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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 04 Apr 2011 06:50:47 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Apr/04/t1301899859sk0n2wso9ricdf6.htm/, Retrieved Wed, 08 May 2024 03:35:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=120038, Retrieved Wed, 08 May 2024 03:35:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact126
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-04-04 06:50:47] [39dfb880f237820275004e8a4e7fff84] [Current]
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Dataseries X:
1,3014
1,3201
1,2938
1,2694
1,2165
1,2037
1,2292
1,2256
1,2015
1,1786
1,1856
1,2103
1,1938
1,202
1,2271
1,277
1,265
1,2684
1,2811
1,2727
1,2611
1,2881
1,3213
1,2999
1,3074
1,3242
1,3516
1,3511
1,3419
1,3716
1,3622
1,3896
1,4227
1,4684
1,457
1,4718
1,4748
1,5527
1,5751
1,5557
1,5553
1,577
1,4975
1,437
1,3322
1,2732
1,3449
1,3239
1,2785
1,305
1,319
1,365
1,4016
1,4088
1,4268
1,4562
1,4816
1,4914
1,4614
1,4272
1,3686
1,3569
1,3406
1,2565
1,2209
1,277
1,2894
1,3067
1,3898
1,3661
1,322
1,336




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120038&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120038&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120038&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.343958333333330.0120375676536271111.647001454515
Geometric Mean1.34021129545952
Harmonic Mean1.33654523068255
Quadratic Mean1.3477804410297
Winsorized Mean ( 1 / 24 )1.344029166666670.0120119592593563111.890919511718
Winsorized Mean ( 2 / 24 )1.343718055555560.0118294201567808113.591202083165
Winsorized Mean ( 3 / 24 )1.344022222222220.0117692120134334114.198148583623
Winsorized Mean ( 4 / 24 )1.343905555555560.0117281058112114114.588457606757
Winsorized Mean ( 5 / 24 )1.340190277777780.0108314068636905123.731874782622
Winsorized Mean ( 6 / 24 )1.340231944444440.0106323541843895126.052228998559
Winsorized Mean ( 7 / 24 )1.339881944444440.0103424371767132129.551857221941
Winsorized Mean ( 8 / 24 )1.339615277777780.0101169307302711132.413210438368
Winsorized Mean ( 9 / 24 )1.339827777777780.00995056407642572134.64842470107
Winsorized Mean ( 10 / 24 )1.339563888888890.00982923749057619136.283601873818
Winsorized Mean ( 11 / 24 )1.338815277777780.00958244916511656139.715354050771
Winsorized Mean ( 12 / 24 )1.342631944444440.0087653618395569153.17473129122
Winsorized Mean ( 13 / 24 )1.343318055555560.00862553718505612155.737321251467
Winsorized Mean ( 14 / 24 )1.340343055555560.00785487195346159170.638434782489
Winsorized Mean ( 15 / 24 )1.339009722222220.00741130685682268180.671202540961
Winsorized Mean ( 16 / 24 )1.339143055555560.0073666836154259181.783706952119
Winsorized Mean ( 17 / 24 )1.338954166666670.00710201125866692188.531687419205
Winsorized Mean ( 18 / 24 )1.335604166666670.00652156061731912204.798244628708
Winsorized Mean ( 19 / 24 )1.334706944444440.00608978573698084219.171412934826
Winsorized Mean ( 20 / 24 )1.331429166666670.00559487016240717237.973201882816
Winsorized Mean ( 21 / 24 )1.331808333333330.00552659551806936240.981690984793
Winsorized Mean ( 22 / 24 )1.327102777777780.00463769805402487286.155494022738
Winsorized Mean ( 23 / 24 )1.328380555555560.00420087070809589316.215529555696
Winsorized Mean ( 24 / 24 )1.327980555555560.00403069872770524329.466587623532
Trimmed Mean ( 1 / 24 )1.342991428571430.0116809472627835114.972818416047
Trimmed Mean ( 2 / 24 )1.341892647058820.0112858396666168118.900559169567
Trimmed Mean ( 3 / 24 )1.340896969696970.0109308920400454122.670406475938
Trimmed Mean ( 4 / 24 )1.3397250.0105303322276838127.225330695447
Trimmed Mean ( 5 / 24 )1.338511290322580.0100590817089474133.064958517237
Trimmed Mean ( 6 / 24 )1.338108333333330.00978903032185439136.69467652439
Trimmed Mean ( 7 / 24 )1.337668965517240.0095160641100076140.569562169141
Trimmed Mean ( 8 / 24 )1.33726250.0092576590132627144.449314679252
Trimmed Mean ( 9 / 24 )1.336870370370370.00899382489826749148.643139653285
Trimmed Mean ( 10 / 24 )1.336415384615380.00870381861057821153.543570288927
Trimmed Mean ( 11 / 24 )1.3359620.00836723585401623159.665870940969
Trimmed Mean ( 12 / 24 )1.335572916666670.00800005470924519166.945472900732
Trimmed Mean ( 13 / 24 )1.334652173913040.00771941259506541172.895561349605
Trimmed Mean ( 14 / 24 )1.333561363636360.00738240309333234180.640551156142
Trimmed Mean ( 15 / 24 )1.332730952380950.00713583934192509186.765829290856
Trimmed Mean ( 16 / 24 )1.33197750.00691519182994021192.61613166435
Trimmed Mean ( 17 / 24 )1.331128947368420.00662253997150477200.999760378338
