Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 19 Oct 2012 08:56:31 -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/2012/Oct/19/t1350651425t9oeumths9wuhgl.htm/, Retrieved Mon, 29 Apr 2024 13:58:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=180118, Retrieved Mon, 29 Apr 2024 13:58:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-19 12:56:31] [946b987ea445738c2c70467dba74cc4f] [Current]
Feedback Forum

Post a new message
Dataseries X:
3,43
3,43
3,43
3,43
3,43
3,43
3,43
3,43
3,5
3,52
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,58
3,58
3,59
3,59
3,59
3,59
3,59
3,59
3,59
3,59
3,59
3,61
3,71
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
4,09
4,09
4,09
4,09




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=180118&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=180118&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180118&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 Mean3.747777777777780.0251833823651289148.819476408668
Geometric Mean3.74174211318093
Harmonic Mean3.73568791109276
Quadratic Mean3.75378031678289
Winsorized Mean ( 1 / 24 )3.747777777777780.0251833823651289148.819476408668
Winsorized Mean ( 2 / 24 )3.747777777777780.0251833823651289148.819476408668
Winsorized Mean ( 3 / 24 )3.747777777777780.0251833823651289148.819476408668
Winsorized Mean ( 4 / 24 )3.741666666666670.024170915928835154.80036742021
Winsorized Mean ( 5 / 24 )3.741666666666670.024170915928835154.80036742021
Winsorized Mean ( 6 / 24 )3.741666666666670.024170915928835154.80036742021
Winsorized Mean ( 7 / 24 )3.741666666666670.024170915928835154.80036742021
Winsorized Mean ( 8 / 24 )3.749444444444440.0228640680103425163.988509951439
Winsorized Mean ( 9 / 24 )3.751944444444440.0224903377696406166.824726372458
Winsorized Mean ( 10 / 24 )3.753333333333330.0222914609924258168.375385292541
Winsorized Mean ( 11 / 24 )3.753333333333330.0222914609924258168.375385292541
Winsorized Mean ( 12 / 24 )3.753333333333330.0222914609924258168.375385292541
Winsorized Mean ( 13 / 24 )3.753333333333330.0222914609924258168.375385292541
Winsorized Mean ( 14 / 24 )3.753333333333330.0222914609924258168.375385292541
Winsorized Mean ( 15 / 24 )3.753333333333330.0222914609924258168.375385292541
Winsorized Mean ( 16 / 24 )3.740.0205070696615408182.376129877495
Winsorized Mean ( 17 / 24 )3.740.0205070696615408182.376129877495
Winsorized Mean ( 18 / 24 )3.740.0205070696615408182.376129877495
Winsorized Mean ( 19 / 24 )3.740.0205070696615408182.376129877495
Winsorized Mean ( 20 / 24 )3.753888888888890.0185861311348446201.972581687602
Winsorized Mean ( 21 / 24 )3.753888888888890.0185861311348446201.972581687602
Winsorized Mean ( 22 / 24 )3.756944444444440.0181872529361047206.570198239575
Winsorized Mean ( 23 / 24 )3.756944444444440.0181872529361047206.570198239575
Winsorized Mean ( 24 / 24 )3.756944444444440.0181872529361047206.570198239575
Trimmed Mean ( 1 / 24 )3.747428571428570.0250214696335073149.768523844428
Trimmed Mean ( 2 / 24 )3.747058823529410.0248163215779584150.991709700342
Trimmed Mean ( 3 / 24 )3.746666666666670.0245598392337105152.552572963265
Trimmed Mean ( 4 / 24 )3.746250.0242419803463148154.535642158026
Trimmed Mean ( 5 / 24 )3.747580645161290.0241991620492383154.864066678674
Trimmed Mean ( 6 / 24 )3.7490.0241215144140479155.421419055541
Trimmed Mean ( 7 / 24 )3.750517241379310.0240014397806097156.262177421926
Trimmed Mean ( 8 / 24 )3.752142857142860.0238293640280526157.458791293201
Trimmed Mean ( 9 / 24 )3.752592592592590.0238900129205381157.077880412802
Trimmed Mean ( 10 / 24 )3.752692307692310.0240005583529435156.358541851676
Trimmed Mean ( 11 / 24 )3.75260.0241285841157033155.525081041027
Trimmed Mean ( 12 / 24 )3.75250.0242356559902264154.833853125877
Trimmed Mean ( 13 / 24 )3.752391304347830.0243151307391251154.32330365018
Trimmed Mean ( 14 / 24 )3.752272727272730.0243582833095637154.045040021334
Trimmed Mean ( 15 / 24 )3.752142857142860.0243535126602914154.069883448919
Trimmed Mean ( 16 / 24 )3.7520.0242851648289492154.497613107712
Trimmed Mean ( 17 / 24 )3.753421052631580.0244782724098168153.336844602085
Trimmed Mean ( 18 / 24 )3.7550.0246354371161699152.422706457087
Trimmed Mean ( 19 / 24 )3.756764705882350.0247400769219206151.849354298237
Trimmed Mean ( 20 / 24 )3.758750.0247680774645575151.757842544649
Trimmed Mean ( 21 / 24 )3.759333333333330.0251566738172576149.436819853124
Trimmed Mean ( 22 / 24 )3.760.0255262081317869147.299590310784
