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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 03 Mar 2013 04:13:58 -0500
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/Mar/03/t13623020457f0ba84hse6uvaj.htm/, Retrieved Sat, 04 May 2024 21:51:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207246, Retrieved Sat, 04 May 2024 21:51:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-03-03 09:13:58] [d299705eb289d47d3db9039788329b5a] [Current]
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Dataseries X:
16,68
16,68
16,69
16,61
16,58
16,6
16,6
16,62
16,62
16,6
16,63
16,66
16,66
16,65
16,5
16,39
16,34
16,35
16,35
16,38
16,36
16,38
16,39
16,41
16,41
16,41
16,45
16,41
16,44
16,47
16,47
16,49
16,54
16,62
16,69
16,72
16,72
16,71
16,89
16,93
16,91
16,93
16,93
16,93
16,95
16,93
16,95
16,95
16,95
16,95
16,92
16,91
16,9
16,96
16,96
16,95
16,92
16,87
16,87
16,88
16,88
16,86
16,88
16,88
16,88
16,88
16,88
16,87
16,92
16,94
17,03
17,02




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207246&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207246&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207246&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean16.71583333333330.0255133139013434655.18079689574
Geometric Mean16.7144467905913
Harmonic Mean16.7130562033862
Quadratic Mean16.7172156772592
Winsorized Mean ( 1 / 24 )16.71583333333330.0254611229002714656.523806856734
Winsorized Mean ( 2 / 24 )16.71416666666670.0252063083616117663.094588342088
Winsorized Mean ( 3 / 24 )16.71458333333330.025122499174818665.323271264647
Winsorized Mean ( 4 / 24 )16.71513888888890.0248311930384636673.15085759259
Winsorized Mean ( 5 / 24 )16.71513888888890.0248311930384636673.15085759259
Winsorized Mean ( 6 / 24 )16.71597222222220.0246744529347659677.460702631008
Winsorized Mean ( 7 / 24 )16.71597222222220.0246744529347659677.460702631008
Winsorized Mean ( 8 / 24 )16.71819444444440.0242689082092413688.87295218655
Winsorized Mean ( 9 / 24 )16.71819444444440.0242689082092413688.87295218655
Winsorized Mean ( 10 / 24 )16.71680555555560.0240848350563272694.080134510364
Winsorized Mean ( 11 / 24 )16.71527777777780.0238884112118782699.723293839916
Winsorized Mean ( 12 / 24 )16.72027777777780.0230091260915864726.680262050101
Winsorized Mean ( 13 / 24 )16.72208333333330.0227018312395178736.596231242557
Winsorized Mean ( 14 / 24 )16.72597222222220.0220556095106226758.354567991718
Winsorized Mean ( 15 / 24 )16.72597222222220.0220556095106226758.354567991718
Winsorized Mean ( 16 / 24 )16.72819444444440.0210505821895717794.666593721643
Winsorized Mean ( 17 / 24 )16.73055555555560.0206770087034771809.138100945042
Winsorized Mean ( 18 / 24 )16.74055555555560.0191525145638709874.065674234483
Winsorized Mean ( 19 / 24 )16.74847222222220.0172997821300092968.131973937947
Winsorized Mean ( 20 / 24 )16.75402777777780.01655438672865121012.05970673508
Winsorized Mean ( 21 / 24 )16.75111111111110.01617170624171151035.82830783218
Winsorized Mean ( 22 / 24 )16.74805555555560.01577998039464661061.34831201928
Winsorized Mean ( 23 / 24 )16.74805555555560.01496035304068951119.49601122405
Winsorized Mean ( 24 / 24 )16.75138888888890.01453142075588231152.7702053571
Trimmed Mean ( 1 / 24 )16.71671428571430.0252832577674692661.177228008288
Trimmed Mean ( 2 / 24 )16.71764705882350.0250592954816711667.123585778825
Trimmed Mean ( 3 / 24 )16.71954545454550.0249329467375092670.580402331367
Trimmed Mean ( 4 / 24 )16.721406250.0247986606656193674.28666714983
Trimmed Mean ( 5 / 24 )16.72322580645160.0247170922236625676.585484049854
Trimmed Mean ( 6 / 24 )16.72516666666670.0245932925340383680.070252631617
Trimmed Mean ( 7 / 24 )16.72706896551720.0244603072675032683.845414637945
Trimmed Mean ( 8 / 24 )16.72910714285710.0242715653015878689.247147227162
Trimmed Mean ( 9 / 24 )16.73092592592590.0241099689396821693.94224305237
Trimmed Mean ( 10 / 24 )16.73288461538460.0238812050814737700.671702215123
Trimmed Mean ( 11 / 24 )16.73520.0236042887836002708.989800685176
Trimmed Mean ( 12 / 24 )16.73791666666670.0232641292637806719.473163034972
Trimmed Mean ( 13 / 24 )16.74021739130430.0230007122982221727.812998756493
Trimmed Mean ( 14 / 24 )16.74250.0226964643193697737.669963233503
Trimmed Mean ( 15 / 24 )16.74452380952380.0224130851448156747.086967337782
Trimmed Mean ( 16 / 24 )16.746750.022000546321888761.197006427924
Trimmed Mean ( 17 / 24 )16.74894736842110.021648916850701773.662141340745
Trimmed Mean ( 18 / 24 )16.75111111111110.0212235934070454789.268376464014
