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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 11:00:14 -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/2008/Oct/20/t12245221675fr55n17ot9iso6.htm/, Retrieved Sun, 19 May 2024 00:27:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17678, Retrieved Sun, 19 May 2024 00:27:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Investigating Ass...] [2007-10-22 10:34:53] [b9964c45117f7aac638ab9056d451faa]
F    D    [Central Tendency] [Central Tendency:...] [2008-10-20 17:00:14] [0f30549460cf4ec26d9cf94b1fcf7789] [Current]
Feedback Forum
2008-10-25 13:18:13 [Astrid Sniekers] [reply
Het antwoord van de student is correct.

Post a new message
Dataseries X:
0,33
0,33
0,32
0,33
0,34
0,36
0,34
0,33
0,35
0,31
0,28
0,26
0,26
0,26
0,29
0,30
0,30
0,28
0,29
0,29
0,32
0,33
0,29
0,31
0,33
0,36
0,39
0,30
0,27
0,28
0,29
0,30
0,30
0,30
0,31
0,30
0,31
0,29
0,32
0,33
0,35
0,35
0,36
0,40
0,40
0,47
0,43
0,38
0,38
0,40
0,45
0,47
0,45
0,50
0,54
0,55
0,59
0,51
0,50
0,50




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17678&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17678&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17678&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.3560.010464359744330134.0202371380523
Geometric Mean0.348010596252580
Harmonic Mean0.341034576107742
Quadratic Mean0.364961185150787
Winsorized Mean ( 1 / 20 )0.3553333333333330.010230304673370334.7334067438163
Winsorized Mean ( 2 / 20 )0.3550.010124925890779935.0619850287768
Winsorized Mean ( 3 / 20 )0.3540.0096087295526421836.8414989786718
Winsorized Mean ( 4 / 20 )0.3540.0093343421569398737.9244722389793
Winsorized Mean ( 5 / 20 )0.3540.0093343421569398737.9244722389793
Winsorized Mean ( 6 / 20 )0.3540.0093343421569398737.9244722389793
Winsorized Mean ( 7 / 20 )0.3516666666666670.0082925555978087742.407513886261
Winsorized Mean ( 8 / 20 )0.3516666666666670.0082925555978087742.407513886261
Winsorized Mean ( 9 / 20 )0.3486666666666670.0075892678709692345.9420687996006
Winsorized Mean ( 10 / 20 )0.3486666666666670.0075892678709692345.9420687996006
Winsorized Mean ( 11 / 20 )0.3450.0067835793761510950.8581061515858
Winsorized Mean ( 12 / 20 )0.3390.0055829644030231660.7204301385895
Winsorized Mean ( 13 / 20 )0.3411666666666670.005278094945371364.6382208349355
Winsorized Mean ( 14 / 20 )0.3411666666666670.005278094945371364.6382208349355
Winsorized Mean ( 15 / 20 )0.3386666666666670.0048156211599656470.3266838102113
Winsorized Mean ( 16 / 20 )0.3360.0043452682232749977.3254912551197
Winsorized Mean ( 17 / 20 )0.3360.0043452682232749977.3254912551197
Winsorized Mean ( 18 / 20 )0.330.003369856406939397.9270212583703
Winsorized Mean ( 19 / 20 )0.330.003369856406939397.9270212583703
Winsorized Mean ( 20 / 20 )0.3333333333333330.00288838181845652115.404871753229
Trimmed Mean ( 1 / 20 )0.3536206896551720.0098895848465396535.7568790947684
Trimmed Mean ( 2 / 20 )0.3517857142857140.0094632136123961837.174022345316
Trimmed Mean ( 3 / 20 )0.350.0089995729380779438.8907343057492
Trimmed Mean ( 4 / 20 )0.3484615384615380.0086771514576878440.158517476701
Trimmed Mean ( 5 / 20 )0.34680.008376059177616841.4037189382266
Trimmed Mean ( 6 / 20 )0.3450.0079838045286550643.2124808118415
Trimmed Mean ( 7 / 20 )0.3430434782608700.0074656674099558245.9494723543946
Trimmed Mean ( 8 / 20 )0.3413636363636360.0071349933374210847.8435816573616
Trimmed Mean ( 9 / 20 )0.3395238095238100.0066865474265064550.7771481853083
Trimmed Mean ( 10 / 20 )0.3380.0063164417117104753.51114051656
Trimmed Mean ( 11 / 20 )0.3363157894736840.0057991642679340957.9938373764147
Trimmed Mean ( 12 / 20 )0.3350.0053674504012169362.4132455744812
Trimmed Mean ( 13 / 20 )0.3344117647058820.0051741710173401164.6309840910117
Trimmed Mean ( 14 / 20 )0.33343750.0049718841555743967.0646156600724
Trimmed Mean ( 15 / 20 )0.3323333333333330.00466543497703171.2330865116514
Trimmed Mean ( 16 / 20 )0.3314285714285710.0043859529776660675.5659199075448
Trimmed Mean ( 17 / 20 )0.3307692307692310.0041481442346808579.7390862168705
Trimmed Mean ( 18 / 20 )0.330.0037590470577805687.7882066724753
Trimmed Mean ( 19 / 20 )0.330.0036037498507822491.5712837083766
Trimmed Mean ( 20 / 20 )0.330.0033245498310218499.2615592405094
Median0.33
Midrange0.425
Midmean - Weighted Average at Xnp0.3303125
Midmean - Weighted Average at X(n+1)p0.3303125
Midmean - Empirical Distribution Function0.3303125
Midmean - Empirical Distribution Function - Averaging0.3303125
Midmean - Empirical Distribution Function - Interpolation0.3303125
Midmean - Closest Observation0.3303125
Midmean - True Basic - Statistics Graphics Toolkit0.3303125
Midmean - MS Excel (old versions)0.336285714285714
