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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 10 Oct 2014 16:46:46 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/10/t1412956145tf391w4gjtbaf0v.htm/, Retrieved Sun, 12 May 2024 17:45:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240351, Retrieved Sun, 12 May 2024 17:45:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-10 15:46:46] [7686dea5cfa8a11058319f854e13a03d] [Current]
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Dataseries X:
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
4,09
4,09
4,09
4,09
4,09
4,09
4,09
4,09
4,21
4,21
4,21
4,21
4,21
4,21
4,21
4,21
4,21
4,21
4,21
4,21
4,23
4,23
4,23
4,23




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240351&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240351&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240351&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.970833333333330.0225052158795253176.440579578972
Geometric Mean3.96622699372836
Harmonic Mean3.96154191331954
Quadratic Mean3.97535882377651
Winsorized Mean ( 1 / 24 )3.970833333333330.0225052158795253176.440579578972
Winsorized Mean ( 2 / 24 )3.970833333333330.0225052158795253176.440579578972
Winsorized Mean ( 3 / 24 )3.970833333333330.0225052158795253176.440579578972
Winsorized Mean ( 4 / 24 )3.969722222222220.0223308913791994177.768193611828
Winsorized Mean ( 5 / 24 )3.969722222222220.0223308913791994177.768193611828
Winsorized Mean ( 6 / 24 )3.969722222222220.0223308913791994177.768193611828
Winsorized Mean ( 7 / 24 )3.971666666666670.0218715484645663181.590556932953
Winsorized Mean ( 8 / 24 )3.982777777777780.0194699140144515204.560624911932
Winsorized Mean ( 9 / 24 )3.997777777777780.0169116064984744236.392549586488
Winsorized Mean ( 10 / 24 )3.997777777777780.0169116064984744236.392549586488
Winsorized Mean ( 11 / 24 )3.997777777777780.0169116064984744236.392549586488
Winsorized Mean ( 12 / 24 )3.997777777777780.0169116064984744236.392549586488
Winsorized Mean ( 13 / 24 )3.997777777777780.0169116064984744236.392549586488
Winsorized Mean ( 14 / 24 )3.997777777777780.0169116064984744236.392549586488
Winsorized Mean ( 15 / 24 )3.997777777777780.0169116064984744236.392549586488
Winsorized Mean ( 16 / 24 )3.971111111111110.012713829228845312.345796032992
Winsorized Mean ( 17 / 24 )3.971111111111110.012713829228845312.345796032992
Winsorized Mean ( 18 / 24 )3.971111111111110.012713829228845312.345796032992
Winsorized Mean ( 19 / 24 )3.971111111111110.012713829228845312.345796032992
Winsorized Mean ( 20 / 24 )3.996111111111110.00922793344658823433.045072793472
Winsorized Mean ( 21 / 24 )3.996111111111110.00922793344658823433.045072793471
Winsorized Mean ( 22 / 24 )3.996111111111110.00922793344658823433.045072793472
Winsorized Mean ( 23 / 24 )3.996111111111110.00922793344658823433.045072793471
Winsorized Mean ( 24 / 24 )3.996111111111110.00922793344658823433.045072793472
Trimmed Mean ( 1 / 24 )3.972571428571430.0221828330789211179.08314120374
Trimmed Mean ( 2 / 24 )3.974411764705880.0217933691143602182.367936955973
Trimmed Mean ( 3 / 24 )3.976363636363640.021322953874665186.482776248378
Trimmed Mean ( 4 / 24 )3.97843750.0207536795719171191.697934152526
Trimmed Mean ( 5 / 24 )3.980967741935480.0201248215910836197.813815338332
Trimmed Mean ( 6 / 24 )3.983666666666670.019353924355212205.83250164424
Trimmed Mean ( 7 / 24 )3.986551724137930.0184002546803338216.657420964872
Trimmed Mean ( 8 / 24 )3.989285714285710.017350207047788229.927268492989
Trimmed Mean ( 9 / 24 )3.990370370370370.0167230972621086238.614313355207
Trimmed Mean ( 10 / 24 )3.989230769230770.0165497698895527241.044485564058
Trimmed Mean ( 11 / 24 )3.9880.0163157617545934244.426221710258
Trimmed Mean ( 12 / 24 )3.986666666666670.0160045797228174249.095367433045
Trimmed Mean ( 13 / 24 )3.985217391304350.0155936910642795255.566009027413
Trimmed Mean ( 14 / 24 )3.983636363636360.0150513248385815264.670147402904
Trimmed Mean ( 15 / 24 )3.981904761904760.0143307459049617277.857467316206
Trimmed Mean ( 16 / 24 )3.980.0133589497514415297.927612129131
Trimmed Mean ( 17 / 24 )3.981052631578950.0131669954302653302.350878198697
Trimmed Mean ( 18 / 24 )3.982222222222220.0128798545239191309.182236090234
Trimmed Mean ( 19 / 24 )3.983529411764710.0124594340187645319.719933165931
Trimmed Mean ( 20 / 24 )3.9850.011845783243212336.406628264412
Trimmed Mean ( 21 / 24 )3.983666666666670.0119335645004258333.820349026857
Trimmed Mean ( 22 / 24 )3.982142857142860.0119783440267669332.445190106773