Trimmed Mean ( 19 / 24 )16.75235294117650.0209917173358341798.04585175979
Trimmed Mean ( 20 / 24 )16.75281250.0210569234984064795.596398555937
Trimmed Mean ( 21 / 24 )16.75266666666670.0212209684490531789.43930890271
Trimmed Mean ( 22 / 24 )16.75285714285710.0214171045156721782.218582843361
Trimmed Mean ( 23 / 24 )16.75346153846150.021647116046626773.935036074831
Trimmed Mean ( 24 / 24 )16.75416666666670.0220335438171006760.393643698089
Median16.715
Midrange16.685
Midmean - Weighted Average at Xnp16.7533333333333
Midmean - Weighted Average at X(n+1)p16.76
Midmean - Empirical Distribution Function16.7533333333333
Midmean - Empirical Distribution Function - Averaging16.76
Midmean - Empirical Distribution Function - Interpolation16.76
Midmean - Closest Observation16.7533333333333
Midmean - True Basic - Statistics Graphics Toolkit16.76
Midmean - MS Excel (old versions)16.7533333333333
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 16.7158333333333 & 0.0255133139013434 & 655.18079689574 \tabularnewline
Geometric Mean & 16.7144467905913 &  &  \tabularnewline
Harmonic Mean & 16.7130562033862 &  &  \tabularnewline
Quadratic Mean & 16.7172156772592 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 16.7158333333333 & 0.0254611229002714 & 656.523806856734 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 16.7141666666667 & 0.0252063083616117 & 663.094588342088 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 16.7145833333333 & 0.025122499174818 & 665.323271264647 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 16.7151388888889 & 0.0248311930384636 & 673.15085759259 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 16.7151388888889 & 0.0248311930384636 & 673.15085759259 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 16.7159722222222 & 0.0246744529347659 & 677.460702631008 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 16.7159722222222 & 0.0246744529347659 & 677.460702631008 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 16.7181944444444 & 0.0242689082092413 & 688.87295218655 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 16.7181944444444 & 0.0242689082092413 & 688.87295218655 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 16.7168055555556 & 0.0240848350563272 & 694.080134510364 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 16.7152777777778 & 0.0238884112118782 & 699.723293839916 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 16.7202777777778 & 0.0230091260915864 & 726.680262050101 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 16.7220833333333 & 0.0227018312395178 & 736.596231242557 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 16.7259722222222 & 0.0220556095106226 & 758.354567991718 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 16.7259722222222 & 0.0220556095106226 & 758.354567991718 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 16.7281944444444 & 0.0210505821895717 & 794.666593721643 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 16.7305555555556 & 0.0206770087034771 & 809.138100945042 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 16.7405555555556 & 0.0191525145638709 & 874.065674234483 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 16.7484722222222 & 0.0172997821300092 & 968.131973937947 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 16.7540277777778 & 0.0165543867286512 & 1012.05970673508 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 16.7511111111111 & 0.0161717062417115 & 1035.82830783218 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 16.7480555555556 & 0.0157799803946466 & 1061.34831201928 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 16.7480555555556 & 0.0149603530406895 & 1119.49601122405 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 16.7513888888889 & 0.0145314207558823 & 1152.7702053571 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 16.7167142857143 & 0.0252832577674692 & 661.177228008288 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 16.7176470588235 & 0.0250592954816711 & 667.123585778825 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 16.7195454545455 & 0.0249329467375092 & 670.580402331367 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 16.72140625 & 0.0247986606656193 & 674.28666714983 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 16.7232258064516 & 0.0247170922236625 & 676.585484049854 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 16.7251666666667 & 0.0245932925340383 & 680.070252631617 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 