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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 11:34:58 -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/07/t1331138106dwex0j5pv99hgau.htm/, Retrieved Mon, 29 Apr 2024 04:22:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163660, Retrieved Mon, 29 Apr 2024 04:22:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-03-07 16:34:58] [f26bc165187ae19198203e315c1ca52f] [Current]
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Dataseries X:
101,65
101,18
102,13
102,59
103,25
103,48
104,03
103,64
103,29
103,3
104,51
104,62
105,93
105,2
106
108,05
109,36
110,05
110,23
110,45
110,64
112,31
116,13
119,08
120,55
121,13
121,16
122,23
122,49
122,94
122,56
123,3
123,75
123,32
123,66
124,01
124,42
124,63
125,36
125,84
123,79
125,66
123,23
123,44
122,98
123,34
122,85
122,72
123,18
122,7
122,24
121
121,25
120,48
120,4
120,7
121,42
121,76
121,64
120,52




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163660&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]1 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=163660&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163660&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean116.2958333333331.09632527678766106.077854625492
Geometric Mean115.980784118892
Harmonic Mean115.656278327711
Quadratic Mean116.600320189669
Winsorized Mean ( 1 / 20 )116.3006666666671.09408220357213106.29975178003
Winsorized Mean ( 2 / 20 )116.3066666666671.08907185038082106.794300693749
Winsorized Mean ( 3 / 20 )116.2931666666671.07909719777277107.768945102158
Winsorized Mean ( 4 / 20 )116.3231666666671.06798055092605108.918806214029
Winsorized Mean ( 5 / 20 )116.2923333333331.06299160422796109.400989500566
Winsorized Mean ( 6 / 20 )116.2713333333331.06010828427475109.678732878574
Winsorized Mean ( 7 / 20 )116.2876666666671.05521043411428110.203294913659
Winsorized Mean ( 8 / 20 )116.2971.04940277069448110.822082090594
Winsorized Mean ( 9 / 20 )116.32251.03363864520927112.536910785151
Winsorized Mean ( 10 / 20 )116.3858333333331.01570821613303114.585893354721
Winsorized Mean ( 11 / 20 )116.4023333333331.01129349868851115.102424255955
Winsorized Mean ( 12 / 20 )116.5143333333330.988116949283531117.91552955125
Winsorized Mean ( 13 / 20 )116.6573333333330.955956109276217122.032101893944
Winsorized Mean ( 14 / 20 )116.6620.951494714693884122.609193932867
Winsorized Mean ( 15 / 20 )117.12450.850538793177927137.706240960956
Winsorized Mean ( 16 / 20 )117.4631666666670.787184946992845149.219274473416
Winsorized Mean ( 17 / 20 )117.6331666666670.750373710722783156.766108654525
Winsorized Mean ( 18 / 20 )117.6481666666670.736566146924176159.725188508803
Winsorized Mean ( 19 / 20 )117.71150.723958664776577162.59422771924
Winsorized Mean ( 20 / 20 )117.7281666666670.707774721240004166.335647676721
Trimmed Mean ( 1 / 20 )116.3918965517241.09095082925445106.688489921462
Trimmed Mean ( 2 / 20 )116.4896428571431.08576354019342107.288224871127
Trimmed Mean ( 3 / 20 )116.5912962962961.08117708476922107.837372747484
Trimmed Mean ( 4 / 20 )116.7059615384621.07840740837243108.220660051472
Trimmed Mean ( 5 / 20 )116.82081.07721257220397108.447304658714
Trimmed Mean ( 6 / 20 )116.9529166666671.07505215766316108.788132587806
Trimmed Mean ( 7 / 20 )117.1010869565221.07073166678091109.365483985898
Trimmed Mean ( 8 / 20 )117.2595454545451.06410251390547110.195722613397
Trimmed Mean ( 9 / 20 )117.4314285714291.05445234732498111.367221922677
Trimmed Mean ( 10 / 20 )117.616251.04316214829153112.749729457332
Trimmed Mean ( 11 / 20 )117.8105263157891.02999219343866114.380018670312
Trimmed Mean ( 12 / 20 )118.0238888888891.01011536963098116.841988981918
Trimmed Mean ( 13 / 20 )118.2458823529410.986384412852951119.878092974862
Trimmed Mean ( 14 / 20 )118.4750.959593117739442123.463786692319
Trimmed Mean ( 15 / 20 )118.7340.918317627168191129.295133282086
Trimmed Mean ( 16 / 20 )118.9639285714290.890886149901416133.534378758266
Trimmed Mean ( 17 / 20 )119.1803846153850.868914350168642137.16010627774
Trimmed Mean ( 18 / 20 )119.4079166666670.843437363800412141.572951106447
Trimmed Mean ( 19 / 20 )119.6745454545450.800321019810237149.533177927679
Trimmed Mean ( 20 / 20 )119.98450.725023221043734165.490561567493
Median121.065
Midrange113.51
Midmean - Weighted Average at Xnp118.323225806452
Midmean - Weighted Average at X(n+1)p118.734
Midmean - Empirical Distribution Function118.323225806452
Midmean - Empirical Distribution Function - Averaging118.734
Midmean - Empirical Distribution Function - Interpolation118.734
Midmean - Closest Observation118.323225806452
Midmean - True Basic - Statistics Graphics Toolkit118.734
Midmean - MS Excel (old versions)118.475
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 116.295833333333 & 1.09632527678766 & 106.077854625492 \tabularnewline
