Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 17 Oct 2011 13:31:57 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/17/t1318872824rfa7keosscy9tum.htm/, Retrieved Wed, 15 May 2024 21:35:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=130765, Retrieved Wed, 15 May 2024 21:35:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Opdracht 5 gemidd...] [2011-10-15 14:13:51] [78ad7246c13d73188e9e2bc44b7acf73]
- RM    [Mean versus Median] [opdracht 5 gemidd...] [2011-10-17 17:25:16] [78ad7246c13d73188e9e2bc44b7acf73]
- RM D      [Central Tendency] [Opdracht 5(2) gem...] [2011-10-17 17:31:57] [5c7e349a99f3f4c38d746f616922f776] [Current]
- RM          [Mean versus Median] [Opdracht 5(2) gem...] [2011-10-17 17:43:26] [78ad7246c13d73188e9e2bc44b7acf73]
Feedback Forum

Post a new message
Dataseries X:
6
6
5
3
2
3
3
2
0
4
4
5
6
6
5
5
3
5
5
5
3
6
6
4
6
5
4
5
5
4
3
2
3
2
-1
0
-2
1
-2
-2
-2
-6
-4
-2
0
-5
-4
-5
-1
-2
-4
-1
1
1
-2
1
1
3
3
1
1
0
2
2
-1
1
0
1
1
3
2
0




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130765&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130765&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130765&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'AstonUniversity' @ aston.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.666666666666670.3636452552618994.58322126454346
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean3.48807492274273
Winsorized Mean ( 1 / 24 )1.680555555555560.359765610582044.67125124282084
Winsorized Mean ( 2 / 24 )1.680555555555560.359765610582044.67125124282084
Winsorized Mean ( 3 / 24 )1.722222222222220.3495034607854784.92762566170785
Winsorized Mean ( 4 / 24 )1.722222222222220.3495034607854784.92762566170785
Winsorized Mean ( 5 / 24 )1.722222222222220.3495034607854784.92762566170785
Winsorized Mean ( 6 / 24 )1.888888888888890.3155810124405015.98543262879295
Winsorized Mean ( 7 / 24 )1.791666666666670.2992802398619585.98658524028539
Winsorized Mean ( 8 / 24 )1.791666666666670.2992802398619585.98658524028539
Winsorized Mean ( 9 / 24 )1.791666666666670.2992802398619585.98658524028539
Winsorized Mean ( 10 / 24 )1.791666666666670.2992802398619585.98658524028539
Winsorized Mean ( 11 / 24 )1.791666666666670.2992802398619585.98658524028539
Winsorized Mean ( 12 / 24 )1.791666666666670.2992802398619585.98658524028539
Winsorized Mean ( 13 / 24 )1.972222222222220.2690127303116477.33133417120235
Winsorized Mean ( 14 / 24 )1.972222222222220.2690127303116477.33133417120235
Winsorized Mean ( 15 / 24 )1.972222222222220.2690127303116477.33133417120235
Winsorized Mean ( 16 / 24 )1.972222222222220.2690127303116477.33133417120235
Winsorized Mean ( 17 / 24 )1.972222222222220.1977694693266379.9723290401558
Winsorized Mean ( 18 / 24 )1.972222222222220.1977694693266379.9723290401558
Winsorized Mean ( 19 / 24 )1.972222222222220.1977694693266379.9723290401558
Winsorized Mean ( 20 / 24 )1.972222222222220.1977694693266379.9723290401558
Winsorized Mean ( 21 / 24 )1.972222222222220.1977694693266379.9723290401558
Winsorized Mean ( 22 / 24 )1.666666666666670.1569964564056910.6159508617181
Winsorized Mean ( 23 / 24 )1.986111111111110.11274955897875817.6152450537327
Winsorized Mean ( 24 / 24 )1.986111111111110.11274955897875817.6152450537327
Trimmed Mean ( 1 / 24 )1.714285714285710.3519498229946214.87082419789117
Trimmed Mean ( 2 / 24 )1.750.342596986774255.10804259102589
Trimmed Mean ( 3 / 24 )1.787878787878790.3313567162947465.39563165603212
Trimmed Mean ( 4 / 24 )1.81250.3226525417510495.61749797526306
Trimmed Mean ( 5 / 24 )1.838709677419350.3120983285400145.89144352685508
Trimmed Mean ( 6 / 24 )1.866666666666670.2992142881066286.23856126149116
Trimmed Mean ( 7 / 24 )1.862068965517240.2935568181497336.3431296784511
Trimmed Mean ( 8 / 24 )1.8750.2906134353934266.45186963727836
Trimmed Mean ( 9 / 24 )1.888888888888890.286752298977746.58717958189942
Trimmed Mean ( 10 / 24 )1.903846153846150.2817468877139776.75729258020729
Trimmed Mean ( 11 / 24 )1.920.2752957593244786.97431738400659
Trimmed Mean ( 12 / 24 )1.93750.2669871467408557.25690365117311
Trimmed Mean ( 13 / 24 )1.956521739130430.256239097544217.63553164946997
Trimmed Mean ( 14 / 24 )1.954545454545450.2496393708753957.8294759664374
Trimmed Mean ( 15 / 24 )1.952380952380950.2408665659986998.1056536189896
Trimmed Mean ( 16 / 24 )1.950.2291287847477928.5104977192037