16.7270689655172 & 0.0244603072675032 & 683.845414637945 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 16.7291071428571 & 0.0242715653015878 & 689.247147227162 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 16.7309259259259 & 0.0241099689396821 & 693.94224305237 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 16.7328846153846 & 0.0238812050814737 & 700.671702215123 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 16.7352 & 0.0236042887836002 & 708.989800685176 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 16.7379166666667 & 0.0232641292637806 & 719.473163034972 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 16.7402173913043 & 0.0230007122982221 & 727.812998756493 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 16.7425 & 0.0226964643193697 & 737.669963233503 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 16.7445238095238 & 0.0224130851448156 & 747.086967337782 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 16.74675 & 0.022000546321888 & 761.197006427924 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 16.7489473684211 & 0.021648916850701 & 773.662141340745 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 16.7511111111111 & 0.0212235934070454 & 789.268376464014 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 16.7523529411765 & 0.0209917173358341 & 798.04585175979 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 16.7528125 & 0.0210569234984064 & 795.596398555937 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 16.7526666666667 & 0.0212209684490531 & 789.43930890271 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 16.7528571428571 & 0.0214171045156721 & 782.218582843361 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 16.7534615384615 & 0.021647116046626 & 773.935036074831 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 16.7541666666667 & 0.0220335438171006 & 760.393643698089 \tabularnewline
Median & 16.715 &  &  \tabularnewline
Midrange & 16.685 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 16.7533333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 16.76 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 16.7533333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 16.76 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 16.76 &  &  \tabularnewline
Midmean - Closest Observation & 16.7533333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 16.76 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 16.7533333333333 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207246&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]16.7158333333333[/C][C]0.0255133139013434[/C][C]655.18079689574[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]16.7144467905913[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]16.7130562033862[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]16.7172156772592[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]16.7158333333333[/C][C]0.0254611229002714[/C][C]656.523806856734[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]16.7141666666667[/C][C]0.0252063083616117[/C][C]663.094588342088[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]16.7145833333333[/C][C]0.025122499174818[/C][C]665.323271264647[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]16.7151388888889[/C][C]0.0248311930384636[/C][C]673.15085759259[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]16.7151388888889[/C][C]0.0248311930384636[/C][C]673.15085759259[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]16.7159722222222[/C][C]0.0246744529347659[/C][C]677.460702631008[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]16.7159722222222[/C][C]0.0246744529347659[/C][C]677.460702631008[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]16.7181944444444[/C][C]0.0242689082092413[/C][C]688.87295218655[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]16.7181944444444[/C][C]0.0242689082092413[/C][C]688.87295218655[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]16.7168055555556[/C][C]0.0240848350563272[/C][C]694.080134510364[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]16.7152777777778[/C][C]0.0238884112118782[/C][C]699.723293839916[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]16.7202777777778[/C][C]0.0230091260915864[/C][C]726.680262050101[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]16.7220833333333[/C][C]0.0227018312395178[/C][C]736.596231242557[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]16.7259722222222[/C][C]0.0220556095106226[/C][C]758.354