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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 22 May 2013 06:47:21 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/22/t1369219704tu3rjfhbrqzd8w8.htm/, Retrieved Sat, 27 Apr 2024 23:41:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=209436, Retrieved Sat, 27 Apr 2024 23:41:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-05-22 10:47:21] [5b48cba8ffed7710e2defc0d8d22bd89] [Current]
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Dataseries X:
13,29
13,34
13,41
13,45
13,52
13,52
13,53
13,55
13,52
13,51
13,55
13,56
13,62
13,69
13,67
13,66
13,69
13,69
13,7
13,73
13,79
13,8
13,84
13,84
13,88
13,97
14,06
14,11
14,13
14,15
14,2
14,28
14,3
14,33
14,4
14,4
14,42
14,51
14,64
14,68
14,72
14,73
14,76
14,78
14,83
14,84
14,85
14,87
14,87
14,96
15,08
15,08
15,12
15,12
15,1
15,16
15,22
15,28
15,29
15,32
15,4
15,44
15,48
15,52
15,6
15,61
15,66
15,69
15,75
15,82
15,81
15,82




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209436&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209436&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209436&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 Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean14.47930555555560.0914515885658007158.327545564039
Geometric Mean14.458881547723
Harmonic Mean14.4385625464322
Quadratic Mean14.4997962150431
Winsorized Mean ( 1 / 24 )14.480.0913269419647811158.551241161496
Winsorized Mean ( 2 / 24 )14.48166666666670.090937346227868159.248837439999
Winsorized Mean ( 3 / 24 )14.48083333333330.0901597760160683160.61301362098
Winsorized Mean ( 4 / 24 )14.48083333333330.0889857099357529162.732121188766
Winsorized Mean ( 5 / 24 )14.47944444444440.088484211850627163.638734431942
Winsorized Mean ( 6 / 24 )14.47527777777780.0877130699371657165.02988423672
Winsorized Mean ( 7 / 24 )14.47430555555560.0875364503530407165.351753437336
Winsorized Mean ( 8 / 24 )14.46652777777780.0857917100687407168.623842165944
Winsorized Mean ( 9 / 24 )14.46402777777780.0845536609815119171.063294124431
Winsorized Mean ( 10 / 24 )14.45847222222220.083624294800244172.89798684413
Winsorized Mean ( 11 / 24 )14.45388888888890.0823912845498792175.429828140846
Winsorized Mean ( 12 / 24 )14.45055555555560.0787686160247679183.455750333505
Winsorized Mean ( 13 / 24 )14.45236111111110.0768711533652313188.007600750373
Winsorized Mean ( 14 / 24 )14.45236111111110.0762918201731662189.435264204044
Winsorized Mean ( 15 / 24 )14.44402777777780.0738102449413556195.691367631336
Winsorized Mean ( 16 / 24 )14.43069444444440.0718698197123159200.78935083194
Winsorized Mean ( 17 / 24 )14.421250.0705358812507398204.452680597207
Winsorized Mean ( 18 / 24 )14.423750.0701717760175148205.549165470742
Winsorized Mean ( 19 / 24 )14.42638888888890.0682927583520507211.243318281574
Winsorized Mean ( 20 / 24 )14.43750.0651571322107893221.579733639801
Winsorized Mean ( 21 / 24 )14.44041666666670.0647498610278809223.018496679842
Winsorized Mean ( 22 / 24 )14.41597222222220.0580680283828781248.260060203334
Winsorized Mean ( 23 / 24 )14.38722222222220.0543701386840711264.616250214518
Winsorized Mean ( 24 / 24 )14.40055555555560.0524937170727712274.32912658085
Trimmed Mean ( 1 / 24 )14.47714285714290.0904800042783421160.003781748364
Trimmed Mean ( 2 / 24 )14.47411764705880.089438359567721161.833442798102
Trimmed Mean ( 3 / 24 )14.470.0884025545728835163.683052711675
Trimmed Mean ( 4 / 24 )14.46593750.0874667506980714165.387846062046
Trimmed Mean ( 5 / 24 )14.46161290322580.0867066492382515166.787818815237
Trimmed Mean ( 6 / 24 )14.45733333333330.0858809011958256168.341658413292
Trimmed Mean ( 7 / 24 )14.45362068965520.0850275562164649169.987487972239
Trimmed Mean ( 8 / 24 )14.44982142857140.0839656280447536172.092102030961
Trimmed Mean ( 9 / 24 )14.4470370370370.083013907563918174.031526294715
Trimmed Mean ( 10 / 24 )14.44442307692310.082043293881986176.058546572989
Trimmed Mean ( 11 / 24 )14.44240.0809623545676807178.384140099666
Trimmed Mean ( 12 / 24 )14.44083333333330.0797929686670434180.978770116843
Trimmed Mean ( 13 / 24 )14.43956521739130.0789942555984885182.792598119851
Trimmed Mean ( 14 / 24 )14.43795454545450.0782536529589658184.501988080038
Trimmed Mean ( 15 / 24 )14.43619047619050.0772907631295698186.777693629312
Trimmed Mean ( 16 / 24 )14.435250.0764425270114577188.837948774723
Trimmed Mean ( 17 / 24 )14.43578947368420.0755968490192718190.957555254771
Trimmed Mean ( 18 / 24 )14.43750.0745924109931954193.55186147981
