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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 24 Jan 2017 19:07:01 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Jan/24/t1485281233s2c6x1ftn7zzja5.htm/, Retrieved Mon, 13 May 2024 20:49:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=305235, Retrieved Mon, 13 May 2024 20:49:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact52

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [sdfq] [2017-01-24 18:07:01] [3e1967f5210cd535e22e7f22478b75ce] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4.2
11.5
7.3
5.8
6.4
10
11.2
11.2
5.2
7
16.5
16.5
15.2
17.3
22.5
17.3
13.6
14.5
18.8
15.5
23.6
18.5
33.9
25.5
26.4
32.5
26.7
21.5
23.3
29.5
15.2
21.5
17.6
9.7
14.5
10
8.2
9.4
16.5
9.7
19.7
23.3
23.6
26.4
20
25.2
25.8
21.2
14.5
27.3
25.5
26.4
22.4
24.5
24.8
30.9
26.4
27.3
29.4
23

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=305235&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=305235&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305235&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean18.81330.98752219.051
Geometric Mean16.9307
Harmonic Mean14.6992
Quadratic Mean20.2849
Winsorized Mean ( 1 / 20 )18.80670.97767419.2361
Winsorized Mean ( 2 / 20 )18.77330.96098719.5355
Winsorized Mean ( 3 / 20 )18.73330.93992919.9306
Winsorized Mean ( 4 / 20 )18.76670.92989820.1814
Winsorized Mean ( 5 / 20 )18.61670.89310320.8449
Winsorized Mean ( 6 / 20 )18.70670.87426821.397
Winsorized Mean ( 7 / 20 )18.77670.83520522.4815
Winsorized Mean ( 8 / 20 )18.77670.82128922.8624
Winsorized Mean ( 9 / 20 )18.77670.82128922.8624
Winsorized Mean ( 10 / 20 )18.82670.81223.1856
Winsorized Mean ( 11 / 20 )18.82670.81223.1856
Winsorized Mean ( 12 / 20 )18.94670.75005625.2603
Winsorized Mean ( 13 / 20 )18.88170.74009725.5124
Winsorized Mean ( 14 / 20 )18.95170.72786526.0373
Winsorized Mean ( 15 / 20 )19.40170.62941330.825
Winsorized Mean ( 16 / 20 )19.5350.57626233.8995
Winsorized Mean ( 17 / 20 )19.450.56322134.5335
Winsorized Mean ( 18 / 20 )19.180.52333636.6495
Winsorized Mean ( 19 / 20 )19.40170.49041939.5614
Winsorized Mean ( 20 / 20 )19.30170.47604540.5459
Trimmed Mean ( 1 / 20 )18.80520.95434919.7047
Trimmed Mean ( 2 / 20 )18.80360.92553920.3163
Trimmed Mean ( 3 / 20 )18.82040.90092120.8901
Trimmed Mean ( 4 / 20 )18.85380.88018921.4202
Trimmed Mean ( 5 / 20 )18.880.85781422.0094
Trimmed Mean ( 6 / 20 )18.94580.84152522.5137
Trimmed Mean ( 7 / 20 )18.99780.82597623.0005
Trimmed Mean ( 8 / 20 )19.04090.81629423.3261
Trimmed Mean ( 9 / 20 )19.08810.80619123.6769
Trimmed Mean ( 10 / 20 )19.140.79158124.1795
Trimmed Mean ( 11 / 20 )19.18950.77347424.8095
Trimmed Mean ( 12 / 20 )19.24440.74780625.7346
Trimmed Mean ( 13 / 20 )19.28820.72935426.4457
Trimmed Mean ( 14 / 20 )19.34690.70477927.451
Trimmed Mean ( 15 / 20 )19.40330.67228428.8618
Trimmed Mean ( 16 / 20 )19.40360.656629.5516
Trimmed Mean ( 17 / 20 )19.38460.64778229.9246
Trimmed Mean ( 18 / 20 )19.3750.63520730.5019
Trimmed Mean ( 19 / 20 )19.40450.62607430.994
Trimmed Mean ( 20 / 20 )19.4050.61944331.3265
Median19.25
Midrange19.05
Midmean - Weighted Average at Xnp19.1484
Midmean - Weighted Average at X(n+1)p19.4033
Midmean - Empirical Distribution Function19.1484
Midmean - Empirical Distribution Function - Averaging19.4033
Midmean - Empirical Distribution Function - Interpolation19.4033
Midmean - Closest Observation19.1484
Midmean - True Basic - Statistics Graphics Toolkit19.4033
Midmean - MS Excel (old versions)19.5333
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 18.8133 & 0.987522 & 19.051 \tabularnewline
Geometric Mean & 16.9307 &  &  \tabularnewline
Harmonic Mean & 14.6992 &  &  \tabularnewline
Quadratic Mean & 20.2849 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 18.8067 & 0.977674 & 19.2361 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 18.7733 & 0.960987 & 19.5355 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 18.7333 & 0.939929 & 19.9306 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 18.7667 & 0.929898 & 20.1814 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 18.6167 & 0.893103 & 20.8449 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 18.7067 & 0.874268 & 21.397 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 18.7767 & 0.835205 & 22.4815 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 18.7767 & 0.821289 & 22.8624 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 18.7767 & 0.821289 & 22.8624 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 18.8267 & 0.812 & 23.1856 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 18.8267 & 0.812 & 23.1856 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 18.9467 & 0.750056 & 25.2603 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 18.8817 & 0.740097 & 25.5124 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 18.9517 & 0.727865 & 26.0373 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 19.4017 & 0.629413 & 30.825 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 19.535 & 0.576262 & 33.8995 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 19.45 & 0.563221 & 34.5335 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 19.18 & 0.523336 & 36.6495 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 19.4017 & 0.490419 & 39.5614 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 19.3017 & 0.476045 & 40.5459 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 18.8052 & 0.954349 & 19.7047 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 18.8036 & 0.925539 & 20.3163 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 18.8204 & 0.900921 & 20.8901 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 