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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 12 Dec 2015 16:56:37 +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/2015/Dec/12/t1449939833qotfwciyi17411r.htm/, Retrieved Thu, 16 May 2024 23:41:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286117, Retrieved Thu, 16 May 2024 23:41:58 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact46
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Getrimde gemiddel...] [2015-12-12 16:56:37] [18106851e169be8e7181c7a62bb5da83] [Current]
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Dataseries X:
12,2
12,6
10,6
12
11,9
9,6
13,8
9,9
11,5
8,3
10,3
9,3
12,3
7,9
9,3
12,5
15,9
9,1
12,2
12,3
14,6
12,6
12,6
17,1
16,1
13,35
14,5
8,6
17,65
16,35
13,6
14,35
18,25
18,25
18,95
15,9
13,35
15,35
14,85
13,6
15,25
13,2
15,65
15,6
15,2
18,4
19,05
18,55
12,4
14,6
14,05
11,85
7,85
15,2




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286117&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286117&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286117&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean13.52314814814810.40856208661784633.0993711631329
Geometric Mean13.1785456373631
Harmonic Mean12.8171087086583
Quadratic Mean13.8463877492906
Winsorized Mean ( 1 / 18 )13.52222222222220.40785154623253233.1547651274875
Winsorized Mean ( 2 / 18 )13.52222222222220.40048596149872633.7645348956015
Winsorized Mean ( 3 / 18 )13.53055555555560.39451253583009334.2968963637263
Winsorized Mean ( 4 / 18 )13.55648148148150.38350430581563735.3489681234466
Winsorized Mean ( 5 / 18 )13.5750.37950588990843435.7701958282527
Winsorized Mean ( 6 / 18 )13.50833333333330.3646019387286237.0495378615851
Winsorized Mean ( 7 / 18 )13.47592592592590.34140320859632939.4721712819627
Winsorized Mean ( 8 / 18 )13.40925925925930.31080606322020343.1434931491633
Winsorized Mean ( 9 / 18 )13.43425925925930.28954476448304646.3978662616982
Winsorized Mean ( 10 / 18 )13.45277777777780.27200634275842849.4575885302989
Winsorized Mean ( 11 / 18 )13.63611111111110.23818120765000557.2509949279822
Winsorized Mean ( 12 / 18 )13.65833333333330.21559463055458863.3519178942403
Winsorized Mean ( 13 / 18 )13.65833333333330.21160739690822664.5456327751008
Winsorized Mean ( 14 / 18 )13.61944444444440.19655673590832369.2901435379797
Winsorized Mean ( 15 / 18 )13.64722222222220.18350200296457374.370971443058
Winsorized Mean ( 16 / 18 )13.63240740740740.18107122334455375.287542413445
Winsorized Mean ( 17 / 18 )13.66388888888890.17642509821646577.4486681714862
Winsorized Mean ( 18 / 18 )13.54722222222220.15772345670734685.8922477672992
Trimmed Mean ( 1 / 18 )13.52596153846150.39558386689520934.1923993124942
Trimmed Mean ( 2 / 18 )13.530.38008055000196535.5977173784085
Trimmed Mean ( 3 / 18 )13.5343750.36549768196066237.0299886100418
Trimmed Mean ( 4 / 18 )13.53586956521740.34984697497923538.6908292290388
Trimmed Mean ( 5 / 18 )13.52954545454550.33430657059701940.4704742428
Trimmed Mean ( 6 / 18 )13.51785714285710.31537646617014842.8626057835405
Trimmed Mean ( 7 / 18 )13.520.29570537138622745.7211850316416
Trimmed Mean ( 8 / 18 )13.52894736842110.27743895551289548.7636905329694
Trimmed Mean ( 9 / 18 )13.55138888888890.26288604350457451.5485291962756
Trimmed Mean ( 10 / 18 )13.57205882352940.2497698689142254.3382549805898
Trimmed Mean ( 11 / 18 )13.59218750.2370231777045357.3453939468479
Trimmed Mean ( 12 / 18 )13.5850.23000687146157259.0634528163202
Trimmed Mean ( 13 / 18 )13.57321428571430.22639167117080659.9545655346733
Trimmed Mean ( 14 / 18 )13.55961538461540.2213076388331861.2704353817472
Trimmed Mean ( 15 / 18 )13.550.21784102034494762.2013245188801
Trimmed Mean ( 16 / 18 )13.53409090909090.21560812927002562.7717097444919
Trimmed Mean ( 17 / 18 )13.51750.21098999103225164.0670201172423
Trimmed Mean ( 18 / 18 )13.49166666666670.20284939195618466.510757249797
Median13.475
Midrange13.45
Midmean - Weighted Average at Xnp13.4981481481482
Midmean - Weighted Average at X(n+1)p13.5732142857143
Midmean - Empirical Distribution Function13.5732142857143
Midmean - Empirical Distribution Function - Averaging13.5732142857143
Midmean - Empirical Distribution Function - Interpolation13.5596153846154
Midmean - Closest Observation13.5732142857143
Midmean - True Basic - Statistics Graphics Toolkit13.5732142857143
Midmean - MS Excel (old versions)13.5732142857143