Trimmed Mean ( 19 / 24 )14.43911764705880.0731325654520645197.437592374947
Trimmed Mean ( 20 / 24 )14.4406250.0714283104113894202.169488775943
Trimmed Mean ( 21 / 24 )14.4410.0697208720542134207.125923335712
Trimmed Mean ( 22 / 24 )14.44107142857140.0671595653532907215.026278871887
Trimmed Mean ( 23 / 24 )14.44423076923080.0653868325415942220.904273961312
Trimmed Mean ( 24 / 24 )14.45166666666670.0635788528632041227.303042062756
Median14.41
Midrange14.555
Midmean - Weighted Average at Xnp14.3985
Midmean - Weighted Average at X(n+1)p14.4559459459459
Midmean - Empirical Distribution Function14.3985
Midmean - Empirical Distribution Function - Averaging14.4559459459459
Midmean - Empirical Distribution Function - Interpolation14.4559459459459
Midmean - Closest Observation14.3985
Midmean - True Basic - Statistics Graphics Toolkit14.4559459459459
Midmean - MS Excel (old versions)14.3985
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 14.4793055555556 & 0.0914515885658007 & 158.327545564039 \tabularnewline
Geometric Mean & 14.458881547723 &  &  \tabularnewline
Harmonic Mean & 14.4385625464322 &  &  \tabularnewline
Quadratic Mean & 14.4997962150431 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 14.48 & 0.0913269419647811 & 158.551241161496 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 14.4816666666667 & 0.090937346227868 & 159.248837439999 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 14.4808333333333 & 0.0901597760160683 & 160.61301362098 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 14.4808333333333 & 0.0889857099357529 & 162.732121188766 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 14.4794444444444 & 0.088484211850627 & 163.638734431942 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 14.4752777777778 & 0.0877130699371657 & 165.02988423672 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 14.4743055555556 & 0.0875364503530407 & 165.351753437336 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 14.4665277777778 & 0.0857917100687407 & 168.623842165944 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 14.4640277777778 & 0.0845536609815119 & 171.063294124431 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 14.4584722222222 & 0.083624294800244 & 172.89798684413 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 14.4538888888889 & 0.0823912845498792 & 175.429828140846 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 14.4505555555556 & 0.0787686160247679 & 183.455750333505 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 14.4523611111111 & 0.0768711533652313 & 188.007600750373 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 14.4523611111111 & 0.0762918201731662 & 189.435264204044 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 14.4440277777778 & 0.0738102449413556 & 195.691367631336 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 14.4306944444444 & 0.0718698197123159 & 200.78935083194 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 14.42125 & 0.0705358812507398 & 204.452680597207 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 14.42375 & 0.0701717760175148 & 205.549165470742 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 14.4263888888889 & 0.0682927583520507 & 211.243318281574 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 14.4375 & 0.0651571322107893 & 221.579733639801 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 14.4404166666667 & 0.0647498610278809 & 223.018496679842 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 14.4159722222222 & 0.0580680283828781 & 248.260060203334 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 14.3872222222222 & 0.0543701386840711 & 264.616250214518 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 14.4005555555556 & 0.0524937170727712 & 274.32912658085 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 14.4771428571429 & 0.0904800042783421 & 160.003781748364 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 14.4741176470588 & 0.089438359567721 & 161.833442798102 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 14.47 & 0.0884025545728835 & 163.683052711675 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 14.4659375 & 0.0874667506980714 & 165.387846062046 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 14.4616129032258 & 0.0867066492382515 & 166.787818815237 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 14.4573333333333 & 0.0858809011958256 & 168.341658413292 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 