94.45
94.35
95.52
96.89
97.54
97.65
97.35
98.2
99.46
100.35
99.72
99.69
99.62
99.77
100.19
100.82
100.36
101.08
100.73
101.51
102.12
102.88
103.47
103.53
103.67
103.68
103.76
103.67
103.01
103.39
103.43
103.4
104.8




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=&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=&T=0

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

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean97.27209677419350.530303143955905183.427343176909
Geometric Mean97.184827487058
Harmonic Mean97.0985422138063
Quadratic Mean97.3602347868057
Winsorized Mean ( 1 / 20 )97.25870967741940.526139441590732184.853485576689
Winsorized Mean ( 2 / 20 )97.26451612903230.524406928868141185.475268869853
Winsorized Mean ( 3 / 20 )97.26838709677420.523702152622528185.732265200145
Winsorized Mean ( 4 / 20 )97.26903225806450.523613008064701185.765118054602
Winsorized Mean ( 5 / 20 )97.26177419354840.520813367670859186.749765330554
Winsorized Mean ( 6 / 20 )97.27435483870970.517194493290885188.080801517738
Winsorized Mean ( 7 / 20 )97.27209677419360.516010974814356188.507806077553
Winsorized Mean ( 8 / 20 )97.26951612903230.515084587808191188.84182992727
Winsorized Mean ( 9 / 20 )97.27677419354840.513659621724999189.379834581641
Winsorized Mean ( 10 / 20 )97.21548387096770.501878263633884193.703315953698
Winsorized Mean ( 11 / 20 )97.20129032258060.496369020316041195.824651306183
Winsorized Mean ( 12 / 20 )97.06967741935480.467496169865393207.637374756042
Winsorized Mean ( 13 / 20 )96.95854838709680.443181961522871218.778192266504
Winsorized Mean ( 14 / 20 )96.86822580645160.42624450099308227.259766591157
Winsorized Mean ( 15 / 20 )96.81016129032260.415532158465451232.978746212663
Winsorized Mean ( 16 / 20 )96.79209677419360.411187876728024235.396280513921
Winsorized Mean ( 17 / 20 )96.72354838709680.391147148582499247.281742274279
Winsorized Mean ( 18 / 20 )96.72354838709680.390323740989749247.803395565521
Winsorized Mean ( 19 / 20 )96.67451612903230.382899309750862252.480256994808
Winsorized Mean ( 20 / 20 )96.58096774193550.357277568873812270.324745117282
Trimmed Mean ( 1 / 20 )97.22966666666670.526683685271767184.607325773716
Trimmed Mean ( 2 / 20 )97.19862068965520.526637649671742184.564511766753
Trimmed Mean ( 3 / 20 )97.16214285714290.526913871709952184.398529007844
Trimmed Mean ( 4 / 20 )97.12148148148150.526744441846889184.380647930429
Trimmed Mean ( 5 / 20 )97.07750.525713540458507184.658549816565
Trimmed Mean ( 6 / 20 )97.03180.524438879145305185.020226109353
Trimmed Mean ( 7 / 20 )96.97958333333330.522879961131573185.471983136356
Trimmed Mean ( 8 / 20 )96.92326086956520.520195063223136186.320993261696
Trimmed Mean ( 9 / 20 )96.86227272727270.515944182990332187.737890881673
Trimmed Mean ( 10 / 20 )96.79428571428570.509694876142795189.906334642391
Trimmed Mean ( 11 / 20 )96.7290.503551464026346192.093573170386
Trimmed Mean ( 12 / 20 )96.65894736842110.495617750293439195.027210609774
Trimmed Mean ( 13 / 20 )96.60.491409375778662196.577445936868
Trimmed Mean ( 14 / 20 )96.54970588235290.490402265905622196.878588446273
Trimmed Mean ( 15 / 20 )96.5056250.491373555729407196.399712346637
Trimmed Mean ( 16 / 20 )96.46366666666670.493070250603959195.638788891662
Trimmed Mean ( 17 / 20 )96.41821428571430.493732424795079195.284347236729
Trimmed Mean ( 18 / 20 )96.37538461538460.497234267885635193.822893633613
Trimmed Mean ( 19 / 20 )96.32541666666670.498452307243751193.249013530119
Trimmed Mean ( 20 / 20 )96.27363636363640.498319924295647193.196442024097
Median95.4
Midrange98.545
Midmean - Weighted Average at Xnp96.3664516129032
Midmean - Weighted Average at X(n+1)p96.505625
Midmean - Empirical Distribution Function96.505625
Midmean - Empirical Distribution Function - Averaging96.505625
Midmean - Empirical Distribution Function - Interpolation96.4636666666667
Midmean - Closest Observation96.505625
Midmean - True Basic - Statistics Graphics Toolkit96.505625
Midmean - MS Excel (old versions)96.505625
Number of observations62

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 97.2720967741935 & 0.530303143955905 & 183.427343176909 \tabularnewline
Geometric Mean & 97.184827487058 &  &  \tabularnewline
Harmonic Mean & 97.0985422138063 &  &  \tabularnewline