567991718[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]16.7259722222222[/C][C]0.0220556095106226[/C][C]758.354567991718[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]16.7281944444444[/C][C]0.0210505821895717[/C][C]794.666593721643[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]16.7305555555556[/C][C]0.0206770087034771[/C][C]809.138100945042[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]16.7405555555556[/C][C]0.0191525145638709[/C][C]874.065674234483[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]16.7484722222222[/C][C]0.0172997821300092[/C][C]968.131973937947[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]16.7540277777778[/C][C]0.0165543867286512[/C][C]1012.05970673508[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]16.7511111111111[/C][C]0.0161717062417115[/C][C]1035.82830783218[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]16.7480555555556[/C][C]0.0157799803946466[/C][C]1061.34831201928[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]16.7480555555556[/C][C]0.0149603530406895[/C][C]1119.49601122405[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]16.7513888888889[/C][C]0.0145314207558823[/C][C]1152.7702053571[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]16.7167142857143[/C][C]0.0252832577674692[/C][C]661.177228008288[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]16.7176470588235[/C][C]0.0250592954816711[/C][C]667.123585778825[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]16.7195454545455[/C][C]0.0249329467375092[/C][C]670.580402331367[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]16.72140625[/C][C]0.0247986606656193[/C][C]674.28666714983[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]16.7232258064516[/C][C]0.0247170922236625[/C][C]676.585484049854[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]16.7251666666667[/C][C]0.0245932925340383[/C][C]680.070252631617[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]16.7270689655172[/C][C]0.0244603072675032[/C][C]683.845414637945[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]16.7291071428571[/C][C]0.0242715653015878[/C][C]689.247147227162[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]16.7309259259259[/C][C]0.0241099689396821[/C][C]693.94224305237[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]16.7328846153846[/C][C]0.0238812050814737[/C][C]700.671702215123[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]16.7352[/C][C]0.0236042887836002[/C][C]708.989800685176[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]16.7379166666667[/C][C]0.0232641292637806[/C][C]719.473163034972[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]16.7402173913043[/C][C]0.0230007122982221[/C][C]727.812998756493[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]16.7425[/C][C]0.0226964643193697[/C][C]737.669963233503[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]16.7445238095238[/C][C]0.0224130851448156[/C][C]747.086967337782[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]16.74675[/C][C]0.022000546321888[/C][C]761.197006427924[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]16.7489473684211[/C][C]0.021648916850701[/C][C]773.662141340745[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]16.7511111111111[/C][C]0.0212235934070454[/C][C]789.268376464014[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]16.7523529411765[/C][C]0.0209917173358341[/C][C]798.04585175979[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]16.7528125[/C][C]0.0210569234984064[/C][C]795.596398555937[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]16.7526666666667[/C][C]0.0212209684490531[/C][C]789.43930890271[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]16.7528571428571[/C][C]0.0214171045156721[/C][C]782.218582843361[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]16.7534615384615[/C][C]0.021647116046626[/C][C]773.935036074831[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]16.7541666666667[/C][C]0.0220335438171006[/C][C]760.393643698089[/C][/ROW]
[ROW][C]Median[/C][C]16.715[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16.685[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]16.7533333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]16.76[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]16.7533333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]16.76[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]16.76[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]16.7533333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]16.76[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]16.7533333333333[/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=207246&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207246&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 Mean16.71583333333330.0255133139013434655.18079689574
