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of Irreproducible Research!

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, 20 Oct 2008 14:07:38 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224533305n06nz1a8y5dcw60.htm/, Retrieved Sun, 19 May 2024 14:46:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18050, Retrieved Sun, 19 May 2024 14:46:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact168
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Werkloosheid BELGIE] [2008-10-19 10:57:42] [46c5a5fbda57fdfa1d4ef48658f82a0c]
- RMP   [Histogram] [Histogram - Werkl...] [2008-10-19 11:37:28] [46c5a5fbda57fdfa1d4ef48658f82a0c]
- RM      [Central Tendency] [] [2008-10-19 12:22:19] [46c5a5fbda57fdfa1d4ef48658f82a0c]
F   PD        [Central Tendency] [Voorspelling tijd...] [2008-10-20 20:07:38] [96c9291ce335a5c9abba7b920811c2df] [Current]
Feedback Forum
2008-10-26 12:40:40 [Julie Leurentop] [reply
Aan de hand van deze grafieken kunnen we besluiten dat de werkloosheid vrij constant, licht stijgend verloopt.
2008-10-27 10:57:54 [Karen Van den Broeck] [reply
We kunnen op deze grafieken zien dat de werkloosheid vrij constant is.

Post a new message
Dataseries X:
23
23
19
11
13
8
0
2
7
5
9
6
10
11
16
14
14
9
17
16
21
41
14
13
19
18
27
26
30
27
33
26
26
35
39
37
39
40
44
45
46
34
34
39
40
41
40
41
32
30
33
30
40
39
36
34
35
41
44
59




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18050&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18050&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18050&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean26.68333333333331.7552973361313315.2016030470047
Geometric Mean0
Harmonic Mean0
Quadratic Mean29.8962093472288
Winsorized Mean ( 1 / 20 )26.51.6917045861437115.6646734997672
Winsorized Mean ( 2 / 20 )26.56666666666671.6620331070602115.9844389102799
Winsorized Mean ( 3 / 20 )26.56666666666671.6420269041793916.1791908518962
Winsorized Mean ( 4 / 20 )26.63333333333331.6281365499353616.3581693036685
Winsorized Mean ( 5 / 20 )26.46666666666671.5690269514536516.868203979636
Winsorized Mean ( 6 / 20 )26.56666666666671.5494425217026517.1459517178302
Winsorized Mean ( 7 / 20 )26.56666666666671.5494425217026517.1459517178302
Winsorized Mean ( 8 / 20 )26.71.5242484486898217.5168293744699
Winsorized Mean ( 9 / 20 )26.71.4733604312767418.1218386439652
Winsorized Mean ( 10 / 20 )26.71.4733604312767418.1218386439652
Winsorized Mean ( 11 / 20 )27.06666666666671.4091842947776019.2073292095115
Winsorized Mean ( 12 / 20 )27.06666666666671.4091842947776019.2073292095115
Winsorized Mean ( 13 / 20 )27.06666666666671.3397163597830820.2032814401469
Winsorized Mean ( 14 / 20 )27.06666666666671.3397163597830820.2032814401469
Winsorized Mean ( 15 / 20 )27.06666666666671.3397163597830820.2032814401469
Winsorized Mean ( 16 / 20 )27.61.2537401671716822.0141307766051
Winsorized Mean ( 17 / 20 )27.03333333333331.1690371398184723.1244435378084
Winsorized Mean ( 18 / 20 )27.03333333333331.0785443911895725.0646459748562
Winsorized Mean ( 19 / 20 )27.03333333333330.98490490139070227.447658444142
Winsorized Mean ( 20 / 20 )27.36666666666670.93366620375681629.3109749036119
Trimmed Mean ( 1 / 20 )26.58620689655171.6636453830463815.9806934623703
Trimmed Mean ( 2 / 20 )26.67857142857141.6285016503620516.3822808669799
Trimmed Mean ( 3 / 20 )26.74074074074071.6038879180474016.6724497640056
Trimmed Mean ( 4 / 20 )26.80769230769231.5816248927324916.9494628156605
Trimmed Mean ( 5 / 20 )26.861.5578661491846817.2415326015379
Trimmed Mean ( 6 / 20 )26.95833333333331.5456867271956617.4410071970041
Trimmed Mean ( 7 / 20 )27.04347826086961.5338236524612017.6314129838037
Trimmed Mean ( 8 / 20 )27.13636363636361.5161536502665617.8981619914266
Trimmed Mean ( 9 / 20 )27.21428571428571.4977860991937818.1696743806973
Trimmed Mean ( 10 / 20 )27.31.4841901875502718.3938690802558
Trimmed Mean ( 11 / 20 )27.39473684210531.4629319698269318.7259130343198
Trimmed Mean ( 12 / 20 )27.44444444444441.4482854912611418.9496094589377
Trimmed Mean ( 13 / 20 )27.51.4244178220969119.30613305548
Trimmed Mean ( 14 / 20 )27.56251.4063060024691119.5992194811139
Trimmed Mean ( 15 / 20 )27.63333333333331.3758870353701320.0840131660224
Trimmed Mean ( 16 / 20 )27.71428571428571.3272252382152020.8813733466632
Trimmed Mean ( 17 / 20 )27.73076923076921.2812946485221021.6427730052218
Trimmed Mean ( 18 / 20 )27.83333333333331.2360330811826122.5182754062723
Trimmed Mean ( 19 / 20 )27.95454545454551.1942815999356723.4069966882612
Trimmed Mean ( 20 / 20 )28.11.1582654908821324.2604137144751
Median28.5
Midrange29.5
Midmean - Weighted Average at Xnp27.5
Midmean - Weighted Average at X(n+1)p27.5
Midmean - Empirical Distribution Function27.5