Geometric Mean & 115.980784118892 &  &  \tabularnewline
Harmonic Mean & 115.656278327711 &  &  \tabularnewline
Quadratic Mean & 116.600320189669 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 116.300666666667 & 1.09408220357213 & 106.29975178003 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 116.306666666667 & 1.08907185038082 & 106.794300693749 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 116.293166666667 & 1.07909719777277 & 107.768945102158 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 116.323166666667 & 1.06798055092605 & 108.918806214029 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 116.292333333333 & 1.06299160422796 & 109.400989500566 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 116.271333333333 & 1.06010828427475 & 109.678732878574 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 116.287666666667 & 1.05521043411428 & 110.203294913659 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 116.297 & 1.04940277069448 & 110.822082090594 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 116.3225 & 1.03363864520927 & 112.536910785151 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 116.385833333333 & 1.01570821613303 & 114.585893354721 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 116.402333333333 & 1.01129349868851 & 115.102424255955 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 116.514333333333 & 0.988116949283531 & 117.91552955125 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 116.657333333333 & 0.955956109276217 & 122.032101893944 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 116.662 & 0.951494714693884 & 122.609193932867 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 117.1245 & 0.850538793177927 & 137.706240960956 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 117.463166666667 & 0.787184946992845 & 149.219274473416 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 117.633166666667 & 0.750373710722783 & 156.766108654525 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 117.648166666667 & 0.736566146924176 & 159.725188508803 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 117.7115 & 0.723958664776577 & 162.59422771924 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 117.728166666667 & 0.707774721240004 & 166.335647676721 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 116.391896551724 & 1.09095082925445 & 106.688489921462 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 116.489642857143 & 1.08576354019342 & 107.288224871127 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 116.591296296296 & 1.08117708476922 & 107.837372747484 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 116.705961538462 & 1.07840740837243 & 108.220660051472 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 116.8208 & 1.07721257220397 & 108.447304658714 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 116.952916666667 & 1.07505215766316 & 108.788132587806 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 117.101086956522 & 1.07073166678091 & 109.365483985898 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 117.259545454545 & 1.06410251390547 & 110.195722613397 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 117.431428571429 & 1.05445234732498 & 111.367221922677 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 117.61625 & 1.04316214829153 & 112.749729457332 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 117.810526315789 & 1.02999219343866 & 114.380018670312 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 118.023888888889 & 1.01011536963098 & 116.841988981918 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 118.245882352941 & 0.986384412852951 & 119.878092974862 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 118.475 & 0.959593117739442 & 123.463786692319 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 118.734 & 0.918317627168191 & 129.295133282086 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 118.963928571429 & 0.890886149901416 & 133.534378758266 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 119.180384615385 & 0.868914350168642 & 137.16010627774 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 119.407916666667 & 0.843437363800412 & 141.572951106447 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 119.674545454545 & 0.800321019810237 & 149.533177927679 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 119.9845 & 0.725023221043734 & 165.490561567493 \tabularnewline
Median & 121.065 &  &  \tabularnewline
Midrange & 113.51 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 118.323225806452 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 118.734 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 118.323225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 118.734 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 118.734 &  &  \tabularnewline