Number of observations54

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 13.5231481481481 & 0.408562086617846 & 33.0993711631329 \tabularnewline
Geometric Mean & 13.1785456373631 &  &  \tabularnewline
Harmonic Mean & 12.8171087086583 &  &  \tabularnewline
Quadratic Mean & 13.8463877492906 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & 13.5222222222222 & 0.407851546232532 & 33.1547651274875 \tabularnewline
Winsorized Mean ( 2 / 18 ) & 13.5222222222222 & 0.400485961498726 & 33.7645348956015 \tabularnewline
Winsorized Mean ( 3 / 18 ) & 13.5305555555556 & 0.394512535830093 & 34.2968963637263 \tabularnewline
Winsorized Mean ( 4 / 18 ) & 13.5564814814815 & 0.383504305815637 & 35.3489681234466 \tabularnewline
Winsorized Mean ( 5 / 18 ) & 13.575 & 0.379505889908434 & 35.7701958282527 \tabularnewline
Winsorized Mean ( 6 / 18 ) & 13.5083333333333 & 0.36460193872862 & 37.0495378615851 \tabularnewline
Winsorized Mean ( 7 / 18 ) & 13.4759259259259 & 0.341403208596329 & 39.4721712819627 \tabularnewline
Winsorized Mean ( 8 / 18 ) & 13.4092592592593 & 0.310806063220203 & 43.1434931491633 \tabularnewline
Winsorized Mean ( 9 / 18 ) & 13.4342592592593 & 0.289544764483046 & 46.3978662616982 \tabularnewline
Winsorized Mean ( 10 / 18 ) & 13.4527777777778 & 0.272006342758428 & 49.4575885302989 \tabularnewline
Winsorized Mean ( 11 / 18 ) & 13.6361111111111 & 0.238181207650005 & 57.2509949279822 \tabularnewline
Winsorized Mean ( 12 / 18 ) & 13.6583333333333 & 0.215594630554588 & 63.3519178942403 \tabularnewline
Winsorized Mean ( 13 / 18 ) & 13.6583333333333 & 0.211607396908226 & 64.5456327751008 \tabularnewline
Winsorized Mean ( 14 / 18 ) & 13.6194444444444 & 0.196556735908323 & 69.2901435379797 \tabularnewline
Winsorized Mean ( 15 / 18 ) & 13.6472222222222 & 0.183502002964573 & 74.370971443058 \tabularnewline
Winsorized Mean ( 16 / 18 ) & 13.6324074074074 & 0.181071223344553 & 75.287542413445 \tabularnewline
Winsorized Mean ( 17 / 18 ) & 13.6638888888889 & 0.176425098216465 & 77.4486681714862 \tabularnewline
Winsorized Mean ( 18 / 18 ) & 13.5472222222222 & 0.157723456707346 & 85.8922477672992 \tabularnewline
Trimmed Mean ( 1 / 18 ) & 13.5259615384615 & 0.395583866895209 & 34.1923993124942 \tabularnewline
Trimmed Mean ( 2 / 18 ) & 13.53 & 0.380080550001965 & 35.5977173784085 \tabularnewline
Trimmed Mean ( 3 / 18 ) & 13.534375 & 0.365497681960662 & 37.0299886100418 \tabularnewline
Trimmed Mean ( 4 / 18 ) & 13.5358695652174 & 0.349846974979235 & 38.6908292290388 \tabularnewline
Trimmed Mean ( 5 / 18 ) & 13.5295454545455 & 0.334306570597019 & 40.4704742428 \tabularnewline
Trimmed Mean ( 6 / 18 ) & 13.5178571428571 & 0.315376466170148 & 42.8626057835405 \tabularnewline
Trimmed Mean ( 7 / 18 ) & 13.52 & 0.295705371386227 & 45.7211850316416 \tabularnewline
Trimmed Mean ( 8 / 18 ) & 13.5289473684211 & 0.277438955512895 & 48.7636905329694 \tabularnewline
Trimmed Mean ( 9 / 18 ) & 13.5513888888889 & 0.262886043504574 & 51.5485291962756 \tabularnewline
Trimmed Mean ( 10 / 18 ) & 13.5720588235294 & 0.24976986891422 & 54.3382549805898 \tabularnewline
Trimmed Mean ( 11 / 18 ) & 13.5921875 & 0.23702317770453 & 57.3453939468479 \tabularnewline
Trimmed Mean ( 12 / 18 ) & 13.585 & 0.230006871461572 & 59.0634528163202 \tabularnewline
Trimmed Mean ( 13 / 18 ) & 13.5732142857143 & 0.226391671170806 & 59.9545655346733 \tabularnewline
Trimmed Mean ( 14 / 18 ) & 13.5596153846154 & 0.22130763883318 & 61.2704353817472 \tabularnewline
Trimmed Mean ( 15 / 18 ) & 13.55 & 0.217841020344947 & 62.2013245188801 \tabularnewline
Trimmed Mean ( 16 / 18 ) & 13.5340909090909 & 0.215608129270025 & 62.7717097444919 \tabularnewline
Trimmed Mean ( 17 / 18 ) & 13.5175 & 0.210989991032251 & 64.0670201172423 \tabularnewline
Trimmed Mean ( 18 / 18 ) & 13.4916666666667 & 0.202849391956184 & 66.510757249797 \tabularnewline
Median & 13.475 &  &  \tabularnewline
Midrange & 13.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13.4981481481482 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13.5732142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13.5732142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13.5732142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13.5596153846154 &  &  \tabularnewline
Midmean - Closest Observation & 13.5732142857143 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13.5732142857143 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13.5732142857143 &  &  \tabularnewline
