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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 01 Mar 2012 09:58:54 -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/2012/Mar/01/t1330613957b5ttqoea52sxrae.htm/, Retrieved Sun, 28 Apr 2024 07:06:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163384, Retrieved Sun, 28 Apr 2024 07:06:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [KDG2011W52a] [2012-03-01 14:58:54] [73066c1738da8cd0d8960e0866962dc1] [Current]
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Dataseries X:
4.95
4.95
4.96
4.93
4.95
4.96
4.97
5.01
5.04
5.07
5.07
5.08
5.07
5.08
5.09
5.09
5.14
5.17
5.17
5.18
5.18
5.18
5.17
5.17
5.18
5.18
5.26
5.26
5.26
5.28
5.28
5.31
5.37
5.42
5.43
5.43
5.44
5.5
5.52
5.55
5.55
5.55
5.55
5.55
5.55
5.55
5.55
5.56
5.57
5.59
5.69
5.73
5.76
5.77
5.77
5.79
5.79
5.79
5.79
5.79




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163384&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163384&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163384&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean5.342333333333330.0355738800472985150.175727984416
Geometric Mean5.33538062701759
Harmonic Mean5.32847008836342
Quadratic Mean5.34931677880456
Winsorized Mean ( 1 / 20 )5.342666666666670.035509898887785150.455699227701
Winsorized Mean ( 2 / 20 )5.342666666666670.035509898887785150.455699227701
Winsorized Mean ( 3 / 20 )5.342666666666670.035509898887785150.455699227701
Winsorized Mean ( 4 / 20 )5.343333333333330.0353862198806088151.000399346453
Winsorized Mean ( 5 / 20 )5.341666666666670.0350352257494439152.465598619739
Winsorized Mean ( 6 / 20 )5.342666666666670.0348522844671628153.2945902499
Winsorized Mean ( 7 / 20 )5.346166666666670.0337932327550601158.202285807242
Winsorized Mean ( 8 / 20 )5.346166666666670.0323164890016474165.431543828729
Winsorized Mean ( 9 / 20 )5.344666666666670.030428639002806175.645932313101
Winsorized Mean ( 10 / 20 )5.3280.0274652322591826193.990713412542
Winsorized Mean ( 11 / 20 )5.324333333333330.0268847368819709198.042977199597
Winsorized Mean ( 12 / 20 )5.324333333333330.0262596408625433202.757279172388
Winsorized Mean ( 13 / 20 )5.322166666666670.0259335217775966205.223444478889
Winsorized Mean ( 14 / 20 )5.32450.0255674857520957208.25278056774
Winsorized Mean ( 15 / 20 )5.32450.0255674857520957208.25278056774
Winsorized Mean ( 16 / 20 )5.337833333333330.0235795224606584226.375803082498
Winsorized Mean ( 17 / 20 )5.346333333333330.0224073316626736238.597500756385
Winsorized Mean ( 18 / 20 )5.346333333333330.0224073316626736238.597500756385
Winsorized Mean ( 19 / 20 )5.346333333333330.0224073316626736238.597500756385
Winsorized Mean ( 20 / 20 )5.346333333333330.0224073316626736238.597500756385
Trimmed Mean ( 1 / 20 )5.341724137931030.0352565036335062151.510319725933
Trimmed Mean ( 2 / 20 )5.340714285714290.0349162794082932152.957714172885
Trimmed Mean ( 3 / 20 )5.339629629629630.0344690819064666154.910700671372
Trimmed Mean ( 4 / 20 )5.338461538461540.0338887192923822157.529161618733
Trimmed Mean ( 5 / 20 )5.3370.0331874699738517160.813704817059
Trimmed Mean ( 6 / 20 )5.335833333333330.032403475501654164.668550231934
Trimmed Mean ( 7 / 20 )5.334347826086960.0314414603259965169.659671363178
Trimmed Mean ( 8 / 20 )5.332045454545450.0304972524070954174.836912629707
Trimmed Mean ( 9 / 20 )5.329523809523810.0296690071652782179.632698183476
Trimmed Mean ( 10 / 20 )5.3270.0290693247432004183.251590708038
Trimmed Mean ( 11 / 20 )5.326842105263160.029007050850211183.639561731744
Trimmed Mean ( 12 / 20 )5.327222222222220.0289762111271898183.848129724021
Trimmed Mean ( 13 / 20 )5.327647058823530.0289847794083252183.808439035189
Trimmed Mean ( 14 / 20 )5.32843750.0289573844800842184.00962641031
Trimmed Mean ( 15 / 20 )5.3290.0288848287745199184.491313471135
Trimmed Mean ( 16 / 20 )5.329642857142860.0286350977100075186.122740390728
Trimmed Mean ( 17 / 20 )5.328461538461540.0286983907760713185.671091457309
Trimmed Mean ( 18 / 20 )5.325833333333330.0288983517574881184.295401275033
Trimmed Mean ( 19 / 20 )5.322727272727270.0289138279219538184.089332173338
Trimmed Mean ( 20 / 20 )5.3190.0286071393371066185.932607148198
Median5.28
Midrange5.36
Midmean - Weighted Average at Xnp5.33515151515152
Midmean - Weighted Average at X(n+1)p5.33515151515152
Midmean - Empirical Distribution Function5.33515151515152
Midmean - Empirical Distribution Function - Averaging5.33515151515152
Midmean - Empirical Distribution Function - Interpolation5.33515151515152
Midmean - Closest Observation5.33515151515152
Midmean - True Basic - Statistics Graphics Toolkit5.33515151515152
Midmean - MS Excel (old versions)5.33515151515152
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 5.34233333333333 & 0.0355738800472985 & 150.175727984416 \tabularnewline
Geometric Mean & 5.33538062701759 &  &  \tabularnewline
