Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 19 Aug 2009 07:41:18 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Aug/19/t1250689322rgzu5zzw66fpkt2.htm/, Retrieved Tue, 07 May 2024 14:59:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42942, Retrieved Tue, 07 May 2024 14:59:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Thomas Van den Bo...] [2009-04-22 20:03:59] [29fb2afdd4eca1705c3ee13bfc104084]
-   PD    [Central Tendency] [Thomas Van den Bo...] [2009-08-19 13:41:18] [50e97696ebad247f45d73cd9926afb25] [Current]
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Dataseries X:
5,93
5,9
5,9
5,94
5,86
5,92
5,9
5,91
5,84
5,84
5,83
5,82
5,8
5,91
5,92
5,96
5,9
5,92
6,09
6,31
6,25
6,23
6,22
6,19
6,15
6,12
6,13
6,1
6,05
6,07
6,09
6,17
6,12
6,12
6,13
6,19
6,24
6,41
6,5
6,53
6,58
6,53
6,51
6,51
6,49
6,49
6,49
6,53
6,65
6,61
6,52
6,62
6,6
6,61
6,63
6,62
6,6
6,59
6,59
6,52
6,52
6,61
6,59
6,6
6,48
6,53
6,56
6,56
6,49
6,45
6,44
6,43




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42942&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]6 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=42942&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42942&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.277222222222220.0334307392670722187.767975218095
Geometric Mean6.27084813996112
Harmonic Mean6.26442685072195
Quadratic Mean6.28353956337067
Winsorized Mean ( 1 / 24 )6.277222222222220.0333334637451805188.315929907819
Winsorized Mean ( 2 / 24 )6.277222222222220.0332394347777394188.848645116737
Winsorized Mean ( 3 / 24 )6.277638888888890.0331612300351992189.306575245413
Winsorized Mean ( 4 / 24 )6.277083333333330.0330814648069205189.746233123879
Winsorized Mean ( 5 / 24 )6.278472222222220.0328275356063116191.256276362551
Winsorized Mean ( 6 / 24 )6.281805555555560.0322501994928314194.783463493052
Winsorized Mean ( 7 / 24 )6.280833333333330.0321124722867818195.588594899891
Winsorized Mean ( 8 / 24 )6.280833333333330.0321124722867818195.588594899891
Winsorized Mean ( 9 / 24 )6.280833333333330.0321124722867818195.588594899891
Winsorized Mean ( 10 / 24 )6.280833333333330.0316893605363852198.200065480078
Winsorized Mean ( 11 / 24 )6.280833333333330.0316893605363852198.200065480078
Winsorized Mean ( 12 / 24 )6.28250.0314165748245877199.974059396287
Winsorized Mean ( 13 / 24 )6.280694444444440.0311700158809573201.497954586591
Winsorized Mean ( 14 / 24 )6.276805555555550.0306539486723221204.763360918099
Winsorized Mean ( 15 / 24 )6.278888888888890.0303143129989131207.126214244539
Winsorized Mean ( 16 / 24 )6.274444444444440.0291063352471841215.569716735516
Winsorized Mean ( 17 / 24 )6.279166666666670.0283497259952589221.489501087833
Winsorized Mean ( 18 / 24 )6.301666666666670.0249561430650314252.50963861866
Winsorized Mean ( 19 / 24 )6.306944444444440.0242175188539226260.429009366617
Winsorized Mean ( 20 / 24 )6.309722222222220.0231041496301831273.099089264002
Winsorized Mean ( 21 / 24 )6.309722222222220.0231041496301831273.099089264002
Winsorized Mean ( 22 / 24 )6.312777777777780.0226977677942401278.123286615864
Winsorized Mean ( 23 / 24 )6.315972222222220.0214558721385597294.370332813058
Winsorized Mean ( 24 / 24 )6.315972222222220.0214558721385597294.370332813058
Trimmed Mean ( 1 / 24 )6.278714285714290.0332702849461247188.718380256783
Trimmed Mean ( 2 / 24 )6.280294117647060.0331688754934934189.342991711583
Trimmed Mean ( 3 / 24 )6.28196969696970.0330784331015764189.911344279192
Trimmed Mean ( 4 / 24 )6.283593750.0329752847469414190.554647161397
Trimmed Mean ( 5 / 24 )6.285483870967740.0328479642945314191.350788578827
Trimmed Mean ( 6 / 24 )6.287166666666670.0327385566039836192.041657264195
Trimmed Mean ( 7 / 24 )6.288275862068970.0327229085436985192.167387983606
Trimmed Mean ( 8 / 24 )6.289642857142860.0326929480120974192.385307523062
Trimmed Mean ( 9 / 24 )6.291111111111110.0326113280754500192.911834088938
Trimmed Mean ( 10 / 24 )6.29269230769230.0324654537179797193.82733296616
Trimmed Mean ( 11 / 24 )6.29440.0323263461136768194.71424261392
Trimmed Mean ( 12 / 24 )6.296250.0321022096077844196.131359084804
Trimmed Mean ( 13 / 24 )6.298043478260870.0318277665141154197.878901602088
Trimmed Mean ( 14 / 24 )6.300227272727270.0314744915616746200.169310451987
Trimmed Mean ( 15 / 24 )6.303095238095240.0310660158332044202.893582232655
Trimmed Mean ( 16 / 24 )6.3060.030554281247709206.386789100884
Trimmed Mean ( 17 / 24 )6.309736842105260.0300745561049251209.803157861803
Trimmed Mean ( 18 / 24 )6.313333333333330.0295522136790687213.633178275405
