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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sun, 20 Apr 2008 11:29:33 -0600

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/2008/Apr/20/t1208712612wpp15suaicw5kei.htm/, Retrieved Sun, 10 Nov 2024 19:18:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10383, Retrieved Sun, 10 Nov 2024 19:18:28 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

207

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

-       [Central Tendency] [Bruin brood centr...] [2008-04-20 17:29:33] [d697b8fe067a6665f759724e14415da5] [Current]

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Dataseries X:

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1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,44
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,57
1,58
1,58
1,58
1,58
1,59
1,6
1,6
1,61
1,61
1,61
1,62
1,63
1,63
1,64
1,64
1,64
1,64
1,64
1,65
1,65
1,65
1,65

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10383&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10383&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10383&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.51069444444444	0.00913583459480834	165.359215818436
Geometric Mean	1.50877442467608
Harmonic Mean	1.50689715841029
Quadratic Mean	1.51265449165072
Winsorized Mean ( 1 / 24 )	1.51069444444444	0.00913583459480834	165.359215818436
Winsorized Mean ( 2 / 24 )	1.51069444444444	0.00913583459480834	165.359215818436
Winsorized Mean ( 3 / 24 )	1.51069444444444	0.00913583459480834	165.359215818436
Winsorized Mean ( 4 / 24 )	1.51013888888889	0.00901982917202266	167.424333663987
Winsorized Mean ( 5 / 24 )	1.51013888888889	0.00901982917202266	167.424333663987
Winsorized Mean ( 6 / 24 )	1.51013888888889	0.00901982917202266	167.424333663987
Winsorized Mean ( 7 / 24 )	1.51013888888889	0.00901982917202266	167.424333663987
Winsorized Mean ( 8 / 24 )	1.51013888888889	0.00901982917202266	167.424333663987
Winsorized Mean ( 9 / 24 )	1.50888888888889	0.00877147611598796	172.02223080088
Winsorized Mean ( 10 / 24 )	1.50888888888889	0.00877147611598796	172.02223080088
Winsorized Mean ( 11 / 24 )	1.50736111111111	0.008479915181472	177.756625963027
Winsorized Mean ( 12 / 24 )	1.50569444444444	0.00817412802030692	184.202454464117
Winsorized Mean ( 13 / 24 )	1.50569444444444	0.00817412802030692	184.202454464117
Winsorized Mean ( 14 / 24 )	1.50569444444444	0.00817412802030692	184.202454464117
Winsorized Mean ( 15 / 24 )	1.50361111111111	0.00780560358975859	192.632266527593
Winsorized Mean ( 16 / 24 )	1.50361111111111	0.00780560358975859	192.632266527593
Winsorized Mean ( 17 / 24 )	1.50125	0.00740071872963566	202.851919501865
Winsorized Mean ( 18 / 24 )	1.50125	0.00664885384359514	225.790795724312
Winsorized Mean ( 19 / 24 )	1.51180555555556	0.00551114388494218	274.31792512008
Winsorized Mean ( 20 / 24 )	1.51180555555556	0.00551114388494218	274.31792512008
Winsorized Mean ( 21 / 24 )	1.51180555555556	0.00551114388494218	274.31792512008
Winsorized Mean ( 22 / 24 )	1.50875	0.0049801542766985	302.952462147457
Winsorized Mean ( 23 / 24 )	1.48	0	Inf
Winsorized Mean ( 24 / 24 )	1.48	0	Inf
Trimmed Mean ( 1 / 24 )	1.50985714285714	0.00910825816253568	165.767934539617
Trimmed Mean ( 2 / 24 )	1.50897058823529	0.00906793138142844	166.407367321475
Trimmed Mean ( 3 / 24 )	1.50803030303030	0.00901234506080913	167.329401266279
Trimmed Mean ( 4 / 24 )	1.50703125	0.00893839055808423	168.602081124882
Trimmed Mean ( 5 / 24 )	1.50612903225806	0.00888362637038576	169.53988939459
Trimmed Mean ( 6 / 24 )	1.50516666666667	0.00880899535967095	170.867006419094
Trimmed Mean ( 7 / 24 )	1.50413793103448	0.00871000315940351	172.690859406932
Trimmed Mean ( 8 / 24 )	1.50303571428571	0.00858085926000854	175.161445811223
Trimmed Mean ( 9 / 24 )	1.50185185185185	0.00841396660127913	178.495104986931
Trimmed Mean ( 10 / 24 )	1.50076923076923	0.00826067641297375	181.676312657909
Trimmed Mean ( 11 / 24 )	1.4996	0.00806078944834886	186.036368969688
Trimmed Mean ( 12 / 24 )	1.49854166666667	0.00787192236007356	190.365402264036
Trimmed Mean ( 13 / 24 )	1.49760869565217	0.00769707129577486	194.568640214396
Trimmed Mean ( 14 / 24 )	1.49659090909091	0.0074633932693401	200.524192559832
Trimmed Mean ( 15 / 24 )	1.49547619047619	0.00715030583357336	209.148563052278
Trimmed Mean ( 16 / 24 )	1.4945	0.00683083131179921	218.787425978223