Trimmed Mean ( 23 / 24 )3.980384615384620.0119547965170183332.952937318365
Trimmed Mean ( 24 / 24 )3.978333333333330.0118209263392049336.550048547289
Median3.98
Midrange3.91
Midmean - Weighted Average at Xnp3.95765957446809
Midmean - Weighted Average at X(n+1)p3.95765957446809
Midmean - Empirical Distribution Function3.95765957446809
Midmean - Empirical Distribution Function - Averaging3.95765957446809
Midmean - Empirical Distribution Function - Interpolation3.95765957446809
Midmean - Closest Observation3.95765957446809
Midmean - True Basic - Statistics Graphics Toolkit3.95765957446809
Midmean - MS Excel (old versions)3.95765957446809
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.97083333333333 & 0.0225052158795253 & 176.440579578972 \tabularnewline
Geometric Mean & 3.96622699372836 &  &  \tabularnewline
Harmonic Mean & 3.96154191331954 &  &  \tabularnewline
Quadratic Mean & 3.97535882377651 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 3.97083333333333 & 0.0225052158795253 & 176.440579578972 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 3.97083333333333 & 0.0225052158795253 & 176.440579578972 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 3.97083333333333 & 0.0225052158795253 & 176.440579578972 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 3.96972222222222 & 0.0223308913791994 & 177.768193611828 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3.96972222222222 & 0.0223308913791994 & 177.768193611828 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3.96972222222222 & 0.0223308913791994 & 177.768193611828 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3.97166666666667 & 0.0218715484645663 & 181.590556932953 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3.98277777777778 & 0.0194699140144515 & 204.560624911932 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3.99777777777778 & 0.0169116064984744 & 236.392549586488 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 3.99777777777778 & 0.0169116064984744 & 236.392549586488 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 3.99777777777778 & 0.0169116064984744 & 236.392549586488 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 3.99777777777778 & 0.0169116064984744 & 236.392549586488 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 3.99777777777778 & 0.0169116064984744 & 236.392549586488 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 3.99777777777778 & 0.0169116064984744 & 236.392549586488 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 3.99777777777778 & 0.0169116064984744 & 236.392549586488 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 3.97111111111111 & 0.012713829228845 & 312.345796032992 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 3.97111111111111 & 0.012713829228845 & 312.345796032992 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 3.97111111111111 & 0.012713829228845 & 312.345796032992 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3.97111111111111 & 0.012713829228845 & 312.345796032992 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 3.99611111111111 & 0.00922793344658823 & 433.045072793472 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 3.99611111111111 & 0.00922793344658823 & 433.045072793471 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 3.99611111111111 & 0.00922793344658823 & 433.045072793472 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 3.99611111111111 & 0.00922793344658823 & 433.045072793471 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 3.99611111111111 & 0.00922793344658823 & 433.045072793472 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 3.97257142857143 & 0.0221828330789211 & 179.08314120374 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 3.97441176470588 & 0.0217933691143602 & 182.367936955973 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 3.97636363636364 & 0.021322953874665 & 186.482776248378 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 3.9784375 & 0.0207536795719171 & 191.697934152526 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 3.98096774193548 & 0.0201248215910836 & 197.813815338332 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 3.98366666666667 & 0.019353924355212 & 205.83250164424 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 3.98655172413793 & 0.0184002546803338 & 216.657420964872 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 3.98928571428571 & 0.017350207047788 & 229.927268492989 