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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 15 Oct 2012 12:21:52 -0400

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/15/t13503181392idm9f2pbsmnt50.htm/, Retrieved Tue, 07 May 2024 19:08:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=177405, Retrieved Tue, 07 May 2024 19:08:26 +0000

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Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Central Tendency] [Prijs tonijn in b...] [2012-10-15 16:21:52] [99829035b61c7d7eb141f248bedbb510] [Current]

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1,41
1,43
1,43
1,45
1,49
1,54
1,54
1,55
1,55
1,55
1,55
1,56
1,56
1,59
1,62
1,62
1,64
1,65
1,64
1,65
1,65
1,65
1,66
1,67
1,68
1,68
1,68
1,71
1,71
1,71
1,71
1,71
1,72
1,79
1,8
1,8
1,84
1,9
1,9
1,92
1,93
1,93
1,94
1,94
1,95
1,95
1,96
1,95
1,95
1,94
1,94
1,93
1,93
1,9
1,91
1,9
1,91
1,91
1,91
1,91
1,93
1,94
1,93
1,91
1,88
1,88
1,89
1,9
1,92
1,93
1,96
1,96

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=177405&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=177405&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=177405&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.77125	0.0198743485439636	89.1224180798609
Geometric Mean	1.76303320544125
Harmonic Mean	1.75453519483045
Quadratic Mean	1.77914890701519
Winsorized Mean ( 1 / 24 )	1.77152777777778	0.0198050551179404	89.4482629423758
Winsorized Mean ( 2 / 24 )	1.77152777777778	0.0198050551179404	89.4482629423758
Winsorized Mean ( 3 / 24 )	1.77194444444444	0.0195525443602129	90.624749996739
Winsorized Mean ( 4 / 24 )	1.77416666666667	0.0190612532943613	93.0771255839457
Winsorized Mean ( 5 / 24 )	1.77763888888889	0.0183796821885881	96.7176075543144
Winsorized Mean ( 6 / 24 )	1.77763888888889	0.0183796821885881	96.7176075543144
Winsorized Mean ( 7 / 24 )	1.77763888888889	0.0180792173714761	98.3249911964385
Winsorized Mean ( 8 / 24 )	1.77763888888889	0.0180792173714761	98.3249911964385
Winsorized Mean ( 9 / 24 )	1.77763888888889	0.0180792173714761	98.3249911964385
Winsorized Mean ( 10 / 24 )	1.77763888888889	0.0180792173714761	98.3249911964385
Winsorized Mean ( 11 / 24 )	1.77916666666667	0.0178113374068062	99.8895605664515
Winsorized Mean ( 12 / 24 )	1.7775	0.0176036501229882	100.973376974745
Winsorized Mean ( 13 / 24 )	1.78291666666667	0.0166906371052652	106.821366699311
Winsorized Mean ( 14 / 24 )	1.78875	0.0157753912624558	113.388629812123
Winsorized Mean ( 15 / 24 )	1.78875	0.0157753912624558	113.388629812123
Winsorized Mean ( 16 / 24 )	1.79319444444444	0.0151231594786584	118.57273918026
Winsorized Mean ( 17 / 24 )	1.79319444444444	0.0151231594786584	118.57273918026
Winsorized Mean ( 18 / 24 )	1.79569444444444	0.014771110180549	121.568008260412
Winsorized Mean ( 19 / 24 )	1.79305555555556	0.0144386876092768	124.184108977019
Winsorized Mean ( 20 / 24 )	1.79305555555556	0.0144386876092768	124.184108977019
Winsorized Mean ( 21 / 24 )	1.79013888888889	0.0140832160391198	127.111512307722
Winsorized Mean ( 22 / 24 )	1.79319444444444	0.0136592021136739	131.281053572618
Winsorized Mean ( 23 / 24 )	1.79638888888889	0.0132247715878455	135.83515427517
Winsorized Mean ( 24 / 24 )	1.79972222222222	0.0127804566151585	140.818303791089
Trimmed Mean ( 1 / 24 )	1.77371428571429	0.0195848966067254	90.5654148363078
Trimmed Mean ( 2 / 24 )	1.77602941176471	0.0193134348762729	91.9582364888708
Trimmed Mean ( 3 / 24 )	1.77848484848485	0.0189801054281209	93.7025800631144
Trimmed Mean ( 4 / 24 )	1.7809375	0.0186853631256898	95.3119020497629
Trimmed Mean ( 5 / 24 )	1.78290322580645	0.0184991990290314	96.3773200671274
Trimmed Mean ( 6 / 24 )	1.78416666666667	0.018467090390619	96.6133066404981
Trimmed Mean ( 7 / 24 )	1.78551724137931	0.0184062057412126	97.006263348531
Trimmed Mean ( 8 / 24 )	1.78696428571429	0.0183807487568068	97.2193412443297
Trimmed Mean ( 9 / 24 )	1.78851851851852	0.0183231483189755	97.6097823028765
Trimmed Mean ( 10 / 24 )	1.79019230769231	0.0182253581331369	98.2253569238468
Trimmed Mean ( 11 / 24 )	1.792	0.0180769330972951	99.1318599429981
Trimmed Mean ( 12 / 24 )	1.79375	0.017923262846475	100.079433938156
Trimmed Mean ( 13 / 24 )	1.79586956521739	0.0177382364556397	101.242847320733
Trimmed Mean ( 14 / 24 )	1.7975	0.017671314891056	101.718520160023
Trimmed Mean ( 15 / 24 )	1.79857142857143	0.0177365264449807	101.404941613041
Trimmed Mean ( 16 / 24 )	1.79975	0.0177680478849261	101.291374925146
Trimmed Mean ( 17 / 24 )	1.80052631578947	0.0178899248822677	100.644710787698