Harmonic Mean & 5.32847008836342 &  &  \tabularnewline
Quadratic Mean & 5.34931677880456 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 5.34266666666667 & 0.035509898887785 & 150.455699227701 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 5.34266666666667 & 0.035509898887785 & 150.455699227701 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 5.34266666666667 & 0.035509898887785 & 150.455699227701 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 5.34333333333333 & 0.0353862198806088 & 151.000399346453 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 5.34166666666667 & 0.0350352257494439 & 152.465598619739 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 5.34266666666667 & 0.0348522844671628 & 153.2945902499 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 5.34616666666667 & 0.0337932327550601 & 158.202285807242 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 5.34616666666667 & 0.0323164890016474 & 165.431543828729 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 5.34466666666667 & 0.030428639002806 & 175.645932313101 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 5.328 & 0.0274652322591826 & 193.990713412542 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 5.32433333333333 & 0.0268847368819709 & 198.042977199597 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 5.32433333333333 & 0.0262596408625433 & 202.757279172388 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 5.32216666666667 & 0.0259335217775966 & 205.223444478889 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 5.3245 & 0.0255674857520957 & 208.25278056774 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 5.3245 & 0.0255674857520957 & 208.25278056774 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 5.33783333333333 & 0.0235795224606584 & 226.375803082498 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 5.34633333333333 & 0.0224073316626736 & 238.597500756385 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 5.34633333333333 & 0.0224073316626736 & 238.597500756385 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 5.34633333333333 & 0.0224073316626736 & 238.597500756385 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 5.34633333333333 & 0.0224073316626736 & 238.597500756385 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 5.34172413793103 & 0.0352565036335062 & 151.510319725933 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 5.34071428571429 & 0.0349162794082932 & 152.957714172885 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 5.33962962962963 & 0.0344690819064666 & 154.910700671372 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 5.33846153846154 & 0.0338887192923822 & 157.529161618733 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 5.337 & 0.0331874699738517 & 160.813704817059 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 5.33583333333333 & 0.032403475501654 & 164.668550231934 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 5.33434782608696 & 0.0314414603259965 & 169.659671363178 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 5.33204545454545 & 0.0304972524070954 & 174.836912629707 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 5.32952380952381 & 0.0296690071652782 & 179.632698183476 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 5.327 & 0.0290693247432004 & 183.251590708038 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 5.32684210526316 & 0.029007050850211 & 183.639561731744 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 5.32722222222222 & 0.0289762111271898 & 183.848129724021 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 5.32764705882353 & 0.0289847794083252 & 183.808439035189 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 5.3284375 & 0.0289573844800842 & 184.00962641031 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 5.329 & 0.0288848287745199 & 184.491313471135 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 5.32964285714286 & 0.0286350977100075 & 186.122740390728 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 5.32846153846154 & 0.0286983907760713 & 185.671091457309 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 5.32583333333333 & 0.0288983517574881 & 184.295401275033 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 5.32272727272727 & 0.0289138279219538 & 184.089332173338 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 5.319 & 0.0286071393371066 & 185.932607148198 \tabularnewline
Median & 5.28 &  &  \tabularnewline
Midrange & 5.36 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5.33515151515152 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5.33515151515152 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5.33515151515152 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5.33515151515152 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5.33515151515152 &  &  \tabularnewline
