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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 31 May 2009 02:01:53 -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/2009/May/31/t1243757039xv82xkpt3mt4hjd.htm/, Retrieved Sun, 05 May 2024 23:50:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40809, Retrieved Sun, 05 May 2024 23:50:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opgave 5 - Sofie ...] [2009-05-31 08:01:53] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
30,06
30,46
30,46
30,49
30,49
30,5
30,5
30,5
30,51
30,51
30,61
30,88
30,95
31,09
31,28
31,31
31,32
31,34
31,34
31,34
31,34
31,36
31,36
31,36
31,72
32,07
32,13
32,19
32,26
32,27
32,28
32,28
32,28
32,29
32,61
32,68
32,69
32,74
32,86
32,86
32,9
32,95
32,95
32,96
32,99
33
33,06
33,42
33,48
33,5
33,51
33,52
33,55
33,56
33,56
33,56
33,6
33,61
33,62
33,72
33,83
33,96
34,06
34,11
34,11
34,21
34,19
34,17
34,12
34,15
34,15
34,15




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40809&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]3 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=40809&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40809&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean32.44166666666670.149925646673664216.385037426457
Geometric Mean32.4168913330953
Harmonic Mean32.3919517424162
Quadratic Mean32.4662540613755
Winsorized Mean ( 1 / 24 )32.44694444444440.148735099579700218.152571492096
Winsorized Mean ( 2 / 24 )32.44638888888890.148643883593361218.282704303200
Winsorized Mean ( 3 / 24 )32.44680555555550.148274613369354218.829136143017
Winsorized Mean ( 4 / 24 )32.44680555555560.148274613369354218.829136143017
Winsorized Mean ( 5 / 24 )32.44750.148145784002394219.024120183371
Winsorized Mean ( 6 / 24 )32.4450.147743856932686219.603039162450
Winsorized Mean ( 7 / 24 )32.44402777777780.147588950887887219.826942210757
Winsorized Mean ( 8 / 24 )32.44513888888890.147383145544506220.141446764626
Winsorized Mean ( 9 / 24 )32.43888888888890.146398543272942221.579314682186
Winsorized Mean ( 10 / 24 )32.43888888888890.141713683934275228.904421847742
Winsorized Mean ( 11 / 24 )32.46027777777780.131504471951639246.837824570065
Winsorized Mean ( 12 / 24 )32.45361111111110.126909408122234255.722657534209
Winsorized Mean ( 13 / 24 )32.46083333333330.120273838243752269.891057002329
Winsorized Mean ( 14 / 24 )32.49583333333330.114269769420625284.378217424389
Winsorized Mean ( 15 / 24 )32.50.113052330453513287.477488253672
Winsorized Mean ( 16 / 24 )32.49333333333330.111515032636467291.380745403714
Winsorized Mean ( 17 / 24 )32.49805555555560.110817604321596293.257156699085
Winsorized Mean ( 18 / 24 )32.49805555555560.110817604321596293.257156699085
Winsorized Mean ( 19 / 24 )32.49541666666670.110462099785607294.177068240928
Winsorized Mean ( 20 / 24 )32.48708333333330.109347445109414297.099610336818
Winsorized Mean ( 21 / 24 )32.490.108099241483878300.557150577654
Winsorized Mean ( 22 / 24 )32.48694444444440.107693785536712301.660344490072
Winsorized Mean ( 23 / 24 )32.48055555555560.106849697883288303.983597511282
Winsorized Mean ( 24 / 24 )32.58055555555560.0868936376274391374.947538682249
Trimmed Mean ( 1 / 24 )32.45042857142860.148213157969218218.944316523962
Trimmed Mean ( 2 / 24 )32.45411764705880.147493282728865220.037936959603
Trimmed Mean ( 3 / 24 )32.45833333333330.146593420468420221.417395334777
Trimmed Mean ( 4 / 24 )32.462656250.145580774875218222.987247305318
Trimmed Mean ( 5 / 24 )32.46725806451610.144265892612483225.051517559507
Trimmed Mean ( 6 / 24 )32.4720.142625066536425227.673863988746
Trimmed Mean ( 7 / 24 )32.47758620689660.140653412173359230.905071587364
Trimmed Mean ( 8 / 24 )32.483750.138200532471205235.047936640679
Trimmed Mean ( 9 / 24 )32.49018518518520.135159788640929240.383515777018
Trimmed Mean ( 10 / 24 )32.49807692307690.131551261582499247.037364234600
Trimmed Mean ( 11 / 24 )32.50660.128077020832412253.805091567008
Trimmed Mean ( 12 / 24 )32.51291666666670.125953793147623258.133684219896
Trimmed Mean ( 13 / 24 )32.52065217391300.124115188112434262.019924140574
Trimmed Mean ( 14 / 24 )32.52818181818180.123012002339548264.430959577383
Trimmed Mean ( 15 / 24 )32.53214285714290.122642003647078265.261018979757
Trimmed Mean ( 16 / 24 )32.5360.122123728768021266.418331050172
Trimmed Mean ( 17 / 24 )32.54105263157890.121447990655996267.942289170943
Trimmed Mean ( 18 / 24 )32.54611111111110.120370643060334270.382464392068
Trimmed Mean ( 19 / 24 )32.55176470588240.118564250043077274.549577077877