Trimmed Mean ( 19 / 24 )6.314705882352940.029614984205703213.226717883473
Trimmed Mean ( 20 / 24 )6.3156250.0297467045477581212.313434244802
Trimmed Mean ( 21 / 24 )6.316333333333330.0300401391755402210.263118170782
Trimmed Mean ( 22 / 24 )6.317142857142860.0302627695853846208.743051072025
Trimmed Mean ( 23 / 24 )6.317692307692310.0304848395729251207.240464316017
Trimmed Mean ( 24 / 24 )6.317916666666670.0309275636095257204.28109845422
Median6.28
Midrange6.225
Midmean - Weighted Average at Xnp6.31538461538462
Midmean - Weighted Average at X(n+1)p6.32473684210526
Midmean - Empirical Distribution Function6.31538461538462
Midmean - Empirical Distribution Function - Averaging6.32473684210526
Midmean - Empirical Distribution Function - Interpolation6.32473684210526
Midmean - Closest Observation6.31538461538462
Midmean - True Basic - Statistics Graphics Toolkit6.32473684210526
Midmean - MS Excel (old versions)6.31538461538462
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.27722222222222 & 0.0334307392670722 & 187.767975218095 \tabularnewline
Geometric Mean & 6.27084813996112 &  &  \tabularnewline
Harmonic Mean & 6.26442685072195 &  &  \tabularnewline
Quadratic Mean & 6.28353956337067 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 6.27722222222222 & 0.0333334637451805 & 188.315929907819 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 6.27722222222222 & 0.0332394347777394 & 188.848645116737 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 6.27763888888889 & 0.0331612300351992 & 189.306575245413 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 6.27708333333333 & 0.0330814648069205 & 189.746233123879 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 6.27847222222222 & 0.0328275356063116 & 191.256276362551 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 6.28180555555556 & 0.0322501994928314 & 194.783463493052 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 6.28083333333333 & 0.0321124722867818 & 195.588594899891 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 6.28083333333333 & 0.0321124722867818 & 195.588594899891 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 6.28083333333333 & 0.0321124722867818 & 195.588594899891 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 6.28083333333333 & 0.0316893605363852 & 198.200065480078 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 6.28083333333333 & 0.0316893605363852 & 198.200065480078 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 6.2825 & 0.0314165748245877 & 199.974059396287 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 6.28069444444444 & 0.0311700158809573 & 201.497954586591 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 6.27680555555555 & 0.0306539486723221 & 204.763360918099 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 6.27888888888889 & 0.0303143129989131 & 207.126214244539 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 6.27444444444444 & 0.0291063352471841 & 215.569716735516 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 6.27916666666667 & 0.0283497259952589 & 221.489501087833 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 6.30166666666667 & 0.0249561430650314 & 252.50963861866 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 6.30694444444444 & 0.0242175188539226 & 260.429009366617 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 6.30972222222222 & 0.0231041496301831 & 273.099089264002 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 6.30972222222222 & 0.0231041496301831 & 273.099089264002 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 6.31277777777778 & 0.0226977677942401 & 278.123286615864 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 6.31597222222222 & 0.0214558721385597 & 294.370332813058 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 6.31597222222222 & 0.0214558721385597 & 294.370332813058 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 6.27871428571429 & 0.0332702849461247 & 188.718380256783 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 6.28029411764706 & 0.0331688754934934 & 189.342991711583 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 6.2819696969697 & 0.0330784331015764 & 189.911344279192 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 6.28359375 & 0.0329752847469414 & 190.554647161397 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 6.28548387096774 & 0.0328479642945314 & 191.350788578827 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 6.28716666666667 & 0.0327385566039836 & 192.041657264195 