Trimmed Mean ( 17 / 24 )1.947368421052630.2131767724285699.1349934557488
Trimmed Mean ( 18 / 24 )1.944444444444440.2106092614842189.23247358991452
Trimmed Mean ( 19 / 24 )1.941176470588240.2065814461343679.39666415794974
Trimmed Mean ( 20 / 24 )1.93750.2004908291684319.66378366549781
Trimmed Mean ( 21 / 24 )1.933333333333330.19138535077278410.1017832635927
Trimmed Mean ( 22 / 24 )1.928571428571430.17764308956824910.8564393540931
Trimmed Mean ( 23 / 24 )1.961538461538460.17079694854749611.4846224023316
Trimmed Mean ( 24 / 24 )1.958333333333330.17527583506430111.172865515745
Median2
Midrange0
Midmean - Weighted Average at Xnp1.94736842105263
Midmean - Weighted Average at X(n+1)p1.94736842105263
Midmean - Empirical Distribution Function1.94736842105263
Midmean - Empirical Distribution Function - Averaging1.94736842105263
Midmean - Empirical Distribution Function - Interpolation1.94736842105263
Midmean - Closest Observation1.94736842105263
Midmean - True Basic - Statistics Graphics Toolkit1.94736842105263
Midmean - MS Excel (old versions)1.94736842105263
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.66666666666667 & 0.363645255261899 & 4.58322126454346 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 3.48807492274273 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.68055555555556 & 0.35976561058204 & 4.67125124282084 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.68055555555556 & 0.35976561058204 & 4.67125124282084 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.72222222222222 & 0.349503460785478 & 4.92762566170785 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.72222222222222 & 0.349503460785478 & 4.92762566170785 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.72222222222222 & 0.349503460785478 & 4.92762566170785 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.88888888888889 & 0.315581012440501 & 5.98543262879295 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.79166666666667 & 0.299280239861958 & 5.98658524028539 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.79166666666667 & 0.299280239861958 & 5.98658524028539 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.79166666666667 & 0.299280239861958 & 5.98658524028539 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.79166666666667 & 0.299280239861958 & 5.98658524028539 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.79166666666667 & 0.299280239861958 & 5.98658524028539 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.79166666666667 & 0.299280239861958 & 5.98658524028539 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.97222222222222 & 0.269012730311647 & 7.33133417120235 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.97222222222222 & 0.269012730311647 & 7.33133417120235 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.97222222222222 & 0.269012730311647 & 7.33133417120235 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.97222222222222 & 0.269012730311647 & 7.33133417120235 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.97222222222222 & 0.197769469326637 & 9.9723290401558 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.97222222222222 & 0.197769469326637 & 9.9723290401558 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.97222222222222 & 0.197769469326637 & 9.9723290401558 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.97222222222222 & 0.197769469326637 & 9.9723290401558 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.97222222222222 & 0.197769469326637 & 9.9723290401558 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.66666666666667 & 0.15699645640569 & 10.6159508617181 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.98611111111111 & 0.112749558978758 & 17.6152450537327 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.98611111111111 & 0.112749558978758 & 17.6152450537327 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.71428571428571 & 0.351949822994621 & 4.87082419789117 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.75 & 0.34259698677425 & 5.10804259102589 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.78787878787879 & 0.331356716294746 & 5.39563165603212 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.8125 & 0.322652541751049 & 5.61749797526306 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.83870967741935 & 0.312098328540014 & 5.89144352685508 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.86666666666667 & 0.299214288106628 & 6.23856126149116 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.86206896551724 & 0.293556818149733 & 6.3431296784511 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.875 & 0.290613435393426 & 6.45186963727836 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.88888888888889 & 0.28675229897774 & 6.58717958189942 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.90384615384615 & 0.281746887713977 & 6.75729258020729 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.92 & 0.275295759324478 & 6.97431738400659 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.9375 & 0.266987146740855 & 7.25690365117311 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.95652173913043 & 0.25623909754421 & 7.63553164946997 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.95454545454545 & 0.249639370875395 & 7.8294759664374 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.95238095238095 & 0.240866565998699 & 8.1056536189896 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.95 & 0.229128784747792 & 8.5104977192037 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.94736842105263 & 0.213176772428569 & 9.1349934557488 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.94444444444444 & 0.210609261484218 & 9.23247358991452 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.94117647058824 & 0.206581446134367 & 9.39666415794974 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.9375 & 0.200490829168431 & 9.66378366549781 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.93333333333333 & 0.191385350772784 & 10.1017832635927 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.92857142857143 & 0.177643089568249 & 10.8564393540931 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.96153846153846 & 0.170796948547496 & 11.4846224023316 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.95833333333333 & 0.175275835064301 & 11.172865515745 \tabularnewline
Median & 2 &  &  \tabularnewline
Midrange & 0 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.94736842105263 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.94736842105263 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.94736842105263 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.94736842105263 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.94736842105263 &  &  \tabularnewline
Midmean - Closest Observation & 1.94736842105263 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.94736842105263 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.94736842105263 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130765&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]1.66666666666667[/C][C]0.363645255261899[/C][C]4.58322126454346[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.48807492274273[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.68055555555556[/C][C]0.35976561058204[/C][C]4.67125124282084[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.68055555555556[/C][C]0.35976561058204[/C][C]4.67125124282084[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.72222222222222[/C][C]0.349503460785478[/C][C]4.92762566170785[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.72222222222222[/C][C]0.349503460785478[/C][C]4.92762566170785[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.72222222222222[/C][C]0.349503460785478[/C][C]4.92762566170785[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.88888888888889[/C][C]0.315581012440501[/C][C]5.98543262879295[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.79166666666667[/C][C]0.299280239861958[/C][C]5.98658524028539[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.79166666666667[/C][C]0.299280239861958[/C][C]5.98658524028539[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.79166666666667[/C][C]0.299280239861958[/C][C]5.98658524028539[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.79166666666667[/C][C]0.299280239861958[/C][C]5.98658524028539[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.79166666666667[/C][C]0.299280239861958[/C][C]5.98658524028539[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.79166666666667[/C][C]0.299280239861958[/C][C]5.98658524028539[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.97222222222222[/C][C]0.269012730311647[/C][C]7.33133417120235[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.97222222222222[/C][C]0.269012