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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 16 Oct 2008 08:32:46 -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/16/t1224167588ptip6bdsw8cu8xp.htm/, Retrieved Wed, 15 May 2024 10:31:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16352, Retrieved Wed, 15 May 2024 10:31:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact218
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
-    D  [Central Tendency] [] [2008-10-16 14:20:24] [7c33e759a6f7358dc2f6505c3a7a1eae]
-    D    [Central Tendency] [] [2008-10-16 14:30:25] [7c33e759a6f7358dc2f6505c3a7a1eae]
-    D      [Central Tendency] [] [2008-10-16 14:31:36] [7c33e759a6f7358dc2f6505c3a7a1eae]
-    D          [Central Tendency] [] [2008-10-16 14:32:46] [1e28c3a908c2cc51d131d1d2a5af4149] [Current]
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Dataseries X:
2.9
2.7
2.7
2.5
2.2
2.2
2
1.9
1.9
1.8
1.7
1.7
1.8
1.6
1.5
1.5
1.6
1.6
1.6
1.7
1.6
1.4
1.6
1.2
1.5
1.2
1.2
1
0.9
0.6
0.9
0.7
0.6
0.6
0.6
0.4
0.3
0.7
0.7
1
1
0.1
1.1
1
1.3
1.4
1.4
0.6
1.7
1.5
1.7
1.6
1.7
2.1
1.6
1.6
1.5
1.4
1.4
1.4
1.4
1.5
1.4
1.3
1.2
1.2
1.6
1.6
1.6
1.7
1.7
2
1.8
1.8
1.9
2
2
1.7
1.7
1.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16352&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16352&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16352&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.473750.059951028274244324.5825641765204
Geometric Mean1.33847255723942
Harmonic Mean1.08719588155218
Quadratic Mean1.56712316044400
Winsorized Mean ( 1 / 26 )1.473750.058562520686134425.1654126689416
Winsorized Mean ( 2 / 26 )1.476250.057951413248240625.4739257811770
Winsorized Mean ( 3 / 26 )1.476250.05440250104777527.1357009616817
Winsorized Mean ( 4 / 26 )1.461250.051234560811223828.520787079332
Winsorized Mean ( 5 / 26 )1.461250.051234560811223828.520787079332
Winsorized Mean ( 6 / 26 )1.453750.049934886399658929.1129129315478
Winsorized Mean ( 7 / 26 )1.4450.048584390888171929.7420626992319
Winsorized Mean ( 8 / 26 )1.4550.04645332487998131.3217623013898
Winsorized Mean ( 9 / 26 )1.4550.04645332487998131.3217623013898
Winsorized Mean ( 10 / 26 )1.4550.04645332487998131.3217623013898
Winsorized Mean ( 11 / 26 )1.468750.039079347632635937.5837901340354
Winsorized Mean ( 12 / 26 )1.468750.039079347632635937.5837901340354
Winsorized Mean ( 13 / 26 )1.4850.03620004196095241.0220518971174
Winsorized Mean ( 14 / 26 )1.4850.03620004196095241.0220518971174
Winsorized Mean ( 15 / 26 )1.466250.033656104737119443.5656476426064
Winsorized Mean ( 16 / 26 )1.466250.033656104737119443.5656476426064
Winsorized Mean ( 17 / 26 )1.48750.030051380052137049.4985587157494
Winsorized Mean ( 18 / 26 )1.510.026541107357207956.892878645846
Winsorized Mean ( 19 / 26 )1.486250.023515666068238763.2025474288988
Winsorized Mean ( 20 / 26 )1.486250.023515666068238763.2025474288988
Winsorized Mean ( 21 / 26 )1.486250.023515666068238763.2025474288988
Winsorized Mean ( 22 / 26 )1.486250.023515666068238763.2025474288988
Winsorized Mean ( 23 / 26 )1.5150.019250184940752278.7005426006467
Winsorized Mean ( 24 / 26 )1.5150.019250184940752278.7005426006467
Winsorized Mean ( 25 / 26 )1.546250.0150887406676869102.477074399678
Winsorized Mean ( 26 / 26 )1.546250.0150887406676869102.477074399678
Trimmed Mean ( 1 / 26 )1.473076923076920.055938488317689826.333870781615
Trimmed Mean ( 2 / 26 )1.472368421052630.05283535114450627.8671077064609
Trimmed Mean ( 3 / 26 )1.470270270270270.049534289102116129.6818688008073
Trimmed Mean ( 4 / 26 )1.468055555555560.047298968749775231.0377920356357
Trimmed Mean ( 5 / 26 )1.470.045834791996363432.0717065786321
Trimmed Mean ( 6 / 26 )1.472058823529410.044090934259920333.386882093527
Trimmed Mean ( 7 / 26 )1.475757575757580.042369261742552134.8308541396050
Trimmed Mean ( 8 / 26 )1.481250.040634537952377136.4529800175407
Trimmed Mean ( 9 / 26 )1.485483870967740.039083009341847738.0084311823239
Trimmed Mean ( 10 / 26 )1.490.037181794950031940.0733746717282
Trimmed Mean ( 11 / 26 )1.494827586206900.034820637450465642.9293572908703
Trimmed Mean ( 12 / 26 )1.498214285714290.033660940351991644.5089848960694
Trimmed Mean ( 13 / 26 )1.501851851851850.032212903381098346.6226789334704
Trimmed Mean ( 14 / 26 )1.503846153846150.031064757262083648.4100403926764
Trimmed Mean ( 15 / 26 )1.5060.029611084521351350.8593327243413
Trimmed Mean ( 16 / 26 )1.510416666666670.028284205948666353.4014166566301
Trimmed Mean ( 17 / 26 )1.515217391304350.026551816318294757.0664309040257
Trimmed Mean ( 18 / 26 )1.518181818181820.025241482198986860.1463022739115
Trimmed Mean ( 19 / 26 )1.519047619047620.024394668035234862.2696573223936