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.356 & 0.0104643597443301 & 34.0202371380523 \tabularnewline
Geometric Mean & 0.348010596252580 &  &  \tabularnewline
Harmonic Mean & 0.341034576107742 &  &  \tabularnewline
Quadratic Mean & 0.364961185150787 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.355333333333333 & 0.0102303046733703 & 34.7334067438163 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.355 & 0.0101249258907799 & 35.0619850287768 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.354 & 0.00960872955264218 & 36.8414989786718 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.354 & 0.00933434215693987 & 37.9244722389793 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.354 & 0.00933434215693987 & 37.9244722389793 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.354 & 0.00933434215693987 & 37.9244722389793 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.351666666666667 & 0.00829255559780877 & 42.407513886261 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.351666666666667 & 0.00829255559780877 & 42.407513886261 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.348666666666667 & 0.00758926787096923 & 45.9420687996006 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.348666666666667 & 0.00758926787096923 & 45.9420687996006 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.345 & 0.00678357937615109 & 50.8581061515858 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.339 & 0.00558296440302316 & 60.7204301385895 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.341166666666667 & 0.0052780949453713 & 64.6382208349355 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.341166666666667 & 0.0052780949453713 & 64.6382208349355 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.338666666666667 & 0.00481562115996564 & 70.3266838102113 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.336 & 0.00434526822327499 & 77.3254912551197 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.336 & 0.00434526822327499 & 77.3254912551197 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.33 & 0.0033698564069393 & 97.9270212583703 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.33 & 0.0033698564069393 & 97.9270212583703 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.333333333333333 & 0.00288838181845652 & 115.404871753229 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.353620689655172 & 0.00988958484653965 & 35.7568790947684 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.351785714285714 & 0.00946321361239618 & 37.174022345316 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.35 & 0.00899957293807794 & 38.8907343057492 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.348461538461538 & 0.00867715145768784 & 40.158517476701 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.3468 & 0.0083760591776168 & 41.4037189382266 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.345 & 0.00798380452865506 & 43.2124808118415 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.343043478260870 & 0.00746566740995582 & 45.9494723543946 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.341363636363636 & 0.00713499333742108 & 47.8435816573616 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.339523809523810 & 0.00668654742650645 & 50.7771481853083 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.338 & 0.00631644171171047 & 53.51114051656 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.336315789473684 & 0.00579916426793409 & 57.9938373764147 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.335 & 0.00536745040121693 & 62.4132455744812 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.334411764705882 & 0.00517417101734011 & 64.6309840910117 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.3334375 & 0.00497188415557439 & 67.0646156600724 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.332333333333333 & 0.004665434977031 & 71.2330865116514 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.331428571428571 & 0.00438595297766606 & 75.5659199075448 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.330769230769231 & 0.00414814423468085 & 79.7390862168705 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.33 & 0.00375904705778056 & 87.7882066724753 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.33 & 0.00360374985078224 & 91.5712837083766 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.33 & 0.00332454983102184 & 99.2615592405094 \tabularnewline
Median & 0.33 &  &  \tabularnewline
Midrange & 0.425 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.3303125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.3303125 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.3303125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.3303125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.3303125 &  &  \tabularnewline