Geometric Mean16.7144467905913
Harmonic Mean16.7130562033862
Quadratic Mean16.7172156772592
Winsorized Mean ( 1 / 24 )16.71583333333330.0254611229002714656.523806856734
Winsorized Mean ( 2 / 24 )16.71416666666670.0252063083616117663.094588342088
Winsorized Mean ( 3 / 24 )16.71458333333330.025122499174818665.323271264647
Winsorized Mean ( 4 / 24 )16.71513888888890.0248311930384636673.15085759259
Winsorized Mean ( 5 / 24 )16.71513888888890.0248311930384636673.15085759259
Winsorized Mean ( 6 / 24 )16.71597222222220.0246744529347659677.460702631008
Winsorized Mean ( 7 / 24 )16.71597222222220.0246744529347659677.460702631008
Winsorized Mean ( 8 / 24 )16.71819444444440.0242689082092413688.87295218655
Winsorized Mean ( 9 / 24 )16.71819444444440.0242689082092413688.87295218655
Winsorized Mean ( 10 / 24 )16.71680555555560.0240848350563272694.080134510364
Winsorized Mean ( 11 / 24 )16.71527777777780.0238884112118782699.723293839916
Winsorized Mean ( 12 / 24 )16.72027777777780.0230091260915864726.680262050101
Winsorized Mean ( 13 / 24 )16.72208333333330.0227018312395178736.596231242557
Winsorized Mean ( 14 / 24 )16.72597222222220.0220556095106226758.354567991718
Winsorized Mean ( 15 / 24 )16.72597222222220.0220556095106226758.354567991718
Winsorized Mean ( 16 / 24 )16.72819444444440.0210505821895717794.666593721643
Winsorized Mean ( 17 / 24 )16.73055555555560.0206770087034771809.138100945042
Winsorized Mean ( 18 / 24 )16.74055555555560.0191525145638709874.065674234483
Winsorized Mean ( 19 / 24 )16.74847222222220.0172997821300092968.131973937947
Winsorized Mean ( 20 / 24 )16.75402777777780.01655438672865121012.05970673508
Winsorized Mean ( 21 / 24 )16.75111111111110.01617170624171151035.82830783218
Winsorized Mean ( 22 / 24 )16.74805555555560.01577998039464661061.34831201928
Winsorized Mean ( 23 / 24 )16.74805555555560.01496035304068951119.49601122405
Winsorized Mean ( 24 / 24 )16.75138888888890.01453142075588231152.7702053571
Trimmed Mean ( 1 / 24 )16.71671428571430.0252832577674692661.177228008288
Trimmed Mean ( 2 / 24 )16.71764705882350.0250592954816711667.123585778825
Trimmed Mean ( 3 / 24 )16.71954545454550.0249329467375092670.580402331367
Trimmed Mean ( 4 / 24 )16.721406250.0247986606656193674.28666714983
Trimmed Mean ( 5 / 24 )16.72322580645160.0247170922236625676.585484049854
Trimmed Mean ( 6 / 24 )16.72516666666670.0245932925340383680.070252631617
Trimmed Mean ( 7 / 24 )16.72706896551720.0244603072675032683.845414637945
Trimmed Mean ( 8 / 24 )16.72910714285710.0242715653015878689.247147227162
Trimmed Mean ( 9 / 24 )16.73092592592590.0241099689396821693.94224305237
Trimmed Mean ( 10 / 24 )16.73288461538460.0238812050814737700.671702215123
Trimmed Mean ( 11 / 24 )16.73520.0236042887836002708.989800685176
Trimmed Mean ( 12 / 24 )16.73791666666670.0232641292637806719.473163034972
Trimmed Mean ( 13 / 24 )16.74021739130430.0230007122982221727.812998756493
Trimmed Mean ( 14 / 24 )16.74250.0226964643193697737.669963233503
Trimmed Mean ( 15 / 24 )16.74452380952380.0224130851448156747.086967337782
Trimmed Mean ( 16 / 24 )16.746750.022000546321888761.197006427924
Trimmed Mean ( 17 / 24 )16.74894736842110.021648916850701773.662141340745
Trimmed Mean ( 18 / 24 )16.75111111111110.0212235934070454789.268376464014
Trimmed Mean ( 19 / 24 )16.75235294117650.0209917173358341798.04585175979
Trimmed Mean ( 20 / 24 )16.75281250.0210569234984064795.596398555937
Trimmed Mean ( 21 / 24 )16.75266666666670.0212209684490531789.43930890271
Trimmed Mean ( 22 / 24 )16.75285714285710.0214171045156721782.218582843361
Trimmed Mean ( 23 / 24 )16.75346153846150.021647116046626773.935036074831
Trimmed Mean ( 24 / 24 )16.75416666666670.0220335438171006760.393643698089
Median16.715
Midrange16.685
Midmean - Weighted Average at Xnp16.7533333333333
Midmean - Weighted Average at X(n+1)p16.76
Midmean - Empirical Distribution Function16.7533333333333
Midmean - Empirical Distribution Function - Averaging16.76
Midmean - Empirical Distribution Function - Interpolation16.76
Midmean - Closest Observation16.7533333333333
Midmean - True Basic - Statistics Graphics Toolkit16.76
Midmean - MS Excel (old versions)16.7533333333333
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')