Quadratic Mean & 97.3602347868057 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 97.2587096774194 & 0.526139441590732 & 184.853485576689 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 97.2645161290323 & 0.524406928868141 & 185.475268869853 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 97.2683870967742 & 0.523702152622528 & 185.732265200145 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 97.2690322580645 & 0.523613008064701 & 185.765118054602 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 97.2617741935484 & 0.520813367670859 & 186.749765330554 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 97.2743548387097 & 0.517194493290885 & 188.080801517738 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 97.2720967741936 & 0.516010974814356 & 188.507806077553 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 97.2695161290323 & 0.515084587808191 & 188.84182992727 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 97.2767741935484 & 0.513659621724999 & 189.379834581641 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 97.2154838709677 & 0.501878263633884 & 193.703315953698 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 97.2012903225806 & 0.496369020316041 & 195.824651306183 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 97.0696774193548 & 0.467496169865393 & 207.637374756042 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 96.9585483870968 & 0.443181961522871 & 218.778192266504 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 96.8682258064516 & 0.42624450099308 & 227.259766591157 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 96.8101612903226 & 0.415532158465451 & 232.978746212663 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 96.7920967741936 & 0.411187876728024 & 235.396280513921 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 96.7235483870968 & 0.391147148582499 & 247.281742274279 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 96.7235483870968 & 0.390323740989749 & 247.803395565521 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 96.6745161290323 & 0.382899309750862 & 252.480256994808 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 96.5809677419355 & 0.357277568873812 & 270.324745117282 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 97.2296666666667 & 0.526683685271767 & 184.607325773716 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 97.1986206896552 & 0.526637649671742 & 184.564511766753 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 97.1621428571429 & 0.526913871709952 & 184.398529007844 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 97.1214814814815 & 0.526744441846889 & 184.380647930429 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 97.0775 & 0.525713540458507 & 184.658549816565 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 97.0318 & 0.524438879145305 & 185.020226109353 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 96.9795833333333 & 0.522879961131573 & 185.471983136356 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 96.9232608695652 & 0.520195063223136 & 186.320993261696 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 96.8622727272727 & 0.515944182990332 & 187.737890881673 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 96.7942857142857 & 0.509694876142795 & 189.906334642391 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 96.729 & 0.503551464026346 & 192.093573170386 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 96.6589473684211 & 0.495617750293439 & 195.027210609774 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 96.6 & 0.491409375778662 & 196.577445936868 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 96.5497058823529 & 0.490402265905622 & 196.878588446273 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 96.505625 & 0.491373555729407 & 196.399712346637 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 96.4636666666667 & 0.493070250603959 & 195.638788891662 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 96.4182142857143 & 0.493732424795079 & 195.284347236729 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 96.3753846153846 & 0.497234267885635 & 193.822893633613 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 96.3254166666667 & 0.498452307243751 & 193.249013530119 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 96.2736363636364 & 0.498319924295647 & 193.196442024097 \tabularnewline
Median & 95.4 &  &  \tabularnewline
Midrange & 98.545 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 96.3664516129032 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 96.505625 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 96.505625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 96.505625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 96.4636666666667 &  &  \tabularnewline
Midmean - Closest Observation & 96.505625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 96.505625 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 96.505625 &  &  \tabularnewline