Trimmed Mean ( 18 / 24 )	1.80138888888889	0.0179821462504966	100.176523079893
Trimmed Mean ( 19 / 24 )	1.80205882352941	0.01810929096374	99.5101811074576
Trimmed Mean ( 20 / 24 )	1.803125	0.0182635141082061	98.7282616760934
Trimmed Mean ( 21 / 24 )	1.80433333333333	0.0183746660511265	98.1967959751145
Trimmed Mean ( 22 / 24 )	1.80607142857143	0.0184973849554191	97.6392843055533
Trimmed Mean ( 23 / 24 )	1.80769230769231	0.0186655395545884	96.8465070300062
Trimmed Mean ( 24 / 24 )	1.80916666666667	0.0188905760826477	95.7708573180315
Median	1.82
Midrange	1.685
Midmean - Weighted Average at Xnp	1.81159090909091
Midmean - Weighted Average at X(n+1)p	1.81976190476191
Midmean - Empirical Distribution Function	1.81159090909091
Midmean - Empirical Distribution Function - Averaging	1.81976190476191
Midmean - Empirical Distribution Function - Interpolation	1.81976190476191
Midmean - Closest Observation	1.81159090909091
Midmean - True Basic - Statistics Graphics Toolkit	1.81976190476191
Midmean - MS Excel (old versions)	1.81159090909091
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.77125 & 0.0198743485439636 & 89.1224180798609 \tabularnewline
Geometric Mean & 1.76303320544125 &  &  \tabularnewline
Harmonic Mean & 1.75453519483045 &  &  \tabularnewline
Quadratic Mean & 1.77914890701519 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.77152777777778 & 0.0198050551179404 & 89.4482629423758 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.77152777777778 & 0.0198050551179404 & 89.4482629423758 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.77194444444444 & 0.0195525443602129 & 90.624749996739 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.77416666666667 & 0.0190612532943613 & 93.0771255839457 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.77763888888889 & 0.0183796821885881 & 96.7176075543144 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.77763888888889 & 0.0183796821885881 & 96.7176075543144 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.77763888888889 & 0.0180792173714761 & 98.3249911964385 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.77763888888889 & 0.0180792173714761 & 98.3249911964385 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.77763888888889 & 0.0180792173714761 & 98.3249911964385 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.77763888888889 & 0.0180792173714761 & 98.3249911964385 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.77916666666667 & 0.0178113374068062 & 99.8895605664515 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.7775 & 0.0176036501229882 & 100.973376974745 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.78291666666667 & 0.0166906371052652 & 106.821366699311 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.78875 & 0.0157753912624558 & 113.388629812123 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.78875 & 0.0157753912624558 & 113.388629812123 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.79319444444444 & 0.0151231594786584 & 118.57273918026 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.79319444444444 & 0.0151231594786584 & 118.57273918026 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.79569444444444 & 0.014771110180549 & 121.568008260412 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.79305555555556 & 0.0144386876092768 & 124.184108977019 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.79305555555556 & 0.0144386876092768 & 124.184108977019 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.79013888888889 & 0.0140832160391198 & 127.111512307722 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.79319444444444 & 0.0136592021136739 & 131.281053572618 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.79638888888889 & 0.0132247715878455 & 135.83515427517 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.79972222222222 & 0.0127804566151585 & 140.818303791089 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.77371428571429 & 0.0195848966067254 & 90.5654148363078 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.77602941176471 & 0.0193134348762729 & 91.9582364888708 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.77848484848485 & 0.0189801054281209 & 93.7025800631144 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.7809375 & 0.0186853631256898 & 95.3119020497629 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.78290322580645 & 0.0184991990290314 & 96.3773200671274 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.78416666666667 & 0.018467090390619 & 96.6133066404981 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.78551724137931 & 0.0184062057412126 & 97.006263348531 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.78696428571429 & 0.0183807487568068 & 97.2193412443297 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.78851851851852 & 0.0183231483189755 & 97.6097823028765 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.79019230769231 & 0.0182253581331369 & 98.2253569238468 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.792 & 0.0180769330972951 & 99.1318599429981 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.79375 & 0.017923262846475 & 100.079433938156 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.79586956521739 & 0.0177382364556397 & 101.242847320733 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.7975 & 0.017671314891056 & 101.718520160023 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.79857142857143 & 0.0177365264449807 & 101.404941613041 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.79975 & 0.0177680478849261 & 101.291374925146 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.80052631578947 & 0.0178899248822677 & 100.644710787698 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.80138888888889 & 0.0179821462504966 & 100.176523079893 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.80205882352941 & 0.01810929096374 & 99.5101811074576 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.803125 & 0.0182635141082061 & 98.7282616760934 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.80433333333333 & 0.0183746660511265 & 98.1967959751145 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.80607142857143 & 0.0184973849554191 & 97.6392843055533 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.80769230769231 & 0.0186655395545884 & 96.8465070300062 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.80916666666667 & 0.0188905760826477 & 95.7708573180315 \tabularnewline
Median & 1.82 &  &  \tabularnewline
Midrange & 1.685 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.81159090909091 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.81976190476191 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.81159090909091 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.81976190476191 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.81976190476191 &  &  \tabularnewline
Midmean - Closest Observation & 1.81159090909091 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.81976190476191 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.81159090909091 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=177405&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]1.77125[/C][C]0.0198743485439636[/C][C]89.1224180798609[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.76303320544125[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.75453519483045[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.77914890701519[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.77152777777778[/C][C]0.0198050551179404[/C][C]89.4482629423758[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.77152777777778[/C][C]0.0198050551179404[/C][C]89.4482629423758[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.77194444444444[/C][C]0.0195525443602129[/C][C]90.624749996739[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.77416666666667[/C][C]0.0190612532943613[/C][C]93.0771255839457[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.77763888888889[/C][C]0.0183796821885881[/C][C]96.7176075543144[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.77763888888889[/C][C]0.0183796821885881[/C][C]96.7176075543144[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.77763888888889[/C][C]0.0180792173714761[/C][C]98.3249911964385[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.77763888888889[/C][C]0.0180792173714761[/C][C]98.3249911964385[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.77763888888889[/C][C]0.0180792173714761[/C][C]98.3249911964385[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.77763888888889[/C][C]0.0180792173714761[/C][C]98.3249911964385[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.77916666666667[/C][C]0.0178113374068062[/C][C]99.8895605664515[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.7775[/C][C]0.0176036501229882[/C][C]100.973376974745[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.78291666666667[/C][C]0.0166906371052652[/C][C]106.821366699311[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.78875[/C][C]0.0157753912624558[/C][C]113.388629812123[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.78875