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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 computationThu, 24 Nov 2011 10:59:11 -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/2011/Nov/24/t1322150410zy3pixd6ear6fzu.htm/, Retrieved Sat, 20 Apr 2024 00:22:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147020, Retrieved Sat, 20 Apr 2024 00:22:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Central Tendency] [Workshop 8, Robus...] [2010-11-28 19:41:12] [d946de7cca328fbcf207448a112523ab]
-         [Central Tendency] [Workshop 8, Centr...] [2010-11-29 20:08:54] [3635fb7041b1998c5a1332cf9de22bce]
- R  D        [Central Tendency] [] [2011-11-24 15:59:11] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
9,676
8.642
9.402
9.610
9.294
9.448
10.319
9.548
9.801
9.596
8.923
9.746
9.829
9.125
9.782
9.441
9.162
9.915
10.444
10.209
9.985
9.842
9.429
10.132
9.849
9.172
10.313
9.819
9.955
10.048
10.082
10.541
10.208
10.233
9.439
9.963
10.158
9.225
10.474
9.757
10.490
10.281
10.444
10.640
10.695
10.786
9.832
9.747
10.411
9.511
10.402
9.701
10.540
10.112
10.915
11.183
10.384
10.834
9.886
10.216




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=147020&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=147020&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147020&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 Mean9.95910.0673467697898715147.877916506959
Geometric Mean9.94558446764261
Harmonic Mean9.93198306476949
Quadratic Mean9.97252588197527
Winsorized Mean ( 1 / 20 )9.959316666666670.0646820580946501153.973404063505
Winsorized Mean ( 2 / 20 )9.963350.062339759895606159.823361794858
Winsorized Mean ( 3 / 20 )9.96280.0613673057473543162.347032816078
Winsorized Mean ( 4 / 20 )9.95740.0598960266737238166.244750327792
Winsorized Mean ( 5 / 20 )9.957233333333330.0579964365097915171.68698514179
Winsorized Mean ( 6 / 20 )9.954233333333330.0546599987321039182.111847131947
Winsorized Mean ( 7 / 20 )9.966716666666660.0521902489521499190.968942796279
Winsorized Mean ( 8 / 20 )9.963650.0503238485376309197.99062054146
Winsorized Mean ( 9 / 20 )9.962750.0496323865982186200.730826841955
Winsorized Mean ( 10 / 20 )9.958083333333330.0487133219500056204.422177234254
Winsorized Mean ( 11 / 20 )9.959366666666670.0484831671334692205.419060995944
Winsorized Mean ( 12 / 20 )9.965366666666670.0451698174730222220.620033999883
Winsorized Mean ( 13 / 20 )9.971433333333330.0434980639004601229.238555448162
Winsorized Mean ( 14 / 20 )9.978433333333330.0409827052311126243.479128014177
Winsorized Mean ( 15 / 20 )9.965683333333330.0377727556413116263.832573613824
Winsorized Mean ( 16 / 20 )9.981683333333330.034798357741517286.843517371639
Winsorized Mean ( 17 / 20 )9.97970.0323040402573603308.930397575461
Winsorized Mean ( 18 / 20 )9.97880.028123534990093354.820260095867
Winsorized Mean ( 19 / 20 )9.973733333333330.0272611027157854365.85949722269
Winsorized Mean ( 20 / 20 )9.974733333333330.0264425917627926377.222226278468
Trimmed Mean ( 1 / 20 )9.960706896551720.0622796078302896159.935286100298
Trimmed Mean ( 2 / 20 )9.962196428571430.0593129243906258167.959960344594
Trimmed Mean ( 3 / 20 )9.961555555555560.0572321926548104174.055109431812
Trimmed Mean ( 4 / 20 )9.961076923076920.0551138260387432180.736443811297
Trimmed Mean ( 5 / 20 )9.962180.0530467386521797187.800046772351
Trimmed Mean ( 6 / 20 )9.963416666666670.0511015436170697194.972910042164
Trimmed Mean ( 7 / 20 )9.965413043478260.0496817949539111200.584802797946
Trimmed Mean ( 8 / 20 )9.965159090909090.0485615163495855205.206917740619
Trimmed Mean ( 9 / 20 )9.965428571428570.0475828410553666209.433240016773
Trimmed Mean ( 10 / 20 )9.9658750.0464305821451049214.640319797297
Trimmed Mean ( 11 / 20 )9.96710526315790.045092693996732221.035923555161
Trimmed Mean ( 12 / 20 )9.968277777777780.0432961674155436230.234645993149
Trimmed Mean ( 13 / 20 )9.968705882352940.0417618989290479238.703366896449
Trimmed Mean ( 14 / 20 )9.96831250.0400615564027571248.824893366199
Trimmed Mean ( 15 / 20 )9.966866666666670.038366254728807259.782111574813
Trimmed Mean ( 16 / 20 )9.967035714285710.0368979173120276270.124615164573
Trimmed Mean ( 17 / 20 )9.964923076923080.0356209066993365279.749282100915
Trimmed Mean ( 18 / 20 )9.962750.0344490408145637289.202536977115
Trimmed Mean ( 19 / 20 )9.960318181818180.0340273881517716292.714743117879
Trimmed Mean ( 20 / 20 )9.95820.0334020642286796298.131275115916
Median9.935
Midrange9.9125
Midmean - Weighted Average at Xnp9.95490322580645
Midmean - Weighted Average at X(n+1)p9.96686666666667
Midmean - Empirical Distribution Function9.95490322580645
Midmean - Empirical Distribution Function - Averaging9.96686666666667
Midmean - Empirical Distribution Function - Interpolation9.96686666666667
Midmean - Closest Observation9.95490322580645
Midmean - True Basic - Statistics Graphics Toolkit9.96686666666667
