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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 19 Dec 2010 21:03:16 +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/2010/Dec/19/t12927924809d8820l6ogyex7n.htm/, Retrieved Sun, 05 May 2024 02:22:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112743, Retrieved Sun, 05 May 2024 02:22:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-  M D  [Central Tendency] [Robustness of Cen...] [2010-12-18 14:20:59] [1afa3497b02a8d7c9f6727c1b17b89b2]
-         [Central Tendency] [Central tendency ...] [2010-12-19 18:22:32] [1afa3497b02a8d7c9f6727c1b17b89b2]
-    D        [Central Tendency] [Central tendencey...] [2010-12-19 21:03:16] [214713b86cef2e1efaaf6d85aa84ff3c] [Current]
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Dataseries X:
1,3119
1,3014
1,3201
1,2938
1,2694
1,2165
1,2037
1,2292
1,2256
1,2015
1,1786
1,1856
1,2103
1,1938
1,202
1,2271
1,277
1,265
1,2684
1,2811
1,2727
1,2611
1,2881
1,3213
1,2999
1,3074
1,3242
1,3516
1,3511
1,3419
1,3716
1,3622
1,3896
1,4227
1,4684
1,457
1,4718
1,4748
1,5527
1,5751
1,5557
1,5553
1,577
1,4975
1,437
1,3322
1,2732
1,3449
1,3239
1,2785
1,305
1,319
1,365
1,4016
1,4088
1,4268
1,4562
1,4816
1,4914
1,4614




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time8 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 8 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112743&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]8 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112743&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112743&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 time8 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.346986666666670.014049236556990495.8761468071698
Geometric Mean1.34274941291818
Harmonic Mean1.33860142463567
Quadratic Mean1.35130254273423
Winsorized Mean ( 1 / 20 )1.347071666666670.014017237389040596.1010810675065
Winsorized Mean ( 2 / 20 )1.346698333333330.013792624634318297.6390186087235
Winsorized Mean ( 3 / 20 )1.347063333333330.013716685778213098.2061815160157
Winsorized Mean ( 4 / 20 )1.346923333333330.013666273874746898.5581985022448
Winsorized Mean ( 5 / 20 )1.3424650.0125680066029483106.816064186748
Winsorized Mean ( 6 / 20 )1.3425150.0123199539182589108.970780971048
Winsorized Mean ( 7 / 20 )1.3420950.0119595973386576112.219079120823
Winsorized Mean ( 8 / 20 )1.342401666666670.0115701636286440116.022703719013
Winsorized Mean ( 9 / 20 )1.342176666666670.0114449086617130117.272815916539
Winsorized Mean ( 10 / 20 )1.341960.0112771891657552118.997737847216
Winsorized Mean ( 11 / 20 )1.3465250.0101134121455614133.142502314708
Winsorized Mean ( 12 / 20 )1.3464250.00983425887389946136.911689763778
Winsorized Mean ( 13 / 20 )1.346988333333330.0096989195308505138.880246304633
Winsorized Mean ( 14 / 20 )1.342741666666670.00883279466164814152.017760867558
Winsorized Mean ( 15 / 20 )1.341016666666670.00826171798069065162.316926068029
Winsorized Mean ( 16 / 20 )1.340056666666670.00805166942954295166.432151542358
Winsorized Mean ( 17 / 20 )1.3371950.00722596519660861185.054171119948
Winsorized Mean ( 18 / 20 )1.3354850.00680285783458056196.312348791328
Winsorized Mean ( 19 / 20 )1.332508333333330.0060688485359077219.565264390642
Winsorized Mean ( 20 / 20 )1.328841666666670.00479920149412041276.888075713148
Trimmed Mean ( 1 / 20 )1.345924137931030.013665735875747098.488961748462
Trimmed Mean ( 2 / 20 )1.344694642857140.0132298998287289101.640576290466
Trimmed Mean ( 3 / 20 )1.343581481481480.0128384822021758104.652673137155
Trimmed Mean ( 4 / 20 )1.342242307692310.0123826111917376108.397355526105
Trimmed Mean ( 5 / 20 )1.3408380.0118247357100379113.392640045374
Trimmed Mean ( 6 / 20 )1.340431250.0115164845451558116.392397762026
Trimmed Mean ( 7 / 20 )1.339978260869570.0111960314367542119.683324259943
Trimmed Mean ( 8 / 20 )1.339565909090910.0108848901921206123.066552390267
Trimmed Mean ( 9 / 20 )1.339059523809520.0105834025491937126.524481855936
Trimmed Mean ( 10 / 20 )1.338540.0102128851495022131.063845368440
Trimmed Mean ( 11 / 20 )1.3380.00975819967421935137.115456197820
Trimmed Mean ( 12 / 20 )1.336708333333330.00945673303013121141.349906894304
Trimmed Mean ( 13 / 20 )1.335279411764710.00910426608530756146.665244540642
Trimmed Mean ( 14 / 20 )1.3335906250.00862608380214294154.599776165947
Trimmed Mean ( 15 / 20 )1.332283333333330.00823148159640965161.852191216031
Trimmed Mean ( 16 / 20 )1.331035714285710.00783609241224686169.859624448209
Trimmed Mean ( 17 / 20 )1.329734615384620.00729914208300736182.176836710753
Trimmed Mean ( 18 / 20 )1.32863750.0068059538419883195.216942525113
Trimmed Mean ( 19 / 20 )1.32760.00619108072306286214.437520585777
Trimmed Mean ( 20 / 20 )1.3268250.00554644445141494239.220821847682
Median1.3226
Midrange1.3778
Midmean - Weighted Average at Xnp1.33025483870968
Midmean - Weighted Average at X(n+1)p1.33228333333333
Midmean - Empirical Distribution Function1.33025483870968
