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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 10 Oct 2014 14:56:52 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/10/t1412949423y28nk58ymzkzhot.htm/, Retrieved Mon, 13 May 2024 11:11:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240313, Retrieved Mon, 13 May 2024 11:11:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact53
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-10 13:56:52] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
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
1,3649
1,3999
1,4442
1,4349
1,4388
1,4264
1,4343
1,377
1,3706
1,3556
1,3179
1,2905
1,3224
1,3201
1,3162
1,2789
1,2526
1,2288
1,24
1,2856
1,2974
1,2828
1,3119
1,3288
1,3359
1,2964
1,3026
1,2982
1,3189
1,308
1,331
1,3348
1,3635
1,3493
1,3704




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240313&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240313&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240313&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.366022222222220.0100621766605429135.758123545857
Geometric Mean1.3634612298369
Harmonic Mean1.36096895558034
Quadratic Mean1.36865089666593
Winsorized Mean ( 1 / 24 )1.366105555555560.0100326889208793136.165445408411
Winsorized Mean ( 2 / 24 )1.365877777777780.00982214873236728139.060995205331
Winsorized Mean ( 3 / 24 )1.366386111111110.0097269490577291140.474274410368
Winsorized Mean ( 4 / 24 )1.366458333333330.00965233248992634141.567681672739
Winsorized Mean ( 5 / 24 )1.363784722222220.00852157017767987160.03913525166
Winsorized Mean ( 6 / 24 )1.363593055555560.00836388234500108163.033505172457
Winsorized Mean ( 7 / 24 )1.362786111111110.0081421151277865167.374949840779
Winsorized Mean ( 8 / 24 )1.3620750.00798281035414439170.626000064358
Winsorized Mean ( 9 / 24 )1.36218750.00783803273717118173.792014613558
Winsorized Mean ( 10 / 24 )1.361131944444440.00750442170814417181.377326245842
Winsorized Mean ( 11 / 24 )1.360918055555560.00727501628842345187.067355123472
Winsorized Mean ( 12 / 24 )1.359101388888890.00689078433959236197.234642953474
Winsorized Mean ( 13 / 24 )1.359191666666670.0065764487535552206.675626557858
Winsorized Mean ( 14 / 24 )1.359036111111110.00649092821426706209.37469438099
Winsorized Mean ( 15 / 24 )1.358765277777780.00639497772173688212.473809433184
Winsorized Mean ( 16 / 24 )1.359609722222220.00624446269877635217.730457816434
Winsorized Mean ( 17 / 24 )1.35850.00589285229220241230.533523095022
Winsorized Mean ( 18 / 24 )1.3588250.0058224518730318233.376768006233
Winsorized Mean ( 19 / 24 )1.35906250.00576204815102732235.864481583288
Winsorized Mean ( 20 / 24 )1.355256944444440.00484117577545429279.943758976045
Winsorized Mean ( 21 / 24 )1.354411111111110.00436081909451653310.586401718476
Winsorized Mean ( 22 / 24 )1.354411111111110.00421805937194355321.098161898808
Winsorized Mean ( 23 / 24 )1.351504166666670.00369779754982389365.488956184482
Winsorized Mean ( 24 / 24 )1.347270833333330.00309147854324324435.801450499451
Trimmed Mean ( 1 / 24 )1.365081428571430.00967315409343563141.120612303467
Trimmed Mean ( 2 / 24 )1.363997058823530.00924239809844462147.580427102904
Trimmed Mean ( 3 / 24 )1.362971212121210.00886294945438647153.783028904294
Trimmed Mean ( 4 / 24 )1.3616906250.00844729244178122161.198470916543
Trimmed Mean ( 5 / 24 )1.36030645161290.00796678020516955170.747330361922
Trimmed Mean ( 6 / 24 )1.359471666666670.00776764551856427175.017212541123
Trimmed Mean ( 7 / 24 )1.358618965517240.00756783657160022179.525410289081
Trimmed Mean ( 8 / 24 )1.357853571428570.00738033406675607183.982670587349
Trimmed Mean ( 9 / 24 )1.357150.00718694841106518188.835361321156
Trimmed Mean ( 10 / 24 )1.3563750.006977795463102194.384459557807
Trimmed Mean ( 11 / 24 )1.355690.00679321645436963199.565258829339
Trimmed Mean ( 12 / 24 )1.354977083333330.00660905061232747205.018415323674
Trimmed Mean ( 13 / 24 )1.354439130434780.00646094657986231209.63478241042
Trimmed Mean ( 14 / 24 )1.353840909090910.006334103738577213.738354306628
Trimmed Mean ( 15 / 24 )1.353204761904760.00618109773822485218.926284490914
Trimmed Mean ( 16 / 24 )1.35253750.00599536325913404225.597256002693
Trimmed Mean ( 17 / 24 )1.35170.00577356757157619234.118676752749
Trimmed Mean ( 18 / 24 )1.35090.00556088522129745242.928948582904
Trimmed Mean ( 19 / 24 )1.349967647058820.00527493099293085255.921385297357