Trimmed Mean ( 20 / 26 )1.52250.023882055273836163.7507945837462
Trimmed Mean ( 21 / 26 )1.526315789473680.023152721522271465.923817552311
Trimmed Mean ( 22 / 26 )1.530555555555560.022117810263771569.2001394940335
Trimmed Mean ( 23 / 26 )1.535294117647060.020632750449426674.4105407279679
Trimmed Mean ( 24 / 26 )1.53750.019954585534933377.0499591338739
Trimmed Mean ( 25 / 26 )1.540.018937283058960081.3210635974185
Trimmed Mean ( 26 / 26 )1.539285714285710.018785397426261381.940545592815
Median1.6
Midrange1.5
Midmean - Weighted Average at Xnp1.51162790697675
Midmean - Weighted Average at X(n+1)p1.51162790697675
Midmean - Empirical Distribution Function1.51162790697675
Midmean - Empirical Distribution Function - Averaging1.51162790697675
Midmean - Empirical Distribution Function - Interpolation1.51162790697675
Midmean - Closest Observation1.51162790697675
Midmean - True Basic - Statistics Graphics Toolkit1.51162790697675
Midmean - MS Excel (old versions)1.51162790697675
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.47375 & 0.0599510282742443 & 24.5825641765204 \tabularnewline
Geometric Mean & 1.33847255723942 &  &  \tabularnewline
Harmonic Mean & 1.08719588155218 &  &  \tabularnewline
Quadratic Mean & 1.56712316044400 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 1.47375 & 0.0585625206861344 & 25.1654126689416 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 1.47625 & 0.0579514132482406 & 25.4739257811770 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 1.47625 & 0.054402501047775 & 27.1357009616817 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 1.46125 & 0.0512345608112238 & 28.520787079332 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 1.46125 & 0.0512345608112238 & 28.520787079332 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 1.45375 & 0.0499348863996589 & 29.1129129315478 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 1.445 & 0.0485843908881719 & 29.7420626992319 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 1.455 & 0.046453324879981 & 31.3217623013898 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 1.455 & 0.046453324879981 & 31.3217623013898 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 1.455 & 0.046453324879981 & 31.3217623013898 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 1.46875 & 0.0390793476326359 & 37.5837901340354 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 1.46875 & 0.0390793476326359 & 37.5837901340354 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 1.485 & 0.036200041960952 & 41.0220518971174 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 1.485 & 0.036200041960952 & 41.0220518971174 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 1.46625 & 0.0336561047371194 & 43.5656476426064 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 1.46625 & 0.0336561047371194 & 43.5656476426064 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 1.4875 & 0.0300513800521370 & 49.4985587157494 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 1.51 & 0.0265411073572079 & 56.892878645846 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 1.48625 & 0.0235156660682387 & 63.2025474288988 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 1.48625 & 0.0235156660682387 & 63.2025474288988 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 1.48625 & 0.0235156660682387 & 63.2025474288988 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 1.48625 & 0.0235156660682387 & 63.2025474288988 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 1.515 & 0.0192501849407522 & 78.7005426006467 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 1.515 & 0.0192501849407522 & 78.7005426006467 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 1.54625 & 0.0150887406676869 & 102.477074399678 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 1.54625 & 0.0150887406676869 & 102.477074399678 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 1.47307692307692 & 0.0559384883176898 & 26.333870781615 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 1.47236842105263 & 0.052835351144506 & 27.8671077064609 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 1.47027027027027 & 0.0495342891021161 & 29.6818688008073 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 1.46805555555556 & 0.0472989687497752 & 31.0377920356357 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 1.47 & 0.0458347919963634 & 32.0717065786321 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 1.47205882352941 & 0.0440909342599203 & 33.386882093527 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 1.47575757575758 & 0.0423692617425521 & 34.8308541396050 