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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 05 Mar 2016 09:46:30 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/05/t1457171243fg5l21di54xhx1v.htm/, Retrieved Sat, 27 Apr 2024 06:34:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293421, Retrieved Sat, 27 Apr 2024 06:34:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-05 09:46:30] [808bf237864283e5d6c581b9d5be65c1] [Current]
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Dataseries X:
4
7
9
6
9
13
18
8
15
4
8
14
8
3
5
6
12
7
3
11
6
9
6
10
10
6
13
10
9
15
8
12
13
9
6
7
8
7
6
8
3
7
8
8
7
12
7
5
9
9
8
11
9
8
9
11
8
9
9
5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293421&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293421&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293421&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.50.39808865378353421.3520277938441
Geometric Mean7.93808087671123
Harmonic Mean7.33702374379733
Quadratic Mean9.03327183250897
Winsorized Mean ( 1 / 20 )8.450.38062170373736222.2005206666583
Winsorized Mean ( 2 / 20 )8.450.38062170373736222.2005206666583
Winsorized Mean ( 3 / 20 )8.450.35528694538263323.7835926982896
Winsorized Mean ( 4 / 20 )8.383333333333330.33873448984999424.748980645714
Winsorized Mean ( 5 / 20 )8.466666666666670.32195261140805726.297866104076
Winsorized Mean ( 6 / 20 )8.466666666666670.32195261140805726.297866104076
Winsorized Mean ( 7 / 20 )8.350.29575623647258828.2327098139617
Winsorized Mean ( 8 / 20 )8.483333333333330.27256022676246431.1246194431976
Winsorized Mean ( 9 / 20 )8.483333333333330.27256022676246431.1246194431976
Winsorized Mean ( 10 / 20 )8.316666666666670.23827495235341234.9036547254505
Winsorized Mean ( 11 / 20 )8.316666666666670.23827495235341234.9036547254505
Winsorized Mean ( 12 / 20 )8.316666666666670.23827495235341234.9036547254505
Winsorized Mean ( 13 / 20 )8.10.19985870715297540.528632029027
Winsorized Mean ( 14 / 20 )8.10.19985870715297540.528632029027
Winsorized Mean ( 15 / 20 )8.350.15913786085360852.470228990204
Winsorized Mean ( 16 / 20 )8.083333333333330.11714992727865368.999900564226
Winsorized Mean ( 17 / 20 )8.083333333333330.11714992727865368.999900564226
Winsorized Mean ( 18 / 20 )8.083333333333330.11714992727865368.999900564226
Winsorized Mean ( 19 / 20 )8.083333333333330.11714992727865368.999900564226
Winsorized Mean ( 20 / 20 )8.083333333333330.11714992727865368.999900564226
Trimmed Mean ( 1 / 20 )8.431034482758620.36490977841053223.1044356209976
Trimmed Mean ( 2 / 20 )8.410714285714290.34544981565944824.3471378604114
Trimmed Mean ( 3 / 20 )8.388888888888890.32096189579314526.136712796261
Trimmed Mean ( 4 / 20 )8.365384615384610.30336082055258827.5756922075389
Trimmed Mean ( 5 / 20 )8.360.28821760486670829.0058617476411
Trimmed Mean ( 6 / 20 )8.333333333333330.27504566566901230.2979991088521
Trimmed Mean ( 7 / 20 )8.304347826086960.25795472998593632.1930434326198
Trimmed Mean ( 8 / 20 )8.295454545454540.24455928660866433.9200144901006
Trimmed Mean ( 9 / 20 )8.261904761904760.23378798531666435.3393043304345
Trimmed Mean ( 10 / 20 )8.2250.21922795769677237.5180250111007
Trimmed Mean ( 11 / 20 )8.210526315789470.21052631578947439
Trimmed Mean ( 12 / 20 )8.194444444444440.19848411413161141.2851400239058
Trimmed Mean ( 13 / 20 )8.176470588235290.18145081897419645.061635072576
Trimmed Mean ( 14 / 20 )8.18750.17061026611322647.989491995554
Trimmed Mean ( 15 / 20 )8.20.15462226869701453.0324646579084
Trimmed Mean ( 16 / 20 )8.178571428571430.14596487426785356.0310928885762
Trimmed Mean ( 17 / 20 )8.192307692307690.14696133211186855.7446477558577
Trimmed Mean ( 18 / 20 )8.208333333333330.1471857579489155.7685298341334
Trimmed Mean ( 19 / 20 )8.227272727272730.14611592062110556.3064770238621
Trimmed Mean ( 20 / 20 )8.250.1428101426443757.7690060890451
Median8
Midrange10.5
Midmean - Weighted Average at Xnp7.8974358974359
Midmean - Weighted Average at X(n+1)p8.3125
Midmean - Empirical Distribution Function7.8974358974359
Midmean - Empirical Distribution Function - Averaging8.3125
Midmean - Empirical Distribution Function - Interpolation8.3125
Midmean - Closest Observation7.8974358974359
Midmean - True Basic - Statistics Graphics Toolkit8.3125
Midmean - MS Excel (old versions)7.8974358974359
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.5 & 0.398088653783534 & 21.3520277938441 \tabularnewline
Geometric Mean & 7.93808087671123 &  &  \tabularnewline
Harmonic Mean & 7.33702374379733 &  &  \tabularnewline