Midmean - Empirical Distribution Function - Averaging27.5
Midmean - Empirical Distribution Function - Interpolation27.5
Midmean - Closest Observation27.5
Midmean - True Basic - Statistics Graphics Toolkit27.5
Midmean - MS Excel (old versions)27.5
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 26.6833333333333 & 1.75529733613133 & 15.2016030470047 \tabularnewline
Geometric Mean & 0 &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 29.8962093472288 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 26.5 & 1.69170458614371 & 15.6646734997672 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 26.5666666666667 & 1.66203310706021 & 15.9844389102799 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 26.5666666666667 & 1.64202690417939 & 16.1791908518962 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 26.6333333333333 & 1.62813654993536 & 16.3581693036685 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 26.4666666666667 & 1.56902695145365 & 16.868203979636 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 26.5666666666667 & 1.54944252170265 & 17.1459517178302 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 26.5666666666667 & 1.54944252170265 & 17.1459517178302 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 26.7 & 1.52424844868982 & 17.5168293744699 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 26.7 & 1.47336043127674 & 18.1218386439652 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 26.7 & 1.47336043127674 & 18.1218386439652 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 27.0666666666667 & 1.40918429477760 & 19.2073292095115 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 27.0666666666667 & 1.40918429477760 & 19.2073292095115 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 27.0666666666667 & 1.33971635978308 & 20.2032814401469 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 27.0666666666667 & 1.33971635978308 & 20.2032814401469 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 27.0666666666667 & 1.33971635978308 & 20.2032814401469 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 27.6 & 1.25374016717168 & 22.0141307766051 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 27.0333333333333 & 1.16903713981847 & 23.1244435378084 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 27.0333333333333 & 1.07854439118957 & 25.0646459748562 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 27.0333333333333 & 0.984904901390702 & 27.447658444142 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 27.3666666666667 & 0.933666203756816 & 29.3109749036119 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 26.5862068965517 & 1.66364538304638 & 15.9806934623703 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 26.6785714285714 & 1.62850165036205 & 16.3822808669799 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 26.7407407407407 & 1.60388791804740 & 16.6724497640056 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 26.8076923076923 & 1.58162489273249 & 16.9494628156605 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 26.86 & 1.55786614918468 & 17.2415326015379 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 26.9583333333333 & 1.54568672719566 & 17.4410071970041 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 27.0434782608696 & 1.53382365246120 & 17.6314129838037 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 27.1363636363636 & 1.51615365026656 & 17.8981619914266 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 27.2142857142857 & 1.49778609919378 & 18.1696743806973 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 27.3 & 1.48419018755027 & 18.3938690802558 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 27.3947368421053 & 1.46293196982693 & 18.7259130343198 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 27.4444444444444 & 1.44828549126114 & 18.9496094589377 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 27.5 & 1.42441782209691 & 19.30613305548 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 27.5625 & 1.40630600246911 & 19.5992194811139 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 27.6333333333333 & 1.37588703537013 & 20.0840131660224 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 27.7142857142857 & 1.32722523821520 & 20.8813733466632 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 27.7307692307692 & 1.28129464852210 & 21.6427730052218 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 27.8333333333333 & 1.23603308118261 & 22.5182754062723 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 27.9545454545455 & 1.19428159993567 & 23.4069966882612 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 28.1 & 1.15826549088213 & 24.2604137144751 \tabularnewline