Trimmed Mean ( 18 / 24 )1.330208333333330.00628898555298979211.513975048162
Trimmed Mean ( 19 / 24 )1.329573529411760.00600017722379906221.589043093286
Trimmed Mean ( 20 / 24 )1.3289656250.0057177190096124232.429334629036
Trimmed Mean ( 21 / 24 )1.328670.00546955029776399242.92125086466
Trimmed Mean ( 22 / 24 )1.328285714285710.00511679389295761259.593359059053
Trimmed Mean ( 23 / 24 )1.328434615384620.00491310317826083270.386060944656
Trimmed Mean ( 24 / 24 )1.328441666666670.00474913003729221279.72316113376
Median1.32405
Midrange1.3778
Midmean - Weighted Average at Xnp1.32865405405405
Midmean - Weighted Average at X(n+1)p1.33020833333333
Midmean - Empirical Distribution Function1.32865405405405
Midmean - Empirical Distribution Function - Averaging1.33020833333333
Midmean - Empirical Distribution Function - Interpolation1.33020833333333
Midmean - Closest Observation1.32865405405405
Midmean - True Basic - Statistics Graphics Toolkit1.33020833333333
Midmean - MS Excel (old versions)1.33112894736842
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.34395833333333 & 0.0120375676536271 & 111.647001454515 \tabularnewline
Geometric Mean & 1.34021129545952 &  &  \tabularnewline
Harmonic Mean & 1.33654523068255 &  &  \tabularnewline
Quadratic Mean & 1.3477804410297 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.34402916666667 & 0.0120119592593563 & 111.890919511718 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.34371805555556 & 0.0118294201567808 & 113.591202083165 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.34402222222222 & 0.0117692120134334 & 114.198148583623 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.34390555555556 & 0.0117281058112114 & 114.588457606757 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.34019027777778 & 0.0108314068636905 & 123.731874782622 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.34023194444444 & 0.0106323541843895 & 126.052228998559 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.33988194444444 & 0.0103424371767132 & 129.551857221941 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.33961527777778 & 0.0101169307302711 & 132.413210438368 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.33982777777778 & 0.00995056407642572 & 134.64842470107 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.33956388888889 & 0.00982923749057619 & 136.283601873818 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.33881527777778 & 0.00958244916511656 & 139.715354050771 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.34263194444444 & 0.0087653618395569 & 153.17473129122 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.34331805555556 & 0.00862553718505612 & 155.737321251467 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.34034305555556 & 0.00785487195346159 & 170.638434782489 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.33900972222222 & 0.00741130685682268 & 180.671202540961 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.33914305555556 & 0.0073666836154259 & 181.783706952119 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.33895416666667 & 0.00710201125866692 & 188.531687419205 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.33560416666667 & 0.00652156061731912 & 204.798244628708 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.33470694444444 & 0.00608978573698084 & 219.171412934826 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.33142916666667 & 0.00559487016240717 & 237.973201882816 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.33180833333333 & 0.00552659551806936 & 240.981690984793 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.32710277777778 & 0.00463769805402487 & 286.155494022738 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.32838055555556 & 0.00420087070809589 & 316.215529555696 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.32798055555556 & 0.00403069872770524 & 329.466587623532 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.34299142857143 & 0.0116809472627835 & 114.972818416047 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.34189264705882 & 0.0112858396666168 & 118.900559169567 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.34089696969697 & 0.0109308920400454 & 122.670406475938 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.339725 & 0.0105303322276838 & 127.225330695447 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.33851129032258 & 0.0100590817089474 & 133.064958517237 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.33810833333333 & 0.00978903032185439 & 