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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 computationMon, 02 Nov 2009 09:04:27 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/02/t12571779628eatj2ze0mlk102.htm/, Retrieved Sat, 04 May 2024 01:05:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=52739, Retrieved Sat, 04 May 2024 01:05:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMP       [Univariate Explorative Data Analysis] [workshop 3] [2009-10-19 08:29:32] [3e19a07d230ba260a720e0e03e0f40f2]
-             [Univariate Explorative Data Analysis] [Tijdreeks Worksho...] [2009-10-21 16:48:54] [436fa41bc7abf585320106c16117fff6]
- RMPD            [Central Tendency] [Workshop 3 Part 2...] [2009-11-02 16:04:27] [fd0d141bb5380cffe1d2cd25afb62297] [Current]
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Dataseries X:
25.6
23.7
22
21.3
20.7
20.4
20.3
20.4
19.8
19.5
23.1
23.5
23.5
22.9
21.9
21.5
20.5
20.2
19.4
19.2
18.8
18.8
22.6
23.3
23
21.4
19.9
18.8
18.6
18.4
18.6
19.9
19.2
18.4
21.1
20.5
19.1
18.1
17
17.1
17.4
16.8
15.3
14.3
13.4
15.3
22.1
23.7
22.2
19.5
16.6
17.3
19.8
21.2
21.5
20.6
19.1
19.6
23.5
24




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 4 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=52739&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=52739&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=52739&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 time4 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean20.08666666666670.32748370095005861.3363859281959
Geometric Mean19.9213092867914
Harmonic Mean19.746849908298
Quadratic Mean20.2435586463118
Winsorized Mean ( 1 / 20 )20.0750.31592948687636963.5426600995171
Winsorized Mean ( 2 / 20 )20.09833333333330.30424020084741666.0607417341706
Winsorized Mean ( 3 / 20 )20.09833333333330.30424020084741666.0607417341706
Winsorized Mean ( 4 / 20 )20.17166666666670.28053713276948571.9037314865607
Winsorized Mean ( 5 / 20 )20.18833333333330.27701079612103372.8792293153534
Winsorized Mean ( 6 / 20 )20.20833333333330.27294472512858374.0381896877225
Winsorized Mean ( 7 / 20 )20.19666666666670.26593791666080875.9450435660389
Winsorized Mean ( 8 / 20 )20.19666666666670.25553717284248879.0361200368912
Winsorized Mean ( 9 / 20 )20.19666666666670.24980180467639980.8507636397186
Winsorized Mean ( 10 / 20 )20.29666666666670.22583137885617889.8753165723381
Winsorized Mean ( 11 / 20 )20.29666666666670.20642185244689798.3261530989706
Winsorized Mean ( 12 / 20 )20.21666666666670.19182687973555105.390165833574
Winsorized Mean ( 13 / 20 )20.23833333333330.181240104606819111.665866543380
Winsorized Mean ( 14 / 20 )20.2150.177216790853609114.069326628867
Winsorized Mean ( 15 / 20 )20.240.165399704192277122.370230943527
Winsorized Mean ( 16 / 20 )20.13333333333330.147936210613041136.094694124594
Winsorized Mean ( 17 / 20 )20.13333333333330.147936210613041136.094694124594
Winsorized Mean ( 18 / 20 )20.19333333333330.129903629352766155.44856932747
Winsorized Mean ( 19 / 20 )20.16166666666670.124965343594981161.338064511803
Winsorized Mean ( 20 / 20 )20.16166666666670.115080214389266175.196638046472
Trimmed Mean ( 1 / 20 )20.10689655172410.3034970812646366.250708138416
Trimmed Mean ( 2 / 20 )20.14107142857140.2880608790466169.9194958205778
Trimmed Mean ( 3 / 20 )20.16481481481480.27690206710811172.8229118164793
Trimmed Mean ( 4 / 20 )20.19038461538460.26286304515503876.8095211081353
Trimmed Mean ( 5 / 20 )20.1960.25507037844325279.1781473147154
Trimmed Mean ( 6 / 20 )20.19791666666670.24638322769155181.977644565776
Trimmed Mean ( 7 / 20 )20.19565217391300.23654020956581885.3793619739463
Trimmed Mean ( 8 / 20 )20.19545454545450.22595707990768489.3773921742373
Trimmed Mean ( 9 / 20 )20.19523809523810.21524241205213493.8255518635732
Trimmed Mean ( 10 / 20 )20.1950.20270447100175899.6277975527479
Trimmed Mean ( 11 / 20 )20.17894736842110.193020385082569104.543089372602
Trimmed Mean ( 12 / 20 )20.16111111111110.185475698052066108.699475580092
Trimmed Mean ( 13 / 20 )20.15294117647060.179335041015813112.375925320103
Trimmed Mean ( 14 / 20 )20.1406250.173545765031832116.053681841823
Trimmed Mean ( 15 / 20 )20.130.166239682939748121.090221323966
Trimmed Mean ( 16 / 20 )20.11428571428570.159090860009220126.432692067414
Trimmed Mean ( 17 / 20 )20.11153846153850.154354927964682130.294113228054
Trimmed Mean ( 18 / 20 )20.10833333333330.146445402927669137.309419970424
Trimmed Mean ( 19 / 20 )20.09545454545450.140727434925016142.796993039503
Trimmed Mean ( 20 / 20 )20.0850.132838445608111151.198697847257
Median20.05
Midrange19.5
Midmean - Weighted Average at Xnp20.034375
Midmean - Weighted Average at X(n+1)p20.13
Midmean - Empirical Distribution Function20.034375
Midmean - Empirical Distribution Function - Averaging20.13
Midmean - Empirical Distribution Function - Interpolation20.13