Trimmed Mean ( 20 / 24 )32.55843750.115816795482898281.120172288032
Trimmed Mean ( 21 / 24 )32.5670.111905286306985291.022891542946
Trimmed Mean ( 22 / 24 )32.57642857142860.106322876389984306.391528121764
Trimmed Mean ( 23 / 24 )32.58769230769230.0977458363343936333.392127273924
Trimmed Mean ( 24 / 24 )32.60166666666670.0840778337351997387.755787920804
Median32.685
Midrange32.135
Midmean - Weighted Average at Xnp32.5671794871795
Midmean - Weighted Average at X(n+1)p32.5671794871795
Midmean - Empirical Distribution Function32.5671794871795
Midmean - Empirical Distribution Function - Averaging32.5671794871795
Midmean - Empirical Distribution Function - Interpolation32.5671794871795
Midmean - Closest Observation32.5671794871795
Midmean - True Basic - Statistics Graphics Toolkit32.5671794871795
Midmean - MS Excel (old versions)32.5671794871795
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 32.4416666666667 & 0.149925646673664 & 216.385037426457 \tabularnewline
Geometric Mean & 32.4168913330953 &  &  \tabularnewline
Harmonic Mean & 32.3919517424162 &  &  \tabularnewline
Quadratic Mean & 32.4662540613755 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 32.4469444444444 & 0.148735099579700 & 218.152571492096 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 32.4463888888889 & 0.148643883593361 & 218.282704303200 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 32.4468055555555 & 0.148274613369354 & 218.829136143017 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 32.4468055555556 & 0.148274613369354 & 218.829136143017 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 32.4475 & 0.148145784002394 & 219.024120183371 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 32.445 & 0.147743856932686 & 219.603039162450 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 32.4440277777778 & 0.147588950887887 & 219.826942210757 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 32.4451388888889 & 0.147383145544506 & 220.141446764626 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 32.4388888888889 & 0.146398543272942 & 221.579314682186 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 32.4388888888889 & 0.141713683934275 & 228.904421847742 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 32.4602777777778 & 0.131504471951639 & 246.837824570065 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 32.4536111111111 & 0.126909408122234 & 255.722657534209 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 32.4608333333333 & 0.120273838243752 & 269.891057002329 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 32.4958333333333 & 0.114269769420625 & 284.378217424389 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 32.5 & 0.113052330453513 & 287.477488253672 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 32.4933333333333 & 0.111515032636467 & 291.380745403714 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 32.4980555555556 & 0.110817604321596 & 293.257156699085 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 32.4980555555556 & 0.110817604321596 & 293.257156699085 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 32.4954166666667 & 0.110462099785607 & 294.177068240928 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 32.4870833333333 & 0.109347445109414 & 297.099610336818 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 32.49 & 0.108099241483878 & 300.557150577654 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 32.4869444444444 & 0.107693785536712 & 301.660344490072 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 32.4805555555556 & 0.106849697883288 & 303.983597511282 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 32.5805555555556 & 0.0868936376274391 & 374.947538682249 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 32.4504285714286 & 0.148213157969218 & 218.944316523962 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 32.4541176470588 & 0.147493282728865 & 220.037936959603 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 32.4583333333333 & 0.146593420468420 & 221.417395334777 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 32.46265625 & 0.145580774875218 & 222.987247305318 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 32.4672580645161 & 0.144265892612483 & 225.051517559507 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 32.472 & 0.142625066536425 & 227.673863988746 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 32.4775862068966 & 0.140653412173359 & 230.905071587364 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 32.48375 & 0.138200532471205 & 235.047936640679 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 32.4901851851852 & 0.135159788640929 & 240.383515777018 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 32.4980769230769 & 0.131551261582499 & 247.037364234600 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 32.5066 & 0.128077020832412 & 253.805091567008 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 32.5129166666667 & 0.125953793147623 & 258.133684219896 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 32.5206521739130 & 0.124115188112434 & 262.019924140574 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 32.5281818181818 & 0.123012002339548 & 264.430959577383 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 32.5321428571429 & 0.122642003647078 & 265.261018979757 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 32.536 & 0.122123728768021 & 266.418331050172 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 32.5410526315789 & 0.121447990655996 & 267.942289170943 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 32.5461111111111 & 0.120370643060334 & 270.382464392068 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 32.5517647058824 & 0.118564250043077 & 274.549577077877 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 32.5584375 & 0.115816795482898 & 281.120172288032 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 32.567 & 0.111905286306985 & 291.022891542946 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 32.5764285714286 & 0.106322876389984 & 306.391528121764 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 32.5876923076923 & 0.0977458363343936 & 333.392127273924 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 32.6016666666667 & 0.0840778337351997 & 387.755787920804 \tabularnewline
Median & 32.685 &  &  \tabularnewline
Midrange & 32.135 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 32.5671794871795 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 32.5671794871795 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 32.5671794871795 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 32.5671794871795 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 32.5671794871795 &  &  \tabularnewline
Midmean - Closest Observation & 32.5671794871795 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 32.5671794871795 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 32.5671794871795 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40809&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]32.4416666666667[/C][C]0.149925646673664[/C][C]216.385037426457[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]32.4168913330953[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]32.3919517424162[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]32.4662540613755[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]32.4469444444444[/C][C]0.148735099579700[/C][C]218.152571492096[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]32.4463888888889[/C][C]0.148643883593361[/C][C]218.282704303200[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]32.4468055555555[/C][C]0.148274613369354[/C][C]218.829136143017[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]32.4468055555556[/C][C]0.148274613369354[/C][C]218.829136143017[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]32.4475[/C][C]0.148145784002394[/C][C]219.024120183371[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]32.445[/C][C]0.147743856932686[/C][C]219.603039162450[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]32.4440277777778[/C][C]0.147588950887887[/C][C]219.826942210757[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]32.4451388888889[/C][C]0.147383145544506[/C][C]220.141446764626[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]32.4388888888889[/C][C]0.146398543272942[/C][C]221.579314682186[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]32.4388888888889[/C][C]0.141713683934275[/C][C]228.904421847742[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]32.4602777777778[/C][C]0.131504471951639[/C][C]246.837824570065[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]32.4536111111111[/C][C]0.126909408122234[/C][C]255.722657534209[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]32.4608333333333[/C][C]0.120273838243752[/C][C]269.891057002329[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]32.4958333333333[/C][C]0.114269769420625