Number of observations & 54 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286117&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]13.5231481481481[/C][C]0.408562086617846[/C][C]33.0993711631329[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]13.1785456373631[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]12.8171087086583[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13.8463877492906[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]13.5222222222222[/C][C]0.407851546232532[/C][C]33.1547651274875[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]13.5222222222222[/C][C]0.400485961498726[/C][C]33.7645348956015[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]13.5305555555556[/C][C]0.394512535830093[/C][C]34.2968963637263[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]13.5564814814815[/C][C]0.383504305815637[/C][C]35.3489681234466[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]13.575[/C][C]0.379505889908434[/C][C]35.7701958282527[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]13.5083333333333[/C][C]0.36460193872862[/C][C]37.0495378615851[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]13.4759259259259[/C][C]0.341403208596329[/C][C]39.4721712819627[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]13.4092592592593[/C][C]0.310806063220203[/C][C]43.1434931491633[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]13.4342592592593[/C][C]0.289544764483046[/C][C]46.3978662616982[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]13.4527777777778[/C][C]0.272006342758428[/C][C]49.4575885302989[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]13.6361111111111[/C][C]0.238181207650005[/C][C]57.2509949279822[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]13.6583333333333[/C][C]0.215594630554588[/C][C]63.3519178942403[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]13.6583333333333[/C][C]0.211607396908226[/C][C]64.5456327751008[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]13.6194444444444[/C][C]0.196556735908323[/C][C]69.2901435379797[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]13.6472222222222[/C][C]0.183502002964573[/C][C]74.370971443058[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]13.6324074074074[/C][C]0.181071223344553[/C][C]75.287542413445[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]13.6638888888889[/C][C]0.176425098216465[/C][C]77.4486681714862[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]13.5472222222222[/C][C]0.157723456707346[/C][C]85.8922477672992[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]13.5259615384615[/C][C]0.395583866895209[/C][C]34.1923993124942[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]13.53[/C][C]0.380080550001965[/C][C]35.5977173784085[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]13.534375[/C][C]0.365497681960662[/C][C]37.0299886100418[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]13.5358695652174[/C][C]0.349846974979235[/C][C]38.6908292290388[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]13.5295454545455[/C][C]0.334306570597019[/C][C]40.4704742428[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]13.5178571428571[/C][C]0.315376466170148[/C][C]42.8626057835405[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]13.52[/C][C]0.295705371386227[/C][C]45.7211850316416[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]13.5289473684211[/C][C]0.277438955512895[/C][C]48.7636905329694[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]13.5513888888889[/C][C]0.262886043504574[/C][C]51.5485291962756[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]13.5720588235294[/C][C]0.24976986891422[/C][C]54.3382549805898[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]13.5921875[/C][C]0.23702317770453[/C][C]57.3453939468479[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]13.585[/C][C]0.230006871461572[/C][C]59.0634528163202[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]13.5732142857143[/C][C]0.226391671170806[/C][C]59.9545655346733[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]13.5596153846154[/C][C]0.22130763883318[/C][C]61.2704353817472[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]13.55[/C][C]0.217841020344947[/C][C]62.2013245188801[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]13.5340909090909[/C][C]0.215608129270025[/C][C]62.7717097444919[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]13.5175[/C][C]0.210989991032251[/C][C]64.0670201172423[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]13.4916666666667[/C][C]0.202849391956184[/C][C]66.510757249797[/C][/ROW]