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 1.48125 & 0.0406345379523771 & 36.4529800175407 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 1.48548387096774 & 0.0390830093418477 & 38.0084311823239 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 1.49 & 0.0371817949500319 & 40.0733746717282 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 1.49482758620690 & 0.0348206374504656 & 42.9293572908703 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 1.49821428571429 & 0.0336609403519916 & 44.5089848960694 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 1.50185185185185 & 0.0322129033810983 & 46.6226789334704 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 1.50384615384615 & 0.0310647572620836 & 48.4100403926764 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 1.506 & 0.0296110845213513 & 50.8593327243413 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 1.51041666666667 & 0.0282842059486663 & 53.4014166566301 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 1.51521739130435 & 0.0265518163182947 & 57.0664309040257 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 1.51818181818182 & 0.0252414821989868 & 60.1463022739115 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 1.51904761904762 & 0.0243946680352348 & 62.2696573223936 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 1.5225 & 0.0238820552738361 & 63.7507945837462 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 1.52631578947368 & 0.0231527215222714 & 65.923817552311 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 1.53055555555556 & 0.0221178102637715 & 69.2001394940335 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 1.53529411764706 & 0.0206327504494266 & 74.4105407279679 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 1.5375 & 0.0199545855349333 & 77.0499591338739 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 1.54 & 0.0189372830589600 & 81.3210635974185 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 1.53928571428571 & 0.0187853974262613 & 81.940545592815 \tabularnewline
Median & 1.6 &  &  \tabularnewline
Midrange & 1.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.51162790697675 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.51162790697675 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.51162790697675 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.51162790697675 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.51162790697675 &  &  \tabularnewline
Midmean - Closest Observation & 1.51162790697675 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.51162790697675 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.51162790697675 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16352&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]1.47375[/C][C]0.0599510282742443[/C][C]24.5825641765204[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.33847255723942[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.08719588155218[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.56712316044400[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]1.47375[/C][C]0.0585625206861344[/C][C]25.1654126689416[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]1.47625[/C][C]0.0579514132482406[/C][C]25.4739257811770[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]1.47625[/C][C]0.054402501047775[/C][C]27.1357009616817[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]1.46125[/C][C]0.0512345608112238[/C][C]28.520787079332[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]1.46125[/C][C]0.0512345608112238[/C][C]28.520787079332[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]1.45375[/C][C]0.0499348863996589[/C][C]29.1129129315478[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]1.445[/C][C]0.0485843908881719[/C][C]29.7420626992319[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]1.455[/C][C]0.046453324879981[/C][C]31.3217623013898[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]1.455[/C][C]0.046453324879981[/C][C]31.3217623013898[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]1.455[/C][C]0.046453324879981[/C][C]31.3217623013898[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]1.46875[/C][C]0.0390793476326359[/C][C]37.5837901340354[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]1.46875[/C][C]0.0390793476326359[/C][C]37.5837901340354[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]1.485[/C][C]0.036200041960952[/C][C]41.0220518971174[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]1.485[/C][C]0.036200041960952[/C][C]41.0220518971174[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]1.46625[/C][C]0.0336561047371194[/C][C