Quadratic Mean & 9.03327183250897 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8.45 & 0.380621703737362 & 22.2005206666583 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8.45 & 0.380621703737362 & 22.2005206666583 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8.45 & 0.355286945382633 & 23.7835926982896 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8.38333333333333 & 0.338734489849994 & 24.748980645714 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8.46666666666667 & 0.321952611408057 & 26.297866104076 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8.46666666666667 & 0.321952611408057 & 26.297866104076 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8.35 & 0.295756236472588 & 28.2327098139617 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8.48333333333333 & 0.272560226762464 & 31.1246194431976 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8.48333333333333 & 0.272560226762464 & 31.1246194431976 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8.31666666666667 & 0.238274952353412 & 34.9036547254505 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8.31666666666667 & 0.238274952353412 & 34.9036547254505 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.31666666666667 & 0.238274952353412 & 34.9036547254505 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.1 & 0.199858707152975 & 40.528632029027 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.1 & 0.199858707152975 & 40.528632029027 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8.35 & 0.159137860853608 & 52.470228990204 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8.08333333333333 & 0.117149927278653 & 68.999900564226 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8.08333333333333 & 0.117149927278653 & 68.999900564226 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8.08333333333333 & 0.117149927278653 & 68.999900564226 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8.08333333333333 & 0.117149927278653 & 68.999900564226 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8.08333333333333 & 0.117149927278653 & 68.999900564226 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8.43103448275862 & 0.364909778410532 & 23.1044356209976 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8.41071428571429 & 0.345449815659448 & 24.3471378604114 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8.38888888888889 & 0.320961895793145 & 26.136712796261 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8.36538461538461 & 0.303360820552588 & 27.5756922075389 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8.36 & 0.288217604866708 & 29.0058617476411 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8.33333333333333 & 0.275045665669012 & 30.2979991088521 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8.30434782608696 & 0.257954729985936 & 32.1930434326198 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8.29545454545454 & 0.244559286608664 & 33.9200144901006 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8.26190476190476 & 0.233787985316664 & 35.3393043304345 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8.225 & 0.219227957696772 & 37.5180250111007 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8.21052631578947 & 0.210526315789474 & 39 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8.19444444444444 & 0.198484114131611 & 41.2851400239058 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.17647058823529 & 0.181450818974196 & 45.061635072576 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8.1875 & 0.170610266113226 & 47.989491995554 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8.2 & 0.154622268697014 & 53.0324646579084 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8.17857142857143 & 0.145964874267853 & 56.0310928885762 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8.19230769230769 & 0.146961332111868 & 55.7446477558577 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8.20833333333333 & 0.14718575794891 & 55.7685298341334 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8.22727272727273 & 0.146115920621105 & 56.3064770238621 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8.25 & 0.14281014264437 & 57.7690060890451 \tabularnewline
Median & 8 &  &  \tabularnewline
Midrange & 10.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.8974358974359 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.3125 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.8974358974359 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.3125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.3125 &  &  \tabularnewline