Midmean - Closest Observation20.034375
Midmean - True Basic - Statistics Graphics Toolkit20.13
Midmean - MS Excel (old versions)20.0939393939394
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 20.0866666666667 & 0.327483700950058 & 61.3363859281959 \tabularnewline
Geometric Mean & 19.9213092867914 &  &  \tabularnewline
Harmonic Mean & 19.746849908298 &  &  \tabularnewline
Quadratic Mean & 20.2435586463118 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 20.075 & 0.315929486876369 & 63.5426600995171 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 20.0983333333333 & 0.304240200847416 & 66.0607417341706 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 20.0983333333333 & 0.304240200847416 & 66.0607417341706 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 20.1716666666667 & 0.280537132769485 & 71.9037314865607 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 20.1883333333333 & 0.277010796121033 & 72.8792293153534 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 20.2083333333333 & 0.272944725128583 & 74.0381896877225 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 20.1966666666667 & 0.265937916660808 & 75.9450435660389 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 20.1966666666667 & 0.255537172842488 & 79.0361200368912 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 20.1966666666667 & 0.249801804676399 & 80.8507636397186 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 20.2966666666667 & 0.225831378856178 & 89.8753165723381 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 20.2966666666667 & 0.206421852446897 & 98.3261530989706 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 20.2166666666667 & 0.19182687973555 & 105.390165833574 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 20.2383333333333 & 0.181240104606819 & 111.665866543380 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 20.215 & 0.177216790853609 & 114.069326628867 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 20.24 & 0.165399704192277 & 122.370230943527 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 20.1333333333333 & 0.147936210613041 & 136.094694124594 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 20.1333333333333 & 0.147936210613041 & 136.094694124594 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 20.1933333333333 & 0.129903629352766 & 155.44856932747 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 20.1616666666667 & 0.124965343594981 & 161.338064511803 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 20.1616666666667 & 0.115080214389266 & 175.196638046472 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 20.1068965517241 & 0.30349708126463 & 66.250708138416 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 20.1410714285714 & 0.28806087904661 & 69.9194958205778 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 20.1648148148148 & 0.276902067108111 & 72.8229118164793 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 20.1903846153846 & 0.262863045155038 & 76.8095211081353 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 20.196 & 0.255070378443252 & 79.1781473147154 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 20.1979166666667 & 0.246383227691551 & 81.977644565776 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 20.1956521739130 & 0.236540209565818 & 85.3793619739463 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 20.1954545454545 & 0.225957079907684 & 89.3773921742373 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 20.1952380952381 & 0.215242412052134 & 93.8255518635732 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 20.195 & 0.202704471001758 & 99.6277975527479 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 20.1789473684211 & 0.193020385082569 & 104.543089372602 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 20.1611111111111 & 0.185475698052066 & 108.699475580092 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 20.1529411764706 & 0.179335041015813 & 112.375925320103 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 20.140625 & 0.173545765031832 & 116.053681841823 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 20.13 & 0.166239682939748 & 121.090221323966 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 20.1142857142857 & 0.159090860009220 & 126.432692067414 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 20.1115384615385 & 0.154354927964682 & 130.294113228054 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 20.1083333333333 & 0.146445402927669 & 137.309419970424 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 20.0954545454545 & 0.140727434925016 & 142.796993039503 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 20.085 & 0.132838445608111 & 151.198697847257 \tabularnewline
Median & 20.05 &  &  \tabularnewline