Number of observations & 62 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]97.2720967741935[/C][C]0.530303143955905[/C][C]183.427343176909[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]97.184827487058[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]97.0985422138063[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]97.3602347868057[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]97.2587096774194[/C][C]0.526139441590732[/C][C]184.853485576689[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]97.2645161290323[/C][C]0.524406928868141[/C][C]185.475268869853[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]97.2683870967742[/C][C]0.523702152622528[/C][C]185.732265200145[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]97.2690322580645[/C][C]0.523613008064701[/C][C]185.765118054602[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]97.2617741935484[/C][C]0.520813367670859[/C][C]186.749765330554[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]97.2743548387097[/C][C]0.517194493290885[/C][C]188.080801517738[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]97.2720967741936[/C][C]0.516010974814356[/C][C]188.507806077553[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]97.2695161290323[/C][C]0.515084587808191[/C][C]188.84182992727[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]97.2767741935484[/C][C]0.513659621724999[/C][C]189.379834581641[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]97.2154838709677[/C][C]0.501878263633884[/C][C]193.703315953698[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]97.2012903225806[/C][C]0.496369020316041[/C][C]195.824651306183[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]97.0696774193548[/C][C]0.467496169865393[/C][C]207.637374756042[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]96.9585483870968[/C][C]0.443181961522871[/C][C]218.778192266504[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]96.8682258064516[/C][C]0.42624450099308[/C][C]227.259766591157[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]96.8101612903226[/C][C]0.415532158465451[/C][C]232.978746212663[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]96.7920967741936[/C][C]0.411187876728024[/C][C]235.396280513921[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]96.7235483870968[/C][C]0.391147148582499[/C][C]247.281742274279[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]96.7235483870968[/C][C]0.390323740989749[/C][C]247.803395565521[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]96.6745161290323[/C][C]0.382899309750862[/C][C]252.480256994808[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]96.5809677419355[/C][C]0.357277568873812[/C][C]270.324745117282[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]97.2296666666667[/C][C]0.526683685271767[/C][C]184.607325773716[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]97.1986206896552[/C][C]0.526637649671742[/C][C]184.564511766753[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]97.1621428571429[/C][C]0.526913871709952[/C][C]184.398529007844[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]97.1214814814815[/C][C]0.526744441846889[/C][C]184.380647930429[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]97.0775[/C][C]0.525713540458507[/C][C]184.658549816565[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]97.0318[/C][C]0.524438879145305[/C][C]185.020226109353[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]96.9795833333333[/C][C]0.522879961131573[/C][C]185.471983136356[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]96.9232608695652[/C][C]0.520195063223136[/C][C]186.320993261696[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]96.8622727272727[/C][C]0.515944182990332[/C][C]187.737890881673[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]96.7942857142857[/C][C]0.509694876142795[/C][C]189.906334642391[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]96.729[/C][C]0.503551464026346[/C][C]192.093573170386[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]96.6589473684211[/C][C]0.495617750293439[/C][C]195.027210609774[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]96.6[/C][C]0.491409375778662[/C][C]196.577445936868[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]96.5497058823529[/C][C]0.490402265905622[/C][C]196.878588446273[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]96.505625[/C][C]0.491373555729407[/C][C]196.399712346637[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]96.4636666666667[/C][C]0.493070250603959[/C][C]195.638788891662[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]96.4182142857143[/C][C]0.493732424795079[/C][C]195.284347236729[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]96.3753846153846[/C][C]0.497234267885635[/C][C]193.822893633613[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]96.3254166666667[/C][C]0.498452307243751[/C][C]193.249013530119[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]96.2736363636364[/C][C]0.498319924295647[/C][C]193.196442024097[/C][/ROW]