Midmean - Closest Observation & 7.8974358974359 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.3125 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.8974358974359 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293421&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]8.5[/C][C]0.398088653783534[/C][C]21.3520277938441[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.93808087671123[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.33702374379733[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9.03327183250897[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8.45[/C][C]0.380621703737362[/C][C]22.2005206666583[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8.45[/C][C]0.380621703737362[/C][C]22.2005206666583[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8.45[/C][C]0.355286945382633[/C][C]23.7835926982896[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8.38333333333333[/C][C]0.338734489849994[/C][C]24.748980645714[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8.46666666666667[/C][C]0.321952611408057[/C][C]26.297866104076[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8.46666666666667[/C][C]0.321952611408057[/C][C]26.297866104076[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8.35[/C][C]0.295756236472588[/C][C]28.2327098139617[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8.48333333333333[/C][C]0.272560226762464[/C][C]31.1246194431976[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8.48333333333333[/C][C]0.272560226762464[/C][C]31.1246194431976[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8.31666666666667[/C][C]0.238274952353412[/C][C]34.9036547254505[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8.31666666666667[/C][C]0.238274952353412[/C][C]34.9036547254505[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.31666666666667[/C][C]0.238274952353412[/C][C]34.9036547254505[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.1[/C][C]0.199858707152975[/C][C]40.528632029027[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.1[/C][C]0.199858707152975[/C][C]40.528632029027[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8.35[/C][C]0.159137860853608[/C][C]52.470228990204[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8.08333333333333[/C][C]0.117149927278653[/C][C]68.999900564226[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8.08333333333333[/C][C]0.117149927278653[/C][C]68.999900564226[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8.08333333333333[/C][C]0.117149927278653[/C][C]68.999900564226[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8.08333333333333[/C][C]0.117149927278653[/C][C]68.999900564226[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8.08333333333333[/C][C]0.117149927278653[/C][C]68.999900564226[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8.43103448275862[/C][C]0.364909778410532[/C][C]23.1044356209976[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8.41071428571429[/C][C]0.345449815659448[/C][C]24.3471378604114[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8.38888888888889[/C][C]0.320961895793145[/C][C]26.136712796261[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8.36538461538461[/C][C]0.303360820552588[/C][C]27.5756922075389[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8.36[/C][C]0.288217604866708[/C][C]29.0058617476411[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8.33333333333333[/C][C]0.275045665669012[/C][C]30.2979991088521[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8.30434782608696[/C][C]0.257954729985936[/C][C]32.1930434326198[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8.29545454545454[/C][C]0.244559286608664[/C][C]33.9200144901006[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8.26190476190476[/C][C]0.233787985316664[/C][C]35.3393043304345[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8.225[/C][C]0.219227957696772[/C][C]37.5180250111007[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8.21052631578947[/C][C]0.210526315789474[/C][C]39[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8.19444444444444[/C][C]0.198484114131611[/C][C]41.2851400239058[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.17647058823529[/C][C]0.181450818974196[/C][C]45.061635072576[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8.1875[/C][C]0.170610266113226[/C][C]47.989491995554[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8.2[/C][C]0.154622268697014[/C][C]53.0324646579084[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8.17857142857143[/C][C]0.145964874267853[/C][C]56.0310928885762[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8.19230769230769[/C][C]0.146961332111868[/C][C]55.7446477558577[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8.20833333333333[/C][C]0.14718575794891[/C][C]55.7685298341334[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8.22727272727273[/C][C]0.146115920621105[/C][C]56.3064770238621[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8.25[/C][C]0.14281014264437[/C][C]57.7690060890451[/C][/ROW]