Trimmed Mean ( 23 / 24 )3.760384615384620.0259613960110052144.845239207882
Trimmed Mean ( 24 / 24 )3.760833333333330.0263609055799525142.667076513238
Median3.83
Midrange3.76
Midmean - Weighted Average at Xnp3.72304347826087
Midmean - Weighted Average at X(n+1)p3.72304347826087
Midmean - Empirical Distribution Function3.72304347826087
Midmean - Empirical Distribution Function - Averaging3.72304347826087
Midmean - Empirical Distribution Function - Interpolation3.72304347826087
Midmean - Closest Observation3.72304347826087
Midmean - True Basic - Statistics Graphics Toolkit3.72304347826087
Midmean - MS Excel (old versions)3.72304347826087
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.74777777777778 & 0.0251833823651289 & 148.819476408668 \tabularnewline
Geometric Mean & 3.74174211318093 &  &  \tabularnewline
Harmonic Mean & 3.73568791109276 &  &  \tabularnewline
Quadratic Mean & 3.75378031678289 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 3.74777777777778 & 0.0251833823651289 & 148.819476408668 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 3.74777777777778 & 0.0251833823651289 & 148.819476408668 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 3.74777777777778 & 0.0251833823651289 & 148.819476408668 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 3.74166666666667 & 0.024170915928835 & 154.80036742021 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3.74166666666667 & 0.024170915928835 & 154.80036742021 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3.74166666666667 & 0.024170915928835 & 154.80036742021 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3.74166666666667 & 0.024170915928835 & 154.80036742021 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3.74944444444444 & 0.0228640680103425 & 163.988509951439 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3.75194444444444 & 0.0224903377696406 & 166.824726372458 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 3.75333333333333 & 0.0222914609924258 & 168.375385292541 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 3.75333333333333 & 0.0222914609924258 & 168.375385292541 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 3.75333333333333 & 0.0222914609924258 & 168.375385292541 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 3.75333333333333 & 0.0222914609924258 & 168.375385292541 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 3.75333333333333 & 0.0222914609924258 & 168.375385292541 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 3.75333333333333 & 0.0222914609924258 & 168.375385292541 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 3.74 & 0.0205070696615408 & 182.376129877495 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 3.74 & 0.0205070696615408 & 182.376129877495 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 3.74 & 0.0205070696615408 & 182.376129877495 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3.74 & 0.0205070696615408 & 182.376129877495 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 3.75388888888889 & 0.0185861311348446 & 201.972581687602 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 3.75388888888889 & 0.0185861311348446 & 201.972581687602 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 3.75694444444444 & 0.0181872529361047 & 206.570198239575 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 3.75694444444444 & 0.0181872529361047 & 206.570198239575 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 3.75694444444444 & 0.0181872529361047 & 206.570198239575 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 3.74742857142857 & 0.0250214696335073 & 149.768523844428 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 3.74705882352941 & 0.0248163215779584 & 150.991709700342 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 3.74666666666667 & 0.0245598392337105 & 152.552572963265 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 3.74625 & 0.0242419803463148 & 154.535642158026 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 3.74758064516129 & 0.0241991620492383 & 154.864066678674 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 3.749 & 0.0241215144140479 & 155.421419055541 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 3.75051724137931 & 0.0240014397806097 & 156.262177421926 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 3.75214285714286 & 0.0238293640280526 & 157.458791293201 