Midmean - Closest Observation & 0.3303125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.3303125 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.336285714285714 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17678&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]0.356[/C][C]0.0104643597443301[/C][C]34.0202371380523[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.348010596252580[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.341034576107742[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.364961185150787[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.355333333333333[/C][C]0.0102303046733703[/C][C]34.7334067438163[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.355[/C][C]0.0101249258907799[/C][C]35.0619850287768[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.354[/C][C]0.00960872955264218[/C][C]36.8414989786718[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.354[/C][C]0.00933434215693987[/C][C]37.9244722389793[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.354[/C][C]0.00933434215693987[/C][C]37.9244722389793[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.354[/C][C]0.00933434215693987[/C][C]37.9244722389793[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.351666666666667[/C][C]0.00829255559780877[/C][C]42.407513886261[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.351666666666667[/C][C]0.00829255559780877[/C][C]42.407513886261[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.348666666666667[/C][C]0.00758926787096923[/C][C]45.9420687996006[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.348666666666667[/C][C]0.00758926787096923[/C][C]45.9420687996006[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.345[/C][C]0.00678357937615109[/C][C]50.8581061515858[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.339[/C][C]0.00558296440302316[/C][C]60.7204301385895[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.341166666666667[/C][C]0.0052780949453713[/C][C]64.6382208349355[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.341166666666667[/C][C]0.0052780949453713[/C][C]64.6382208349355[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.338666666666667[/C][C]0.00481562115996564[/C][C]70.3266838102113[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.336[/C][C]0.00434526822327499[/C][C]77.3254912551197[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.336[/C][C]0.00434526822327499[/C][C]77.3254912551197[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.33[/C][C]0.0033698564069393[/C][C]97.9270212583703[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.33[/C][C]0.0033698564069393[/C][C]97.9270212583703[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.333333333333333[/C][C]0.00288838181845652[/C][C]115.404871753229[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.353620689655172[/C][C]0.00988958484653965[/C][C]35.7568790947684[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.351785714285714[/C][C]0.00946321361239618[/C][C]37.174022345316[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.35[/C][C]0.00899957293807794[/C][C]38.8907343057492[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.348461538461538[/C][C]0.00867715145768784[/C][C]40.158517476701[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.3468[/C][C]0.0083760591776168[/C][C]41.4037189382266[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.345[/C][C]0.00798380452865506[/C][C]43.2124808118415[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.343043478260870[/C][C]0.00746566740995582[/C][C]45.9494723543946[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.341363636363636[/C][C]0.00713499333742108[/C][C]47.8435816573616[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.339523809523810[/C][C]0.00668654742650645[/C][C]50.7771481853083[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.338[/C][C]0.00631644171171047[/C][C]53.51114051656[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.336315789473684[/C][C]0.00579916426793409[/C][C]57.9938373764147[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.335[/C][C]0.00536745040121693[/C][C]62.4132455744812[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.334411764705882[/C][C]0.00517417101734011[/C][C]64.6309840910117[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.3334375[/C][C]0.00497188415557439[/C][C]67.0646156600724[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.332333333333333[/C][C]0.004665434977031[/C][C]71.2330865116514[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.331428571428571[/C][C]0.00438595297766606[/C][C]75.5659199075448[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.330769230769231[/C][C]0.00414814423468085[/C][C]79.7390862168705[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.33[/C][C]0.00375904705778056[/C][C]87.7882066724753[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.33[/C][C]0.00360374985078224[/C][C]91.5712837083766[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.33[/C][C]0.00332454983102184[/C][C]99.2615592405094[/C][/ROW]