[/C][C]0.0157753912624558[/C][C]113.388629812123[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.79319444444444[/C][C]0.0151231594786584[/C][C]118.57273918026[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.79319444444444[/C][C]0.0151231594786584[/C][C]118.57273918026[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.79569444444444[/C][C]0.014771110180549[/C][C]121.568008260412[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.79305555555556[/C][C]0.0144386876092768[/C][C]124.184108977019[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.79305555555556[/C][C]0.0144386876092768[/C][C]124.184108977019[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.79013888888889[/C][C]0.0140832160391198[/C][C]127.111512307722[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.79319444444444[/C][C]0.0136592021136739[/C][C]131.281053572618[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.79638888888889[/C][C]0.0132247715878455[/C][C]135.83515427517[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.79972222222222[/C][C]0.0127804566151585[/C][C]140.818303791089[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.77371428571429[/C][C]0.0195848966067254[/C][C]90.5654148363078[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.77602941176471[/C][C]0.0193134348762729[/C][C]91.9582364888708[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.77848484848485[/C][C]0.0189801054281209[/C][C]93.7025800631144[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.7809375[/C][C]0.0186853631256898[/C][C]95.3119020497629[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.78290322580645[/C][C]0.0184991990290314[/C][C]96.3773200671274[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.78416666666667[/C][C]0.018467090390619[/C][C]96.6133066404981[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.78551724137931[/C][C]0.0184062057412126[/C][C]97.006263348531[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.78696428571429[/C][C]0.0183807487568068[/C][C]97.2193412443297[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.78851851851852[/C][C]0.0183231483189755[/C][C]97.6097823028765[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.79019230769231[/C][C]0.0182253581331369[/C][C]98.2253569238468[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.792[/C][C]0.0180769330972951[/C][C]99.1318599429981[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.79375[/C][C]0.017923262846475[/C][C]100.079433938156[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.79586956521739[/C][C]0.0177382364556397[/C][C]101.242847320733[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.7975[/C][C]0.017671314891056[/C][C]101.718520160023[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.79857142857143[/C][C]0.0177365264449807[/C][C]101.404941613041[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.79975[/C][C]0.0177680478849261[/C][C]101.291374925146[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.80052631578947[/C][C]0.0178899248822677[/C][C]100.644710787698[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.80138888888889[/C][C]0.0179821462504966[/C][C]100.176523079893[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.80205882352941[/C][C]0.01810929096374[/C][C]99.5101811074576[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.803125[/C][C]0.0182635141082061[/C][C]98.7282616760934[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.80433333333333[/C][C]0.0183746660511265[/C][C]98.1967959751145[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.80607142857143[/C][C]0.0184973849554191[/C][C]97.6392843055533[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.80769230769231[/C][C]0.0186655395545884[/C][C]96.8465070300062[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.80916666666667[/C][C]0.0188905760826477[/C][C]95.7708573180315[/C][/ROW]
[ROW][C]Median[/C][C]1.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.685[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.81159090909091[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.81976190476191[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.81159090909091[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.81976190476191[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.81976190476191[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.81159090909091[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.81976190476191[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.81159090909091[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=177405&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=177405&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.77125	0.0198743485439636	89.1224180798609
