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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sun, 14 Oct 2012 05:38:18 -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/14/t1350207505abkaevcedbrfxzi.htm/, Retrieved Sat, 27 Apr 2024 15:06:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=176014, Retrieved Sat, 27 Apr 2024 15:06:35 +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] [] [2012-10-14 09:38:18] [eb7c3df32e1deded9387ee1ff8d7fc91] [Current]

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1,26
1,26
1,28
1,34
1,39
1,47
1,57
1,63
1,72
1,43
1,35
1,41
1,44
1,43
1,43
1,42
1,45
1,51
1,48
1,48
1,45
1,38
1,46
1,45
1,41
1,45
1,47
1,47
1,53
1,56
1,66
1,79
1,78
1,46
1,41
1,43
1,43
1,45
1,35
1,35
1,29
1,29
1,26
1,3
1,3
1,16
1,24
1,15
1,21
1,22
1,17
1,13
1,15
1,2
1,23
1,25
1,38
1,28
1,26
1,25
1,26
1,28
1,31
1,22
1,23
1,36
1,54
1,58
1,44
1,29
1,28
1,23

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=176014&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=176014&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=176014&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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.37819444444444	0.0172234763413334	80.0183666253838
Geometric Mean	1.37080016419255
Harmonic Mean	1.36363595227197
Quadratic Mean	1.38581454186498
Winsorized Mean ( 1 / 24 )	1.37833333333333	0.0171228644876642	80.4966560546179
Winsorized Mean ( 2 / 24 )	1.37666666666667	0.016604343568841	82.9100326043637
Winsorized Mean ( 3 / 24 )	1.37458333333333	0.0158422108791641	86.7671402569955
Winsorized Mean ( 4 / 24 )	1.37347222222222	0.0153291478802583	89.598732620425
Winsorized Mean ( 5 / 24 )	1.37208333333333	0.0141862437225157	96.7192838478891
Winsorized Mean ( 6 / 24 )	1.37208333333333	0.0138767454738216	98.8764502398466
Winsorized Mean ( 7 / 24 )	1.37208333333333	0.0135269647530538	101.433200897753
Winsorized Mean ( 8 / 24 )	1.36986111111111	0.0131061828454209	104.520219751834
Winsorized Mean ( 9 / 24 )	1.36986111111111	0.0126829229998395	108.008312526099
Winsorized Mean ( 10 / 24 )	1.36708333333333	0.0122065516093172	111.995867226732
Winsorized Mean ( 11 / 24 )	1.3625	0.0114973460909964	118.505608965444
Winsorized Mean ( 12 / 24 )	1.36416666666667	0.0112322717209173	121.450646900417
Winsorized Mean ( 13 / 24 )	1.36416666666667	0.0106988766906304	127.50559765413
Winsorized Mean ( 14 / 24 )	1.36416666666667	0.0106988766906304	127.50559765413
Winsorized Mean ( 15 / 24 )	1.36625	0.0103922248458016	131.468479586636
Winsorized Mean ( 16 / 24 )	1.36402777777778	0.0100869842112585	135.226520554611
Winsorized Mean ( 17 / 24 )	1.36402777777778	0.0100869842112585	135.226520554611
Winsorized Mean ( 18 / 24 )	1.36152777777778	0.00975975039570541	139.504364617449
Winsorized Mean ( 19 / 24 )	1.36152777777778	0.00975975039570541	139.504364617449
Winsorized Mean ( 20 / 24 )	1.36708333333333	0.00897186852793937	152.374427810226
Winsorized Mean ( 21 / 24 )	1.36708333333333	0.00897186852793937	152.374427810226
Winsorized Mean ( 22 / 24 )	1.36708333333333	0.00897186852793937	152.374427810226
Winsorized Mean ( 23 / 24 )	1.36388888888889	0.00856384371829834	159.261300620733
Winsorized Mean ( 24 / 24 )	1.36722222222222	0.00811021068168632	168.580358252536
Trimmed Mean ( 1 / 24 )	1.37585714285714	0.0163102590092866	84.3553215233289
Trimmed Mean ( 2 / 24 )	1.37323529411765	0.0153256159066426	89.6039221185522
Trimmed Mean ( 3 / 24 )	1.37136363636364	0.0144823441476516	94.6921038736681
Trimmed Mean ( 4 / 24 )	1.37015625	0.0138345025816452	99.0390685833434
Trimmed Mean ( 5 / 24 )	1.3691935483871	0.0132508211674874	103.328958340075
Trimmed Mean ( 6 / 24 )	1.3685	0.0129204978826949	105.916971035064
Trimmed Mean ( 7 / 24 )	1.36775862068966	0.012604177145507	108.516296216704
Trimmed Mean ( 8 / 24 )	1.36696428571429	0.0123054196772106	111.086360447005
Trimmed Mean ( 9 / 24 )	1.36648148148148	0.0120392945257173	113.501790205607
Trimmed Mean ( 10 / 24 )	1.36596153846154	0.0118029945307646	115.730083149759
Trimmed Mean ( 11 / 24 )	1.3658	0.0116096019373128	117.643999111664
Trimmed Mean ( 12 / 24 )	1.36625	0.0115071092733921	118.730948628356
Trimmed Mean ( 13 / 24 )	1.36652173913043	0.0114174939562921	119.686661920881
Trimmed Mean ( 14 / 24 )	1.36681818181818	0.0113923527226544	119.976813841111
Trimmed Mean ( 15 / 24 )	1.36714285714286	0.0113352754072477	120.609584507202
Trimmed Mean ( 16 / 24 )	1.36725	0.01130003120032	120.995241142457
Trimmed Mean ( 17 / 24 )	1.36763157894737	0.0112859774682939	121.179719061951