[ROW][C]Median[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]10.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.8974358974359[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.3125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.8974358974359[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.3125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.3125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.8974358974359[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.3125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.8974358974359[/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=293421&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293421&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 Mean8.50.39808865378353421.3520277938441
Geometric Mean7.93808087671123
Harmonic Mean7.33702374379733
Quadratic Mean9.03327183250897
Winsorized Mean ( 1 / 20 )8.450.38062170373736222.2005206666583
Winsorized Mean ( 2 / 20 )8.450.38062170373736222.2005206666583
Winsorized Mean ( 3 / 20 )8.450.35528694538263323.7835926982896
Winsorized Mean ( 4 / 20 )8.383333333333330.33873448984999424.748980645714
Winsorized Mean ( 5 / 20 )8.466666666666670.32195261140805726.297866104076
Winsorized Mean ( 6 / 20 )8.466666666666670.32195261140805726.297866104076
Winsorized Mean ( 7 / 20 )8.350.29575623647258828.2327098139617
Winsorized Mean ( 8 / 20 )8.483333333333330.27256022676246431.1246194431976
Winsorized Mean ( 9 / 20 )8.483333333333330.27256022676246431.1246194431976
Winsorized Mean ( 10 / 20 )8.316666666666670.23827495235341234.9036547254505
Winsorized Mean ( 11 / 20 )8.316666666666670.23827495235341234.9036547254505
Winsorized Mean ( 12 / 20 )8.316666666666670.23827495235341234.9036547254505
Winsorized Mean ( 13 / 20 )8.10.19985870715297540.528632029027
Winsorized Mean ( 14 / 20 )8.10.19985870715297540.528632029027
Winsorized Mean ( 15 / 20 )8.350.15913786085360852.470228990204
Winsorized Mean ( 16 / 20 )8.083333333333330.11714992727865368.999900564226
Winsorized Mean ( 17 / 20 )8.083333333333330.11714992727865368.999900564226
Winsorized Mean ( 18 / 20 )8.083333333333330.11714992727865368.999900564226
Winsorized Mean ( 19 / 20 )8.083333333333330.11714992727865368.999900564226
Winsorized Mean ( 20 / 20 )8.083333333333330.11714992727865368.999900564226
Trimmed Mean ( 1 / 20 )8.431034482758620.36490977841053223.1044356209976
Trimmed Mean ( 2 / 20 )8.410714285714290.34544981565944824.3471378604114
Trimmed Mean ( 3 / 20 )8.388888888888890.32096189579314526.136712796261
Trimmed Mean ( 4 / 20 )8.365384615384610.30336082055258827.5756922075389
Trimmed Mean ( 5 / 20 )8.360.28821760486670829.0058617476411
Trimmed Mean ( 6 / 20 )8.333333333333330.27504566566901230.2979991088521
Trimmed Mean ( 7 / 20 )8.304347826086960.25795472998593632.1930434326198
Trimmed Mean ( 8 / 20 )8.295454545454540.24455928660866433.9200144901006
Trimmed Mean ( 9 / 20 )8.261904761904760.23378798531666435.3393043304345
Trimmed Mean ( 10 / 20 )8.2250.21922795769677237.5180250111007
Trimmed Mean ( 11 / 20 )8.210526315789470.21052631578947439
Trimmed Mean ( 12 / 20 )8.194444444444440.19848411413161141.2851400239058
Trimmed Mean ( 13 / 20 )8.176470588235290.18145081897419645.061635072576
Trimmed Mean ( 14 / 20 )8.18750.17061026611322647.989491995554
Trimmed Mean ( 15 / 20 )8.20.15462226869701453.0324646579084
Trimmed Mean ( 16 / 20 )8.178571428571430.14596487426785356.0310928885762
Trimmed Mean ( 17 / 20 )8.192307692307690.14696133211186855.7446477558577
Trimmed Mean ( 18 / 20 )8.208333333333330.1471857579489155.7685298341334
Trimmed Mean ( 19 / 20 )8.227272727272730.14611592062110556.3064770238621
Trimmed Mean ( 20 / 20 )8.250.1428101426443757.7690060890451
Median8
Midrange10.5
Midmean - Weighted Average at Xnp7.8974358974359
Midmean - Weighted Average at X(n+1)p8.3125
Midmean - Empirical Distribution Function7.8974358974359
Midmean - Empirical Distribution Function - Averaging8.3125
Midmean - Empirical Distribution Function - Interpolation8.3125
Midmean - Closest Observation7.8974358974359
Midmean - True Basic - Statistics Graphics Toolkit8.3125
Midmean - MS Excel (old versions)7.8974358974359
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')