Median & 28.5 &  &  \tabularnewline
Midrange & 29.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 27.5 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 27.5 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 27.5 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 27.5 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 27.5 &  &  \tabularnewline
Midmean - Closest Observation & 27.5 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 27.5 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 27.5 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18050&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]26.6833333333333[/C][C]1.75529733613133[/C][C]15.2016030470047[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]29.8962093472288[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]26.5[/C][C]1.69170458614371[/C][C]15.6646734997672[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]26.5666666666667[/C][C]1.66203310706021[/C][C]15.9844389102799[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]26.5666666666667[/C][C]1.64202690417939[/C][C]16.1791908518962[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]26.6333333333333[/C][C]1.62813654993536[/C][C]16.3581693036685[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]26.4666666666667[/C][C]1.56902695145365[/C][C]16.868203979636[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]26.5666666666667[/C][C]1.54944252170265[/C][C]17.1459517178302[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]26.5666666666667[/C][C]1.54944252170265[/C][C]17.1459517178302[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]26.7[/C][C]1.52424844868982[/C][C]17.5168293744699[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]26.7[/C][C]1.47336043127674[/C][C]18.1218386439652[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]26.7[/C][C]1.47336043127674[/C][C]18.1218386439652[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]27.0666666666667[/C][C]1.40918429477760[/C][C]19.2073292095115[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]27.0666666666667[/C][C]1.40918429477760[/C][C]19.2073292095115[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]27.0666666666667[/C][C]1.33971635978308[/C][C]20.2032814401469[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]27.0666666666667[/C][C]1.33971635978308[/C][C]20.2032814401469[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]27.0666666666667[/C][C]1.33971635978308[/C][C]20.2032814401469[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]27.6[/C][C]1.25374016717168[/C][C]22.0141307766051[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]27.0333333333333[/C][C]1.16903713981847[/C][C]23.1244435378084[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]27.0333333333333[/C][C]1.07854439118957[/C][C]25.0646459748562[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]27.0333333333333[/C][C]0.984904901390702[/C][C]27.447658444142[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]27.3666666666667[/C][C]0.933666203756816[/C][C]29.3109749036119[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]26.5862068965517[/C][C]1.66364538304638[/C][C]15.9806934623703[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]26.6785714285714[/C][C]1.62850165036205[/C][C]16.3822808669799[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]26.7407407407407[/C][C]1.60388791804740[/C][C]16.6724497640056[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]26.8076923076923[/C][C]1.58162489273249[/C][C]16.9494628156605[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]26.86[/C][C]1.55786614918468[/C][C]17.2415326015379[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]26.9583333333333[/C][C]1.54568672719566[/C][C]17.4410071970041[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]27.0434782608696[/C][C]1.53382365246120[/C][C]17.6314129838037[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]27.1363636363636[/C][C]1.51615365026656[/C][C]17.8981619914266[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]27.2142857142857[/C][C]1.49778609919378[/C][C]18.1696743806973[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]27.3[/C][C]1.48419018755027[/C][C]18.3938690802558[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]27.3947368421053[/C][C]1.46293196982693[/C][C]18.7259130343198[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]27.4444444444444[/C][C]1.44828549126114[/C][C]18.9496094589377[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]27.5[/C][C]1.42441782209691[/C][C]19.30613305548[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]27.5625[/C][C]1.40630600246911[/C][C]19.5992194811139[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]27.6333333333333[/C][C]1.37588703537013[/C][C]20.0840131660224[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]27.7142857142857[/C][C]1.32722523821520[/C][C]20.8813733466632[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]27.7307692307692[/C][C]1.28129464852210[/C][C]21.6427730052218[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]27.8333333333333[/C][C]1.23603308118261[/C][C]22.5182754062723[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]27.9545454545455[/C][C]1.19428159993567[/C][C]23.4069966882612[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]28.1[/C][C]1.15826549088213[/C][C]24.2604137144751[/C][/ROW]