Midrange & 19.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 20.034375 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 20.13 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 20.034375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 20.13 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 20.13 &  &  \tabularnewline
Midmean - Closest Observation & 20.034375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 20.13 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 20.0939393939394 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=52739&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]20.0866666666667[/C][C]0.327483700950058[/C][C]61.3363859281959[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]19.9213092867914[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]19.746849908298[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]20.2435586463118[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]20.075[/C][C]0.315929486876369[/C][C]63.5426600995171[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]20.0983333333333[/C][C]0.304240200847416[/C][C]66.0607417341706[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]20.0983333333333[/C][C]0.304240200847416[/C][C]66.0607417341706[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]20.1716666666667[/C][C]0.280537132769485[/C][C]71.9037314865607[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]20.1883333333333[/C][C]0.277010796121033[/C][C]72.8792293153534[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]20.2083333333333[/C][C]0.272944725128583[/C][C]74.0381896877225[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]20.1966666666667[/C][C]0.265937916660808[/C][C]75.9450435660389[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]20.1966666666667[/C][C]0.255537172842488[/C][C]79.0361200368912[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]20.1966666666667[/C][C]0.249801804676399[/C][C]80.8507636397186[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]20.2966666666667[/C][C]0.225831378856178[/C][C]89.8753165723381[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]20.2966666666667[/C][C]0.206421852446897[/C][C]98.3261530989706[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]20.2166666666667[/C][C]0.19182687973555[/C][C]105.390165833574[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]20.2383333333333[/C][C]0.181240104606819[/C][C]111.665866543380[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]20.215[/C][C]0.177216790853609[/C][C]114.069326628867[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]20.24[/C][C]0.165399704192277[/C][C]122.370230943527[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]20.1333333333333[/C][C]0.147936210613041[/C][C]136.094694124594[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]20.1333333333333[/C][C]0.147936210613041[/C][C]136.094694124594[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]20.1933333333333[/C][C]0.129903629352766[/C][C]155.44856932747[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]20.1616666666667[/C][C]0.124965343594981[/C][C]161.338064511803[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]20.1616666666667[/C][C]0.115080214389266[/C][C]175.196638046472[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]20.1068965517241[/C][C]0.30349708126463[/C][C]66.250708138416[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]20.1410714285714[/C][C]0.28806087904661[/C][C]69.9194958205778[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]20.1648148148148[/C][C]0.276902067108111[/C][C]72.8229118164793[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]20.1903846153846[/C][C]0.262863045155038[/C][C]76.8095211081353[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]20.196[/C][C]0.255070378443252[/C][C]79.1781473147154[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]20.1979166666667[/C][C]0.246383227691551[/C][C]81.977644565776[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]20.1956521739130[/C][C]0.236540209565818[/C][C]85.3793619739463[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]20.1954545454545[/C][C]0.225957079907684[/C][C]89.3773921742373[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]20.1952380952381[/C][C]0.215242412052134[/C][C]93.8255518635732[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]20.195[/C][C]0.202704471001758[/C][C]99.6277975527479[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]20.1789473684211[/C][C]0.193020385082569[/C][C]104.543089372602[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]20.1611111111111[/C][C]0.185475698052066[/C][C]108.699475580092[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]20.1529411764706[/C][C]0.179335041015813[/C][C]112.375925320103[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]20.140625[/C][C]0.173545765031832[/C][C]116.053681841823[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]20.13[/C][C]0.166239682939748[/C][C]121.090221323966[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]20.1142857142857[/C][C]0.159090860009220[/C][C]126.432692067414[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]20.1115384615385[/C][C]0.154354927964682[/C][C]130.294113228054[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]20.1083333333333[/C][C]0.146445402927669[/C][C]137.309419970424[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]20.0954545454545[/C][C]0.140727434925016[/C][C]142.796993039503[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]20.085[/C][C]0.132838445608111[/C][C]151.198697847257[/C][/ROW]