Midmean - Empirical Distribution Function - Averaging1.33228333333333
Midmean - Empirical Distribution Function - Interpolation1.33228333333333
Midmean - Closest Observation1.33025483870968
Midmean - True Basic - Statistics Graphics Toolkit1.33228333333333
Midmean - MS Excel (old versions)1.333590625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.34698666666667 & 0.0140492365569904 & 95.8761468071698 \tabularnewline
Geometric Mean & 1.34274941291818 &  &  \tabularnewline
Harmonic Mean & 1.33860142463567 &  &  \tabularnewline
Quadratic Mean & 1.35130254273423 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.34707166666667 & 0.0140172373890405 & 96.1010810675065 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.34669833333333 & 0.0137926246343182 & 97.6390186087235 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.34706333333333 & 0.0137166857782130 & 98.2061815160157 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.34692333333333 & 0.0136662738747468 & 98.5581985022448 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.342465 & 0.0125680066029483 & 106.816064186748 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.342515 & 0.0123199539182589 & 108.970780971048 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.342095 & 0.0119595973386576 & 112.219079120823 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.34240166666667 & 0.0115701636286440 & 116.022703719013 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.34217666666667 & 0.0114449086617130 & 117.272815916539 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.34196 & 0.0112771891657552 & 118.997737847216 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.346525 & 0.0101134121455614 & 133.142502314708 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.346425 & 0.00983425887389946 & 136.911689763778 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.34698833333333 & 0.0096989195308505 & 138.880246304633 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.34274166666667 & 0.00883279466164814 & 152.017760867558 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.34101666666667 & 0.00826171798069065 & 162.316926068029 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.34005666666667 & 0.00805166942954295 & 166.432151542358 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.337195 & 0.00722596519660861 & 185.054171119948 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.335485 & 0.00680285783458056 & 196.312348791328 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.33250833333333 & 0.0060688485359077 & 219.565264390642 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.32884166666667 & 0.00479920149412041 & 276.888075713148 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.34592413793103 & 0.0136657358757470 & 98.488961748462 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.34469464285714 & 0.0132298998287289 & 101.640576290466 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.34358148148148 & 0.0128384822021758 & 104.652673137155 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.34224230769231 & 0.0123826111917376 & 108.397355526105 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.340838 & 0.0118247357100379 & 113.392640045374 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.34043125 & 0.0115164845451558 & 116.392397762026 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.33997826086957 & 0.0111960314367542 & 119.683324259943 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.33956590909091 & 0.0108848901921206 & 123.066552390267 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.33905952380952 & 0.0105834025491937 & 126.524481855936 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.33854 & 0.0102128851495022 & 131.063845368440 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.338 & 0.00975819967421935 & 137.115456197820 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.33670833333333 & 0.00945673303013121 & 141.349906894304 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.33527941176471 & 0.00910426608530756 & 146.665244540642 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.333590625 & 0.00862608380214294 & 154.599776165947 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.33228333333333 & 0.00823148159640965 & 161.852191216031 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.33103571428571 & 0.00783609241224686 & 169.859624448209 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.32973461538462 & 0.00729914208300736 & 182.176836710753 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.3286375 & 0.0068059538419883 & 195.216942525113 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.3276 & 0.00619108072306286 & 214.437520585777 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.326825 & 0.00554644445141494 & 239.220821847682 \tabularnewline
Median & 1.3226 &  &  \tabularnewline