Trimmed Mean ( 18 / 24 )	1.36805555555556	0.0112321777308981	121.797890696853
Trimmed Mean ( 19 / 24 )	1.36882352941176	0.0111924081880776	122.299285945438
Trimmed Mean ( 20 / 24 )	1.3696875	0.0110942114283865	123.459653607774
Trimmed Mean ( 21 / 24 )	1.37	0.0111210683353507	123.189603614354
Trimmed Mean ( 22 / 24 )	1.37035714285714	0.011097000677493	123.4889663147
Trimmed Mean ( 23 / 24 )	1.37076923076923	0.0109954266985881	124.667215592938
Trimmed Mean ( 24 / 24 )	1.37166666666667	0.0108958619100686	125.888771167257
Median	1.38
Midrange	1.46
Midmean - Weighted Average at Xnp	1.35974358974359
Midmean - Weighted Average at X(n+1)p	1.35974358974359
Midmean - Empirical Distribution Function	1.35974358974359
Midmean - Empirical Distribution Function - Averaging	1.35974358974359
Midmean - Empirical Distribution Function - Interpolation	1.35974358974359
Midmean - Closest Observation	1.35974358974359
Midmean - True Basic - Statistics Graphics Toolkit	1.35974358974359
Midmean - MS Excel (old versions)	1.36463414634146
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.37819444444444 & 0.0172234763413334 & 80.0183666253838 \tabularnewline
Geometric Mean & 1.37080016419255 &  &  \tabularnewline
Harmonic Mean & 1.36363595227197 &  &  \tabularnewline
Quadratic Mean & 1.38581454186498 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.37833333333333 & 0.0171228644876642 & 80.4966560546179 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.37666666666667 & 0.016604343568841 & 82.9100326043637 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.37458333333333 & 0.0158422108791641 & 86.7671402569955 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.37347222222222 & 0.0153291478802583 & 89.598732620425 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.37208333333333 & 0.0141862437225157 & 96.7192838478891 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.37208333333333 & 0.0138767454738216 & 98.8764502398466 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.37208333333333 & 0.0135269647530538 & 101.433200897753 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.36986111111111 & 0.0131061828454209 & 104.520219751834 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.36986111111111 & 0.0126829229998395 & 108.008312526099 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.36708333333333 & 0.0122065516093172 & 111.995867226732 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.3625 & 0.0114973460909964 & 118.505608965444 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.36416666666667 & 0.0112322717209173 & 121.450646900417 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.36416666666667 & 0.0106988766906304 & 127.50559765413 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.36416666666667 & 0.0106988766906304 & 127.50559765413 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.36625 & 0.0103922248458016 & 131.468479586636 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.36402777777778 & 0.0100869842112585 & 135.226520554611 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.36402777777778 & 0.0100869842112585 & 135.226520554611 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.36152777777778 & 0.00975975039570541 & 139.504364617449 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.36152777777778 & 0.00975975039570541 & 139.504364617449 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.36708333333333 & 0.00897186852793937 & 152.374427810226 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.36708333333333 & 0.00897186852793937 & 152.374427810226 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.36708333333333 & 0.00897186852793937 & 152.374427810226 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.36388888888889 & 0.00856384371829834 & 159.261300620733 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.36722222222222 & 0.00811021068168632 & 168.580358252536 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.37585714285714 & 0.0163102590092866 & 84.3553215233289 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.37323529411765 & 0.0153256159066426 & 89.6039221185522 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.37136363636364 & 0.0144823441476516 & 94.6921038736681 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.37015625 & 0.0138345025816452 & 99.0390685833434 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.3691935483871 & 0.0132508211674874 & 103.328958340075 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.3685 & 0.0129204978826949 & 105.916971035064 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.36775862068966 & 0.012604177145507 & 108.516296216704 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.36696428571429 & 0.0123054196772106 & 111.086360447005 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.36648148148148 & 0.0120392945257173 & 113.501790205607 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.36596153846154 & 0.0118029945307646 & 115.730083149759 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.3658 & 0.0116096019373128 & 117.643999111664 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.36625 & 0.0115071092733921 & 118.730948628356 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.36652173913043 & 0.0114174939562921 & 119.686661920881 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.36681818181818 & 0.0113923527226544 & 119.976813841111 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.36714285714286 & 0.0113352754072477 & 120.609584507202 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.36725 & 0.01130003120032 & 120.995241142457 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.36763157894737 & 0.0112859774682939 & 121.179719061951 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.36805555555556 & 0.0112321777308981 & 121.797890696853 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.36882352941176 & 0.0111924081880776 & 122.299285945438 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.3696875 & 0.0110942114283865 & 123.459653607774 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.37 & 0.0111210683353507 & 123.189603614354 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.37035714285714 & 0.011097000677493 & 123.4889663147 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.37076923076923 & 0.0109954266985881 & 124.667215592938 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.37166666666667 & 0.0108958619100686 & 125.888771167257 \tabularnewline
Median & 1.38 &  &  \tabularnewline
Midrange & 1.46 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.35974358974359 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.35974358974359 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.35974358974359 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.35974358974359 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.35974358974359 &  &  \tabularnewline
Midmean - Closest Observation & 1.35974358974359 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.35974358974359 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.36463414634146 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=176014&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]1.37819444444444[/C][C]0.0172234763413334[/C][C]80.0183666253838[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.37080016419255[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.36363595227197[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.38581454186498[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.37833333333333[/C][C]0.0171228644876642[/C][C]80.4966560546179[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.37666666666667[/C][C]0.016604343568841[/C][C]82.9100326043637[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.37458333333333[/C][C]0.0158422108791641[/C][C]86.7671402569955[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.37347222222222[/C][C]0.0153291478802583[/C][C]89.598732620425[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.37208333333333[/C][C]0.0141862437225157[/C][C]96.7192838478891[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.37208333333333[/C][C]0.0138767454738216[/C][C]98.8764502398466[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.37208333333333[/C][C]0.0135269647530538[/C][C]101.433200897753[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.36986111111111[/C][C]0.0131061828454209[/C][C]104.520219751834[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.36986111111111[/C][C]0.0126829229998395[/C][C]108.008312526099[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.36708333333333[/C][C]0.0122065516093172[/C][C]111.995867226732[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.3625[/C][C]0.0114973460909964[/C][C]118.505608965444[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.36416666666667[/C][C]0.0112322717209173[/C][C]121.450646900417[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.36416666666667[/C][C]0.0106988766906304[/C][C]127.50559765413[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.36416666666667[/C][C]0.0106988766906304[/C][C]127.50559765413[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