Midmean - MS Excel (old versions)9.9683125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9.9591 & 0.0673467697898715 & 147.877916506959 \tabularnewline
Geometric Mean & 9.94558446764261 &  &  \tabularnewline
Harmonic Mean & 9.93198306476949 &  &  \tabularnewline
Quadratic Mean & 9.97252588197527 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 9.95931666666667 & 0.0646820580946501 & 153.973404063505 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 9.96335 & 0.062339759895606 & 159.823361794858 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 9.9628 & 0.0613673057473543 & 162.347032816078 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 9.9574 & 0.0598960266737238 & 166.244750327792 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 9.95723333333333 & 0.0579964365097915 & 171.68698514179 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 9.95423333333333 & 0.0546599987321039 & 182.111847131947 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 9.96671666666666 & 0.0521902489521499 & 190.968942796279 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 9.96365 & 0.0503238485376309 & 197.99062054146 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 9.96275 & 0.0496323865982186 & 200.730826841955 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 9.95808333333333 & 0.0487133219500056 & 204.422177234254 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 9.95936666666667 & 0.0484831671334692 & 205.419060995944 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 9.96536666666667 & 0.0451698174730222 & 220.620033999883 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 9.97143333333333 & 0.0434980639004601 & 229.238555448162 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 9.97843333333333 & 0.0409827052311126 & 243.479128014177 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 9.96568333333333 & 0.0377727556413116 & 263.832573613824 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 9.98168333333333 & 0.034798357741517 & 286.843517371639 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 9.9797 & 0.0323040402573603 & 308.930397575461 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 9.9788 & 0.028123534990093 & 354.820260095867 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 9.97373333333333 & 0.0272611027157854 & 365.85949722269 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 9.97473333333333 & 0.0264425917627926 & 377.222226278468 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 9.96070689655172 & 0.0622796078302896 & 159.935286100298 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 9.96219642857143 & 0.0593129243906258 & 167.959960344594 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 9.96155555555556 & 0.0572321926548104 & 174.055109431812 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 9.96107692307692 & 0.0551138260387432 & 180.736443811297 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 9.96218 & 0.0530467386521797 & 187.800046772351 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 9.96341666666667 & 0.0511015436170697 & 194.972910042164 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 9.96541304347826 & 0.0496817949539111 & 200.584802797946 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 9.96515909090909 & 0.0485615163495855 & 205.206917740619 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 9.96542857142857 & 0.0475828410553666 & 209.433240016773 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 9.965875 & 0.0464305821451049 & 214.640319797297 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 9.9671052631579 & 0.045092693996732 & 221.035923555161 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 9.96827777777778 & 0.0432961674155436 & 230.234645993149 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 9.96870588235294 & 0.0417618989290479 & 238.703366896449 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 9.9683125 & 0.0400615564027571 & 248.824893366199 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 9.96686666666667 & 0.038366254728807 & 259.782111574813 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 9.96703571428571 & 0.0368979173120276 & 270.124615164573 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 9.96492307692308 & 0.0356209066993365 & 279.749282100915 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 9.96275 & 0.0344490408145637 & 289.202536977115 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 9.96031818181818 & 0.0340273881517716 & 292.714743117879 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 9.9582 & 0.0334020642286796 & 298.131275115916 \tabularnewline
Median & 9.935 &  &  \tabularnewline
Midrange & 9.9125 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 9.95490322580645 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 9.96686666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 9.95490322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 9.96686666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 9.96686666666667 &  &  \tabularnewline