[ROW][C]Median[/C][C]20.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]20.034375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]20.13[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]20.034375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]20.13[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]20.13[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]20.034375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]20.13[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]20.0939393939394[/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=52739&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=52739&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 Mean20.08666666666670.32748370095005861.3363859281959
Geometric Mean19.9213092867914
Harmonic Mean19.746849908298
Quadratic Mean20.2435586463118
Winsorized Mean ( 1 / 20 )20.0750.31592948687636963.5426600995171
Winsorized Mean ( 2 / 20 )20.09833333333330.30424020084741666.0607417341706
Winsorized Mean ( 3 / 20 )20.09833333333330.30424020084741666.0607417341706
Winsorized Mean ( 4 / 20 )20.17166666666670.28053713276948571.9037314865607
Winsorized Mean ( 5 / 20 )20.18833333333330.27701079612103372.8792293153534
Winsorized Mean ( 6 / 20 )20.20833333333330.27294472512858374.0381896877225
Winsorized Mean ( 7 / 20 )20.19666666666670.26593791666080875.9450435660389
Winsorized Mean ( 8 / 20 )20.19666666666670.25553717284248879.0361200368912
Winsorized Mean ( 9 / 20 )20.19666666666670.24980180467639980.8507636397186
Winsorized Mean ( 10 / 20 )20.29666666666670.22583137885617889.8753165723381
Winsorized Mean ( 11 / 20 )20.29666666666670.20642185244689798.3261530989706
Winsorized Mean ( 12 / 20 )20.21666666666670.19182687973555105.390165833574
Winsorized Mean ( 13 / 20 )20.23833333333330.181240104606819111.665866543380
Winsorized Mean ( 14 / 20 )20.2150.177216790853609114.069326628867
Winsorized Mean ( 15 / 20 )20.240.165399704192277122.370230943527
Winsorized Mean ( 16 / 20 )20.13333333333330.147936210613041136.094694124594
Winsorized Mean ( 17 / 20 )20.13333333333330.147936210613041136.094694124594
Winsorized Mean ( 18 / 20 )20.19333333333330.129903629352766155.44856932747
Winsorized Mean ( 19 / 20 )20.16166666666670.124965343594981161.338064511803
Winsorized Mean ( 20 / 20 )20.16166666666670.115080214389266175.196638046472
Trimmed Mean ( 1 / 20 )20.10689655172410.3034970812646366.250708138416
Trimmed Mean ( 2 / 20 )20.14107142857140.2880608790466169.9194958205778
Trimmed Mean ( 3 / 20 )20.16481481481480.27690206710811172.8229118164793
Trimmed Mean ( 4 / 20 )20.19038461538460.26286304515503876.8095211081353
Trimmed Mean ( 5 / 20 )20.1960.25507037844325279.1781473147154
Trimmed Mean ( 6 / 20 )20.19791666666670.24638322769155181.977644565776
Trimmed Mean ( 7 / 20 )20.19565217391300.23654020956581885.3793619739463
Trimmed Mean ( 8 / 20 )20.19545454545450.22595707990768489.3773921742373
Trimmed Mean ( 9 / 20 )20.19523809523810.21524241205213493.8255518635732
Trimmed Mean ( 10 / 20 )20.1950.20270447100175899.6277975527479
Trimmed Mean ( 11 / 20 )20.17894736842110.193020385082569104.543089372602
Trimmed Mean ( 12 / 20 )20.16111111111110.185475698052066108.699475580092
Trimmed Mean ( 13 / 20 )20.15294117647060.179335041015813112.375925320103
Trimmed Mean ( 14 / 20 )20.1406250.173545765031832116.053681841823
Trimmed Mean ( 15 / 20 )20.130.166239682939748121.090221323966
Trimmed Mean ( 16 / 20 )20.11428571428570.159090860009220126.432692067414
Trimmed Mean ( 17 / 20 )20.11153846153850.154354927964682130.294113228054
Trimmed Mean ( 18 / 20 )20.10833333333330.146445402927669137.309419970424
Trimmed Mean ( 19 / 20 )20.09545454545450.140727434925016142.796993039503
Trimmed Mean ( 20 / 20 )20.0850.132838445608111151.198697847257
Median20.05
Midrange19.5
Midmean - Weighted Average at Xnp20.034375
Midmean - Weighted Average at X(n+1)p20.13
Midmean - Empirical Distribution Function20.034375
Midmean - Empirical Distribution Function - Averaging20.13
Midmean - Empirical Distribution Function - Interpolation20.13
Midmean - Closest Observation20.034375
Midmean - True Basic - Statistics Graphics Toolkit20.13
Midmean - MS Excel (old versions)20.0939393939394
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')