Trimmed Mean ( 20 / 24 )1.3488906250.00487538534327941276.673643214564
Trimmed Mean ( 21 / 24 )1.348126666666670.00462430841883307291.530439703428
Trimmed Mean ( 22 / 24 )1.347357142857140.00441093347140843305.458504779245
Trimmed Mean ( 23 / 24 )1.346469230769230.00412497373131317326.418861906446
Trimmed Mean ( 24 / 24 )1.34581250.00390374361619901344.749202897292
Median1.34275
Midrange1.39895
Midmean - Weighted Average at Xnp1.34965945945946
Midmean - Weighted Average at X(n+1)p1.3509
Midmean - Empirical Distribution Function1.34965945945946
Midmean - Empirical Distribution Function - Averaging1.3509
Midmean - Empirical Distribution Function - Interpolation1.3509
Midmean - Closest Observation1.34965945945946
Midmean - True Basic - Statistics Graphics Toolkit1.3509
Midmean - MS Excel (old versions)1.3517
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.36602222222222 & 0.0100621766605429 & 135.758123545857 \tabularnewline
Geometric Mean & 1.3634612298369 &  &  \tabularnewline
Harmonic Mean & 1.36096895558034 &  &  \tabularnewline
Quadratic Mean & 1.36865089666593 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.36610555555556 & 0.0100326889208793 & 136.165445408411 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.36587777777778 & 0.00982214873236728 & 139.060995205331 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.36638611111111 & 0.0097269490577291 & 140.474274410368 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.36645833333333 & 0.00965233248992634 & 141.567681672739 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.36378472222222 & 0.00852157017767987 & 160.03913525166 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.36359305555556 & 0.00836388234500108 & 163.033505172457 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.36278611111111 & 0.0081421151277865 & 167.374949840779 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.362075 & 0.00798281035414439 & 170.626000064358 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.3621875 & 0.00783803273717118 & 173.792014613558 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.36113194444444 & 0.00750442170814417 & 181.377326245842 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.36091805555556 & 0.00727501628842345 & 187.067355123472 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.35910138888889 & 0.00689078433959236 & 197.234642953474 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.35919166666667 & 0.0065764487535552 & 206.675626557858 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.35903611111111 & 0.00649092821426706 & 209.37469438099 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.35876527777778 & 0.00639497772173688 & 212.473809433184 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.35960972222222 & 0.00624446269877635 & 217.730457816434 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.3585 & 0.00589285229220241 & 230.533523095022 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.358825 & 0.0058224518730318 & 233.376768006233 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.3590625 & 0.00576204815102732 & 235.864481583288 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.35525694444444 & 0.00484117577545429 & 279.943758976045 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.35441111111111 & 0.00436081909451653 & 310.586401718476 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.35441111111111 & 0.00421805937194355 & 321.098161898808 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.35150416666667 & 0.00369779754982389 & 365.488956184482 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.34727083333333 & 0.00309147854324324 & 435.801450499451 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.36508142857143 & 0.00967315409343563 & 141.120612303467 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.36399705882353 & 0.00924239809844462 & 147.580427102904 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.36297121212121 & 0.00886294945438647 & 153.783028904294 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.361690625 & 0.00844729244178122 & 161.198470916543 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.3603064516129 & 0.00796678020516955 & 170.747330361922 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.35947166666667 & 0.00776764551856427 & 175.017212541123 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.35861896551724 & 0.00756783657160022 & 179.525410289081 