]43.5656476426064[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]1.46625[/C][C]0.0336561047371194[/C][C]43.5656476426064[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]1.4875[/C][C]0.0300513800521370[/C][C]49.4985587157494[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]1.51[/C][C]0.0265411073572079[/C][C]56.892878645846[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]1.48625[/C][C]0.0235156660682387[/C][C]63.2025474288988[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]1.48625[/C][C]0.0235156660682387[/C][C]63.2025474288988[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]1.48625[/C][C]0.0235156660682387[/C][C]63.2025474288988[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]1.48625[/C][C]0.0235156660682387[/C][C]63.2025474288988[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]1.515[/C][C]0.0192501849407522[/C][C]78.7005426006467[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]1.515[/C][C]0.0192501849407522[/C][C]78.7005426006467[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]1.54625[/C][C]0.0150887406676869[/C][C]102.477074399678[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]1.54625[/C][C]0.0150887406676869[/C][C]102.477074399678[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]1.47307692307692[/C][C]0.0559384883176898[/C][C]26.333870781615[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]1.47236842105263[/C][C]0.052835351144506[/C][C]27.8671077064609[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]1.47027027027027[/C][C]0.0495342891021161[/C][C]29.6818688008073[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]1.46805555555556[/C][C]0.0472989687497752[/C][C]31.0377920356357[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]1.47[/C][C]0.0458347919963634[/C][C]32.0717065786321[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]1.47205882352941[/C][C]0.0440909342599203[/C][C]33.386882093527[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]1.47575757575758[/C][C]0.0423692617425521[/C][C]34.8308541396050[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]1.48125[/C][C]0.0406345379523771[/C][C]36.4529800175407[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]1.48548387096774[/C][C]0.0390830093418477[/C][C]38.0084311823239[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]1.49[/C][C]0.0371817949500319[/C][C]40.0733746717282[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]1.49482758620690[/C][C]0.0348206374504656[/C][C]42.9293572908703[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]1.49821428571429[/C][C]0.0336609403519916[/C][C]44.5089848960694[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]1.50185185185185[/C][C]0.0322129033810983[/C][C]46.6226789334704[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]1.50384615384615[/C][C]0.0310647572620836[/C][C]48.4100403926764[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]1.506[/C][C]0.0296110845213513[/C][C]50.8593327243413[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]1.51041666666667[/C][C]0.0282842059486663[/C][C]53.4014166566301[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]1.51521739130435[/C][C]0.0265518163182947[/C][C]57.0664309040257[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]1.51818181818182[/C][C]0.0252414821989868[/C][C]60.1463022739115[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]1.51904761904762[/C][C]0.0243946680352348[/C][C]62.2696573223936[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]1.5225[/C][C]0.0238820552738361[/C][C]63.7507945837462[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]1.52631578947368[/C][C]0.0231527215222714[/C][C]65.923817552311[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]1.53055555555556[/C][C]0.0221178102637715[/C][C]69.2001394940335[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]1.53529411764706[/C][C]0.0206327504494266[/C][C]74.4105407279679[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]1.5375[/C][C]0.0199545855349333[/C][C]77.0499591338739[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]1.54[/C][C]0.0189372830589600[/C][C]81.3210635974185[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]1.53928571428571[/C][C]0.0187853974262613[/C][C]81.940545592815[/C][/ROW]
[ROW][C]Median[/C][C]1.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.51162790697675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.51162790697675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.51162790697675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.51162790697675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.51162790697675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.51162790697675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.51162790697675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.51162790697675[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16352&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16352&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 Mean1.473750.059951028274244324.5825641765204