Trimmed Mean ( 17 / 24 )	1.49342105263158	0.00639252225612776	233.620000493547
Trimmed Mean ( 18 / 24 )	1.4925	0.00591440265201472	252.350082977794
Trimmed Mean ( 19 / 24 )	1.49147058823529	0.0054744969073698	272.439753546571
Trimmed Mean ( 20 / 24 )	1.4890625	0.00506727671898568	293.858532418586
Trimmed Mean ( 21 / 24 )	1.48633333333333	0.00440697809600835	337.268146324483
Trimmed Mean ( 22 / 24 )	1.48321428571429	0.00321428571428572	461.444444444444
Trimmed Mean ( 23 / 24 )	1.48	0	Inf
Trimmed Mean ( 24 / 24 )	1.48	0	Inf
Median	1.48
Midrange	1.54
Midmean - Weighted Average at Xnp	1.47166666666667
Midmean - Weighted Average at X(n+1)p	1.4925
Midmean - Empirical Distribution Function	1.47166666666667
Midmean - Empirical Distribution Function - Averaging	1.4925
Midmean - Empirical Distribution Function - Interpolation	1.4925
Midmean - Closest Observation	1.47166666666667
Midmean - True Basic - Statistics Graphics Toolkit	1.4925
Midmean - MS Excel (old versions)	1.47381818181818
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.51069444444444 & 0.00913583459480834 & 165.359215818436 \tabularnewline
Geometric Mean & 1.50877442467608 &  &  \tabularnewline
Harmonic Mean & 1.50689715841029 &  &  \tabularnewline
Quadratic Mean & 1.51265449165072 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.51069444444444 & 0.00913583459480834 & 165.359215818436 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.51069444444444 & 0.00913583459480834 & 165.359215818436 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.51069444444444 & 0.00913583459480834 & 165.359215818436 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.51013888888889 & 0.00901982917202266 & 167.424333663987 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.51013888888889 & 0.00901982917202266 & 167.424333663987 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.51013888888889 & 0.00901982917202266 & 167.424333663987 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.51013888888889 & 0.00901982917202266 & 167.424333663987 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.51013888888889 & 0.00901982917202266 & 167.424333663987 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.50888888888889 & 0.00877147611598796 & 172.02223080088 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.50888888888889 & 0.00877147611598796 & 172.02223080088 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.50736111111111 & 0.008479915181472 & 177.756625963027 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.50569444444444 & 0.00817412802030692 & 184.202454464117 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.50569444444444 & 0.00817412802030692 & 184.202454464117 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.50569444444444 & 0.00817412802030692 & 184.202454464117 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.50361111111111 & 0.00780560358975859 & 192.632266527593 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.50361111111111 & 0.00780560358975859 & 192.632266527593 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.50125 & 0.00740071872963566 & 202.851919501865 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.50125 & 0.00664885384359514 & 225.790795724312 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.51180555555556 & 0.00551114388494218 & 274.31792512008 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.51180555555556 & 0.00551114388494218 & 274.31792512008 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.51180555555556 & 0.00551114388494218 & 274.31792512008 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.50875 & 0.0049801542766985 & 302.952462147457 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.48 & 0 & Inf \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.48 & 0 & Inf \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.50985714285714 & 0.00910825816253568 & 165.767934539617 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.50897058823529 & 0.00906793138142844 & 166.407367321475 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.50803030303030 & 0.00901234506080913 & 167.329401266279 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.50703125 & 0.00893839055808423 & 168.602081124882 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.50612903225806 & 0.00888362637038576 & 169.53988939459 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.50516666666667 & 0.00880899535967095 & 170.867006419094 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.50413793103448 & 0.00871000315940351 & 172.690859406932 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.50303571428571 & 0.00858085926000854 & 175.161445811223 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.50185185185185 & 0.00841396660127913 & 178.495104986931 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.50076923076923 & 0.00826067641297375 & 181.676312657909 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.4996 & 0.00806078944834886 & 186.036368969688 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.49854166666667 & 0.00787192236007356 & 190.365402264036 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.49760869565217 & 0.00769707129577486 & 194.568640214396 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.49659090909091 & 0.0074633932693401 & 200.524192559832 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.49547619047619 & 0.00715030583357336 & 209.148563052278 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.4945 & 0.00683083131179921 & 218.787425978223 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.49342105263158 & 0.00639252225612776 & 233.620000493547 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.4925 & 0.00591440265201472 & 252.350082977794 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.49147058823529 & 0.0054744969073698 & 272.439753546571 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.4890625 & 0.00506727671898568 & 293.858532418586 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.48633333333333 & 0.00440697809600835 & 337.268146324483 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.48321428571429 & 0.00321428571428572 & 461.444444444444 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.48 & 0 & Inf \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.48 & 0 & Inf \tabularnewline
Median & 1.48 &  &  \tabularnewline
Midrange & 1.54 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.47166666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.4925 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.47166666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.4925 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.4925 &  &  \tabularnewline
Midmean - Closest Observation & 1.47166666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.4925 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.47381818181818 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10383&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]1.51069444444444[/C][C]0.00913583459480834[/C][C]165.359215818436[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.50877442467608[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.50689715841029[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.51265449165072[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.51069444444444[/C][C]0.00913583459480834[/C][C]165.359215818436[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.51069444444444[/C][C]0.00913583459480834[/C][C]165.359215818436[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.51069444444444[/C][C]0.00913583459480834[/C][C]165.359215818436[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.51013888888889[/C][C]0.00901982917202266[/C][C]167.424333663987[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.51013888888889[/C][C]0.00901982917202266[/C][C]167.424333663987[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.51013888888889[/C][C]0.00901982917202266[/C][C]167.424333663987[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.51013888888889[/C][C]0.00901982917202266[/C][C]167.424333663987[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.51013888888889[/C][C]0.00901982917202266[/C][C]167.424333663987[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.50888888888889[/C][C]0.00877147611598796[/C][C]172.02223080088[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.50888888888889[/C][C]0.00877147611598796[/C][C]172.02223080088[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.50736111111111[/C][C]0.008479915181472[/C][C]177.756625963027[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.50569444444444[/C][C]0.00817412802030692[/C][C]184.202454464117[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.50569444444444[/C][C]0.00817412802030692[/C][C]184.202454464117[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