[ROW][C]Median[/C][C]13.475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]13.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13.4981481481482[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13.5732142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13.5732142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13.5732142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13.5596153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13.5732142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13.5732142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13.5732142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]54[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286117&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286117&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 Mean13.52314814814810.40856208661784633.0993711631329
Geometric Mean13.1785456373631
Harmonic Mean12.8171087086583
Quadratic Mean13.8463877492906
Winsorized Mean ( 1 / 18 )13.52222222222220.40785154623253233.1547651274875
Winsorized Mean ( 2 / 18 )13.52222222222220.40048596149872633.7645348956015
Winsorized Mean ( 3 / 18 )13.53055555555560.39451253583009334.2968963637263
Winsorized Mean ( 4 / 18 )13.55648148148150.38350430581563735.3489681234466
Winsorized Mean ( 5 / 18 )13.5750.37950588990843435.7701958282527
Winsorized Mean ( 6 / 18 )13.50833333333330.3646019387286237.0495378615851
Winsorized Mean ( 7 / 18 )13.47592592592590.34140320859632939.4721712819627
Winsorized Mean ( 8 / 18 )13.40925925925930.31080606322020343.1434931491633
Winsorized Mean ( 9 / 18 )13.43425925925930.28954476448304646.3978662616982
Winsorized Mean ( 10 / 18 )13.45277777777780.27200634275842849.4575885302989
Winsorized Mean ( 11 / 18 )13.63611111111110.23818120765000557.2509949279822
Winsorized Mean ( 12 / 18 )13.65833333333330.21559463055458863.3519178942403
Winsorized Mean ( 13 / 18 )13.65833333333330.21160739690822664.5456327751008
Winsorized Mean ( 14 / 18 )13.61944444444440.19655673590832369.2901435379797
Winsorized Mean ( 15 / 18 )13.64722222222220.18350200296457374.370971443058
Winsorized Mean ( 16 / 18 )13.63240740740740.18107122334455375.287542413445
Winsorized Mean ( 17 / 18 )13.66388888888890.17642509821646577.4486681714862
Winsorized Mean ( 18 / 18 )13.54722222222220.15772345670734685.8922477672992
Trimmed Mean ( 1 / 18 )13.52596153846150.39558386689520934.1923993124942
Trimmed Mean ( 2 / 18 )13.530.38008055000196535.5977173784085
Trimmed Mean ( 3 / 18 )13.5343750.36549768196066237.0299886100418
Trimmed Mean ( 4 / 18 )13.53586956521740.34984697497923538.6908292290388
Trimmed Mean ( 5 / 18 )13.52954545454550.33430657059701940.4704742428
Trimmed Mean ( 6 / 18 )13.51785714285710.31537646617014842.8626057835405
Trimmed Mean ( 7 / 18 )13.520.29570537138622745.7211850316416
Trimmed Mean ( 8 / 18 )13.52894736842110.27743895551289548.7636905329694
Trimmed Mean ( 9 / 18 )13.55138888888890.26288604350457451.5485291962756
Trimmed Mean ( 10 / 18 )13.57205882352940.2497698689142254.3382549805898
Trimmed Mean ( 11 / 18 )13.59218750.2370231777045357.3453939468479
Trimmed Mean ( 12 / 18 )13.5850.23000687146157259.0634528163202
Trimmed Mean ( 13 / 18 )13.57321428571430.22639167117080659.9545655346733
Trimmed Mean ( 14 / 18 )13.55961538461540.2213076388331861.2704353817472
Trimmed Mean ( 15 / 18 )13.550.21784102034494762.2013245188801
Trimmed Mean ( 16 / 18 )13.53409090909090.21560812927002562.7717097444919
Trimmed Mean ( 17 / 18 )13.51750.21098999103225164.0670201172423
Trimmed Mean ( 18 / 18 )13.49166666666670.20284939195618466.510757249797
Median13.475
Midrange13.45
Midmean - Weighted Average at Xnp13.4981481481482
Midmean - Weighted Average at X(n+1)p13.5732142857143
Midmean - Empirical Distribution Function13.5732142857143
Midmean - Empirical Distribution Function - Averaging13.5732142857143
Midmean - Empirical Distribution Function - Interpolation13.5596153846154
Midmean - Closest Observation13.5732142857143
Midmean - True Basic - Statistics Graphics Toolkit13.5732142857143
Midmean - MS Excel (old versions)13.5732142857143
Number of observations54



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')