[/C][C]284.378217424389[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]32.5[/C][C]0.113052330453513[/C][C]287.477488253672[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]32.4933333333333[/C][C]0.111515032636467[/C][C]291.380745403714[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]32.4980555555556[/C][C]0.110817604321596[/C][C]293.257156699085[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]32.4980555555556[/C][C]0.110817604321596[/C][C]293.257156699085[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]32.4954166666667[/C][C]0.110462099785607[/C][C]294.177068240928[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]32.4870833333333[/C][C]0.109347445109414[/C][C]297.099610336818[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]32.49[/C][C]0.108099241483878[/C][C]300.557150577654[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]32.4869444444444[/C][C]0.107693785536712[/C][C]301.660344490072[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]32.4805555555556[/C][C]0.106849697883288[/C][C]303.983597511282[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]32.5805555555556[/C][C]0.0868936376274391[/C][C]374.947538682249[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]32.4504285714286[/C][C]0.148213157969218[/C][C]218.944316523962[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]32.4541176470588[/C][C]0.147493282728865[/C][C]220.037936959603[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]32.4583333333333[/C][C]0.146593420468420[/C][C]221.417395334777[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]32.46265625[/C][C]0.145580774875218[/C][C]222.987247305318[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]32.4672580645161[/C][C]0.144265892612483[/C][C]225.051517559507[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]32.472[/C][C]0.142625066536425[/C][C]227.673863988746[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]32.4775862068966[/C][C]0.140653412173359[/C][C]230.905071587364[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]32.48375[/C][C]0.138200532471205[/C][C]235.047936640679[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]32.4901851851852[/C][C]0.135159788640929[/C][C]240.383515777018[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]32.4980769230769[/C][C]0.131551261582499[/C][C]247.037364234600[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]32.5066[/C][C]0.128077020832412[/C][C]253.805091567008[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]32.5129166666667[/C][C]0.125953793147623[/C][C]258.133684219896[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]32.5206521739130[/C][C]0.124115188112434[/C][C]262.019924140574[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]32.5281818181818[/C][C]0.123012002339548[/C][C]264.430959577383[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]32.5321428571429[/C][C]0.122642003647078[/C][C]265.261018979757[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]32.536[/C][C]0.122123728768021[/C][C]266.418331050172[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]32.5410526315789[/C][C]0.121447990655996[/C][C]267.942289170943[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]32.5461111111111[/C][C]0.120370643060334[/C][C]270.382464392068[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]32.5517647058824[/C][C]0.118564250043077[/C][C]274.549577077877[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]32.5584375[/C][C]0.115816795482898[/C][C]281.120172288032[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]32.567[/C][C]0.111905286306985[/C][C]291.022891542946[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]32.5764285714286[/C][C]0.106322876389984[/C][C]306.391528121764[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]32.5876923076923[/C][C]0.0977458363343936[/C][C]333.392127273924[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]32.6016666666667[/C][C]0.0840778337351997[/C][C]387.755787920804[/C][/ROW]
[ROW][C]Median[/C][C]32.685[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]32.135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]32.5671794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]32.5671794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]32.5671794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]32.5671794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]32.5671794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]32.5671794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]32.5671794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]32.5671794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40809&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40809&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 Mean32.44166666666670.149925646673664216.385037426457