Midmean - Closest Observation & 5.33515151515152 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5.33515151515152 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5.33515151515152 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163384&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]5.34233333333333[/C][C]0.0355738800472985[/C][C]150.175727984416[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]5.33538062701759[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]5.32847008836342[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.34931677880456[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]5.34266666666667[/C][C]0.035509898887785[/C][C]150.455699227701[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]5.34266666666667[/C][C]0.035509898887785[/C][C]150.455699227701[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]5.34266666666667[/C][C]0.035509898887785[/C][C]150.455699227701[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]5.34333333333333[/C][C]0.0353862198806088[/C][C]151.000399346453[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]5.34166666666667[/C][C]0.0350352257494439[/C][C]152.465598619739[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]5.34266666666667[/C][C]0.0348522844671628[/C][C]153.2945902499[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]5.34616666666667[/C][C]0.0337932327550601[/C][C]158.202285807242[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]5.34616666666667[/C][C]0.0323164890016474[/C][C]165.431543828729[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]5.34466666666667[/C][C]0.030428639002806[/C][C]175.645932313101[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]5.328[/C][C]0.0274652322591826[/C][C]193.990713412542[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]5.32433333333333[/C][C]0.0268847368819709[/C][C]198.042977199597[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]5.32433333333333[/C][C]0.0262596408625433[/C][C]202.757279172388[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]5.32216666666667[/C][C]0.0259335217775966[/C][C]205.223444478889[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]5.3245[/C][C]0.0255674857520957[/C][C]208.25278056774[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]5.3245[/C][C]0.0255674857520957[/C][C]208.25278056774[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]5.33783333333333[/C][C]0.0235795224606584[/C][C]226.375803082498[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]5.34633333333333[/C][C]0.0224073316626736[/C][C]238.597500756385[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]5.34633333333333[/C][C]0.0224073316626736[/C][C]238.597500756385[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]5.34633333333333[/C][C]0.0224073316626736[/C][C]238.597500756385[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]5.34633333333333[/C][C]0.0224073316626736[/C][C]238.597500756385[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]5.34172413793103[/C][C]0.0352565036335062[/C][C]151.510319725933[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]5.34071428571429[/C][C]0.0349162794082932[/C][C]152.957714172885[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]5.33962962962963[/C][C]0.0344690819064666[/C][C]154.910700671372[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]5.33846153846154[/C][C]0.0338887192923822[/C][C]157.529161618733[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]5.337[/C][C]0.0331874699738517[/C][C]160.813704817059[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]5.33583333333333[/C][C]0.032403475501654[/C][C]164.668550231934[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]5.33434782608696[/C][C]0.0314414603259965[/C][C]169.659671363178[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]5.33204545454545[/C][C]0.0304972524070954[/C][C]174.836912629707[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]5.32952380952381[/C][C]0.0296690071652782[/C][C]179.632698183476[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]5.327[/C][C]0.0290693247432004[/C][C]183.251590708038[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]5.32684210526316[/C][C]0.029007050850211[/C][C]183.639561731744[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]5.32722222222222[/C][C]0.0289762111271898[/C][C]183.848129724021[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]5.32764705882353[/C][C]0.0289847794083252[/C][C]183.808439035189[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]5.3284375[/C][C]0.0289573844800842[/C][C]184.00962641031[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]5.329[/C][C]0.0288848287745199[/C][C]184.491313471135[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]5.32964285714286[/C][C]0.0286350977100075[/C][C]186.122740390728[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]5.32846153846154[/C][C]0.0286983907760713[/C][C]185.671091457309[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]5.32583333333333[/C][C]0.0288983517574881[/C][C]184.295401275033[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]5.32272727272727[/C][C]0.0289138279219538[/C][C]184.089332173338[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]5.319[/C][C]0.0286071393371066[/C][C]185.932607148198[/C][/ROW]