.36625[/C][C]0.0103922248458016[/C][C]131.468479586636[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.36402777777778[/C][C]0.0100869842112585[/C][C]135.226520554611[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.36402777777778[/C][C]0.0100869842112585[/C][C]135.226520554611[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.36152777777778[/C][C]0.00975975039570541[/C][C]139.504364617449[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.36152777777778[/C][C]0.00975975039570541[/C][C]139.504364617449[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.36708333333333[/C][C]0.00897186852793937[/C][C]152.374427810226[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.36708333333333[/C][C]0.00897186852793937[/C][C]152.374427810226[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.36708333333333[/C][C]0.00897186852793937[/C][C]152.374427810226[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.36388888888889[/C][C]0.00856384371829834[/C][C]159.261300620733[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.36722222222222[/C][C]0.00811021068168632[/C][C]168.580358252536[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.37585714285714[/C][C]0.0163102590092866[/C][C]84.3553215233289[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.37323529411765[/C][C]0.0153256159066426[/C][C]89.6039221185522[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.37136363636364[/C][C]0.0144823441476516[/C][C]94.6921038736681[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.37015625[/C][C]0.0138345025816452[/C][C]99.0390685833434[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.3691935483871[/C][C]0.0132508211674874[/C][C]103.328958340075[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.3685[/C][C]0.0129204978826949[/C][C]105.916971035064[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.36775862068966[/C][C]0.012604177145507[/C][C]108.516296216704[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.36696428571429[/C][C]0.0123054196772106[/C][C]111.086360447005[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.36648148148148[/C][C]0.0120392945257173[/C][C]113.501790205607[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.36596153846154[/C][C]0.0118029945307646[/C][C]115.730083149759[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.3658[/C][C]0.0116096019373128[/C][C]117.643999111664[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.36625[/C][C]0.0115071092733921[/C][C]118.730948628356[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.36652173913043[/C][C]0.0114174939562921[/C][C]119.686661920881[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.36681818181818[/C][C]0.0113923527226544[/C][C]119.976813841111[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.36714285714286[/C][C]0.0113352754072477[/C][C]120.609584507202[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.36725[/C][C]0.01130003120032[/C][C]120.995241142457[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.36763157894737[/C][C]0.0112859774682939[/C][C]121.179719061951[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.36805555555556[/C][C]0.0112321777308981[/C][C]121.797890696853[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.36882352941176[/C][C]0.0111924081880776[/C][C]122.299285945438[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.3696875[/C][C]0.0110942114283865[/C][C]123.459653607774[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.37[/C][C]0.0111210683353507[/C][C]123.189603614354[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.37035714285714[/C][C]0.011097000677493[/C][C]123.4889663147[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.37076923076923[/C][C]0.0109954266985881[/C][C]124.667215592938[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.37166666666667[/C][C]0.0108958619100686[/C][C]125.888771167257[/C][/ROW]
[ROW][C]Median[/C][C]1.38[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.46[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.35974358974359[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.35974358974359[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.35974358974359[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.35974358974359[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.35974358974359[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.35974358974359[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.35974358974359[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.36463414634146[/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=176014&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=176014&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	1.37819444444444	0.0172234763413334	80.0183666253838