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 3.75259259259259 & 0.0238900129205381 & 157.077880412802 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 3.75269230769231 & 0.0240005583529435 & 156.358541851676 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 3.7526 & 0.0241285841157033 & 155.525081041027 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 3.7525 & 0.0242356559902264 & 154.833853125877 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 3.75239130434783 & 0.0243151307391251 & 154.32330365018 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 3.75227272727273 & 0.0243582833095637 & 154.045040021334 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 3.75214285714286 & 0.0243535126602914 & 154.069883448919 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 3.752 & 0.0242851648289492 & 154.497613107712 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 3.75342105263158 & 0.0244782724098168 & 153.336844602085 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3.755 & 0.0246354371161699 & 152.422706457087 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 3.75676470588235 & 0.0247400769219206 & 151.849354298237 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 3.75875 & 0.0247680774645575 & 151.757842544649 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 3.75933333333333 & 0.0251566738172576 & 149.436819853124 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 3.76 & 0.0255262081317869 & 147.299590310784 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 3.76038461538462 & 0.0259613960110052 & 144.845239207882 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 3.76083333333333 & 0.0263609055799525 & 142.667076513238 \tabularnewline
Median & 3.83 &  &  \tabularnewline
Midrange & 3.76 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.72304347826087 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.72304347826087 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.72304347826087 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.72304347826087 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.72304347826087 &  &  \tabularnewline
Midmean - Closest Observation & 3.72304347826087 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.72304347826087 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.72304347826087 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180118&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]3.74777777777778[/C][C]0.0251833823651289[/C][C]148.819476408668[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.74174211318093[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.73568791109276[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.75378031678289[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]3.74777777777778[/C][C]0.0251833823651289[/C][C]148.819476408668[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]3.74777777777778[/C][C]0.0251833823651289[/C][C]148.819476408668[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]3.74777777777778[/C][C]0.0251833823651289[/C][C]148.819476408668[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]3.74166666666667[/C][C]0.024170915928835[/C][C]154.80036742021[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3.74166666666667[/C][C]0.024170915928835[/C][C]154.80036742021[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3.74166666666667[/C][C]0.024170915928835[/C][C]154.80036742021[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3.74166666666667[/C][C]0.024170915928835[/C][C]154.80036742021[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3.74944444444444[/C][C]0.0228640680103425[/C][C]163.988509951439[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3.75194444444444[/C][C]0.0224903377696406[/C][C]166.824726372458[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]3.75333333333333[/C][C]0.0222914609924258[/C][C]168.375385292541[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]3.75333333333333[/C][C]0.0222914609924258[/C][C]168.375385292541[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]3.75333333333333[/C][C]0.0222914609924258[/C][C]168.375385292541[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]3.75333333333333[/C][C]0.0222914609924258[/C][C]168.375385292541[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]3.75333333333333[/C][C]0.0222914609924258[/C][C]168.375385292541[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]3.75333333333333[/C][C]0.0222