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.35785357142857 & 0.00738033406675607 & 183.982670587349 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.35715 & 0.00718694841106518 & 188.835361321156 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.356375 & 0.006977795463102 & 194.384459557807 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.35569 & 0.00679321645436963 & 199.565258829339 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.35497708333333 & 0.00660905061232747 & 205.018415323674 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.35443913043478 & 0.00646094657986231 & 209.63478241042 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.35384090909091 & 0.006334103738577 & 213.738354306628 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.35320476190476 & 0.00618109773822485 & 218.926284490914 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.3525375 & 0.00599536325913404 & 225.597256002693 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.3517 & 0.00577356757157619 & 234.118676752749 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.3509 & 0.00556088522129745 & 242.928948582904 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.34996764705882 & 0.00527493099293085 & 255.921385297357 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.348890625 & 0.00487538534327941 & 276.673643214564 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.34812666666667 & 0.00462430841883307 & 291.530439703428 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.34735714285714 & 0.00441093347140843 & 305.458504779245 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.34646923076923 & 0.00412497373131317 & 326.418861906446 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.3458125 & 0.00390374361619901 & 344.749202897292 \tabularnewline
Median & 1.34275 &  &  \tabularnewline
Midrange & 1.39895 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.34965945945946 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.3509 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.34965945945946 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.3509 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.3509 &  &  \tabularnewline
Midmean - Closest Observation & 1.34965945945946 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.3509 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.3517 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240313&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]1.36602222222222[/C][C]0.0100621766605429[/C][C]135.758123545857[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.3634612298369[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.36096895558034[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.36865089666593[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.36610555555556[/C][C]0.0100326889208793[/C][C]136.165445408411[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.36587777777778[/C][C]0.00982214873236728[/C][C]139.060995205331[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.36638611111111[/C][C]0.0097269490577291[/C][C]140.474274410368[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.36645833333333[/C][C]0.00965233248992634[/C][C]141.567681672739[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.36378472222222[/C][C]0.00852157017767987[/C][C]160.03913525166[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.36359305555556[/C][C]0.00836388234500108[/C][C]163.033505172457[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.36278611111111[/C][C]0.0081421151277865[/C][C]167.374949840779[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.362075[/C][C]0.00798281035414439[/C][C]170.626000064358[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.3621875[/C][C]0.00783803273717118[/C][C]173.792014613558[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.36113194444444[/C][C]0.00750442170814417[/C][C]181.377326245842[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.36091805555556[/C][C]0.00727501628842345[/C][C]187.067355123472[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.35910138888889[/C][C]0.00689078433959236[/C][C]197.234642953474[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.35919166666667[/C][C]0.0065764487535552[/C][C]206.675626557858[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.35903611111111[/C][C]0.00649092821426706[/C][C]209.37469438099[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