Geometric Mean32.4168913330953
Harmonic Mean32.3919517424162
Quadratic Mean32.4662540613755
Winsorized Mean ( 1 / 24 )32.44694444444440.148735099579700218.152571492096
Winsorized Mean ( 2 / 24 )32.44638888888890.148643883593361218.282704303200
Winsorized Mean ( 3 / 24 )32.44680555555550.148274613369354218.829136143017
Winsorized Mean ( 4 / 24 )32.44680555555560.148274613369354218.829136143017
Winsorized Mean ( 5 / 24 )32.44750.148145784002394219.024120183371
Winsorized Mean ( 6 / 24 )32.4450.147743856932686219.603039162450
Winsorized Mean ( 7 / 24 )32.44402777777780.147588950887887219.826942210757
Winsorized Mean ( 8 / 24 )32.44513888888890.147383145544506220.141446764626
Winsorized Mean ( 9 / 24 )32.43888888888890.146398543272942221.579314682186
Winsorized Mean ( 10 / 24 )32.43888888888890.141713683934275228.904421847742
Winsorized Mean ( 11 / 24 )32.46027777777780.131504471951639246.837824570065
Winsorized Mean ( 12 / 24 )32.45361111111110.126909408122234255.722657534209
Winsorized Mean ( 13 / 24 )32.46083333333330.120273838243752269.891057002329
Winsorized Mean ( 14 / 24 )32.49583333333330.114269769420625284.378217424389
Winsorized Mean ( 15 / 24 )32.50.113052330453513287.477488253672
Winsorized Mean ( 16 / 24 )32.49333333333330.111515032636467291.380745403714
Winsorized Mean ( 17 / 24 )32.49805555555560.110817604321596293.257156699085
Winsorized Mean ( 18 / 24 )32.49805555555560.110817604321596293.257156699085
Winsorized Mean ( 19 / 24 )32.49541666666670.110462099785607294.177068240928
Winsorized Mean ( 20 / 24 )32.48708333333330.109347445109414297.099610336818
Winsorized Mean ( 21 / 24 )32.490.108099241483878300.557150577654
Winsorized Mean ( 22 / 24 )32.48694444444440.107693785536712301.660344490072
Winsorized Mean ( 23 / 24 )32.48055555555560.106849697883288303.983597511282
Winsorized Mean ( 24 / 24 )32.58055555555560.0868936376274391374.947538682249
Trimmed Mean ( 1 / 24 )32.45042857142860.148213157969218218.944316523962
Trimmed Mean ( 2 / 24 )32.45411764705880.147493282728865220.037936959603
Trimmed Mean ( 3 / 24 )32.45833333333330.146593420468420221.417395334777
Trimmed Mean ( 4 / 24 )32.462656250.145580774875218222.987247305318
Trimmed Mean ( 5 / 24 )32.46725806451610.144265892612483225.051517559507
Trimmed Mean ( 6 / 24 )32.4720.142625066536425227.673863988746
Trimmed Mean ( 7 / 24 )32.47758620689660.140653412173359230.905071587364
Trimmed Mean ( 8 / 24 )32.483750.138200532471205235.047936640679
Trimmed Mean ( 9 / 24 )32.49018518518520.135159788640929240.383515777018
Trimmed Mean ( 10 / 24 )32.49807692307690.131551261582499247.037364234600
Trimmed Mean ( 11 / 24 )32.50660.128077020832412253.805091567008
Trimmed Mean ( 12 / 24 )32.51291666666670.125953793147623258.133684219896
Trimmed Mean ( 13 / 24 )32.52065217391300.124115188112434262.019924140574
Trimmed Mean ( 14 / 24 )32.52818181818180.123012002339548264.430959577383
Trimmed Mean ( 15 / 24 )32.53214285714290.122642003647078265.261018979757
Trimmed Mean ( 16 / 24 )32.5360.122123728768021266.418331050172
Trimmed Mean ( 17 / 24 )32.54105263157890.121447990655996267.942289170943
Trimmed Mean ( 18 / 24 )32.54611111111110.120370643060334270.382464392068
Trimmed Mean ( 19 / 24 )32.55176470588240.118564250043077274.549577077877
Trimmed Mean ( 20 / 24 )32.55843750.115816795482898281.120172288032
Trimmed Mean ( 21 / 24 )32.5670.111905286306985291.022891542946
Trimmed Mean ( 22 / 24 )32.57642857142860.106322876389984306.391528121764
Trimmed Mean ( 23 / 24 )32.58769230769230.0977458363343936333.392127273924
Trimmed Mean ( 24 / 24 )32.60166666666670.0840778337351997387.755787920804
Median32.685
Midrange32.135
Midmean - Weighted Average at Xnp32.5671794871795
Midmean - Weighted Average at X(n+1)p32.5671794871795
Midmean - Empirical Distribution Function32.5671794871795
Midmean - Empirical Distribution Function - Averaging32.5671794871795
Midmean - Empirical Distribution Function - Interpolation32.5671794871795
Midmean - Closest Observation32.5671794871795
Midmean - True Basic - Statistics Graphics Toolkit32.5671794871795
Midmean - MS Excel (old versions)32.5671794871795
Number of observations72



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')