Midrange & 1.3778 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.33025483870968 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.33228333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.33025483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.33228333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.33228333333333 &  &  \tabularnewline
Midmean - Closest Observation & 1.33025483870968 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.33228333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.333590625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112743&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]1.34698666666667[/C][C]0.0140492365569904[/C][C]95.8761468071698[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.34274941291818[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.33860142463567[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.35130254273423[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.34707166666667[/C][C]0.0140172373890405[/C][C]96.1010810675065[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.34669833333333[/C][C]0.0137926246343182[/C][C]97.6390186087235[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.34706333333333[/C][C]0.0137166857782130[/C][C]98.2061815160157[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.34692333333333[/C][C]0.0136662738747468[/C][C]98.5581985022448[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.342465[/C][C]0.0125680066029483[/C][C]106.816064186748[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.342515[/C][C]0.0123199539182589[/C][C]108.970780971048[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.342095[/C][C]0.0119595973386576[/C][C]112.219079120823[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.34240166666667[/C][C]0.0115701636286440[/C][C]116.022703719013[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.34217666666667[/C][C]0.0114449086617130[/C][C]117.272815916539[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.34196[/C][C]0.0112771891657552[/C][C]118.997737847216[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.346525[/C][C]0.0101134121455614[/C][C]133.142502314708[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.346425[/C][C]0.00983425887389946[/C][C]136.911689763778[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.34698833333333[/C][C]0.0096989195308505[/C][C]138.880246304633[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.34274166666667[/C][C]0.00883279466164814[/C][C]152.017760867558[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.34101666666667[/C][C]0.00826171798069065[/C][C]162.316926068029[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.34005666666667[/C][C]0.00805166942954295[/C][C]166.432151542358[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.337195[/C][C]0.00722596519660861[/C][C]185.054171119948[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.335485[/C][C]0.00680285783458056[/C][C]196.312348791328[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.33250833333333[/C][C]0.0060688485359077[/C][C]219.565264390642[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.32884166666667[/C][C]0.00479920149412041[/C][C]276.888075713148[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.34592413793103[/C][C]0.0136657358757470[/C][C]98.488961748462[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.34469464285714[/C][C]0.0132298998287289[/C][C]101.640576290466[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.34358148148148[/C][C]0.0128384822021758[/C][C]104.652673137155[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.34224230769231[/C][C]0.0123826111917376[/C][C]108.397355526105[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.340838[/C][C]0.0118247357100379[/C][C]113.392640045374[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.34043125[/C][C]0.0115164845451558[/C][C]116.392397762026[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.33997826086957[/C][C]0.0111960314367542[/C][C]119.683324259943[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.33956590909091[/C][C]0.0108848901921206[/C][C]123.066552390267[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.33905952380952[/C][C]0.0105834025491937[/C][C]126.524481855936[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.33854[/C][C]0.0102128851495022[/C][C]131.063845368440[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.338[/C][C]0.00975819967421935[/C][C]137.115456197820[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.33670833333333[/C][C]0.00945673303013121[/C][C]141.349906894304[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.33527941176471[/C][C]0.00910426608530756[/C][C]146.665244540642[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.333590625[/C][C]0.00862608380214294[/C][C]154.599776165947[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.33228333333333[/C][C]0.00823148159640965[/C][C]161.852191216031[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.33103571428571[/C][C]0.00783609241224686[/C][C]169.859624448209[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.32973461538462[/C][C]0.00729914208300736[/C][C]182.176836710753[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.3286375[/C][C]0.0068059538419883[/C][C]195.216942525113[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.3276[/C][C]0.00619108072306286[/C][C]214.437520585777[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.326825[/C][C]0.00554644445141494[/C][C]239.220821847682[/C][/ROW]