Midmean - Closest Observation & 118.323225806452 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 118.734 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 118.475 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163660&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]116.295833333333[/C][C]1.09632527678766[/C][C]106.077854625492[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]115.980784118892[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]115.656278327711[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]116.600320189669[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]116.300666666667[/C][C]1.09408220357213[/C][C]106.29975178003[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]116.306666666667[/C][C]1.08907185038082[/C][C]106.794300693749[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]116.293166666667[/C][C]1.07909719777277[/C][C]107.768945102158[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]116.323166666667[/C][C]1.06798055092605[/C][C]108.918806214029[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]116.292333333333[/C][C]1.06299160422796[/C][C]109.400989500566[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]116.271333333333[/C][C]1.06010828427475[/C][C]109.678732878574[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]116.287666666667[/C][C]1.05521043411428[/C][C]110.203294913659[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]116.297[/C][C]1.04940277069448[/C][C]110.822082090594[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]116.3225[/C][C]1.03363864520927[/C][C]112.536910785151[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]116.385833333333[/C][C]1.01570821613303[/C][C]114.585893354721[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]116.402333333333[/C][C]1.01129349868851[/C][C]115.102424255955[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]116.514333333333[/C][C]0.988116949283531[/C][C]117.91552955125[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]116.657333333333[/C][C]0.955956109276217[/C][C]122.032101893944[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]116.662[/C][C]0.951494714693884[/C][C]122.609193932867[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]117.1245[/C][C]0.850538793177927[/C][C]137.706240960956[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]117.463166666667[/C][C]0.787184946992845[/C][C]149.219274473416[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]117.633166666667[/C][C]0.750373710722783[/C][C]156.766108654525[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]117.648166666667[/C][C]0.736566146924176[/C][C]159.725188508803[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]117.7115[/C][C]0.723958664776577[/C][C]162.59422771924[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]117.728166666667[/C][C]0.707774721240004[/C][C]166.335647676721[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]116.391896551724[/C][C]1.09095082925445[/C][C]106.688489921462[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]116.489642857143[/C][C]1.08576354019342[/C][C]107.288224871127[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]116.591296296296[/C][C]1.08117708476922[/C][C]107.837372747484[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]116.705961538462[/C][C]1.07840740837243[/C][C]108.220660051472[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]116.8208[/C][C]1.07721257220397[/C][C]108.447304658714[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]116.952916666667[/C][C]1.07505215766316[/C][C]108.788132587806[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]117.101086956522[/C][C]1.07073166678091[/C][C]109.365483985898[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]117.259545454545[/C][C]1.06410251390547[/C][C]110.195722613397[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]117.431428571429[/C][C]1.05445234732498[/C][C]111.367221922677[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]117.61625[/C][C]1.04316214829153[/C][C]112.749729457332[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]117.810526315789[/C][C]1.02999219343866[/C][C]114.380018670312[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]118.023888888889[/C][C]1.01011536963098[/C][C]116.841988981918[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]118.245882352941[/C][C]0.986384412852951[/C][C]119.878092974862[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]118.475[/C][C]0.959593117739442[/C][C]123.463786692319[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]118.734[/C][C]0.918317627168191[/C][C]129.295133282086[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]118.963928571429[/C][C]0.890886149901416[/C][C]133.534378758266[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]119.180384615385[/C][C]0.868914350168642[/C][C]137.16010627774[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]119.407916666667[/C][C]0.843437363800412[/C][C]141.572951106447[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]119.674545454545[/C][C]0.800321019810237[/C][C]149.533177927679[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]119.9845[/C][C]0.725023221043734[/C][C]165.490561567493[/C][/ROW]