.50569444444444[/C][C]0.00817412802030692[/C][C]184.202454464117[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.50361111111111[/C][C]0.00780560358975859[/C][C]192.632266527593[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.50361111111111[/C][C]0.00780560358975859[/C][C]192.632266527593[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.50125[/C][C]0.00740071872963566[/C][C]202.851919501865[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.50125[/C][C]0.00664885384359514[/C][C]225.790795724312[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.51180555555556[/C][C]0.00551114388494218[/C][C]274.31792512008[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.51180555555556[/C][C]0.00551114388494218[/C][C]274.31792512008[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.51180555555556[/C][C]0.00551114388494218[/C][C]274.31792512008[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.50875[/C][C]0.0049801542766985[/C][C]302.952462147457[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.48[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.48[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.50985714285714[/C][C]0.00910825816253568[/C][C]165.767934539617[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.50897058823529[/C][C]0.00906793138142844[/C][C]166.407367321475[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.50803030303030[/C][C]0.00901234506080913[/C][C]167.329401266279[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.50703125[/C][C]0.00893839055808423[/C][C]168.602081124882[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.50612903225806[/C][C]0.00888362637038576[/C][C]169.53988939459[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.50516666666667[/C][C]0.00880899535967095[/C][C]170.867006419094[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.50413793103448[/C][C]0.00871000315940351[/C][C]172.690859406932[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.50303571428571[/C][C]0.00858085926000854[/C][C]175.161445811223[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.50185185185185[/C][C]0.00841396660127913[/C][C]178.495104986931[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.50076923076923[/C][C]0.00826067641297375[/C][C]181.676312657909[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.4996[/C][C]0.00806078944834886[/C][C]186.036368969688[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.49854166666667[/C][C]0.00787192236007356[/C][C]190.365402264036[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.49760869565217[/C][C]0.00769707129577486[/C][C]194.568640214396[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.49659090909091[/C][C]0.0074633932693401[/C][C]200.524192559832[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.49547619047619[/C][C]0.00715030583357336[/C][C]209.148563052278[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.4945[/C][C]0.00683083131179921[/C][C]218.787425978223[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.49342105263158[/C][C]0.00639252225612776[/C][C]233.620000493547[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.4925[/C][C]0.00591440265201472[/C][C]252.350082977794[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.49147058823529[/C][C]0.0054744969073698[/C][C]272.439753546571[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.4890625[/C][C]0.00506727671898568[/C][C]293.858532418586[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.48633333333333[/C][C]0.00440697809600835[/C][C]337.268146324483[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.48321428571429[/C][C]0.00321428571428572[/C][C]461.444444444444[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.48[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.48[/C][C]0[/C][C]Inf[/C][/ROW]
[ROW][C]Median[/C][C]1.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.54[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.47166666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.4925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.47166666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.4925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.4925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.47166666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.4925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.47381818181818[/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=10383&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10383&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	1.51069444444444	0.00913583459480834	165.359215818436