18.8538 & 0.880189 & 21.4202 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 18.88 & 0.857814 & 22.0094 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 18.9458 & 0.841525 & 22.5137 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 18.9978 & 0.825976 & 23.0005 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 19.0409 & 0.816294 & 23.3261 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 19.0881 & 0.806191 & 23.6769 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 19.14 & 0.791581 & 24.1795 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 19.1895 & 0.773474 & 24.8095 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 19.2444 & 0.747806 & 25.7346 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 19.2882 & 0.729354 & 26.4457 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 19.3469 & 0.704779 & 27.451 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 19.4033 & 0.672284 & 28.8618 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 19.4036 & 0.6566 & 29.5516 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 19.3846 & 0.647782 & 29.9246 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 19.375 & 0.635207 & 30.5019 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 19.4045 & 0.626074 & 30.994 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 19.405 & 0.619443 & 31.3265 \tabularnewline
Median & 19.25 &  &  \tabularnewline
Midrange & 19.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 19.1484 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 19.4033 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 19.1484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 19.4033 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 19.4033 &  &  \tabularnewline
Midmean - Closest Observation & 19.1484 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 19.4033 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 19.5333 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=305235&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]18.8133[/C][C]0.987522[/C][C]19.051[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]16.9307[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]14.6992[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]20.2849[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]18.8067[/C][C]0.977674[/C][C]19.2361[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]18.7733[/C][C]0.960987[/C][C]19.5355[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]18.7333[/C][C]0.939929[/C][C]19.9306[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]18.7667[/C][C]0.929898[/C][C]20.1814[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]18.6167[/C][C]0.893103[/C][C]20.8449[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]18.7067[/C][C]0.874268[/C][C]21.397[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]18.7767[/C][C]0.835205[/C][C]22.4815[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]18.7767[/C][C]0.821289[/C][C]22.8624[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]18.7767[/C][C]0.821289[/C][C]22.8624[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]18.8267[/C][C]0.812[/C][C]23.1856[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]18.8267[/C][C]0.812[/C][C]23.1856[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]18.9467[/C][C]0.750056[/C][C]25.2603[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]18.8817[/C][C]0.740097[/C][C]25.5124[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]18.9517[/C][C]0.727865[/C][C]26.0373[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]19.4017[/C][C]0.629413[/C][C]30.825[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]19.535[/C][C]0.576262[/C][C]33.8995[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]19.45[/C][C]0.563221[/C][C]34.5335[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]19.18[/C][C]0.523336[/C][C]36.6495[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]19.4017[/C][C]0.490419[/C][C]39.5614[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]19.3017[/C][C]0.476045[/C][C]40.5459[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]18.8052[/C][C]0.954349[/C][C]19.7047[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]18.8036[/C][C]0.925539[/C][C]20.3163[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]18.8204[/C][C]0.900921[/C][C]20.8901[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]18.8538[/C][C]0.880189[/C][C]21.4202[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]18.88[/C][C]0.857814[/C][C]22.0094[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]18.9458[/C][C]0.841525[/C][C]22.5137[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]18.9978[/C][C]0.825976[/C][C]23.0005[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]19.0409[/C][C]0.816294[/C][C]23.3261[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]19.0881[/C][C]0.806191[/C][C]23.6769[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]19.14[/C][C]0.791581[/C][C]24.1795[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]19.1895[/C][C]0.773474[/C][C]24.8095[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]19.2444[/C][C]0.747806[/C][C]25.7346[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]19.2882[/C][C]0.729354[/C][C]26.4457[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]19.3469[/C][C]0.704779[/C][C]27.451[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]19.4033[/C][C]0.672284[/C][C]28.8618[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]19.4036[/C][C]0.6566[/C][C]29.5516[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]19.3846[/C][C]0.647782[/C][C]29.9246[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]19.375[/C][C]0.635207[/C][C]30.5019[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]19.4045[/C][C]0.626074[/C][C]30.994[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]19.405[/C][C]0.619443[/C][C]31.3265[/C][/ROW]