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 3.99037037037037 & 0.0167230972621086 & 238.614313355207 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 3.98923076923077 & 0.0165497698895527 & 241.044485564058 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 3.988 & 0.0163157617545934 & 244.426221710258 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 3.98666666666667 & 0.0160045797228174 & 249.095367433045 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 3.98521739130435 & 0.0155936910642795 & 255.566009027413 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 3.98363636363636 & 0.0150513248385815 & 264.670147402904 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 3.98190476190476 & 0.0143307459049617 & 277.857467316206 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 3.98 & 0.0133589497514415 & 297.927612129131 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 3.98105263157895 & 0.0131669954302653 & 302.350878198697 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3.98222222222222 & 0.0128798545239191 & 309.182236090234 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 3.98352941176471 & 0.0124594340187645 & 319.719933165931 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 3.985 & 0.011845783243212 & 336.406628264412 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 3.98366666666667 & 0.0119335645004258 & 333.820349026857 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 3.98214285714286 & 0.0119783440267669 & 332.445190106773 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 3.98038461538462 & 0.0119547965170183 & 332.952937318365 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 3.97833333333333 & 0.0118209263392049 & 336.550048547289 \tabularnewline
Median & 3.98 &  &  \tabularnewline
Midrange & 3.91 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.95765957446809 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.95765957446809 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.95765957446809 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.95765957446809 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.95765957446809 &  &  \tabularnewline
Midmean - Closest Observation & 3.95765957446809 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.95765957446809 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.95765957446809 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240351&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]3.97083333333333[/C][C]0.0225052158795253[/C][C]176.440579578972[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.96622699372836[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.96154191331954[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.97535882377651[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]3.97083333333333[/C][C]0.0225052158795253[/C][C]176.440579578972[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]3.97083333333333[/C][C]0.0225052158795253[/C][C]176.440579578972[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]3.97083333333333[/C][C]0.0225052158795253[/C][C]176.440579578972[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]3.96972222222222[/C][C]0.0223308913791994[/C][C]177.768193611828[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3.96972222222222[/C][C]0.0223308913791994[/C][C]177.768193611828[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3.96972222222222[/C][C]0.0223308913791994[/C][C]177.768193611828[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3.97166666666667[/C][C]0.0218715484645663[/C][C]181.590556932953[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3.98277777777778[/C][C]0.0194699140144515[/C][C]204.560624911932[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3.99777777777778[/C][C]0.0169116064984744[/C][C]236.392549586488[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]3.99777777777778[/C][C]0.0169116064984744[/C][C]236.392549586488[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]3.99777777777778[/C][C]0.0169116064984744[/C][C]236.392549586488[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]3.99777777777778[/C][C]0.0169116064984744[/C][C]236.392549586488[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]3.99777777777778[/C][C]0.0169116064984744[/C][C]236.392549586488[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]3.99777777777778[/C][C]0.0169116064984744[/C][C]236.392549586488[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]3.99777777777778[/C][C]0.0169116064984744[/C][C]236.392549586488