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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 02 Mar 2012 11:47:28 -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/02/t133070686829ixxxuc15t5f0b.htm/, Retrieved Sun, 28 Apr 2024 22:48:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163436, Retrieved Sun, 28 Apr 2024 22:48:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-03-02 16:47:28] [6ae3a840f5540338367116d7beba32a2] [Current]
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Dataseries X:
13,15
13,47
13,65
13,52
14,13
14,84
15,29
15,51
15,43
15,42
15,56
15,43
15,36
15,18
15,41
15,15
15,21
15,09
15,09
15,5
15,41
15,42
15,47
15,23
15,59
15,22
15,45
15,02
15,5
15,59
15,98
15,76
15,43
15,45
15,32
15,4
15,42
15,54
15,6
15,67
15,61
16,01
16,06
16,15
15,87
15,89
15,73
15,78
16,07
16,2
16,42
16,61
16,89
17,62
17,83
17,94
18,07
17,85
17,86
17,85




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163436&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163436&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163436&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean15.68616666666670.134581605610641116.555056654981
Geometric Mean15.6523899313051
Harmonic Mean15.6187834107715
Quadratic Mean15.7201922698166
Winsorized Mean ( 1 / 20 )15.68933333333330.132333440065989118.559098331531
Winsorized Mean ( 2 / 20 )15.68833333333330.131104212369175119.663076035702
Winsorized Mean ( 3 / 20 )15.69433333333330.129180241677761121.49174772782
Winsorized Mean ( 4 / 20 )15.72633333333330.121296891839273129.651577174557
Winsorized Mean ( 5 / 20 )15.78383333333330.109762478967438143.799898488224
Winsorized Mean ( 6 / 20 )15.78083333333330.100721490945229156.677916353669
Winsorized Mean ( 7 / 20 )15.70383333333330.0747493331477035210.086601071113
Winsorized Mean ( 8 / 20 )15.66650.065114338809851240.599847688692
Winsorized Mean ( 9 / 20 )15.6470.05698215599374274.594734564255
Winsorized Mean ( 10 / 20 )15.61533333333330.0482100316978619323.902158604593
Winsorized Mean ( 11 / 20 )15.61166666666670.0455159788585293342.993099526435
Winsorized Mean ( 12 / 20 )15.59766666666670.0420857120209324370.616675296091
Winsorized Mean ( 13 / 20 )15.59766666666670.0413462482101412377.245030489633
Winsorized Mean ( 14 / 20 )15.60.0370973676864753420.515011518926
Winsorized Mean ( 15 / 20 )15.60.0346524308014889450.184868396872
Winsorized Mean ( 16 / 20 )15.58666666666670.0288309574149281540.62258295301
Winsorized Mean ( 17 / 20 )15.59233333333330.0263616382242866591.478162346083
Winsorized Mean ( 18 / 20 )15.56833333333330.021287866450252731.324267263478
Winsorized Mean ( 19 / 20 )15.5620.0202286366350526769.305429760591
Winsorized Mean ( 20 / 20 )15.55533333333330.0181604068414734856.552029319584
Trimmed Mean ( 1 / 20 )15.68879310344830.125417651352562125.092384797937
Trimmed Mean ( 2 / 20 )15.68821428571430.116790162352244134.328217118134
Trimmed Mean ( 3 / 20 )15.68814814814810.106715814828247147.008652591909
Trimmed Mean ( 4 / 20 )15.68576923076920.094663947242495165.699505331084
Trimmed Mean ( 5 / 20 )15.67360.082446153113807190.107111224031
Trimmed Mean ( 6 / 20 )15.64604166666670.0706860627465384221.34549667548
Trimmed Mean ( 7 / 20 )15.61673913043480.0579196964886372269.627433795315
Trimmed Mean ( 8 / 20 )15.59977272727270.0515760984971785302.461279193619
Trimmed Mean ( 9 / 20 )15.58785714285710.0466440990491564334.187120356418
Trimmed Mean ( 10 / 20 )15.5780.0428057628519027363.922961819324
Trimmed Mean ( 11 / 20 )15.57210526315790.0405494936583823384.027119903108
Trimmed Mean ( 12 / 20 )15.56611111111110.0382707102927805406.736927327099
Trimmed Mean ( 13 / 20 )15.56147058823530.0362087736015633429.770716884027
Trimmed Mean ( 14 / 20 )15.556250.0334770925530646464.683424205425
Trimmed Mean ( 15 / 20 )15.550.030957887599087502.295253519126
Trimmed Mean ( 16 / 20 )15.54285714285710.0280440750179606554.229623651444
Trimmed Mean ( 17 / 20 )15.53653846153850.0260055751874171597.431064284089
Trimmed Mean ( 18 / 20 )15.52833333333330.0236265223929903657.241598024616
Trimmed Mean ( 19 / 20 )15.52227272727270.0223115661013944695.705207636798
Trimmed Mean ( 20 / 20 )15.5160.0205246962923873755.96733705409
Median15.5
Midrange15.61
Midmean - Weighted Average at Xnp15.5416129032258
Midmean - Weighted Average at X(n+1)p15.55
Midmean - Empirical Distribution Function15.5416129032258
Midmean - Empirical Distribution Function - Averaging15.55
Midmean - Empirical Distribution Function - Interpolation15.55
Midmean - Closest Observation15.5416129032258
Midmean - True Basic - Statistics Graphics Toolkit15.55
Midmean - MS Excel (old versions)15.55625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 15.6861666666667 & 0.134581605610641 & 116.555056654981 \tabularnewline
Geometric Mean & 15.6523899313051 &  &  \tabularnewline