Geometric Mean	1.37080016419255
Harmonic Mean	1.36363595227197
Quadratic Mean	1.38581454186498
Winsorized Mean ( 1 / 24 )	1.37833333333333	0.0171228644876642	80.4966560546179
Winsorized Mean ( 2 / 24 )	1.37666666666667	0.016604343568841	82.9100326043637
Winsorized Mean ( 3 / 24 )	1.37458333333333	0.0158422108791641	86.7671402569955
Winsorized Mean ( 4 / 24 )	1.37347222222222	0.0153291478802583	89.598732620425
Winsorized Mean ( 5 / 24 )	1.37208333333333	0.0141862437225157	96.7192838478891
Winsorized Mean ( 6 / 24 )	1.37208333333333	0.0138767454738216	98.8764502398466
Winsorized Mean ( 7 / 24 )	1.37208333333333	0.0135269647530538	101.433200897753
Winsorized Mean ( 8 / 24 )	1.36986111111111	0.0131061828454209	104.520219751834
Winsorized Mean ( 9 / 24 )	1.36986111111111	0.0126829229998395	108.008312526099
Winsorized Mean ( 10 / 24 )	1.36708333333333	0.0122065516093172	111.995867226732
Winsorized Mean ( 11 / 24 )	1.3625	0.0114973460909964	118.505608965444
Winsorized Mean ( 12 / 24 )	1.36416666666667	0.0112322717209173	121.450646900417
Winsorized Mean ( 13 / 24 )	1.36416666666667	0.0106988766906304	127.50559765413
Winsorized Mean ( 14 / 24 )	1.36416666666667	0.0106988766906304	127.50559765413
Winsorized Mean ( 15 / 24 )	1.36625	0.0103922248458016	131.468479586636
Winsorized Mean ( 16 / 24 )	1.36402777777778	0.0100869842112585	135.226520554611
Winsorized Mean ( 17 / 24 )	1.36402777777778	0.0100869842112585	135.226520554611
Winsorized Mean ( 18 / 24 )	1.36152777777778	0.00975975039570541	139.504364617449
Winsorized Mean ( 19 / 24 )	1.36152777777778	0.00975975039570541	139.504364617449
Winsorized Mean ( 20 / 24 )	1.36708333333333	0.00897186852793937	152.374427810226
Winsorized Mean ( 21 / 24 )	1.36708333333333	0.00897186852793937	152.374427810226
Winsorized Mean ( 22 / 24 )	1.36708333333333	0.00897186852793937	152.374427810226
Winsorized Mean ( 23 / 24 )	1.36388888888889	0.00856384371829834	159.261300620733
Winsorized Mean ( 24 / 24 )	1.36722222222222	0.00811021068168632	168.580358252536
Trimmed Mean ( 1 / 24 )	1.37585714285714	0.0163102590092866	84.3553215233289
Trimmed Mean ( 2 / 24 )	1.37323529411765	0.0153256159066426	89.6039221185522
Trimmed Mean ( 3 / 24 )	1.37136363636364	0.0144823441476516	94.6921038736681
Trimmed Mean ( 4 / 24 )	1.37015625	0.0138345025816452	99.0390685833434
Trimmed Mean ( 5 / 24 )	1.3691935483871	0.0132508211674874	103.328958340075
Trimmed Mean ( 6 / 24 )	1.3685	0.0129204978826949	105.916971035064
Trimmed Mean ( 7 / 24 )	1.36775862068966	0.012604177145507	108.516296216704
Trimmed Mean ( 8 / 24 )	1.36696428571429	0.0123054196772106	111.086360447005
Trimmed Mean ( 9 / 24 )	1.36648148148148	0.0120392945257173	113.501790205607
Trimmed Mean ( 10 / 24 )	1.36596153846154	0.0118029945307646	115.730083149759
Trimmed Mean ( 11 / 24 )	1.3658	0.0116096019373128	117.643999111664
Trimmed Mean ( 12 / 24 )	1.36625	0.0115071092733921	118.730948628356
Trimmed Mean ( 13 / 24 )	1.36652173913043	0.0114174939562921	119.686661920881
Trimmed Mean ( 14 / 24 )	1.36681818181818	0.0113923527226544	119.976813841111
Trimmed Mean ( 15 / 24 )	1.36714285714286	0.0113352754072477	120.609584507202
Trimmed Mean ( 16 / 24 )	1.36725	0.01130003120032	120.995241142457
Trimmed Mean ( 17 / 24 )	1.36763157894737	0.0112859774682939	121.179719061951
Trimmed Mean ( 18 / 24 )	1.36805555555556	0.0112321777308981	121.797890696853
Trimmed Mean ( 19 / 24 )	1.36882352941176	0.0111924081880776	122.299285945438
Trimmed Mean ( 20 / 24 )	1.3696875	0.0110942114283865	123.459653607774
Trimmed Mean ( 21 / 24 )	1.37	0.0111210683353507	123.189603614354
Trimmed Mean ( 22 / 24 )	1.37035714285714	0.011097000677493	123.4889663147
Trimmed Mean ( 23 / 24 )	1.37076923076923	0.0109954266985881	124.667215592938
Trimmed Mean ( 24 / 24 )	1.37166666666667	0.0108958619100686	125.888771167257
Median	1.38
Midrange	1.46
Midmean - Weighted Average at Xnp	1.35974358974359
Midmean - Weighted Average at X(n+1)p	1.35974358974359
Midmean - Empirical Distribution Function	1.35974358974359
Midmean - Empirical Distribution Function - Averaging	1.35974358974359
Midmean - Empirical Distribution Function - Interpolation	1.35974358974359
Midmean - Closest Observation	1.35974358974359
Midmean - True Basic - Statistics Graphics Toolkit	1.35974358974359
Midmean - MS Excel (old versions)	1.36463414634146
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