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 6.28827586206897 & 0.0327229085436985 & 192.167387983606 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 6.28964285714286 & 0.0326929480120974 & 192.385307523062 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 6.29111111111111 & 0.0326113280754500 & 192.911834088938 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 6.2926923076923 & 0.0324654537179797 & 193.82733296616 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 6.2944 & 0.0323263461136768 & 194.71424261392 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 6.29625 & 0.0321022096077844 & 196.131359084804 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 6.29804347826087 & 0.0318277665141154 & 197.878901602088 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 6.30022727272727 & 0.0314744915616746 & 200.169310451987 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 6.30309523809524 & 0.0310660158332044 & 202.893582232655 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 6.306 & 0.030554281247709 & 206.386789100884 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 6.30973684210526 & 0.0300745561049251 & 209.803157861803 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 6.31333333333333 & 0.0295522136790687 & 213.633178275405 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 6.31470588235294 & 0.029614984205703 & 213.226717883473 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 6.315625 & 0.0297467045477581 & 212.313434244802 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 6.31633333333333 & 0.0300401391755402 & 210.263118170782 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 6.31714285714286 & 0.0302627695853846 & 208.743051072025 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 6.31769230769231 & 0.0304848395729251 & 207.240464316017 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 6.31791666666667 & 0.0309275636095257 & 204.28109845422 \tabularnewline
Median & 6.28 &  &  \tabularnewline
Midrange & 6.225 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.31538461538462 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.32473684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.31538461538462 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.32473684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.32473684210526 &  &  \tabularnewline
Midmean - Closest Observation & 6.31538461538462 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.32473684210526 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.31538461538462 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42942&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]6.27722222222222[/C][C]0.0334307392670722[/C][C]187.767975218095[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.27084813996112[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.26442685072195[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.28353956337067[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]6.27722222222222[/C][C]0.0333334637451805[/C][C]188.315929907819[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]6.27722222222222[/C][C]0.0332394347777394[/C][C]188.848645116737[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]6.27763888888889[/C][C]0.0331612300351992[/C][C]189.306575245413[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]6.27708333333333[/C][C]0.0330814648069205[/C][C]189.746233123879[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]6.27847222222222[/C][C]0.0328275356063116[/C][C]191.256276362551[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]6.28180555555556[/C][C]0.0322501994928314[/C][C]194.783463493052[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]6.28083333333333[/C][C]0.0321124722867818[/C][C]195.588594899891[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]6.28083333333333[/C][C]0.0321124722867818[/C][C]195.588594899891[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]6.28083333333333[/C][C]0.0321124722867818[/C][C]195.588594899891[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]6.28083333333333[/C][C]0.0316893605363852[/C][C]198.200065480078[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]6.28083333333333[/C][C]0.0316893605363852[/C][C]198.200065480078[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]6.2825[/C][C]0.0314165748245877[/C][C]199.974059396287[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]6.28069444444444[/C][C]0.0311700158809573[/C][C]201.497954586591[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]6.27680555555555[/C][