136.69467652439 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.33766896551724 & 0.0095160641100076 & 140.569562169141 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.3372625 & 0.0092576590132627 & 144.449314679252 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.33687037037037 & 0.00899382489826749 & 148.643139653285 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.33641538461538 & 0.00870381861057821 & 153.543570288927 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.335962 & 0.00836723585401623 & 159.665870940969 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.33557291666667 & 0.00800005470924519 & 166.945472900732 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.33465217391304 & 0.00771941259506541 & 172.895561349605 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.33356136363636 & 0.00738240309333234 & 180.640551156142 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.33273095238095 & 0.00713583934192509 & 186.765829290856 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.3319775 & 0.00691519182994021 & 192.61613166435 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.33112894736842 & 0.00662253997150477 & 200.999760378338 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.33020833333333 & 0.00628898555298979 & 211.513975048162 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.32957352941176 & 0.00600017722379906 & 221.589043093286 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.328965625 & 0.0057177190096124 & 232.429334629036 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.32867 & 0.00546955029776399 & 242.92125086466 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.32828571428571 & 0.00511679389295761 & 259.593359059053 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.32843461538462 & 0.00491310317826083 & 270.386060944656 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.32844166666667 & 0.00474913003729221 & 279.72316113376 \tabularnewline
Median & 1.32405 &  &  \tabularnewline
Midrange & 1.3778 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.32865405405405 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.33020833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.32865405405405 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.33020833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.33020833333333 &  &  \tabularnewline
Midmean - Closest Observation & 1.32865405405405 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.33020833333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.33112894736842 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120038&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]1.34395833333333[/C][C]0.0120375676536271[/C][C]111.647001454515[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.34021129545952[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.33654523068255[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.3477804410297[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.34402916666667[/C][C]0.0120119592593563[/C][C]111.890919511718[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.34371805555556[/C][C]0.0118294201567808[/C][C]113.591202083165[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.34402222222222[/C][C]0.0117692120134334[/C][C]114.198148583623[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.34390555555556[/C][C]0.0117281058112114[/C][C]114.588457606757[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.34019027777778[/C][C]0.0108314068636905[/C][C]123.731874782622[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.34023194444444[/C][C]0.0106323541843895[/C][C]126.052228998559[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.33988194444444[/C][C]0.0103424371767132[/C][C]129.551857221941[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.33961527777778[/C][C]0.0101169307302711[/C][C]132.413210438368[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.33982777777778[/C][C]0.00995056407642572[/C][C]134.64842470107[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.33956388888889[/C][C]0.00982923749057619[/C][C]136.283601873818[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.33881527777778[/C][C]0.00958244916511656[/C][C]139.715354050771[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.34263194444444[/C][C]0.0087653618395569[/C][C]153.17473129122[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.34331805555556[/C][C]0.00862553718505612[/C][C]155.737321251467[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.34034305555556[/C][C]0.00785487195346