[ROW][C]Median[/C][C]5.28[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5.36[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5.33515151515152[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5.33515151515152[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5.33515151515152[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5.33515151515152[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5.33515151515152[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]5.33515151515152[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5.33515151515152[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5.33515151515152[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163384&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163384&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 Mean5.342333333333330.0355738800472985150.175727984416
Geometric Mean5.33538062701759
Harmonic Mean5.32847008836342
Quadratic Mean5.34931677880456
Winsorized Mean ( 1 / 20 )5.342666666666670.035509898887785150.455699227701
Winsorized Mean ( 2 / 20 )5.342666666666670.035509898887785150.455699227701
Winsorized Mean ( 3 / 20 )5.342666666666670.035509898887785150.455699227701
Winsorized Mean ( 4 / 20 )5.343333333333330.0353862198806088151.000399346453
Winsorized Mean ( 5 / 20 )5.341666666666670.0350352257494439152.465598619739
Winsorized Mean ( 6 / 20 )5.342666666666670.0348522844671628153.2945902499
Winsorized Mean ( 7 / 20 )5.346166666666670.0337932327550601158.202285807242
Winsorized Mean ( 8 / 20 )5.346166666666670.0323164890016474165.431543828729
Winsorized Mean ( 9 / 20 )5.344666666666670.030428639002806175.645932313101
Winsorized Mean ( 10 / 20 )5.3280.0274652322591826193.990713412542
Winsorized Mean ( 11 / 20 )5.324333333333330.0268847368819709198.042977199597
Winsorized Mean ( 12 / 20 )5.324333333333330.0262596408625433202.757279172388
Winsorized Mean ( 13 / 20 )5.322166666666670.0259335217775966205.223444478889
Winsorized Mean ( 14 / 20 )5.32450.0255674857520957208.25278056774
Winsorized Mean ( 15 / 20 )5.32450.0255674857520957208.25278056774
Winsorized Mean ( 16 / 20 )5.337833333333330.0235795224606584226.375803082498
Winsorized Mean ( 17 / 20 )5.346333333333330.0224073316626736238.597500756385
Winsorized Mean ( 18 / 20 )5.346333333333330.0224073316626736238.597500756385
Winsorized Mean ( 19 / 20 )5.346333333333330.0224073316626736238.597500756385
Winsorized Mean ( 20 / 20 )5.346333333333330.0224073316626736238.597500756385
Trimmed Mean ( 1 / 20 )5.341724137931030.0352565036335062151.510319725933
Trimmed Mean ( 2 / 20 )5.340714285714290.0349162794082932152.957714172885
Trimmed Mean ( 3 / 20 )5.339629629629630.0344690819064666154.910700671372
Trimmed Mean ( 4 / 20 )5.338461538461540.0338887192923822157.529161618733
Trimmed Mean ( 5 / 20 )5.3370.0331874699738517160.813704817059
Trimmed Mean ( 6 / 20 )5.335833333333330.032403475501654164.668550231934
Trimmed Mean ( 7 / 20 )5.334347826086960.0314414603259965169.659671363178
Trimmed Mean ( 8 / 20 )5.332045454545450.0304972524070954174.836912629707
Trimmed Mean ( 9 / 20 )5.329523809523810.0296690071652782179.632698183476
Trimmed Mean ( 10 / 20 )5.3270.0290693247432004183.251590708038
Trimmed Mean ( 11 / 20 )5.326842105263160.029007050850211183.639561731744
Trimmed Mean ( 12 / 20 )5.327222222222220.0289762111271898183.848129724021
Trimmed Mean ( 13 / 20 )5.327647058823530.0289847794083252183.808439035189
Trimmed Mean ( 14 / 20 )5.32843750.0289573844800842184.00962641031
Trimmed Mean ( 15 / 20 )5.3290.0288848287745199184.491313471135
Trimmed Mean ( 16 / 20 )5.329642857142860.0286350977100075186.122740390728
Trimmed Mean ( 17 / 20 )5.328461538461540.0286983907760713185.671091457309
Trimmed Mean ( 18 / 20 )5.325833333333330.0288983517574881184.295401275033
Trimmed Mean ( 19 / 20 )5.322727272727270.0289138279219538184.089332173338
Trimmed Mean ( 20 / 20 )5.3190.0286071393371066185.932607148198
Median5.28
Midrange5.36
Midmean - Weighted Average at Xnp5.33515151515152
Midmean - Weighted Average at X(n+1)p5.33515151515152
Midmean - Empirical Distribution Function5.33515151515152
Midmean - Empirical Distribution Function - Averaging5.33515151515152
Midmean - Empirical Distribution Function - Interpolation5.33515151515152
Midmean - Closest Observation5.33515151515152
Midmean - True Basic - Statistics Graphics Toolkit5.33515151515152
Midmean - MS Excel (old versions)5.33515151515152
Number of observations60



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')