Midmean - Closest Observation & 9.95490322580645 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 9.96686666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 9.9683125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147020&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]9.9591[/C][C]0.0673467697898715[/C][C]147.877916506959[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]9.94558446764261[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9.93198306476949[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9.97252588197527[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]9.95931666666667[/C][C]0.0646820580946501[/C][C]153.973404063505[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]9.96335[/C][C]0.062339759895606[/C][C]159.823361794858[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]9.9628[/C][C]0.0613673057473543[/C][C]162.347032816078[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]9.9574[/C][C]0.0598960266737238[/C][C]166.244750327792[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]9.95723333333333[/C][C]0.0579964365097915[/C][C]171.68698514179[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]9.95423333333333[/C][C]0.0546599987321039[/C][C]182.111847131947[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]9.96671666666666[/C][C]0.0521902489521499[/C][C]190.968942796279[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]9.96365[/C][C]0.0503238485376309[/C][C]197.99062054146[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]9.96275[/C][C]0.0496323865982186[/C][C]200.730826841955[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]9.95808333333333[/C][C]0.0487133219500056[/C][C]204.422177234254[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]9.95936666666667[/C][C]0.0484831671334692[/C][C]205.419060995944[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]9.96536666666667[/C][C]0.0451698174730222[/C][C]220.620033999883[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]9.97143333333333[/C][C]0.0434980639004601[/C][C]229.238555448162[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]9.97843333333333[/C][C]0.0409827052311126[/C][C]243.479128014177[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]9.96568333333333[/C][C]0.0377727556413116[/C][C]263.832573613824[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]9.98168333333333[/C][C]0.034798357741517[/C][C]286.843517371639[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]9.9797[/C][C]0.0323040402573603[/C][C]308.930397575461[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]9.9788[/C][C]0.028123534990093[/C][C]354.820260095867[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]9.97373333333333[/C][C]0.0272611027157854[/C][C]365.85949722269[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]9.97473333333333[/C][C]0.0264425917627926[/C][C]377.222226278468[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]9.96070689655172[/C][C]0.0622796078302896[/C][C]159.935286100298[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]9.96219642857143[/C][C]0.0593129243906258[/C][C]167.959960344594[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]9.96155555555556[/C][C]0.0572321926548104[/C][C]174.055109431812[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]9.96107692307692[/C][C]0.0551138260387432[/C][C]180.736443811297[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]9.96218[/C][C]0.0530467386521797[/C][C]187.800046772351[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]9.96341666666667[/C][C]0.0511015436170697[/C][C]194.972910042164[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]9.96541304347826[/C][C]0.0496817949539111[/C][C]200.584802797946[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]9.96515909090909[/C][C]0.0485615163495855[/C][C]205.206917740619[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]9.96542857142857[/C][C]0.0475828410553666[/C][C]209.433240016773[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]9.965875[/C][C]0.0464305821451049[/C][C]214.640319797297[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]9.9671052631579[/C][C]0.045092693996732[/C][C]221.035923555161[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]9.96827777777778[/C][C]0.0432961674155436[/C][C]230.234645993149[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]9.96870588235294[/C][C]0.0417618989290479[/C][C]238.703366896449[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]9.9683125[/C][C]0.0400615564027571[/C][C]248.824893366199[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]9.96686666666667[/C][C]0.038366254728807[/C][C]259.782111574813[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]9.96703571428571[/C][C]0.0368979173120276[/C][C]270.124615164573[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]9.96492307692308[/C][C]0.0356209066993365[/C][C]279.749282100915[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]9.96275[/C][C]0.0344490408145637[/C][C]289.202536977115[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]9.96031818181818[/C][C]0.0340273881517716[/C][C]292.714743117879[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]9.9582[/C][C]0.0334020642286796[/C][C]298.131275115916[/C][/ROW]