159[/C][C]170.638434782489[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.33900972222222[/C][C]0.00741130685682268[/C][C]180.671202540961[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.33914305555556[/C][C]0.0073666836154259[/C][C]181.783706952119[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.33895416666667[/C][C]0.00710201125866692[/C][C]188.531687419205[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.33560416666667[/C][C]0.00652156061731912[/C][C]204.798244628708[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.33470694444444[/C][C]0.00608978573698084[/C][C]219.171412934826[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.33142916666667[/C][C]0.00559487016240717[/C][C]237.973201882816[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.33180833333333[/C][C]0.00552659551806936[/C][C]240.981690984793[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.32710277777778[/C][C]0.00463769805402487[/C][C]286.155494022738[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.32838055555556[/C][C]0.00420087070809589[/C][C]316.215529555696[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.32798055555556[/C][C]0.00403069872770524[/C][C]329.466587623532[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.34299142857143[/C][C]0.0116809472627835[/C][C]114.972818416047[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.34189264705882[/C][C]0.0112858396666168[/C][C]118.900559169567[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.34089696969697[/C][C]0.0109308920400454[/C][C]122.670406475938[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.339725[/C][C]0.0105303322276838[/C][C]127.225330695447[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.33851129032258[/C][C]0.0100590817089474[/C][C]133.064958517237[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.33810833333333[/C][C]0.00978903032185439[/C][C]136.69467652439[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.33766896551724[/C][C]0.0095160641100076[/C][C]140.569562169141[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.3372625[/C][C]0.0092576590132627[/C][C]144.449314679252[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.33687037037037[/C][C]0.00899382489826749[/C][C]148.643139653285[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.33641538461538[/C][C]0.00870381861057821[/C][C]153.543570288927[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.335962[/C][C]0.00836723585401623[/C][C]159.665870940969[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.33557291666667[/C][C]0.00800005470924519[/C][C]166.945472900732[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.33465217391304[/C][C]0.00771941259506541[/C][C]172.895561349605[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.33356136363636[/C][C]0.00738240309333234[/C][C]180.640551156142[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.33273095238095[/C][C]0.00713583934192509[/C][C]186.765829290856[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.3319775[/C][C]0.00691519182994021[/C][C]192.61613166435[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.33112894736842[/C][C]0.00662253997150477[/C][C]200.999760378338[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.33020833333333[/C][C]0.00628898555298979[/C][C]211.513975048162[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.32957352941176[/C][C]0.00600017722379906[/C][C]221.589043093286[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.328965625[/C][C]0.0057177190096124[/C][C]232.429334629036[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.32867[/C][C]0.00546955029776399[/C][C]242.92125086466[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.32828571428571[/C][C]0.00511679389295761[/C][C]259.593359059053[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.32843461538462[/C][C]0.00491310317826083[/C][C]270.386060944656[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.32844166666667[/C][C]0.00474913003729221[/C][C]279.72316113376[/C][/ROW]
[ROW][C]Median[/C][C]1.32405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.3778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.32865405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.33020833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.32865405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.33020833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.33020833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.32865405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.33020833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.33112894736842[/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=120038&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120038&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 Mean1.343958333333330.0120375676536271111.647001454515