730311647[/C][C]7.33133417120235[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.97222222222222[/C][C]0.269012730311647[/C][C]7.33133417120235[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.97222222222222[/C][C]0.269012730311647[/C][C]7.33133417120235[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.97222222222222[/C][C]0.197769469326637[/C][C]9.9723290401558[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.97222222222222[/C][C]0.197769469326637[/C][C]9.9723290401558[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.97222222222222[/C][C]0.197769469326637[/C][C]9.9723290401558[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.97222222222222[/C][C]0.197769469326637[/C][C]9.9723290401558[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.97222222222222[/C][C]0.197769469326637[/C][C]9.9723290401558[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.66666666666667[/C][C]0.15699645640569[/C][C]10.6159508617181[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.98611111111111[/C][C]0.112749558978758[/C][C]17.6152450537327[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.98611111111111[/C][C]0.112749558978758[/C][C]17.6152450537327[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.71428571428571[/C][C]0.351949822994621[/C][C]4.87082419789117[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.75[/C][C]0.34259698677425[/C][C]5.10804259102589[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.78787878787879[/C][C]0.331356716294746[/C][C]5.39563165603212[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.8125[/C][C]0.322652541751049[/C][C]5.61749797526306[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.83870967741935[/C][C]0.312098328540014[/C][C]5.89144352685508[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.86666666666667[/C][C]0.299214288106628[/C][C]6.23856126149116[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.86206896551724[/C][C]0.293556818149733[/C][C]6.3431296784511[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.875[/C][C]0.290613435393426[/C][C]6.45186963727836[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.88888888888889[/C][C]0.28675229897774[/C][C]6.58717958189942[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.90384615384615[/C][C]0.281746887713977[/C][C]6.75729258020729[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.92[/C][C]0.275295759324478[/C][C]6.97431738400659[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.9375[/C][C]0.266987146740855[/C][C]7.25690365117311[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.95652173913043[/C][C]0.25623909754421[/C][C]7.63553164946997[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.95454545454545[/C][C]0.249639370875395[/C][C]7.8294759664374[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.95238095238095[/C][C]0.240866565998699[/C][C]8.1056536189896[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.95[/C][C]0.229128784747792[/C][C]8.5104977192037[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.94736842105263[/C][C]0.213176772428569[/C][C]9.1349934557488[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.94444444444444[/C][C]0.210609261484218[/C][C]9.23247358991452[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.94117647058824[/C][C]0.206581446134367[/C][C]9.39666415794974[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.9375[/C][C]0.200490829168431[/C][C]9.66378366549781[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.93333333333333[/C][C]0.191385350772784[/C][C]10.1017832635927[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.92857142857143[/C][C]0.177643089568249[/C][C]10.8564393540931[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.96153846153846[/C][C]0.170796948547496[/C][C]11.4846224023316[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.95833333333333[/C][C]0.175275835064301[/C][C]11.172865515745[/C][/ROW]
[ROW][C]Median[/C][C]2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.94736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.94736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.94736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.94736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.94736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.94736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.94736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.94736842105263[/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=130765&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130765&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 Mean1.666666666666670.3636452552618994.58322126454346