.35876527777778[/C][C]0.00639497772173688[/C][C]212.473809433184[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.35960972222222[/C][C]0.00624446269877635[/C][C]217.730457816434[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.3585[/C][C]0.00589285229220241[/C][C]230.533523095022[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.358825[/C][C]0.0058224518730318[/C][C]233.376768006233[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.3590625[/C][C]0.00576204815102732[/C][C]235.864481583288[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.35525694444444[/C][C]0.00484117577545429[/C][C]279.943758976045[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.35441111111111[/C][C]0.00436081909451653[/C][C]310.586401718476[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.35441111111111[/C][C]0.00421805937194355[/C][C]321.098161898808[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.35150416666667[/C][C]0.00369779754982389[/C][C]365.488956184482[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.34727083333333[/C][C]0.00309147854324324[/C][C]435.801450499451[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.36508142857143[/C][C]0.00967315409343563[/C][C]141.120612303467[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.36399705882353[/C][C]0.00924239809844462[/C][C]147.580427102904[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.36297121212121[/C][C]0.00886294945438647[/C][C]153.783028904294[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.361690625[/C][C]0.00844729244178122[/C][C]161.198470916543[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.3603064516129[/C][C]0.00796678020516955[/C][C]170.747330361922[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.35947166666667[/C][C]0.00776764551856427[/C][C]175.017212541123[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.35861896551724[/C][C]0.00756783657160022[/C][C]179.525410289081[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.35785357142857[/C][C]0.00738033406675607[/C][C]183.982670587349[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.35715[/C][C]0.00718694841106518[/C][C]188.835361321156[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.356375[/C][C]0.006977795463102[/C][C]194.384459557807[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.35569[/C][C]0.00679321645436963[/C][C]199.565258829339[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.35497708333333[/C][C]0.00660905061232747[/C][C]205.018415323674[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.35443913043478[/C][C]0.00646094657986231[/C][C]209.63478241042[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.35384090909091[/C][C]0.006334103738577[/C][C]213.738354306628[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.35320476190476[/C][C]0.00618109773822485[/C][C]218.926284490914[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.3525375[/C][C]0.00599536325913404[/C][C]225.597256002693[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.3517[/C][C]0.00577356757157619[/C][C]234.118676752749[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.3509[/C][C]0.00556088522129745[/C][C]242.928948582904[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.34996764705882[/C][C]0.00527493099293085[/C][C]255.921385297357[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.348890625[/C][C]0.00487538534327941[/C][C]276.673643214564[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.34812666666667[/C][C]0.00462430841883307[/C][C]291.530439703428[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.34735714285714[/C][C]0.00441093347140843[/C][C]305.458504779245[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.34646923076923[/C][C]0.00412497373131317[/C][C]326.418861906446[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.3458125[/C][C]0.00390374361619901[/C][C]344.749202897292[/C][/ROW]
[ROW][C]Median[/C][C]1.34275[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.39895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.34965945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.3509[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.34965945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.3509[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.3509[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.34965945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.3509[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.3517[/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=240313&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240313&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 Mean1.366022222222220.0100621766605429135.758123545857