Geometric Mean	1.50877442467608
Harmonic Mean	1.50689715841029
Quadratic Mean	1.51265449165072
Winsorized Mean ( 1 / 24 )	1.51069444444444	0.00913583459480834	165.359215818436
Winsorized Mean ( 2 / 24 )	1.51069444444444	0.00913583459480834	165.359215818436
Winsorized Mean ( 3 / 24 )	1.51069444444444	0.00913583459480834	165.359215818436
Winsorized Mean ( 4 / 24 )	1.51013888888889	0.00901982917202266	167.424333663987
Winsorized Mean ( 5 / 24 )	1.51013888888889	0.00901982917202266	167.424333663987
Winsorized Mean ( 6 / 24 )	1.51013888888889	0.00901982917202266	167.424333663987
Winsorized Mean ( 7 / 24 )	1.51013888888889	0.00901982917202266	167.424333663987
Winsorized Mean ( 8 / 24 )	1.51013888888889	0.00901982917202266	167.424333663987
Winsorized Mean ( 9 / 24 )	1.50888888888889	0.00877147611598796	172.02223080088
Winsorized Mean ( 10 / 24 )	1.50888888888889	0.00877147611598796	172.02223080088
Winsorized Mean ( 11 / 24 )	1.50736111111111	0.008479915181472	177.756625963027
Winsorized Mean ( 12 / 24 )	1.50569444444444	0.00817412802030692	184.202454464117
Winsorized Mean ( 13 / 24 )	1.50569444444444	0.00817412802030692	184.202454464117
Winsorized Mean ( 14 / 24 )	1.50569444444444	0.00817412802030692	184.202454464117
Winsorized Mean ( 15 / 24 )	1.50361111111111	0.00780560358975859	192.632266527593
Winsorized Mean ( 16 / 24 )	1.50361111111111	0.00780560358975859	192.632266527593
Winsorized Mean ( 17 / 24 )	1.50125	0.00740071872963566	202.851919501865
Winsorized Mean ( 18 / 24 )	1.50125	0.00664885384359514	225.790795724312
Winsorized Mean ( 19 / 24 )	1.51180555555556	0.00551114388494218	274.31792512008
Winsorized Mean ( 20 / 24 )	1.51180555555556	0.00551114388494218	274.31792512008
Winsorized Mean ( 21 / 24 )	1.51180555555556	0.00551114388494218	274.31792512008
Winsorized Mean ( 22 / 24 )	1.50875	0.0049801542766985	302.952462147457
Winsorized Mean ( 23 / 24 )	1.48	0	Inf
Winsorized Mean ( 24 / 24 )	1.48	0	Inf
Trimmed Mean ( 1 / 24 )	1.50985714285714	0.00910825816253568	165.767934539617
Trimmed Mean ( 2 / 24 )	1.50897058823529	0.00906793138142844	166.407367321475
Trimmed Mean ( 3 / 24 )	1.50803030303030	0.00901234506080913	167.329401266279
Trimmed Mean ( 4 / 24 )	1.50703125	0.00893839055808423	168.602081124882
Trimmed Mean ( 5 / 24 )	1.50612903225806	0.00888362637038576	169.53988939459
Trimmed Mean ( 6 / 24 )	1.50516666666667	0.00880899535967095	170.867006419094
Trimmed Mean ( 7 / 24 )	1.50413793103448	0.00871000315940351	172.690859406932
Trimmed Mean ( 8 / 24 )	1.50303571428571	0.00858085926000854	175.161445811223
Trimmed Mean ( 9 / 24 )	1.50185185185185	0.00841396660127913	178.495104986931
Trimmed Mean ( 10 / 24 )	1.50076923076923	0.00826067641297375	181.676312657909
Trimmed Mean ( 11 / 24 )	1.4996	0.00806078944834886	186.036368969688
Trimmed Mean ( 12 / 24 )	1.49854166666667	0.00787192236007356	190.365402264036
Trimmed Mean ( 13 / 24 )	1.49760869565217	0.00769707129577486	194.568640214396
Trimmed Mean ( 14 / 24 )	1.49659090909091	0.0074633932693401	200.524192559832
Trimmed Mean ( 15 / 24 )	1.49547619047619	0.00715030583357336	209.148563052278
Trimmed Mean ( 16 / 24 )	1.4945	0.00683083131179921	218.787425978223
Trimmed Mean ( 17 / 24 )	1.49342105263158	0.00639252225612776	233.620000493547
Trimmed Mean ( 18 / 24 )	1.4925	0.00591440265201472	252.350082977794
Trimmed Mean ( 19 / 24 )	1.49147058823529	0.0054744969073698	272.439753546571
Trimmed Mean ( 20 / 24 )	1.4890625	0.00506727671898568	293.858532418586
Trimmed Mean ( 21 / 24 )	1.48633333333333	0.00440697809600835	337.268146324483
Trimmed Mean ( 22 / 24 )	1.48321428571429	0.00321428571428572	461.444444444444
Trimmed Mean ( 23 / 24 )	1.48	0	Inf
Trimmed Mean ( 24 / 24 )	1.48	0	Inf
Median	1.48
Midrange	1.54
Midmean - Weighted Average at Xnp	1.47166666666667
Midmean - Weighted Average at X(n+1)p	1.4925
Midmean - Empirical Distribution Function	1.47166666666667
Midmean - Empirical Distribution Function - Averaging	1.4925
Midmean - Empirical Distribution Function - Interpolation	1.4925
Midmean - Closest Observation	1.47166666666667
Midmean - True Basic - Statistics Graphics Toolkit	1.4925
Midmean - MS Excel (old versions)	1.47381818181818
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