Harmonic Mean & 15.6187834107715 &  &  \tabularnewline
Quadratic Mean & 15.7201922698166 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 15.6893333333333 & 0.132333440065989 & 118.559098331531 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 15.6883333333333 & 0.131104212369175 & 119.663076035702 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 15.6943333333333 & 0.129180241677761 & 121.49174772782 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 15.7263333333333 & 0.121296891839273 & 129.651577174557 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 15.7838333333333 & 0.109762478967438 & 143.799898488224 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 15.7808333333333 & 0.100721490945229 & 156.677916353669 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 15.7038333333333 & 0.0747493331477035 & 210.086601071113 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 15.6665 & 0.065114338809851 & 240.599847688692 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 15.647 & 0.05698215599374 & 274.594734564255 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 15.6153333333333 & 0.0482100316978619 & 323.902158604593 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 15.6116666666667 & 0.0455159788585293 & 342.993099526435 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 15.5976666666667 & 0.0420857120209324 & 370.616675296091 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 15.5976666666667 & 0.0413462482101412 & 377.245030489633 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 15.6 & 0.0370973676864753 & 420.515011518926 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 15.6 & 0.0346524308014889 & 450.184868396872 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 15.5866666666667 & 0.0288309574149281 & 540.62258295301 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 15.5923333333333 & 0.0263616382242866 & 591.478162346083 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 15.5683333333333 & 0.021287866450252 & 731.324267263478 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 15.562 & 0.0202286366350526 & 769.305429760591 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 15.5553333333333 & 0.0181604068414734 & 856.552029319584 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 15.6887931034483 & 0.125417651352562 & 125.092384797937 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 15.6882142857143 & 0.116790162352244 & 134.328217118134 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 15.6881481481481 & 0.106715814828247 & 147.008652591909 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 15.6857692307692 & 0.094663947242495 & 165.699505331084 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 15.6736 & 0.082446153113807 & 190.107111224031 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 15.6460416666667 & 0.0706860627465384 & 221.34549667548 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 15.6167391304348 & 0.0579196964886372 & 269.627433795315 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 15.5997727272727 & 0.0515760984971785 & 302.461279193619 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 15.5878571428571 & 0.0466440990491564 & 334.187120356418 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 15.578 & 0.0428057628519027 & 363.922961819324 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 15.5721052631579 & 0.0405494936583823 & 384.027119903108 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 15.5661111111111 & 0.0382707102927805 & 406.736927327099 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 15.5614705882353 & 0.0362087736015633 & 429.770716884027 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 15.55625 & 0.0334770925530646 & 464.683424205425 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 15.55 & 0.030957887599087 & 502.295253519126 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 15.5428571428571 & 0.0280440750179606 & 554.229623651444 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 15.5365384615385 & 0.0260055751874171 & 597.431064284089 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 15.5283333333333 & 0.0236265223929903 & 657.241598024616 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 15.5222727272727 & 0.0223115661013944 & 695.705207636798 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 15.516 & 0.0205246962923873 & 755.96733705409 \tabularnewline
Median & 15.5 &  &  \tabularnewline
Midrange & 15.61 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 15.5416129032258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 15.55 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 15.5416129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 15.55 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 15.55 &  &  \tabularnewline