[ROW][C]Median[/C][C]95.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]98.545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]96.3664516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]96.505625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]96.505625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]96.505625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]96.4636666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]96.505625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]96.505625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]96.505625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]62[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean97.27209677419350.530303143955905183.427343176909
Geometric Mean97.184827487058
Harmonic Mean97.0985422138063
Quadratic Mean97.3602347868057
Winsorized Mean ( 1 / 20 )97.25870967741940.526139441590732184.853485576689
Winsorized Mean ( 2 / 20 )97.26451612903230.524406928868141185.475268869853
Winsorized Mean ( 3 / 20 )97.26838709677420.523702152622528185.732265200145
Winsorized Mean ( 4 / 20 )97.26903225806450.523613008064701185.765118054602
Winsorized Mean ( 5 / 20 )97.26177419354840.520813367670859186.749765330554
Winsorized Mean ( 6 / 20 )97.27435483870970.517194493290885188.080801517738
Winsorized Mean ( 7 / 20 )97.27209677419360.516010974814356188.507806077553
Winsorized Mean ( 8 / 20 )97.26951612903230.515084587808191188.84182992727
Winsorized Mean ( 9 / 20 )97.27677419354840.513659621724999189.379834581641
Winsorized Mean ( 10 / 20 )97.21548387096770.501878263633884193.703315953698
Winsorized Mean ( 11 / 20 )97.20129032258060.496369020316041195.824651306183
Winsorized Mean ( 12 / 20 )97.06967741935480.467496169865393207.637374756042
Winsorized Mean ( 13 / 20 )96.95854838709680.443181961522871218.778192266504
Winsorized Mean ( 14 / 20 )96.86822580645160.42624450099308227.259766591157
Winsorized Mean ( 15 / 20 )96.81016129032260.415532158465451232.978746212663
Winsorized Mean ( 16 / 20 )96.79209677419360.411187876728024235.396280513921
Winsorized Mean ( 17 / 20 )96.72354838709680.391147148582499247.281742274279
Winsorized Mean ( 18 / 20 )96.72354838709680.390323740989749247.803395565521
Winsorized Mean ( 19 / 20 )96.67451612903230.382899309750862252.480256994808
Winsorized Mean ( 20 / 20 )96.58096774193550.357277568873812270.324745117282
Trimmed Mean ( 1 / 20 )97.22966666666670.526683685271767184.607325773716
Trimmed Mean ( 2 / 20 )97.19862068965520.526637649671742184.564511766753
Trimmed Mean ( 3 / 20 )97.16214285714290.526913871709952184.398529007844
Trimmed Mean ( 4 / 20 )97.12148148148150.526744441846889184.380647930429
Trimmed Mean ( 5 / 20 )97.07750.525713540458507184.658549816565
Trimmed Mean ( 6 / 20 )97.03180.524438879145305185.020226109353
Trimmed Mean ( 7 / 20 )96.97958333333330.522879961131573185.471983136356
Trimmed Mean ( 8 / 20 )96.92326086956520.520195063223136186.320993261696
Trimmed Mean ( 9 / 20 )96.86227272727270.515944182990332187.737890881673
Trimmed Mean ( 10 / 20 )96.79428571428570.509694876142795189.906334642391
Trimmed Mean ( 11 / 20 )96.7290.503551464026346192.093573170386
Trimmed Mean ( 12 / 20 )96.65894736842110.495617750293439195.027210609774
Trimmed Mean ( 13 / 20 )96.60.491409375778662196.577445936868
Trimmed Mean ( 14 / 20 )96.54970588235290.490402265905622196.878588446273
Trimmed Mean ( 15 / 20 )96.5056250.491373555729407196.399712346637
Trimmed Mean ( 16 / 20 )96.46366666666670.493070250603959195.638788891662
Trimmed Mean ( 17 / 20 )96.41821428571430.493732424795079195.284347236729
Trimmed Mean ( 18 / 20 )96.37538461538460.497234267885635193.822893633613
Trimmed Mean ( 19 / 20 )96.32541666666670.498452307243751193.249013530119
Trimmed Mean ( 20 / 20 )96.27363636363640.498319924295647193.196442024097
Median95.4
Midrange98.545
Midmean - Weighted Average at Xnp96.3664516129032
Midmean - Weighted Average at X(n+1)p96.505625
Midmean - Empirical Distribution Function96.505625
Midmean - Empirical Distribution Function - Averaging96.505625
Midmean - Empirical Distribution Function - Interpolation96.4636666666667
Midmean - Closest Observation96.505625
Midmean - True Basic - Statistics Graphics Toolkit96.505625
Midmean - MS Excel (old versions)96.505625
Number of observations62



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')