C]0.0306539486723221[/C][C]204.763360918099[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]6.27888888888889[/C][C]0.0303143129989131[/C][C]207.126214244539[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]6.27444444444444[/C][C]0.0291063352471841[/C][C]215.569716735516[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]6.27916666666667[/C][C]0.0283497259952589[/C][C]221.489501087833[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]6.30166666666667[/C][C]0.0249561430650314[/C][C]252.50963861866[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]6.30694444444444[/C][C]0.0242175188539226[/C][C]260.429009366617[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]6.30972222222222[/C][C]0.0231041496301831[/C][C]273.099089264002[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]6.30972222222222[/C][C]0.0231041496301831[/C][C]273.099089264002[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]6.31277777777778[/C][C]0.0226977677942401[/C][C]278.123286615864[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]6.31597222222222[/C][C]0.0214558721385597[/C][C]294.370332813058[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]6.31597222222222[/C][C]0.0214558721385597[/C][C]294.370332813058[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]6.27871428571429[/C][C]0.0332702849461247[/C][C]188.718380256783[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]6.28029411764706[/C][C]0.0331688754934934[/C][C]189.342991711583[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]6.2819696969697[/C][C]0.0330784331015764[/C][C]189.911344279192[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]6.28359375[/C][C]0.0329752847469414[/C][C]190.554647161397[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]6.28548387096774[/C][C]0.0328479642945314[/C][C]191.350788578827[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]6.28716666666667[/C][C]0.0327385566039836[/C][C]192.041657264195[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]6.28827586206897[/C][C]0.0327229085436985[/C][C]192.167387983606[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]6.28964285714286[/C][C]0.0326929480120974[/C][C]192.385307523062[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]6.29111111111111[/C][C]0.0326113280754500[/C][C]192.911834088938[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]6.2926923076923[/C][C]0.0324654537179797[/C][C]193.82733296616[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]6.2944[/C][C]0.0323263461136768[/C][C]194.71424261392[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]6.29625[/C][C]0.0321022096077844[/C][C]196.131359084804[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]6.29804347826087[/C][C]0.0318277665141154[/C][C]197.878901602088[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]6.30022727272727[/C][C]0.0314744915616746[/C][C]200.169310451987[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]6.30309523809524[/C][C]0.0310660158332044[/C][C]202.893582232655[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]6.306[/C][C]0.030554281247709[/C][C]206.386789100884[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]6.30973684210526[/C][C]0.0300745561049251[/C][C]209.803157861803[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]6.31333333333333[/C][C]0.0295522136790687[/C][C]213.633178275405[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]6.31470588235294[/C][C]0.029614984205703[/C][C]213.226717883473[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]6.315625[/C][C]0.0297467045477581[/C][C]212.313434244802[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]6.31633333333333[/C][C]0.0300401391755402[/C][C]210.263118170782[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]6.31714285714286[/C][C]0.0302627695853846[/C][C]208.743051072025[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]6.31769230769231[/C][C]0.0304848395729251[/C][C]207.240464316017[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]6.31791666666667[/C][C]0.0309275636095257[/C][C]204.28109845422[/C][/ROW]
[ROW][C]Median[/C][C]6.28[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.31538461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.32473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.31538461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.32473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.32473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.31538461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.32473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.31538461538462[/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=42942&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42942&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.277222222222220.0334307392670722187.767975218095