[ROW][C]Median[/C][C]19.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]19.1484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]19.4033[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]19.1484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]19.4033[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]19.4033[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]19.1484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]19.4033[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]19.5333[/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=305235&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=305235&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean18.81330.98752219.051
Geometric Mean16.9307
Harmonic Mean14.6992
Quadratic Mean20.2849
Winsorized Mean ( 1 / 20 )18.80670.97767419.2361
Winsorized Mean ( 2 / 20 )18.77330.96098719.5355
Winsorized Mean ( 3 / 20 )18.73330.93992919.9306
Winsorized Mean ( 4 / 20 )18.76670.92989820.1814
Winsorized Mean ( 5 / 20 )18.61670.89310320.8449
Winsorized Mean ( 6 / 20 )18.70670.87426821.397
Winsorized Mean ( 7 / 20 )18.77670.83520522.4815
Winsorized Mean ( 8 / 20 )18.77670.82128922.8624
Winsorized Mean ( 9 / 20 )18.77670.82128922.8624
Winsorized Mean ( 10 / 20 )18.82670.81223.1856
Winsorized Mean ( 11 / 20 )18.82670.81223.1856
Winsorized Mean ( 12 / 20 )18.94670.75005625.2603
Winsorized Mean ( 13 / 20 )18.88170.74009725.5124
Winsorized Mean ( 14 / 20 )18.95170.72786526.0373
Winsorized Mean ( 15 / 20 )19.40170.62941330.825
Winsorized Mean ( 16 / 20 )19.5350.57626233.8995
Winsorized Mean ( 17 / 20 )19.450.56322134.5335
Winsorized Mean ( 18 / 20 )19.180.52333636.6495
Winsorized Mean ( 19 / 20 )19.40170.49041939.5614
Winsorized Mean ( 20 / 20 )19.30170.47604540.5459
Trimmed Mean ( 1 / 20 )18.80520.95434919.7047
Trimmed Mean ( 2 / 20 )18.80360.92553920.3163
Trimmed Mean ( 3 / 20 )18.82040.90092120.8901
Trimmed Mean ( 4 / 20 )18.85380.88018921.4202
Trimmed Mean ( 5 / 20 )18.880.85781422.0094
Trimmed Mean ( 6 / 20 )18.94580.84152522.5137
Trimmed Mean ( 7 / 20 )18.99780.82597623.0005
Trimmed Mean ( 8 / 20 )19.04090.81629423.3261
Trimmed Mean ( 9 / 20 )19.08810.80619123.6769
Trimmed Mean ( 10 / 20 )19.140.79158124.1795
Trimmed Mean ( 11 / 20 )19.18950.77347424.8095
Trimmed Mean ( 12 / 20 )19.24440.74780625.7346
Trimmed Mean ( 13 / 20 )19.28820.72935426.4457
Trimmed Mean ( 14 / 20 )19.34690.70477927.451
Trimmed Mean ( 15 / 20 )19.40330.67228428.8618
Trimmed Mean ( 16 / 20 )19.40360.656629.5516
Trimmed Mean ( 17 / 20 )19.38460.64778229.9246
Trimmed Mean ( 18 / 20 )19.3750.63520730.5019
Trimmed Mean ( 19 / 20 )19.40450.62607430.994
Trimmed Mean ( 20 / 20 )19.4050.61944331.3265
Median19.25
Midrange19.05
Midmean - Weighted Average at Xnp19.1484
Midmean - Weighted Average at X(n+1)p19.4033
Midmean - Empirical Distribution Function19.1484
Midmean - Empirical Distribution Function - Averaging19.4033
Midmean - Empirical Distribution Function - Interpolation19.4033
Midmean - Closest Observation19.1484
Midmean - True Basic - Statistics Graphics Toolkit19.4033
Midmean - MS Excel (old versions)19.5333
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par4 = TRUE ;
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,'Arithmetic Mean',header=TRUE)
a<-table.element(a,signif(arm,6))
a<-table.element(a, signif(armse,6))
a<-table.element(a,signif(armose,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Geometric Mean',header=TRUE)
a<-table.element(a,signif(geo,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Harmonic Mean',header=TRUE)
a<-table.element(a,signif(har,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Quadratic Mean',header=TRUE)
a<-table.element(a,signif(qua,6))
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, mylabel,header=TRUE)
a<-table.element(a,signif(win[j,1],6))
a<-table.element(a,signif(win[j,2],6))
a<-table.element(a,signif(win[j,1]/win[j,2],6))
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, mylabel,header=TRUE)
a<-table.element(a,signif(tri[j,1],6))
a<-table.element(a,signif(tri[j,2],6))
a<-table.element(a,signif(tri[j,1]/tri[j,2],6))
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, 'Median',header=TRUE)
a<-table.element(a,signif(median(x),6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Midrange',header=TRUE)
a<-table.element(a,signif(midr,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Weighted Average at Xnp',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[1],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Weighted Average at X(n+1)p',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[2],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[3],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function - Averaging',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[4],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function - Interpolation',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[5],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Closest Observation',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[6],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'True Basic - Statistics Graphics Toolkit',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[7],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'MS Excel (old versions)',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[8],6))
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,signif(length(x),6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')