[ROW][C]Median[/C][C]1.3226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.3778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.33025483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.33228333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.33025483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.33228333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.33228333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.33025483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.33228333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.333590625[/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=112743&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112743&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 Mean1.346986666666670.014049236556990495.8761468071698
Geometric Mean1.34274941291818
Harmonic Mean1.33860142463567
Quadratic Mean1.35130254273423
Winsorized Mean ( 1 / 20 )1.347071666666670.014017237389040596.1010810675065
Winsorized Mean ( 2 / 20 )1.346698333333330.013792624634318297.6390186087235
Winsorized Mean ( 3 / 20 )1.347063333333330.013716685778213098.2061815160157
Winsorized Mean ( 4 / 20 )1.346923333333330.013666273874746898.5581985022448
Winsorized Mean ( 5 / 20 )1.3424650.0125680066029483106.816064186748
Winsorized Mean ( 6 / 20 )1.3425150.0123199539182589108.970780971048
Winsorized Mean ( 7 / 20 )1.3420950.0119595973386576112.219079120823
Winsorized Mean ( 8 / 20 )1.342401666666670.0115701636286440116.022703719013
Winsorized Mean ( 9 / 20 )1.342176666666670.0114449086617130117.272815916539
Winsorized Mean ( 10 / 20 )1.341960.0112771891657552118.997737847216
Winsorized Mean ( 11 / 20 )1.3465250.0101134121455614133.142502314708
Winsorized Mean ( 12 / 20 )1.3464250.00983425887389946136.911689763778
Winsorized Mean ( 13 / 20 )1.346988333333330.0096989195308505138.880246304633
Winsorized Mean ( 14 / 20 )1.342741666666670.00883279466164814152.017760867558
Winsorized Mean ( 15 / 20 )1.341016666666670.00826171798069065162.316926068029
Winsorized Mean ( 16 / 20 )1.340056666666670.00805166942954295166.432151542358
Winsorized Mean ( 17 / 20 )1.3371950.00722596519660861185.054171119948
Winsorized Mean ( 18 / 20 )1.3354850.00680285783458056196.312348791328
Winsorized Mean ( 19 / 20 )1.332508333333330.0060688485359077219.565264390642
Winsorized Mean ( 20 / 20 )1.328841666666670.00479920149412041276.888075713148
Trimmed Mean ( 1 / 20 )1.345924137931030.013665735875747098.488961748462
Trimmed Mean ( 2 / 20 )1.344694642857140.0132298998287289101.640576290466
Trimmed Mean ( 3 / 20 )1.343581481481480.0128384822021758104.652673137155
Trimmed Mean ( 4 / 20 )1.342242307692310.0123826111917376108.397355526105
Trimmed Mean ( 5 / 20 )1.3408380.0118247357100379113.392640045374
Trimmed Mean ( 6 / 20 )1.340431250.0115164845451558116.392397762026
Trimmed Mean ( 7 / 20 )1.339978260869570.0111960314367542119.683324259943
Trimmed Mean ( 8 / 20 )1.339565909090910.0108848901921206123.066552390267
Trimmed Mean ( 9 / 20 )1.339059523809520.0105834025491937126.524481855936
Trimmed Mean ( 10 / 20 )1.338540.0102128851495022131.063845368440
Trimmed Mean ( 11 / 20 )1.3380.00975819967421935137.115456197820
Trimmed Mean ( 12 / 20 )1.336708333333330.00945673303013121141.349906894304
Trimmed Mean ( 13 / 20 )1.335279411764710.00910426608530756146.665244540642
Trimmed Mean ( 14 / 20 )1.3335906250.00862608380214294154.599776165947
Trimmed Mean ( 15 / 20 )1.332283333333330.00823148159640965161.852191216031
Trimmed Mean ( 16 / 20 )1.331035714285710.00783609241224686169.859624448209
Trimmed Mean ( 17 / 20 )1.329734615384620.00729914208300736182.176836710753
Trimmed Mean ( 18 / 20 )1.32863750.0068059538419883195.216942525113
Trimmed Mean ( 19 / 20 )1.32760.00619108072306286214.437520585777
Trimmed Mean ( 20 / 20 )1.3268250.00554644445141494239.220821847682
Median1.3226
Midrange1.3778
Midmean - Weighted Average at Xnp1.33025483870968
Midmean - Weighted Average at X(n+1)p1.33228333333333
Midmean - Empirical Distribution Function1.33025483870968
Midmean - Empirical Distribution Function - Averaging1.33228333333333
Midmean - Empirical Distribution Function - Interpolation1.33228333333333
Midmean - Closest Observation1.33025483870968
Midmean - True Basic - Statistics Graphics Toolkit1.33228333333333
Midmean - MS Excel (old versions)1.333590625
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')