Geometric Mean6.27084813996112
Harmonic Mean6.26442685072195
Quadratic Mean6.28353956337067
Winsorized Mean ( 1 / 24 )6.277222222222220.0333334637451805188.315929907819
Winsorized Mean ( 2 / 24 )6.277222222222220.0332394347777394188.848645116737
Winsorized Mean ( 3 / 24 )6.277638888888890.0331612300351992189.306575245413
Winsorized Mean ( 4 / 24 )6.277083333333330.0330814648069205189.746233123879
Winsorized Mean ( 5 / 24 )6.278472222222220.0328275356063116191.256276362551
Winsorized Mean ( 6 / 24 )6.281805555555560.0322501994928314194.783463493052
Winsorized Mean ( 7 / 24 )6.280833333333330.0321124722867818195.588594899891
Winsorized Mean ( 8 / 24 )6.280833333333330.0321124722867818195.588594899891
Winsorized Mean ( 9 / 24 )6.280833333333330.0321124722867818195.588594899891
Winsorized Mean ( 10 / 24 )6.280833333333330.0316893605363852198.200065480078
Winsorized Mean ( 11 / 24 )6.280833333333330.0316893605363852198.200065480078
Winsorized Mean ( 12 / 24 )6.28250.0314165748245877199.974059396287
Winsorized Mean ( 13 / 24 )6.280694444444440.0311700158809573201.497954586591
Winsorized Mean ( 14 / 24 )6.276805555555550.0306539486723221204.763360918099
Winsorized Mean ( 15 / 24 )6.278888888888890.0303143129989131207.126214244539
Winsorized Mean ( 16 / 24 )6.274444444444440.0291063352471841215.569716735516
Winsorized Mean ( 17 / 24 )6.279166666666670.0283497259952589221.489501087833
Winsorized Mean ( 18 / 24 )6.301666666666670.0249561430650314252.50963861866
Winsorized Mean ( 19 / 24 )6.306944444444440.0242175188539226260.429009366617
Winsorized Mean ( 20 / 24 )6.309722222222220.0231041496301831273.099089264002
Winsorized Mean ( 21 / 24 )6.309722222222220.0231041496301831273.099089264002
Winsorized Mean ( 22 / 24 )6.312777777777780.0226977677942401278.123286615864
Winsorized Mean ( 23 / 24 )6.315972222222220.0214558721385597294.370332813058
Winsorized Mean ( 24 / 24 )6.315972222222220.0214558721385597294.370332813058
Trimmed Mean ( 1 / 24 )6.278714285714290.0332702849461247188.718380256783
Trimmed Mean ( 2 / 24 )6.280294117647060.0331688754934934189.342991711583
Trimmed Mean ( 3 / 24 )6.28196969696970.0330784331015764189.911344279192
Trimmed Mean ( 4 / 24 )6.283593750.0329752847469414190.554647161397
Trimmed Mean ( 5 / 24 )6.285483870967740.0328479642945314191.350788578827
Trimmed Mean ( 6 / 24 )6.287166666666670.0327385566039836192.041657264195
Trimmed Mean ( 7 / 24 )6.288275862068970.0327229085436985192.167387983606
Trimmed Mean ( 8 / 24 )6.289642857142860.0326929480120974192.385307523062
Trimmed Mean ( 9 / 24 )6.291111111111110.0326113280754500192.911834088938
Trimmed Mean ( 10 / 24 )6.29269230769230.0324654537179797193.82733296616
Trimmed Mean ( 11 / 24 )6.29440.0323263461136768194.71424261392
Trimmed Mean ( 12 / 24 )6.296250.0321022096077844196.131359084804
Trimmed Mean ( 13 / 24 )6.298043478260870.0318277665141154197.878901602088
Trimmed Mean ( 14 / 24 )6.300227272727270.0314744915616746200.169310451987
Trimmed Mean ( 15 / 24 )6.303095238095240.0310660158332044202.893582232655
Trimmed Mean ( 16 / 24 )6.3060.030554281247709206.386789100884
Trimmed Mean ( 17 / 24 )6.309736842105260.0300745561049251209.803157861803
Trimmed Mean ( 18 / 24 )6.313333333333330.0295522136790687213.633178275405
Trimmed Mean ( 19 / 24 )6.314705882352940.029614984205703213.226717883473
Trimmed Mean ( 20 / 24 )6.3156250.0297467045477581212.313434244802
Trimmed Mean ( 21 / 24 )6.316333333333330.0300401391755402210.263118170782
Trimmed Mean ( 22 / 24 )6.317142857142860.0302627695853846208.743051072025
Trimmed Mean ( 23 / 24 )6.317692307692310.0304848395729251207.240464316017
Trimmed Mean ( 24 / 24 )6.317916666666670.0309275636095257204.28109845422
Median6.28
Midrange6.225
Midmean - Weighted Average at Xnp6.31538461538462
Midmean - Weighted Average at X(n+1)p6.32473684210526
Midmean - Empirical Distribution Function6.31538461538462
Midmean - Empirical Distribution Function - Averaging6.32473684210526
Midmean - Empirical Distribution Function - Interpolation6.32473684210526
Midmean - Closest Observation6.31538461538462
Midmean - True Basic - Statistics Graphics Toolkit6.32473684210526
Midmean - MS Excel (old versions)6.31538461538462
Number of observations72



Parameters (Session):
par1 = 0 ;
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')