Geometric Mean1.3634612298369
Harmonic Mean1.36096895558034
Quadratic Mean1.36865089666593
Winsorized Mean ( 1 / 24 )1.366105555555560.0100326889208793136.165445408411
Winsorized Mean ( 2 / 24 )1.365877777777780.00982214873236728139.060995205331
Winsorized Mean ( 3 / 24 )1.366386111111110.0097269490577291140.474274410368
Winsorized Mean ( 4 / 24 )1.366458333333330.00965233248992634141.567681672739
Winsorized Mean ( 5 / 24 )1.363784722222220.00852157017767987160.03913525166
Winsorized Mean ( 6 / 24 )1.363593055555560.00836388234500108163.033505172457
Winsorized Mean ( 7 / 24 )1.362786111111110.0081421151277865167.374949840779
Winsorized Mean ( 8 / 24 )1.3620750.00798281035414439170.626000064358
Winsorized Mean ( 9 / 24 )1.36218750.00783803273717118173.792014613558
Winsorized Mean ( 10 / 24 )1.361131944444440.00750442170814417181.377326245842
Winsorized Mean ( 11 / 24 )1.360918055555560.00727501628842345187.067355123472
Winsorized Mean ( 12 / 24 )1.359101388888890.00689078433959236197.234642953474
Winsorized Mean ( 13 / 24 )1.359191666666670.0065764487535552206.675626557858
Winsorized Mean ( 14 / 24 )1.359036111111110.00649092821426706209.37469438099
Winsorized Mean ( 15 / 24 )1.358765277777780.00639497772173688212.473809433184
Winsorized Mean ( 16 / 24 )1.359609722222220.00624446269877635217.730457816434
Winsorized Mean ( 17 / 24 )1.35850.00589285229220241230.533523095022
Winsorized Mean ( 18 / 24 )1.3588250.0058224518730318233.376768006233
Winsorized Mean ( 19 / 24 )1.35906250.00576204815102732235.864481583288
Winsorized Mean ( 20 / 24 )1.355256944444440.00484117577545429279.943758976045
Winsorized Mean ( 21 / 24 )1.354411111111110.00436081909451653310.586401718476
Winsorized Mean ( 22 / 24 )1.354411111111110.00421805937194355321.098161898808
Winsorized Mean ( 23 / 24 )1.351504166666670.00369779754982389365.488956184482
Winsorized Mean ( 24 / 24 )1.347270833333330.00309147854324324435.801450499451
Trimmed Mean ( 1 / 24 )1.365081428571430.00967315409343563141.120612303467
Trimmed Mean ( 2 / 24 )1.363997058823530.00924239809844462147.580427102904
Trimmed Mean ( 3 / 24 )1.362971212121210.00886294945438647153.783028904294
Trimmed Mean ( 4 / 24 )1.3616906250.00844729244178122161.198470916543
Trimmed Mean ( 5 / 24 )1.36030645161290.00796678020516955170.747330361922
Trimmed Mean ( 6 / 24 )1.359471666666670.00776764551856427175.017212541123
Trimmed Mean ( 7 / 24 )1.358618965517240.00756783657160022179.525410289081
Trimmed Mean ( 8 / 24 )1.357853571428570.00738033406675607183.982670587349
Trimmed Mean ( 9 / 24 )1.357150.00718694841106518188.835361321156
Trimmed Mean ( 10 / 24 )1.3563750.006977795463102194.384459557807
Trimmed Mean ( 11 / 24 )1.355690.00679321645436963199.565258829339
Trimmed Mean ( 12 / 24 )1.354977083333330.00660905061232747205.018415323674
Trimmed Mean ( 13 / 24 )1.354439130434780.00646094657986231209.63478241042
Trimmed Mean ( 14 / 24 )1.353840909090910.006334103738577213.738354306628
Trimmed Mean ( 15 / 24 )1.353204761904760.00618109773822485218.926284490914
Trimmed Mean ( 16 / 24 )1.35253750.00599536325913404225.597256002693
Trimmed Mean ( 17 / 24 )1.35170.00577356757157619234.118676752749
Trimmed Mean ( 18 / 24 )1.35090.00556088522129745242.928948582904
Trimmed Mean ( 19 / 24 )1.349967647058820.00527493099293085255.921385297357
Trimmed Mean ( 20 / 24 )1.3488906250.00487538534327941276.673643214564
Trimmed Mean ( 21 / 24 )1.348126666666670.00462430841883307291.530439703428
Trimmed Mean ( 22 / 24 )1.347357142857140.00441093347140843305.458504779245
Trimmed Mean ( 23 / 24 )1.346469230769230.00412497373131317326.418861906446
Trimmed Mean ( 24 / 24 )1.34581250.00390374361619901344.749202897292
Median1.34275
Midrange1.39895
Midmean - Weighted Average at Xnp1.34965945945946
Midmean - Weighted Average at X(n+1)p1.3509
Midmean - Empirical Distribution Function1.34965945945946
Midmean - Empirical Distribution Function - Averaging1.3509
Midmean - Empirical Distribution Function - Interpolation1.3509
Midmean - Closest Observation1.34965945945946
Midmean - True Basic - Statistics Graphics Toolkit1.3509
Midmean - MS Excel (old versions)1.3517
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')