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean3.48807492274273
Winsorized Mean ( 1 / 24 )1.680555555555560.359765610582044.67125124282084
Winsorized Mean ( 2 / 24 )1.680555555555560.359765610582044.67125124282084
Winsorized Mean ( 3 / 24 )1.722222222222220.3495034607854784.92762566170785
Winsorized Mean ( 4 / 24 )1.722222222222220.3495034607854784.92762566170785
Winsorized Mean ( 5 / 24 )1.722222222222220.3495034607854784.92762566170785
Winsorized Mean ( 6 / 24 )1.888888888888890.3155810124405015.98543262879295
Winsorized Mean ( 7 / 24 )1.791666666666670.2992802398619585.98658524028539
Winsorized Mean ( 8 / 24 )1.791666666666670.2992802398619585.98658524028539
Winsorized Mean ( 9 / 24 )1.791666666666670.2992802398619585.98658524028539
Winsorized Mean ( 10 / 24 )1.791666666666670.2992802398619585.98658524028539
Winsorized Mean ( 11 / 24 )1.791666666666670.2992802398619585.98658524028539
Winsorized Mean ( 12 / 24 )1.791666666666670.2992802398619585.98658524028539
Winsorized Mean ( 13 / 24 )1.972222222222220.2690127303116477.33133417120235
Winsorized Mean ( 14 / 24 )1.972222222222220.2690127303116477.33133417120235
Winsorized Mean ( 15 / 24 )1.972222222222220.2690127303116477.33133417120235
Winsorized Mean ( 16 / 24 )1.972222222222220.2690127303116477.33133417120235
Winsorized Mean ( 17 / 24 )1.972222222222220.1977694693266379.9723290401558
Winsorized Mean ( 18 / 24 )1.972222222222220.1977694693266379.9723290401558
Winsorized Mean ( 19 / 24 )1.972222222222220.1977694693266379.9723290401558
Winsorized Mean ( 20 / 24 )1.972222222222220.1977694693266379.9723290401558
Winsorized Mean ( 21 / 24 )1.972222222222220.1977694693266379.9723290401558
Winsorized Mean ( 22 / 24 )1.666666666666670.1569964564056910.6159508617181
Winsorized Mean ( 23 / 24 )1.986111111111110.11274955897875817.6152450537327
Winsorized Mean ( 24 / 24 )1.986111111111110.11274955897875817.6152450537327
Trimmed Mean ( 1 / 24 )1.714285714285710.3519498229946214.87082419789117
Trimmed Mean ( 2 / 24 )1.750.342596986774255.10804259102589
Trimmed Mean ( 3 / 24 )1.787878787878790.3313567162947465.39563165603212
Trimmed Mean ( 4 / 24 )1.81250.3226525417510495.61749797526306
Trimmed Mean ( 5 / 24 )1.838709677419350.3120983285400145.89144352685508
Trimmed Mean ( 6 / 24 )1.866666666666670.2992142881066286.23856126149116
Trimmed Mean ( 7 / 24 )1.862068965517240.2935568181497336.3431296784511
Trimmed Mean ( 8 / 24 )1.8750.2906134353934266.45186963727836
Trimmed Mean ( 9 / 24 )1.888888888888890.286752298977746.58717958189942
Trimmed Mean ( 10 / 24 )1.903846153846150.2817468877139776.75729258020729
Trimmed Mean ( 11 / 24 )1.920.2752957593244786.97431738400659
Trimmed Mean ( 12 / 24 )1.93750.2669871467408557.25690365117311
Trimmed Mean ( 13 / 24 )1.956521739130430.256239097544217.63553164946997
Trimmed Mean ( 14 / 24 )1.954545454545450.2496393708753957.8294759664374
Trimmed Mean ( 15 / 24 )1.952380952380950.2408665659986998.1056536189896
Trimmed Mean ( 16 / 24 )1.950.2291287847477928.5104977192037
Trimmed Mean ( 17 / 24 )1.947368421052630.2131767724285699.1349934557488
Trimmed Mean ( 18 / 24 )1.944444444444440.2106092614842189.23247358991452
Trimmed Mean ( 19 / 24 )1.941176470588240.2065814461343679.39666415794974
Trimmed Mean ( 20 / 24 )1.93750.2004908291684319.66378366549781
Trimmed Mean ( 21 / 24 )1.933333333333330.19138535077278410.1017832635927
Trimmed Mean ( 22 / 24 )1.928571428571430.17764308956824910.8564393540931
Trimmed Mean ( 23 / 24 )1.961538461538460.17079694854749611.4846224023316
Trimmed Mean ( 24 / 24 )1.958333333333330.17527583506430111.172865515745
Median2
Midrange0
Midmean - Weighted Average at Xnp1.94736842105263
Midmean - Weighted Average at X(n+1)p1.94736842105263
Midmean - Empirical Distribution Function1.94736842105263
Midmean - Empirical Distribution Function - Averaging1.94736842105263
Midmean - Empirical Distribution Function - Interpolation1.94736842105263
Midmean - Closest Observation1.94736842105263
Midmean - True Basic - Statistics Graphics Toolkit1.94736842105263
Midmean - MS Excel (old versions)1.94736842105263
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')