[ROW][C]Median[/C][C]28.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]29.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]27.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]27.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]27.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]27.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]27.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]27.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]27.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]27.5[/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=18050&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18050&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 Mean26.68333333333331.7552973361313315.2016030470047
Geometric Mean0
Harmonic Mean0
Quadratic Mean29.8962093472288
Winsorized Mean ( 1 / 20 )26.51.6917045861437115.6646734997672
Winsorized Mean ( 2 / 20 )26.56666666666671.6620331070602115.9844389102799
Winsorized Mean ( 3 / 20 )26.56666666666671.6420269041793916.1791908518962
Winsorized Mean ( 4 / 20 )26.63333333333331.6281365499353616.3581693036685
Winsorized Mean ( 5 / 20 )26.46666666666671.5690269514536516.868203979636
Winsorized Mean ( 6 / 20 )26.56666666666671.5494425217026517.1459517178302
Winsorized Mean ( 7 / 20 )26.56666666666671.5494425217026517.1459517178302
Winsorized Mean ( 8 / 20 )26.71.5242484486898217.5168293744699
Winsorized Mean ( 9 / 20 )26.71.4733604312767418.1218386439652
Winsorized Mean ( 10 / 20 )26.71.4733604312767418.1218386439652
Winsorized Mean ( 11 / 20 )27.06666666666671.4091842947776019.2073292095115
Winsorized Mean ( 12 / 20 )27.06666666666671.4091842947776019.2073292095115
Winsorized Mean ( 13 / 20 )27.06666666666671.3397163597830820.2032814401469
Winsorized Mean ( 14 / 20 )27.06666666666671.3397163597830820.2032814401469
Winsorized Mean ( 15 / 20 )27.06666666666671.3397163597830820.2032814401469
Winsorized Mean ( 16 / 20 )27.61.2537401671716822.0141307766051
Winsorized Mean ( 17 / 20 )27.03333333333331.1690371398184723.1244435378084
Winsorized Mean ( 18 / 20 )27.03333333333331.0785443911895725.0646459748562
Winsorized Mean ( 19 / 20 )27.03333333333330.98490490139070227.447658444142
Winsorized Mean ( 20 / 20 )27.36666666666670.93366620375681629.3109749036119
Trimmed Mean ( 1 / 20 )26.58620689655171.6636453830463815.9806934623703
Trimmed Mean ( 2 / 20 )26.67857142857141.6285016503620516.3822808669799
Trimmed Mean ( 3 / 20 )26.74074074074071.6038879180474016.6724497640056
Trimmed Mean ( 4 / 20 )26.80769230769231.5816248927324916.9494628156605
Trimmed Mean ( 5 / 20 )26.861.5578661491846817.2415326015379
Trimmed Mean ( 6 / 20 )26.95833333333331.5456867271956617.4410071970041
Trimmed Mean ( 7 / 20 )27.04347826086961.5338236524612017.6314129838037
Trimmed Mean ( 8 / 20 )27.13636363636361.5161536502665617.8981619914266
Trimmed Mean ( 9 / 20 )27.21428571428571.4977860991937818.1696743806973
Trimmed Mean ( 10 / 20 )27.31.4841901875502718.3938690802558
Trimmed Mean ( 11 / 20 )27.39473684210531.4629319698269318.7259130343198
Trimmed Mean ( 12 / 20 )27.44444444444441.4482854912611418.9496094589377
Trimmed Mean ( 13 / 20 )27.51.4244178220969119.30613305548
Trimmed Mean ( 14 / 20 )27.56251.4063060024691119.5992194811139
Trimmed Mean ( 15 / 20 )27.63333333333331.3758870353701320.0840131660224
Trimmed Mean ( 16 / 20 )27.71428571428571.3272252382152020.8813733466632
Trimmed Mean ( 17 / 20 )27.73076923076921.2812946485221021.6427730052218
Trimmed Mean ( 18 / 20 )27.83333333333331.2360330811826122.5182754062723
Trimmed Mean ( 19 / 20 )27.95454545454551.1942815999356723.4069966882612
Trimmed Mean ( 20 / 20 )28.11.1582654908821324.2604137144751
Median28.5
Midrange29.5
Midmean - Weighted Average at Xnp27.5
Midmean - Weighted Average at X(n+1)p27.5
Midmean - Empirical Distribution Function27.5
Midmean - Empirical Distribution Function - Averaging27.5
Midmean - Empirical Distribution Function - Interpolation27.5
Midmean - Closest Observation27.5
Midmean - True Basic - Statistics Graphics Toolkit27.5
Midmean - MS Excel (old versions)27.5
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')