Geometric Mean	1.76303320544125
Harmonic Mean	1.75453519483045
Quadratic Mean	1.77914890701519
Winsorized Mean ( 1 / 24 )	1.77152777777778	0.0198050551179404	89.4482629423758
Winsorized Mean ( 2 / 24 )	1.77152777777778	0.0198050551179404	89.4482629423758
Winsorized Mean ( 3 / 24 )	1.77194444444444	0.0195525443602129	90.624749996739
Winsorized Mean ( 4 / 24 )	1.77416666666667	0.0190612532943613	93.0771255839457
Winsorized Mean ( 5 / 24 )	1.77763888888889	0.0183796821885881	96.7176075543144
Winsorized Mean ( 6 / 24 )	1.77763888888889	0.0183796821885881	96.7176075543144
Winsorized Mean ( 7 / 24 )	1.77763888888889	0.0180792173714761	98.3249911964385
Winsorized Mean ( 8 / 24 )	1.77763888888889	0.0180792173714761	98.3249911964385
Winsorized Mean ( 9 / 24 )	1.77763888888889	0.0180792173714761	98.3249911964385
Winsorized Mean ( 10 / 24 )	1.77763888888889	0.0180792173714761	98.3249911964385
Winsorized Mean ( 11 / 24 )	1.77916666666667	0.0178113374068062	99.8895605664515
Winsorized Mean ( 12 / 24 )	1.7775	0.0176036501229882	100.973376974745
Winsorized Mean ( 13 / 24 )	1.78291666666667	0.0166906371052652	106.821366699311
Winsorized Mean ( 14 / 24 )	1.78875	0.0157753912624558	113.388629812123
Winsorized Mean ( 15 / 24 )	1.78875	0.0157753912624558	113.388629812123
Winsorized Mean ( 16 / 24 )	1.79319444444444	0.0151231594786584	118.57273918026
Winsorized Mean ( 17 / 24 )	1.79319444444444	0.0151231594786584	118.57273918026
Winsorized Mean ( 18 / 24 )	1.79569444444444	0.014771110180549	121.568008260412
Winsorized Mean ( 19 / 24 )	1.79305555555556	0.0144386876092768	124.184108977019
Winsorized Mean ( 20 / 24 )	1.79305555555556	0.0144386876092768	124.184108977019
Winsorized Mean ( 21 / 24 )	1.79013888888889	0.0140832160391198	127.111512307722
Winsorized Mean ( 22 / 24 )	1.79319444444444	0.0136592021136739	131.281053572618
Winsorized Mean ( 23 / 24 )	1.79638888888889	0.0132247715878455	135.83515427517
Winsorized Mean ( 24 / 24 )	1.79972222222222	0.0127804566151585	140.818303791089
Trimmed Mean ( 1 / 24 )	1.77371428571429	0.0195848966067254	90.5654148363078
Trimmed Mean ( 2 / 24 )	1.77602941176471	0.0193134348762729	91.9582364888708
Trimmed Mean ( 3 / 24 )	1.77848484848485	0.0189801054281209	93.7025800631144
Trimmed Mean ( 4 / 24 )	1.7809375	0.0186853631256898	95.3119020497629
Trimmed Mean ( 5 / 24 )	1.78290322580645	0.0184991990290314	96.3773200671274
Trimmed Mean ( 6 / 24 )	1.78416666666667	0.018467090390619	96.6133066404981
Trimmed Mean ( 7 / 24 )	1.78551724137931	0.0184062057412126	97.006263348531
Trimmed Mean ( 8 / 24 )	1.78696428571429	0.0183807487568068	97.2193412443297
Trimmed Mean ( 9 / 24 )	1.78851851851852	0.0183231483189755	97.6097823028765
Trimmed Mean ( 10 / 24 )	1.79019230769231	0.0182253581331369	98.2253569238468
Trimmed Mean ( 11 / 24 )	1.792	0.0180769330972951	99.1318599429981
Trimmed Mean ( 12 / 24 )	1.79375	0.017923262846475	100.079433938156
Trimmed Mean ( 13 / 24 )	1.79586956521739	0.0177382364556397	101.242847320733
Trimmed Mean ( 14 / 24 )	1.7975	0.017671314891056	101.718520160023
Trimmed Mean ( 15 / 24 )	1.79857142857143	0.0177365264449807	101.404941613041
Trimmed Mean ( 16 / 24 )	1.79975	0.0177680478849261	101.291374925146
Trimmed Mean ( 17 / 24 )	1.80052631578947	0.0178899248822677	100.644710787698
Trimmed Mean ( 18 / 24 )	1.80138888888889	0.0179821462504966	100.176523079893
Trimmed Mean ( 19 / 24 )	1.80205882352941	0.01810929096374	99.5101811074576
Trimmed Mean ( 20 / 24 )	1.803125	0.0182635141082061	98.7282616760934
Trimmed Mean ( 21 / 24 )	1.80433333333333	0.0183746660511265	98.1967959751145
Trimmed Mean ( 22 / 24 )	1.80607142857143	0.0184973849554191	97.6392843055533
Trimmed Mean ( 23 / 24 )	1.80769230769231	0.0186655395545884	96.8465070300062
Trimmed Mean ( 24 / 24 )	1.80916666666667	0.0188905760826477	95.7708573180315
Median	1.82
Midrange	1.685
Midmean - Weighted Average at Xnp	1.81159090909091
Midmean - Weighted Average at X(n+1)p	1.81976190476191
Midmean - Empirical Distribution Function	1.81159090909091
Midmean - Empirical Distribution Function - Averaging	1.81976190476191
Midmean - Empirical Distribution Function - Interpolation	1.81976190476191
Midmean - Closest Observation	1.81159090909091
Midmean - True Basic - Statistics Graphics Toolkit	1.81976190476191
Midmean - MS Excel (old versions)	1.81159090909091
Number of observations	72

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code