[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]3.97111111111111[/C][C]0.012713829228845[/C][C]312.345796032992[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]3.97111111111111[/C][C]0.012713829228845[/C][C]312.345796032992[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]3.97111111111111[/C][C]0.012713829228845[/C][C]312.345796032992[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3.97111111111111[/C][C]0.012713829228845[/C][C]312.345796032992[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]3.99611111111111[/C][C]0.00922793344658823[/C][C]433.045072793472[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]3.99611111111111[/C][C]0.00922793344658823[/C][C]433.045072793471[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]3.99611111111111[/C][C]0.00922793344658823[/C][C]433.045072793472[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]3.99611111111111[/C][C]0.00922793344658823[/C][C]433.045072793471[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]3.99611111111111[/C][C]0.00922793344658823[/C][C]433.045072793472[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]3.97257142857143[/C][C]0.0221828330789211[/C][C]179.08314120374[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]3.97441176470588[/C][C]0.0217933691143602[/C][C]182.367936955973[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]3.97636363636364[/C][C]0.021322953874665[/C][C]186.482776248378[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]3.9784375[/C][C]0.0207536795719171[/C][C]191.697934152526[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]3.98096774193548[/C][C]0.0201248215910836[/C][C]197.813815338332[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]3.98366666666667[/C][C]0.019353924355212[/C][C]205.83250164424[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]3.98655172413793[/C][C]0.0184002546803338[/C][C]216.657420964872[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]3.98928571428571[/C][C]0.017350207047788[/C][C]229.927268492989[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]3.99037037037037[/C][C]0.0167230972621086[/C][C]238.614313355207[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]3.98923076923077[/C][C]0.0165497698895527[/C][C]241.044485564058[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]3.988[/C][C]0.0163157617545934[/C][C]244.426221710258[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]3.98666666666667[/C][C]0.0160045797228174[/C][C]249.095367433045[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]3.98521739130435[/C][C]0.0155936910642795[/C][C]255.566009027413[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]3.98363636363636[/C][C]0.0150513248385815[/C][C]264.670147402904[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]3.98190476190476[/C][C]0.0143307459049617[/C][C]277.857467316206[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]3.98[/C][C]0.0133589497514415[/C][C]297.927612129131[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]3.98105263157895[/C][C]0.0131669954302653[/C][C]302.350878198697[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3.98222222222222[/C][C]0.0128798545239191[/C][C]309.182236090234[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]3.98352941176471[/C][C]0.0124594340187645[/C][C]319.719933165931[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]3.985[/C][C]0.011845783243212[/C][C]336.406628264412[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]3.98366666666667[/C][C]0.0119335645004258[/C][C]333.820349026857[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]3.98214285714286[/C][C]0.0119783440267669[/C][C]332.445190106773[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]3.98038461538462[/C][C]0.0119547965170183[/C][C]332.952937318365[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]3.97833333333333[/C][C]0.0118209263392049[/C][C]336.550048547289[/C][/ROW]
[ROW][C]Median[/C][C]3.98[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.91[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.95765957446809[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.95765957446809[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.95765957446809[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.95765957446809[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.95765957446809[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.95765957446809[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.95765957446809[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.95765957446809[/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=240351&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240351&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 Mean3.970833333333330.0225052158795253176.440579578972