Geometric Mean1.33847255723942
Harmonic Mean1.08719588155218
Quadratic Mean1.56712316044400
Winsorized Mean ( 1 / 26 )1.473750.058562520686134425.1654126689416
Winsorized Mean ( 2 / 26 )1.476250.057951413248240625.4739257811770
Winsorized Mean ( 3 / 26 )1.476250.05440250104777527.1357009616817
Winsorized Mean ( 4 / 26 )1.461250.051234560811223828.520787079332
Winsorized Mean ( 5 / 26 )1.461250.051234560811223828.520787079332
Winsorized Mean ( 6 / 26 )1.453750.049934886399658929.1129129315478
Winsorized Mean ( 7 / 26 )1.4450.048584390888171929.7420626992319
Winsorized Mean ( 8 / 26 )1.4550.04645332487998131.3217623013898
Winsorized Mean ( 9 / 26 )1.4550.04645332487998131.3217623013898
Winsorized Mean ( 10 / 26 )1.4550.04645332487998131.3217623013898
Winsorized Mean ( 11 / 26 )1.468750.039079347632635937.5837901340354
Winsorized Mean ( 12 / 26 )1.468750.039079347632635937.5837901340354
Winsorized Mean ( 13 / 26 )1.4850.03620004196095241.0220518971174
Winsorized Mean ( 14 / 26 )1.4850.03620004196095241.0220518971174
Winsorized Mean ( 15 / 26 )1.466250.033656104737119443.5656476426064
Winsorized Mean ( 16 / 26 )1.466250.033656104737119443.5656476426064
Winsorized Mean ( 17 / 26 )1.48750.030051380052137049.4985587157494
Winsorized Mean ( 18 / 26 )1.510.026541107357207956.892878645846
Winsorized Mean ( 19 / 26 )1.486250.023515666068238763.2025474288988
Winsorized Mean ( 20 / 26 )1.486250.023515666068238763.2025474288988
Winsorized Mean ( 21 / 26 )1.486250.023515666068238763.2025474288988
Winsorized Mean ( 22 / 26 )1.486250.023515666068238763.2025474288988
Winsorized Mean ( 23 / 26 )1.5150.019250184940752278.7005426006467
Winsorized Mean ( 24 / 26 )1.5150.019250184940752278.7005426006467
Winsorized Mean ( 25 / 26 )1.546250.0150887406676869102.477074399678
Winsorized Mean ( 26 / 26 )1.546250.0150887406676869102.477074399678
Trimmed Mean ( 1 / 26 )1.473076923076920.055938488317689826.333870781615
Trimmed Mean ( 2 / 26 )1.472368421052630.05283535114450627.8671077064609
Trimmed Mean ( 3 / 26 )1.470270270270270.049534289102116129.6818688008073
Trimmed Mean ( 4 / 26 )1.468055555555560.047298968749775231.0377920356357
Trimmed Mean ( 5 / 26 )1.470.045834791996363432.0717065786321
Trimmed Mean ( 6 / 26 )1.472058823529410.044090934259920333.386882093527
Trimmed Mean ( 7 / 26 )1.475757575757580.042369261742552134.8308541396050
Trimmed Mean ( 8 / 26 )1.481250.040634537952377136.4529800175407
Trimmed Mean ( 9 / 26 )1.485483870967740.039083009341847738.0084311823239
Trimmed Mean ( 10 / 26 )1.490.037181794950031940.0733746717282
Trimmed Mean ( 11 / 26 )1.494827586206900.034820637450465642.9293572908703
Trimmed Mean ( 12 / 26 )1.498214285714290.033660940351991644.5089848960694
Trimmed Mean ( 13 / 26 )1.501851851851850.032212903381098346.6226789334704
Trimmed Mean ( 14 / 26 )1.503846153846150.031064757262083648.4100403926764
Trimmed Mean ( 15 / 26 )1.5060.029611084521351350.8593327243413
Trimmed Mean ( 16 / 26 )1.510416666666670.028284205948666353.4014166566301
Trimmed Mean ( 17 / 26 )1.515217391304350.026551816318294757.0664309040257
Trimmed Mean ( 18 / 26 )1.518181818181820.025241482198986860.1463022739115
Trimmed Mean ( 19 / 26 )1.519047619047620.024394668035234862.2696573223936
Trimmed Mean ( 20 / 26 )1.52250.023882055273836163.7507945837462
Trimmed Mean ( 21 / 26 )1.526315789473680.023152721522271465.923817552311
Trimmed Mean ( 22 / 26 )1.530555555555560.022117810263771569.2001394940335
Trimmed Mean ( 23 / 26 )1.535294117647060.020632750449426674.4105407279679
Trimmed Mean ( 24 / 26 )1.53750.019954585534933377.0499591338739
Trimmed Mean ( 25 / 26 )1.540.018937283058960081.3210635974185
Trimmed Mean ( 26 / 26 )1.539285714285710.018785397426261381.940545592815
Median1.6
Midrange1.5
Midmean - Weighted Average at Xnp1.51162790697675
Midmean - Weighted Average at X(n+1)p1.51162790697675
Midmean - Empirical Distribution Function1.51162790697675
Midmean - Empirical Distribution Function - Averaging1.51162790697675
Midmean - Empirical Distribution Function - Interpolation1.51162790697675
Midmean - Closest Observation1.51162790697675
Midmean - True Basic - Statistics Graphics Toolkit1.51162790697675
Midmean - MS Excel (old versions)1.51162790697675
Number of observations80



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')