Midmean - Closest Observation & 15.5416129032258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 15.55 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 15.55625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163436&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]15.6861666666667[/C][C]0.134581605610641[/C][C]116.555056654981[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]15.6523899313051[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]15.6187834107715[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]15.7201922698166[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]15.6893333333333[/C][C]0.132333440065989[/C][C]118.559098331531[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]15.6883333333333[/C][C]0.131104212369175[/C][C]119.663076035702[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]15.6943333333333[/C][C]0.129180241677761[/C][C]121.49174772782[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]15.7263333333333[/C][C]0.121296891839273[/C][C]129.651577174557[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]15.7838333333333[/C][C]0.109762478967438[/C][C]143.799898488224[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]15.7808333333333[/C][C]0.100721490945229[/C][C]156.677916353669[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]15.7038333333333[/C][C]0.0747493331477035[/C][C]210.086601071113[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]15.6665[/C][C]0.065114338809851[/C][C]240.599847688692[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]15.647[/C][C]0.05698215599374[/C][C]274.594734564255[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]15.6153333333333[/C][C]0.0482100316978619[/C][C]323.902158604593[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]15.6116666666667[/C][C]0.0455159788585293[/C][C]342.993099526435[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]15.5976666666667[/C][C]0.0420857120209324[/C][C]370.616675296091[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]15.5976666666667[/C][C]0.0413462482101412[/C][C]377.245030489633[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]15.6[/C][C]0.0370973676864753[/C][C]420.515011518926[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]15.6[/C][C]0.0346524308014889[/C][C]450.184868396872[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]15.5866666666667[/C][C]0.0288309574149281[/C][C]540.62258295301[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]15.5923333333333[/C][C]0.0263616382242866[/C][C]591.478162346083[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]15.5683333333333[/C][C]0.021287866450252[/C][C]731.324267263478[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]15.562[/C][C]0.0202286366350526[/C][C]769.305429760591[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]15.5553333333333[/C][C]0.0181604068414734[/C][C]856.552029319584[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]15.6887931034483[/C][C]0.125417651352562[/C][C]125.092384797937[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]15.6882142857143[/C][C]0.116790162352244[/C][C]134.328217118134[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]15.6881481481481[/C][C]0.106715814828247[/C][C]147.008652591909[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]15.6857692307692[/C][C]0.094663947242495[/C][C]165.699505331084[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]15.6736[/C][C]0.082446153113807[/C][C]190.107111224031[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]15.6460416666667[/C][C]0.0706860627465384[/C][C]221.34549667548[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]15.6167391304348[/C][C]0.0579196964886372[/C][C]269.627433795315[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]15.5997727272727[/C][C]0.0515760984971785[/C][C]302.461279193619[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]15.5878571428571[/C][C]0.0466440990491564[/C][C]334.187120356418[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]15.578[/C][C]0.0428057628519027[/C][C]363.922961819324[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]15.5721052631579[/C][C]0.0405494936583823[/C][C]384.027119903108[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]15.5661111111111[/C][C]0.0382707102927805[/C][C]406.736927327099[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]15.5614705882353[/C][C]0.0362087736015633[/C][C]429.770716884027[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]15.55625[/C][C]0.0334770925530646[/C][C]464.683424205425[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]15.55[/C][C]0.030957887599087[/C][C]502.295253519126[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]15.5428571428571[/C][C]0.0280440750179606[/C][C]554.229623651444[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]15.5365384615385[/C][C]0.0260055751874171[/C][C]597.431064284089[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]15.5283333333333[/C][C]0.0236265223929903[/C][C]657.241598024616[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]15.5222727272727[/C][C]0.0223115661013944[/C][C]695.705207636798[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]15.516[/C][C]0.0205246962923873[/C][C]755.96733705409[/C][/ROW]