Geometric Mean3.96622699372836
Harmonic Mean3.96154191331954
Quadratic Mean3.97535882377651
Winsorized Mean ( 1 / 24 )3.970833333333330.0225052158795253176.440579578972
Winsorized Mean ( 2 / 24 )3.970833333333330.0225052158795253176.440579578972
Winsorized Mean ( 3 / 24 )3.970833333333330.0225052158795253176.440579578972
Winsorized Mean ( 4 / 24 )3.969722222222220.0223308913791994177.768193611828
Winsorized Mean ( 5 / 24 )3.969722222222220.0223308913791994177.768193611828
Winsorized Mean ( 6 / 24 )3.969722222222220.0223308913791994177.768193611828
Winsorized Mean ( 7 / 24 )3.971666666666670.0218715484645663181.590556932953
Winsorized Mean ( 8 / 24 )3.982777777777780.0194699140144515204.560624911932
Winsorized Mean ( 9 / 24 )3.997777777777780.0169116064984744236.392549586488
Winsorized Mean ( 10 / 24 )3.997777777777780.0169116064984744236.392549586488
Winsorized Mean ( 11 / 24 )3.997777777777780.0169116064984744236.392549586488
Winsorized Mean ( 12 / 24 )3.997777777777780.0169116064984744236.392549586488
Winsorized Mean ( 13 / 24 )3.997777777777780.0169116064984744236.392549586488
Winsorized Mean ( 14 / 24 )3.997777777777780.0169116064984744236.392549586488
Winsorized Mean ( 15 / 24 )3.997777777777780.0169116064984744236.392549586488
Winsorized Mean ( 16 / 24 )3.971111111111110.012713829228845312.345796032992
Winsorized Mean ( 17 / 24 )3.971111111111110.012713829228845312.345796032992
Winsorized Mean ( 18 / 24 )3.971111111111110.012713829228845312.345796032992
Winsorized Mean ( 19 / 24 )3.971111111111110.012713829228845312.345796032992
Winsorized Mean ( 20 / 24 )3.996111111111110.00922793344658823433.045072793472
Winsorized Mean ( 21 / 24 )3.996111111111110.00922793344658823433.045072793471
Winsorized Mean ( 22 / 24 )3.996111111111110.00922793344658823433.045072793472
Winsorized Mean ( 23 / 24 )3.996111111111110.00922793344658823433.045072793471
Winsorized Mean ( 24 / 24 )3.996111111111110.00922793344658823433.045072793472
Trimmed Mean ( 1 / 24 )3.972571428571430.0221828330789211179.08314120374
Trimmed Mean ( 2 / 24 )3.974411764705880.0217933691143602182.367936955973
Trimmed Mean ( 3 / 24 )3.976363636363640.021322953874665186.482776248378
Trimmed Mean ( 4 / 24 )3.97843750.0207536795719171191.697934152526
Trimmed Mean ( 5 / 24 )3.980967741935480.0201248215910836197.813815338332
Trimmed Mean ( 6 / 24 )3.983666666666670.019353924355212205.83250164424
Trimmed Mean ( 7 / 24 )3.986551724137930.0184002546803338216.657420964872
Trimmed Mean ( 8 / 24 )3.989285714285710.017350207047788229.927268492989
Trimmed Mean ( 9 / 24 )3.990370370370370.0167230972621086238.614313355207
Trimmed Mean ( 10 / 24 )3.989230769230770.0165497698895527241.044485564058
Trimmed Mean ( 11 / 24 )3.9880.0163157617545934244.426221710258
Trimmed Mean ( 12 / 24 )3.986666666666670.0160045797228174249.095367433045
Trimmed Mean ( 13 / 24 )3.985217391304350.0155936910642795255.566009027413
Trimmed Mean ( 14 / 24 )3.983636363636360.0150513248385815264.670147402904
Trimmed Mean ( 15 / 24 )3.981904761904760.0143307459049617277.857467316206
Trimmed Mean ( 16 / 24 )3.980.0133589497514415297.927612129131
Trimmed Mean ( 17 / 24 )3.981052631578950.0131669954302653302.350878198697
Trimmed Mean ( 18 / 24 )3.982222222222220.0128798545239191309.182236090234
Trimmed Mean ( 19 / 24 )3.983529411764710.0124594340187645319.719933165931
Trimmed Mean ( 20 / 24 )3.9850.011845783243212336.406628264412
Trimmed Mean ( 21 / 24 )3.983666666666670.0119335645004258333.820349026857
Trimmed Mean ( 22 / 24 )3.982142857142860.0119783440267669332.445190106773
Trimmed Mean ( 23 / 24 )3.980384615384620.0119547965170183332.952937318365
Trimmed Mean ( 24 / 24 )3.978333333333330.0118209263392049336.550048547289
Median3.98
Midrange3.91
Midmean - Weighted Average at Xnp3.95765957446809
Midmean - Weighted Average at X(n+1)p3.95765957446809
Midmean - Empirical Distribution Function3.95765957446809
Midmean - Empirical Distribution Function - Averaging3.95765957446809
Midmean - Empirical Distribution Function - Interpolation3.95765957446809
Midmean - Closest Observation3.95765957446809
Midmean - True Basic - Statistics Graphics Toolkit3.95765957446809
Midmean - MS Excel (old versions)3.95765957446809
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')