Geometric Mean1.34021129545952
Harmonic Mean1.33654523068255
Quadratic Mean1.3477804410297
Winsorized Mean ( 1 / 24 )1.344029166666670.0120119592593563111.890919511718
Winsorized Mean ( 2 / 24 )1.343718055555560.0118294201567808113.591202083165
Winsorized Mean ( 3 / 24 )1.344022222222220.0117692120134334114.198148583623
Winsorized Mean ( 4 / 24 )1.343905555555560.0117281058112114114.588457606757
Winsorized Mean ( 5 / 24 )1.340190277777780.0108314068636905123.731874782622
Winsorized Mean ( 6 / 24 )1.340231944444440.0106323541843895126.052228998559
Winsorized Mean ( 7 / 24 )1.339881944444440.0103424371767132129.551857221941
Winsorized Mean ( 8 / 24 )1.339615277777780.0101169307302711132.413210438368
Winsorized Mean ( 9 / 24 )1.339827777777780.00995056407642572134.64842470107
Winsorized Mean ( 10 / 24 )1.339563888888890.00982923749057619136.283601873818
Winsorized Mean ( 11 / 24 )1.338815277777780.00958244916511656139.715354050771
Winsorized Mean ( 12 / 24 )1.342631944444440.0087653618395569153.17473129122
Winsorized Mean ( 13 / 24 )1.343318055555560.00862553718505612155.737321251467
Winsorized Mean ( 14 / 24 )1.340343055555560.00785487195346159170.638434782489
Winsorized Mean ( 15 / 24 )1.339009722222220.00741130685682268180.671202540961
Winsorized Mean ( 16 / 24 )1.339143055555560.0073666836154259181.783706952119
Winsorized Mean ( 17 / 24 )1.338954166666670.00710201125866692188.531687419205
Winsorized Mean ( 18 / 24 )1.335604166666670.00652156061731912204.798244628708
Winsorized Mean ( 19 / 24 )1.334706944444440.00608978573698084219.171412934826
Winsorized Mean ( 20 / 24 )1.331429166666670.00559487016240717237.973201882816
Winsorized Mean ( 21 / 24 )1.331808333333330.00552659551806936240.981690984793
Winsorized Mean ( 22 / 24 )1.327102777777780.00463769805402487286.155494022738
Winsorized Mean ( 23 / 24 )1.328380555555560.00420087070809589316.215529555696
Winsorized Mean ( 24 / 24 )1.327980555555560.00403069872770524329.466587623532
Trimmed Mean ( 1 / 24 )1.342991428571430.0116809472627835114.972818416047
Trimmed Mean ( 2 / 24 )1.341892647058820.0112858396666168118.900559169567
Trimmed Mean ( 3 / 24 )1.340896969696970.0109308920400454122.670406475938
Trimmed Mean ( 4 / 24 )1.3397250.0105303322276838127.225330695447
Trimmed Mean ( 5 / 24 )1.338511290322580.0100590817089474133.064958517237
Trimmed Mean ( 6 / 24 )1.338108333333330.00978903032185439136.69467652439
Trimmed Mean ( 7 / 24 )1.337668965517240.0095160641100076140.569562169141
Trimmed Mean ( 8 / 24 )1.33726250.0092576590132627144.449314679252
Trimmed Mean ( 9 / 24 )1.336870370370370.00899382489826749148.643139653285
Trimmed Mean ( 10 / 24 )1.336415384615380.00870381861057821153.543570288927
Trimmed Mean ( 11 / 24 )1.3359620.00836723585401623159.665870940969
Trimmed Mean ( 12 / 24 )1.335572916666670.00800005470924519166.945472900732
Trimmed Mean ( 13 / 24 )1.334652173913040.00771941259506541172.895561349605
Trimmed Mean ( 14 / 24 )1.333561363636360.00738240309333234180.640551156142
Trimmed Mean ( 15 / 24 )1.332730952380950.00713583934192509186.765829290856
Trimmed Mean ( 16 / 24 )1.33197750.00691519182994021192.61613166435
Trimmed Mean ( 17 / 24 )1.331128947368420.00662253997150477200.999760378338
Trimmed Mean ( 18 / 24 )1.330208333333330.00628898555298979211.513975048162
Trimmed Mean ( 19 / 24 )1.329573529411760.00600017722379906221.589043093286
Trimmed Mean ( 20 / 24 )1.3289656250.0057177190096124232.429334629036
Trimmed Mean ( 21 / 24 )1.328670.00546955029776399242.92125086466
Trimmed Mean ( 22 / 24 )1.328285714285710.00511679389295761259.593359059053
Trimmed Mean ( 23 / 24 )1.328434615384620.00491310317826083270.386060944656
Trimmed Mean ( 24 / 24 )1.328441666666670.00474913003729221279.72316113376
Median1.32405
Midrange1.3778
Midmean - Weighted Average at Xnp1.32865405405405
Midmean - Weighted Average at X(n+1)p1.33020833333333
Midmean - Empirical Distribution Function1.32865405405405
Midmean - Empirical Distribution Function - Averaging1.33020833333333
Midmean - Empirical Distribution Function - Interpolation1.33020833333333
Midmean - Closest Observation1.32865405405405
Midmean - True Basic - Statistics Graphics Toolkit1.33020833333333
Midmean - MS Excel (old versions)1.33112894736842
Number of observations72



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')