[ROW][C]Median[/C][C]121.065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]113.51[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]118.323225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]118.734[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]118.323225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]118.734[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]118.734[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]118.323225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]118.734[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]118.475[/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=163660&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163660&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 Mean116.2958333333331.09632527678766106.077854625492
Geometric Mean115.980784118892
Harmonic Mean115.656278327711
Quadratic Mean116.600320189669
Winsorized Mean ( 1 / 20 )116.3006666666671.09408220357213106.29975178003
Winsorized Mean ( 2 / 20 )116.3066666666671.08907185038082106.794300693749
Winsorized Mean ( 3 / 20 )116.2931666666671.07909719777277107.768945102158
Winsorized Mean ( 4 / 20 )116.3231666666671.06798055092605108.918806214029
Winsorized Mean ( 5 / 20 )116.2923333333331.06299160422796109.400989500566
Winsorized Mean ( 6 / 20 )116.2713333333331.06010828427475109.678732878574
Winsorized Mean ( 7 / 20 )116.2876666666671.05521043411428110.203294913659
Winsorized Mean ( 8 / 20 )116.2971.04940277069448110.822082090594
Winsorized Mean ( 9 / 20 )116.32251.03363864520927112.536910785151
Winsorized Mean ( 10 / 20 )116.3858333333331.01570821613303114.585893354721
Winsorized Mean ( 11 / 20 )116.4023333333331.01129349868851115.102424255955
Winsorized Mean ( 12 / 20 )116.5143333333330.988116949283531117.91552955125
Winsorized Mean ( 13 / 20 )116.6573333333330.955956109276217122.032101893944
Winsorized Mean ( 14 / 20 )116.6620.951494714693884122.609193932867
Winsorized Mean ( 15 / 20 )117.12450.850538793177927137.706240960956
Winsorized Mean ( 16 / 20 )117.4631666666670.787184946992845149.219274473416
Winsorized Mean ( 17 / 20 )117.6331666666670.750373710722783156.766108654525
Winsorized Mean ( 18 / 20 )117.6481666666670.736566146924176159.725188508803
Winsorized Mean ( 19 / 20 )117.71150.723958664776577162.59422771924
Winsorized Mean ( 20 / 20 )117.7281666666670.707774721240004166.335647676721
Trimmed Mean ( 1 / 20 )116.3918965517241.09095082925445106.688489921462
Trimmed Mean ( 2 / 20 )116.4896428571431.08576354019342107.288224871127
Trimmed Mean ( 3 / 20 )116.5912962962961.08117708476922107.837372747484
Trimmed Mean ( 4 / 20 )116.7059615384621.07840740837243108.220660051472
Trimmed Mean ( 5 / 20 )116.82081.07721257220397108.447304658714
Trimmed Mean ( 6 / 20 )116.9529166666671.07505215766316108.788132587806
Trimmed Mean ( 7 / 20 )117.1010869565221.07073166678091109.365483985898
Trimmed Mean ( 8 / 20 )117.2595454545451.06410251390547110.195722613397
Trimmed Mean ( 9 / 20 )117.4314285714291.05445234732498111.367221922677
Trimmed Mean ( 10 / 20 )117.616251.04316214829153112.749729457332
Trimmed Mean ( 11 / 20 )117.8105263157891.02999219343866114.380018670312
Trimmed Mean ( 12 / 20 )118.0238888888891.01011536963098116.841988981918
Trimmed Mean ( 13 / 20 )118.2458823529410.986384412852951119.878092974862
Trimmed Mean ( 14 / 20 )118.4750.959593117739442123.463786692319
Trimmed Mean ( 15 / 20 )118.7340.918317627168191129.295133282086
Trimmed Mean ( 16 / 20 )118.9639285714290.890886149901416133.534378758266
Trimmed Mean ( 17 / 20 )119.1803846153850.868914350168642137.16010627774
Trimmed Mean ( 18 / 20 )119.4079166666670.843437363800412141.572951106447
Trimmed Mean ( 19 / 20 )119.6745454545450.800321019810237149.533177927679
Trimmed Mean ( 20 / 20 )119.98450.725023221043734165.490561567493
Median121.065
Midrange113.51
Midmean - Weighted Average at Xnp118.323225806452
Midmean - Weighted Average at X(n+1)p118.734
Midmean - Empirical Distribution Function118.323225806452
Midmean - Empirical Distribution Function - Averaging118.734
Midmean - Empirical Distribution Function - Interpolation118.734
Midmean - Closest Observation118.323225806452
Midmean - True Basic - Statistics Graphics Toolkit118.734
Midmean - MS Excel (old versions)118.475
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')