914609924258[/C][C]168.375385292541[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]3.74[/C][C]0.0205070696615408[/C][C]182.376129877495[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]3.74[/C][C]0.0205070696615408[/C][C]182.376129877495[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]3.74[/C][C]0.0205070696615408[/C][C]182.376129877495[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3.74[/C][C]0.0205070696615408[/C][C]182.376129877495[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]3.75388888888889[/C][C]0.0185861311348446[/C][C]201.972581687602[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]3.75388888888889[/C][C]0.0185861311348446[/C][C]201.972581687602[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]3.75694444444444[/C][C]0.0181872529361047[/C][C]206.570198239575[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]3.75694444444444[/C][C]0.0181872529361047[/C][C]206.570198239575[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]3.75694444444444[/C][C]0.0181872529361047[/C][C]206.570198239575[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]3.74742857142857[/C][C]0.0250214696335073[/C][C]149.768523844428[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]3.74705882352941[/C][C]0.0248163215779584[/C][C]150.991709700342[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]3.74666666666667[/C][C]0.0245598392337105[/C][C]152.552572963265[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]3.74625[/C][C]0.0242419803463148[/C][C]154.535642158026[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]3.74758064516129[/C][C]0.0241991620492383[/C][C]154.864066678674[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]3.749[/C][C]0.0241215144140479[/C][C]155.421419055541[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]3.75051724137931[/C][C]0.0240014397806097[/C][C]156.262177421926[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]3.75214285714286[/C][C]0.0238293640280526[/C][C]157.458791293201[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]3.75259259259259[/C][C]0.0238900129205381[/C][C]157.077880412802[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]3.75269230769231[/C][C]0.0240005583529435[/C][C]156.358541851676[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]3.7526[/C][C]0.0241285841157033[/C][C]155.525081041027[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]3.7525[/C][C]0.0242356559902264[/C][C]154.833853125877[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]3.75239130434783[/C][C]0.0243151307391251[/C][C]154.32330365018[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]3.75227272727273[/C][C]0.0243582833095637[/C][C]154.045040021334[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]3.75214285714286[/C][C]0.0243535126602914[/C][C]154.069883448919[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]3.752[/C][C]0.0242851648289492[/C][C]154.497613107712[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]3.75342105263158[/C][C]0.0244782724098168[/C][C]153.336844602085[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3.755[/C][C]0.0246354371161699[/C][C]152.422706457087[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]3.75676470588235[/C][C]0.0247400769219206[/C][C]151.849354298237[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]3.75875[/C][C]0.0247680774645575[/C][C]151.757842544649[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]3.75933333333333[/C][C]0.0251566738172576[/C][C]149.436819853124[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]3.76[/C][C]0.0255262081317869[/C][C]147.299590310784[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]3.76038461538462[/C][C]0.0259613960110052[/C][C]144.845239207882[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]3.76083333333333[/C][C]0.0263609055799525[/C][C]142.667076513238[/C][/ROW]
[ROW][C]Median[/C][C]3.83[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.76[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.72304347826087[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.72304347826087[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.72304347826087[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.72304347826087[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.72304347826087[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.72304347826087[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.72304347826087[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.72304347826087[/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=180118&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180118&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 Mean3.747777777777780.0251833823651289148.819476408668