14.4536206896552 & 0.0850275562164649 & 169.987487972239 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 14.4498214285714 & 0.0839656280447536 & 172.092102030961 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 14.447037037037 & 0.083013907563918 & 174.031526294715 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 14.4444230769231 & 0.082043293881986 & 176.058546572989 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 14.4424 & 0.0809623545676807 & 178.384140099666 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 14.4408333333333 & 0.0797929686670434 & 180.978770116843 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 14.4395652173913 & 0.0789942555984885 & 182.792598119851 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 14.4379545454545 & 0.0782536529589658 & 184.501988080038 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 14.4361904761905 & 0.0772907631295698 & 186.777693629312 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 14.43525 & 0.0764425270114577 & 188.837948774723 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 14.4357894736842 & 0.0755968490192718 & 190.957555254771 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 14.4375 & 0.0745924109931954 & 193.55186147981 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 14.4391176470588 & 0.0731325654520645 & 197.437592374947 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 14.440625 & 0.0714283104113894 & 202.169488775943 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 14.441 & 0.0697208720542134 & 207.125923335712 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 14.4410714285714 & 0.0671595653532907 & 215.026278871887 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 14.4442307692308 & 0.0653868325415942 & 220.904273961312 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 14.4516666666667 & 0.0635788528632041 & 227.303042062756 \tabularnewline
Median & 14.41 &  &  \tabularnewline
Midrange & 14.555 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 14.3985 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 14.4559459459459 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 14.3985 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 14.4559459459459 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 14.4559459459459 &  &  \tabularnewline
Midmean - Closest Observation & 14.3985 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 14.4559459459459 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 14.3985 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209436&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]14.4793055555556[/C][C]0.0914515885658007[/C][C]158.327545564039[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]14.458881547723[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]14.4385625464322[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]14.4997962150431[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]14.48[/C][C]0.0913269419647811[/C][C]158.551241161496[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]14.4816666666667[/C][C]0.090937346227868[/C][C]159.248837439999[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]14.4808333333333[/C][C]0.0901597760160683[/C][C]160.61301362098[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]14.4808333333333[/C][C]0.0889857099357529[/C][C]162.732121188766[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]14.4794444444444[/C][C]0.088484211850627[/C][C]163.638734431942[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]14.4752777777778[/C][C]0.0877130699371657[/C][C]165.02988423672[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]14.4743055555556[/C][C]0.0875364503530407[/C][C]165.351753437336[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]14.4665277777778[/C][C]0.0857917100687407[/C][C]168.623842165944[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]14.4640277777778[/C][C]0.0845536609815119[/C][C]171.063294124431[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]14.4584722222222[/C][C]0.083624294800244[/C][C]172.89798684413[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]14.4538888888889[/C][C]0.0823912845498792[/C][C]175.429828140846[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]14.4505555555556[/C][C]0.0787686160247679[/C][C]183.455750333505[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]14.4523611111111[/C][C]0.0768711533652313[/C][C]188.007600750373[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]14.4523611111111[/