[ROW][C]Median[/C][C]0.33[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.3303125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.3303125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.3303125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.3303125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.3303125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.3303125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.3303125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.336285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17678&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17678&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 Mean0.3560.010464359744330134.0202371380523
Geometric Mean0.348010596252580
Harmonic Mean0.341034576107742
Quadratic Mean0.364961185150787
Winsorized Mean ( 1 / 20 )0.3553333333333330.010230304673370334.7334067438163
Winsorized Mean ( 2 / 20 )0.3550.010124925890779935.0619850287768
Winsorized Mean ( 3 / 20 )0.3540.0096087295526421836.8414989786718
Winsorized Mean ( 4 / 20 )0.3540.0093343421569398737.9244722389793
Winsorized Mean ( 5 / 20 )0.3540.0093343421569398737.9244722389793
Winsorized Mean ( 6 / 20 )0.3540.0093343421569398737.9244722389793
Winsorized Mean ( 7 / 20 )0.3516666666666670.0082925555978087742.407513886261
Winsorized Mean ( 8 / 20 )0.3516666666666670.0082925555978087742.407513886261
Winsorized Mean ( 9 / 20 )0.3486666666666670.0075892678709692345.9420687996006
Winsorized Mean ( 10 / 20 )0.3486666666666670.0075892678709692345.9420687996006
Winsorized Mean ( 11 / 20 )0.3450.0067835793761510950.8581061515858
Winsorized Mean ( 12 / 20 )0.3390.0055829644030231660.7204301385895
Winsorized Mean ( 13 / 20 )0.3411666666666670.005278094945371364.6382208349355
Winsorized Mean ( 14 / 20 )0.3411666666666670.005278094945371364.6382208349355
Winsorized Mean ( 15 / 20 )0.3386666666666670.0048156211599656470.3266838102113
Winsorized Mean ( 16 / 20 )0.3360.0043452682232749977.3254912551197
Winsorized Mean ( 17 / 20 )0.3360.0043452682232749977.3254912551197
Winsorized Mean ( 18 / 20 )0.330.003369856406939397.9270212583703
Winsorized Mean ( 19 / 20 )0.330.003369856406939397.9270212583703
Winsorized Mean ( 20 / 20 )0.3333333333333330.00288838181845652115.404871753229
Trimmed Mean ( 1 / 20 )0.3536206896551720.0098895848465396535.7568790947684
Trimmed Mean ( 2 / 20 )0.3517857142857140.0094632136123961837.174022345316
Trimmed Mean ( 3 / 20 )0.350.0089995729380779438.8907343057492
Trimmed Mean ( 4 / 20 )0.3484615384615380.0086771514576878440.158517476701
Trimmed Mean ( 5 / 20 )0.34680.008376059177616841.4037189382266
Trimmed Mean ( 6 / 20 )0.3450.0079838045286550643.2124808118415
Trimmed Mean ( 7 / 20 )0.3430434782608700.0074656674099558245.9494723543946
Trimmed Mean ( 8 / 20 )0.3413636363636360.0071349933374210847.8435816573616
Trimmed Mean ( 9 / 20 )0.3395238095238100.0066865474265064550.7771481853083
Trimmed Mean ( 10 / 20 )0.3380.0063164417117104753.51114051656
Trimmed Mean ( 11 / 20 )0.3363157894736840.0057991642679340957.9938373764147
Trimmed Mean ( 12 / 20 )0.3350.0053674504012169362.4132455744812
Trimmed Mean ( 13 / 20 )0.3344117647058820.0051741710173401164.6309840910117
Trimmed Mean ( 14 / 20 )0.33343750.0049718841555743967.0646156600724
Trimmed Mean ( 15 / 20 )0.3323333333333330.00466543497703171.2330865116514
Trimmed Mean ( 16 / 20 )0.3314285714285710.0043859529776660675.5659199075448
Trimmed Mean ( 17 / 20 )0.3307692307692310.0041481442346808579.7390862168705
Trimmed Mean ( 18 / 20 )0.330.0037590470577805687.7882066724753
Trimmed Mean ( 19 / 20 )0.330.0036037498507822491.5712837083766
Trimmed Mean ( 20 / 20 )0.330.0033245498310218499.2615592405094
Median0.33
Midrange0.425
Midmean - Weighted Average at Xnp0.3303125
Midmean - Weighted Average at X(n+1)p0.3303125
Midmean - Empirical Distribution Function0.3303125
Midmean - Empirical Distribution Function - Averaging0.3303125
Midmean - Empirical Distribution Function - Interpolation0.3303125
Midmean - Closest Observation0.3303125
Midmean - True Basic - Statistics Graphics Toolkit0.3303125
Midmean - MS Excel (old versions)0.336285714285714
Number of observations60



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')