[ROW][C]Median[/C][C]9.935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]9.9125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]9.95490322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]9.96686666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]9.95490322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]9.96686666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]9.96686666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]9.95490322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]9.96686666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]9.9683125[/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=147020&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147020&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 Mean9.95910.0673467697898715147.877916506959
Geometric Mean9.94558446764261
Harmonic Mean9.93198306476949
Quadratic Mean9.97252588197527
Winsorized Mean ( 1 / 20 )9.959316666666670.0646820580946501153.973404063505
Winsorized Mean ( 2 / 20 )9.963350.062339759895606159.823361794858
Winsorized Mean ( 3 / 20 )9.96280.0613673057473543162.347032816078
Winsorized Mean ( 4 / 20 )9.95740.0598960266737238166.244750327792
Winsorized Mean ( 5 / 20 )9.957233333333330.0579964365097915171.68698514179
Winsorized Mean ( 6 / 20 )9.954233333333330.0546599987321039182.111847131947
Winsorized Mean ( 7 / 20 )9.966716666666660.0521902489521499190.968942796279
Winsorized Mean ( 8 / 20 )9.963650.0503238485376309197.99062054146
Winsorized Mean ( 9 / 20 )9.962750.0496323865982186200.730826841955
Winsorized Mean ( 10 / 20 )9.958083333333330.0487133219500056204.422177234254
Winsorized Mean ( 11 / 20 )9.959366666666670.0484831671334692205.419060995944
Winsorized Mean ( 12 / 20 )9.965366666666670.0451698174730222220.620033999883
Winsorized Mean ( 13 / 20 )9.971433333333330.0434980639004601229.238555448162
Winsorized Mean ( 14 / 20 )9.978433333333330.0409827052311126243.479128014177
Winsorized Mean ( 15 / 20 )9.965683333333330.0377727556413116263.832573613824
Winsorized Mean ( 16 / 20 )9.981683333333330.034798357741517286.843517371639
Winsorized Mean ( 17 / 20 )9.97970.0323040402573603308.930397575461
Winsorized Mean ( 18 / 20 )9.97880.028123534990093354.820260095867
Winsorized Mean ( 19 / 20 )9.973733333333330.0272611027157854365.85949722269
Winsorized Mean ( 20 / 20 )9.974733333333330.0264425917627926377.222226278468
Trimmed Mean ( 1 / 20 )9.960706896551720.0622796078302896159.935286100298
Trimmed Mean ( 2 / 20 )9.962196428571430.0593129243906258167.959960344594
Trimmed Mean ( 3 / 20 )9.961555555555560.0572321926548104174.055109431812
Trimmed Mean ( 4 / 20 )9.961076923076920.0551138260387432180.736443811297
Trimmed Mean ( 5 / 20 )9.962180.0530467386521797187.800046772351
Trimmed Mean ( 6 / 20 )9.963416666666670.0511015436170697194.972910042164
Trimmed Mean ( 7 / 20 )9.965413043478260.0496817949539111200.584802797946
Trimmed Mean ( 8 / 20 )9.965159090909090.0485615163495855205.206917740619
Trimmed Mean ( 9 / 20 )9.965428571428570.0475828410553666209.433240016773
Trimmed Mean ( 10 / 20 )9.9658750.0464305821451049214.640319797297
Trimmed Mean ( 11 / 20 )9.96710526315790.045092693996732221.035923555161
Trimmed Mean ( 12 / 20 )9.968277777777780.0432961674155436230.234645993149
Trimmed Mean ( 13 / 20 )9.968705882352940.0417618989290479238.703366896449
Trimmed Mean ( 14 / 20 )9.96831250.0400615564027571248.824893366199
Trimmed Mean ( 15 / 20 )9.966866666666670.038366254728807259.782111574813
Trimmed Mean ( 16 / 20 )9.967035714285710.0368979173120276270.124615164573
Trimmed Mean ( 17 / 20 )9.964923076923080.0356209066993365279.749282100915
Trimmed Mean ( 18 / 20 )9.962750.0344490408145637289.202536977115
Trimmed Mean ( 19 / 20 )9.960318181818180.0340273881517716292.714743117879
Trimmed Mean ( 20 / 20 )9.95820.0334020642286796298.131275115916
Median9.935
Midrange9.9125
Midmean - Weighted Average at Xnp9.95490322580645
Midmean - Weighted Average at X(n+1)p9.96686666666667
Midmean - Empirical Distribution Function9.95490322580645
Midmean - Empirical Distribution Function - Averaging9.96686666666667
Midmean - Empirical Distribution Function - Interpolation9.96686666666667
Midmean - Closest Observation9.95490322580645
Midmean - True Basic - Statistics Graphics Toolkit9.96686666666667
Midmean - MS Excel (old versions)9.9683125
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')