C][C]0.0762918201731662[/C][C]189.435264204044[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]14.4440277777778[/C][C]0.0738102449413556[/C][C]195.691367631336[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]14.4306944444444[/C][C]0.0718698197123159[/C][C]200.78935083194[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]14.42125[/C][C]0.0705358812507398[/C][C]204.452680597207[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]14.42375[/C][C]0.0701717760175148[/C][C]205.549165470742[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]14.4263888888889[/C][C]0.0682927583520507[/C][C]211.243318281574[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]14.4375[/C][C]0.0651571322107893[/C][C]221.579733639801[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]14.4404166666667[/C][C]0.0647498610278809[/C][C]223.018496679842[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]14.4159722222222[/C][C]0.0580680283828781[/C][C]248.260060203334[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]14.3872222222222[/C][C]0.0543701386840711[/C][C]264.616250214518[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]14.4005555555556[/C][C]0.0524937170727712[/C][C]274.32912658085[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]14.4771428571429[/C][C]0.0904800042783421[/C][C]160.003781748364[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]14.4741176470588[/C][C]0.089438359567721[/C][C]161.833442798102[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]14.47[/C][C]0.0884025545728835[/C][C]163.683052711675[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]14.4659375[/C][C]0.0874667506980714[/C][C]165.387846062046[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]14.4616129032258[/C][C]0.0867066492382515[/C][C]166.787818815237[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]14.4573333333333[/C][C]0.0858809011958256[/C][C]168.341658413292[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]14.4536206896552[/C][C]0.0850275562164649[/C][C]169.987487972239[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]14.4498214285714[/C][C]0.0839656280447536[/C][C]172.092102030961[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]14.447037037037[/C][C]0.083013907563918[/C][C]174.031526294715[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]14.4444230769231[/C][C]0.082043293881986[/C][C]176.058546572989[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]14.4424[/C][C]0.0809623545676807[/C][C]178.384140099666[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]14.4408333333333[/C][C]0.0797929686670434[/C][C]180.978770116843[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]14.4395652173913[/C][C]0.0789942555984885[/C][C]182.792598119851[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]14.4379545454545[/C][C]0.0782536529589658[/C][C]184.501988080038[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]14.4361904761905[/C][C]0.0772907631295698[/C][C]186.777693629312[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]14.43525[/C][C]0.0764425270114577[/C][C]188.837948774723[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]14.4357894736842[/C][C]0.0755968490192718[/C][C]190.957555254771[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]14.4375[/C][C]0.0745924109931954[/C][C]193.55186147981[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]14.4391176470588[/C][C]0.0731325654520645[/C][C]197.437592374947[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]14.440625[/C][C]0.0714283104113894[/C][C]202.169488775943[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]14.441[/C][C]0.0697208720542134[/C][C]207.125923335712[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]14.4410714285714[/C][C]0.0671595653532907[/C][C]215.026278871887[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]14.4442307692308[/C][C]0.0653868325415942[/C][C]220.904273961312[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]14.4516666666667[/C][C]0.0635788528632041[/C][C]227.303042062756[/C][/ROW]
[ROW][C]Median[/C][C]14.41[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]14.555[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]14.3985[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]14.4559459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]14.3985[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]14.4559459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]14.4559459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]14.3985[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]14.4559459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]14.3985[/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=209436&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209436&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 Mean14.47930555555560.0914515885658007158.327545564039