Geometric Mean3.74174211318093
Harmonic Mean3.73568791109276
Quadratic Mean3.75378031678289
Winsorized Mean ( 1 / 24 )3.747777777777780.0251833823651289148.819476408668
Winsorized Mean ( 2 / 24 )3.747777777777780.0251833823651289148.819476408668
Winsorized Mean ( 3 / 24 )3.747777777777780.0251833823651289148.819476408668
Winsorized Mean ( 4 / 24 )3.741666666666670.024170915928835154.80036742021
Winsorized Mean ( 5 / 24 )3.741666666666670.024170915928835154.80036742021
Winsorized Mean ( 6 / 24 )3.741666666666670.024170915928835154.80036742021
Winsorized Mean ( 7 / 24 )3.741666666666670.024170915928835154.80036742021
Winsorized Mean ( 8 / 24 )3.749444444444440.0228640680103425163.988509951439
Winsorized Mean ( 9 / 24 )3.751944444444440.0224903377696406166.824726372458
Winsorized Mean ( 10 / 24 )3.753333333333330.0222914609924258168.375385292541
Winsorized Mean ( 11 / 24 )3.753333333333330.0222914609924258168.375385292541
Winsorized Mean ( 12 / 24 )3.753333333333330.0222914609924258168.375385292541
Winsorized Mean ( 13 / 24 )3.753333333333330.0222914609924258168.375385292541
Winsorized Mean ( 14 / 24 )3.753333333333330.0222914609924258168.375385292541
Winsorized Mean ( 15 / 24 )3.753333333333330.0222914609924258168.375385292541
Winsorized Mean ( 16 / 24 )3.740.0205070696615408182.376129877495
Winsorized Mean ( 17 / 24 )3.740.0205070696615408182.376129877495
Winsorized Mean ( 18 / 24 )3.740.0205070696615408182.376129877495
Winsorized Mean ( 19 / 24 )3.740.0205070696615408182.376129877495
Winsorized Mean ( 20 / 24 )3.753888888888890.0185861311348446201.972581687602
Winsorized Mean ( 21 / 24 )3.753888888888890.0185861311348446201.972581687602
Winsorized Mean ( 22 / 24 )3.756944444444440.0181872529361047206.570198239575
Winsorized Mean ( 23 / 24 )3.756944444444440.0181872529361047206.570198239575
Winsorized Mean ( 24 / 24 )3.756944444444440.0181872529361047206.570198239575
Trimmed Mean ( 1 / 24 )3.747428571428570.0250214696335073149.768523844428
Trimmed Mean ( 2 / 24 )3.747058823529410.0248163215779584150.991709700342
Trimmed Mean ( 3 / 24 )3.746666666666670.0245598392337105152.552572963265
Trimmed Mean ( 4 / 24 )3.746250.0242419803463148154.535642158026
Trimmed Mean ( 5 / 24 )3.747580645161290.0241991620492383154.864066678674
Trimmed Mean ( 6 / 24 )3.7490.0241215144140479155.421419055541
Trimmed Mean ( 7 / 24 )3.750517241379310.0240014397806097156.262177421926
Trimmed Mean ( 8 / 24 )3.752142857142860.0238293640280526157.458791293201
Trimmed Mean ( 9 / 24 )3.752592592592590.0238900129205381157.077880412802
Trimmed Mean ( 10 / 24 )3.752692307692310.0240005583529435156.358541851676
Trimmed Mean ( 11 / 24 )3.75260.0241285841157033155.525081041027
Trimmed Mean ( 12 / 24 )3.75250.0242356559902264154.833853125877
Trimmed Mean ( 13 / 24 )3.752391304347830.0243151307391251154.32330365018
Trimmed Mean ( 14 / 24 )3.752272727272730.0243582833095637154.045040021334
Trimmed Mean ( 15 / 24 )3.752142857142860.0243535126602914154.069883448919
Trimmed Mean ( 16 / 24 )3.7520.0242851648289492154.497613107712
Trimmed Mean ( 17 / 24 )3.753421052631580.0244782724098168153.336844602085
Trimmed Mean ( 18 / 24 )3.7550.0246354371161699152.422706457087
Trimmed Mean ( 19 / 24 )3.756764705882350.0247400769219206151.849354298237
Trimmed Mean ( 20 / 24 )3.758750.0247680774645575151.757842544649
Trimmed Mean ( 21 / 24 )3.759333333333330.0251566738172576149.436819853124
Trimmed Mean ( 22 / 24 )3.760.0255262081317869147.299590310784
Trimmed Mean ( 23 / 24 )3.760384615384620.0259613960110052144.845239207882
Trimmed Mean ( 24 / 24 )3.760833333333330.0263609055799525142.667076513238
Median3.83
Midrange3.76
Midmean - Weighted Average at Xnp3.72304347826087
Midmean - Weighted Average at X(n+1)p3.72304347826087
Midmean - Empirical Distribution Function3.72304347826087
Midmean - Empirical Distribution Function - Averaging3.72304347826087
Midmean - Empirical Distribution Function - Interpolation3.72304347826087
Midmean - Closest Observation3.72304347826087
Midmean - True Basic - Statistics Graphics Toolkit3.72304347826087
Midmean - MS Excel (old versions)3.72304347826087
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')