[ROW][C]Median[/C][C]15.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]15.61[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]15.5416129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]15.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]15.5416129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]15.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]15.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]15.5416129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]15.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]15.55625[/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=163436&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163436&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 Mean15.68616666666670.134581605610641116.555056654981
Geometric Mean15.6523899313051
Harmonic Mean15.6187834107715
Quadratic Mean15.7201922698166
Winsorized Mean ( 1 / 20 )15.68933333333330.132333440065989118.559098331531
Winsorized Mean ( 2 / 20 )15.68833333333330.131104212369175119.663076035702
Winsorized Mean ( 3 / 20 )15.69433333333330.129180241677761121.49174772782
Winsorized Mean ( 4 / 20 )15.72633333333330.121296891839273129.651577174557
Winsorized Mean ( 5 / 20 )15.78383333333330.109762478967438143.799898488224
Winsorized Mean ( 6 / 20 )15.78083333333330.100721490945229156.677916353669
Winsorized Mean ( 7 / 20 )15.70383333333330.0747493331477035210.086601071113
Winsorized Mean ( 8 / 20 )15.66650.065114338809851240.599847688692
Winsorized Mean ( 9 / 20 )15.6470.05698215599374274.594734564255
Winsorized Mean ( 10 / 20 )15.61533333333330.0482100316978619323.902158604593
Winsorized Mean ( 11 / 20 )15.61166666666670.0455159788585293342.993099526435
Winsorized Mean ( 12 / 20 )15.59766666666670.0420857120209324370.616675296091
Winsorized Mean ( 13 / 20 )15.59766666666670.0413462482101412377.245030489633
Winsorized Mean ( 14 / 20 )15.60.0370973676864753420.515011518926
Winsorized Mean ( 15 / 20 )15.60.0346524308014889450.184868396872
Winsorized Mean ( 16 / 20 )15.58666666666670.0288309574149281540.62258295301
Winsorized Mean ( 17 / 20 )15.59233333333330.0263616382242866591.478162346083
Winsorized Mean ( 18 / 20 )15.56833333333330.021287866450252731.324267263478
Winsorized Mean ( 19 / 20 )15.5620.0202286366350526769.305429760591
Winsorized Mean ( 20 / 20 )15.55533333333330.0181604068414734856.552029319584
Trimmed Mean ( 1 / 20 )15.68879310344830.125417651352562125.092384797937
Trimmed Mean ( 2 / 20 )15.68821428571430.116790162352244134.328217118134
Trimmed Mean ( 3 / 20 )15.68814814814810.106715814828247147.008652591909
Trimmed Mean ( 4 / 20 )15.68576923076920.094663947242495165.699505331084
Trimmed Mean ( 5 / 20 )15.67360.082446153113807190.107111224031
Trimmed Mean ( 6 / 20 )15.64604166666670.0706860627465384221.34549667548
Trimmed Mean ( 7 / 20 )15.61673913043480.0579196964886372269.627433795315
Trimmed Mean ( 8 / 20 )15.59977272727270.0515760984971785302.461279193619
Trimmed Mean ( 9 / 20 )15.58785714285710.0466440990491564334.187120356418
Trimmed Mean ( 10 / 20 )15.5780.0428057628519027363.922961819324
Trimmed Mean ( 11 / 20 )15.57210526315790.0405494936583823384.027119903108
Trimmed Mean ( 12 / 20 )15.56611111111110.0382707102927805406.736927327099
Trimmed Mean ( 13 / 20 )15.56147058823530.0362087736015633429.770716884027
Trimmed Mean ( 14 / 20 )15.556250.0334770925530646464.683424205425
Trimmed Mean ( 15 / 20 )15.550.030957887599087502.295253519126
Trimmed Mean ( 16 / 20 )15.54285714285710.0280440750179606554.229623651444
Trimmed Mean ( 17 / 20 )15.53653846153850.0260055751874171597.431064284089
Trimmed Mean ( 18 / 20 )15.52833333333330.0236265223929903657.241598024616
Trimmed Mean ( 19 / 20 )15.52227272727270.0223115661013944695.705207636798
Trimmed Mean ( 20 / 20 )15.5160.0205246962923873755.96733705409
Median15.5
Midrange15.61
Midmean - Weighted Average at Xnp15.5416129032258
Midmean - Weighted Average at X(n+1)p15.55
Midmean - Empirical Distribution Function15.5416129032258
Midmean - Empirical Distribution Function - Averaging15.55
Midmean - Empirical Distribution Function - Interpolation15.55
Midmean - Closest Observation15.5416129032258
Midmean - True Basic - Statistics Graphics Toolkit15.55
Midmean - MS Excel (old versions)15.55625
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')