Geometric Mean14.458881547723
Harmonic Mean14.4385625464322
Quadratic Mean14.4997962150431
Winsorized Mean ( 1 / 24 )14.480.0913269419647811158.551241161496
Winsorized Mean ( 2 / 24 )14.48166666666670.090937346227868159.248837439999
Winsorized Mean ( 3 / 24 )14.48083333333330.0901597760160683160.61301362098
Winsorized Mean ( 4 / 24 )14.48083333333330.0889857099357529162.732121188766
Winsorized Mean ( 5 / 24 )14.47944444444440.088484211850627163.638734431942
Winsorized Mean ( 6 / 24 )14.47527777777780.0877130699371657165.02988423672
Winsorized Mean ( 7 / 24 )14.47430555555560.0875364503530407165.351753437336
Winsorized Mean ( 8 / 24 )14.46652777777780.0857917100687407168.623842165944
Winsorized Mean ( 9 / 24 )14.46402777777780.0845536609815119171.063294124431
Winsorized Mean ( 10 / 24 )14.45847222222220.083624294800244172.89798684413
Winsorized Mean ( 11 / 24 )14.45388888888890.0823912845498792175.429828140846
Winsorized Mean ( 12 / 24 )14.45055555555560.0787686160247679183.455750333505
Winsorized Mean ( 13 / 24 )14.45236111111110.0768711533652313188.007600750373
Winsorized Mean ( 14 / 24 )14.45236111111110.0762918201731662189.435264204044
Winsorized Mean ( 15 / 24 )14.44402777777780.0738102449413556195.691367631336
Winsorized Mean ( 16 / 24 )14.43069444444440.0718698197123159200.78935083194
Winsorized Mean ( 17 / 24 )14.421250.0705358812507398204.452680597207
Winsorized Mean ( 18 / 24 )14.423750.0701717760175148205.549165470742
Winsorized Mean ( 19 / 24 )14.42638888888890.0682927583520507211.243318281574
Winsorized Mean ( 20 / 24 )14.43750.0651571322107893221.579733639801
Winsorized Mean ( 21 / 24 )14.44041666666670.0647498610278809223.018496679842
Winsorized Mean ( 22 / 24 )14.41597222222220.0580680283828781248.260060203334
Winsorized Mean ( 23 / 24 )14.38722222222220.0543701386840711264.616250214518
Winsorized Mean ( 24 / 24 )14.40055555555560.0524937170727712274.32912658085
Trimmed Mean ( 1 / 24 )14.47714285714290.0904800042783421160.003781748364
Trimmed Mean ( 2 / 24 )14.47411764705880.089438359567721161.833442798102
Trimmed Mean ( 3 / 24 )14.470.0884025545728835163.683052711675
Trimmed Mean ( 4 / 24 )14.46593750.0874667506980714165.387846062046
Trimmed Mean ( 5 / 24 )14.46161290322580.0867066492382515166.787818815237
Trimmed Mean ( 6 / 24 )14.45733333333330.0858809011958256168.341658413292
Trimmed Mean ( 7 / 24 )14.45362068965520.0850275562164649169.987487972239
Trimmed Mean ( 8 / 24 )14.44982142857140.0839656280447536172.092102030961
Trimmed Mean ( 9 / 24 )14.4470370370370.083013907563918174.031526294715
Trimmed Mean ( 10 / 24 )14.44442307692310.082043293881986176.058546572989
Trimmed Mean ( 11 / 24 )14.44240.0809623545676807178.384140099666
Trimmed Mean ( 12 / 24 )14.44083333333330.0797929686670434180.978770116843
Trimmed Mean ( 13 / 24 )14.43956521739130.0789942555984885182.792598119851
Trimmed Mean ( 14 / 24 )14.43795454545450.0782536529589658184.501988080038
Trimmed Mean ( 15 / 24 )14.43619047619050.0772907631295698186.777693629312
Trimmed Mean ( 16 / 24 )14.435250.0764425270114577188.837948774723
Trimmed Mean ( 17 / 24 )14.43578947368420.0755968490192718190.957555254771
Trimmed Mean ( 18 / 24 )14.43750.0745924109931954193.55186147981
Trimmed Mean ( 19 / 24 )14.43911764705880.0731325654520645197.437592374947
Trimmed Mean ( 20 / 24 )14.4406250.0714283104113894202.169488775943
Trimmed Mean ( 21 / 24 )14.4410.0697208720542134207.125923335712
Trimmed Mean ( 22 / 24 )14.44107142857140.0671595653532907215.026278871887
Trimmed Mean ( 23 / 24 )14.44423076923080.0653868325415942220.904273961312
Trimmed Mean ( 24 / 24 )14.45166666666670.0635788528632041227.303042062756
Median14.41
Midrange14.555
Midmean - Weighted Average at Xnp14.3985
Midmean - Weighted Average at X(n+1)p14.4559459459459
Midmean - Empirical Distribution Function14.3985
Midmean - Empirical Distribution Function - Averaging14.4559459459459
Midmean - Empirical Distribution Function - Interpolation14.4559459459459
Midmean - Closest Observation14.3985
Midmean - True Basic - Statistics Graphics Toolkit14.4559459459459
Midmean - MS Excel (old versions)14.3985
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')