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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 08:31:36 -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/t1224167527yjk3c53bitur65z.htm/, Retrieved Thu, 16 May 2024 00:32:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16351, Retrieved Thu, 16 May 2024 00:32:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact195
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] [1e28c3a908c2cc51d131d1d2a5af4149] [Current]
-    D          [Central Tendency] [] [2008-10-16 14:32:46] [7c33e759a6f7358dc2f6505c3a7a1eae]
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Dataseries X:
2
1.8
1.4
1.5
1.6
1.3
1.1
0.8
1.1
1.3
1.5
1.8
2.7
3
3.2
3.2
3.3
3.2
2.9
2.7
2.6
2.3
2.2
2.1
2.4
2.5
2.4
2.3
2.1
2.3
2.2
2.1
2
2.1
2.1
2.5
2.2
2.3
2.3
2.2
2.2
1.6
1.8
1.7
1.9
1.8
1.9
1.5
1
0.8
1.1
1.5
1.7
2.3
2.4
3
3
3.2
3.2
3.2
3.5
4
4.3
4.1
4
4.1
4.2
4.5
5.6
6.5
7.6
8.5
8.7
8.3
8.3
8.5
8.7
8.7
8.5
7.9




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=16351&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=16351&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16351&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 Mean3.198750.24753527909923112.9224004418283
Geometric Mean2.65137546868119
Harmonic Mean2.26601250174919
Quadratic Mean3.88234787210008
Winsorized Mean ( 1 / 26 )3.198750.24753527909923112.9224004418283
Winsorized Mean ( 2 / 26 )3.203750.24694618225512212.9734745066445
Winsorized Mean ( 3 / 26 )3.20.24444460427050113.0909005316349
Winsorized Mean ( 4 / 26 )3.20.24444460427050113.0909005316349
Winsorized Mean ( 5 / 26 )3.20.24444460427050113.0909005316349
Winsorized Mean ( 6 / 26 )3.20.23878648902685513.4010932236627
Winsorized Mean ( 7 / 26 )3.20.23878648902685513.4010932236627
Winsorized Mean ( 8 / 26 )3.170.22710617602758713.9582289458078
Winsorized Mean ( 9 / 26 )3.14750.21718112810523714.4925115154336
Winsorized Mean ( 10 / 26 )3.010.18260249419456416.4838931323294
Winsorized Mean ( 11 / 26 )2.886250.15370677070565118.7776373594315
Winsorized Mean ( 12 / 26 )2.721250.11934279090295522.8019638170925
Winsorized Mean ( 13 / 26 )2.7050.11124866661126724.3148981681911
Winsorized Mean ( 14 / 26 )2.68750.10811057103549224.8588086646744
Winsorized Mean ( 15 / 26 )2.68750.10247529804231226.2258324819931
Winsorized Mean ( 16 / 26 )2.68750.10247529804231226.2258324819931
Winsorized Mean ( 17 / 26 )2.68750.096248869794449327.9224057980054
Winsorized Mean ( 18 / 26 )2.68750.096248869794449327.9224057980054
Winsorized Mean ( 19 / 26 )2.568750.07675362833133933.4674732106595
Winsorized Mean ( 20 / 26 )2.518750.069334397686369536.3275673265878
Winsorized Mean ( 21 / 26 )2.518750.062264588296207440.4523673716063
Winsorized Mean ( 22 / 26 )2.518750.062264588296207440.4523673716063
Winsorized Mean ( 23 / 26 )2.54750.058757574249160243.3561125106592
Winsorized Mean ( 24 / 26 )2.54750.058757574249160243.3561125106592
Winsorized Mean ( 25 / 26 )2.578750.055195101312170446.7206316990923
Winsorized Mean ( 26 / 26 )2.578750.055195101312170446.7206316990923
Trimmed Mean ( 1 / 26 )3.158974358974360.24178432537722913.0652570386677
Trimmed Mean ( 2 / 26 )3.117105263157890.23497210105311413.2658526233005
Trimmed Mean ( 3 / 26 )3.070270270270270.22721801349400813.5124421829840
Trimmed Mean ( 4 / 26 )3.022222222222220.21908386413326113.7948188661850
Trimmed Mean ( 5 / 26 )2.971428571428570.20924930257946214.2004228200483
Trimmed Mean ( 6 / 26 )2.917647058823530.19722550051397414.7934574952026
Trimmed Mean ( 7 / 26 )2.860606060606060.18411102847456415.5373965606915
Trimmed Mean ( 8 / 26 )2.80.16752753860328816.7136700231149
Trimmed Mean ( 9 / 26 )2.740322580645160.14988907722120418.2823367215814
Trimmed Mean ( 10 / 26 )2.680.12974986800990420.6551269847568
Trimmed Mean ( 11 / 26 )2.634482758620690.11469604545994422.9692553745520
Trimmed Mean ( 12 / 26 )2.601785714285710.10405702331022925.0034609055548
Trimmed Mean ( 13 / 26 )2.587037037037040.099826764562940725.9152647925989
Trimmed Mean ( 14 / 26 )2.573076923076920.096316604332279826.7147802906355
Trimmed Mean ( 15 / 26 )2.560.092582009977255127.6511603132069
Trimmed Mean ( 16 / 26 )2.545833333333330.08902338192604728.5973558659925
Trimmed Mean ( 17 / 26 )2.530434782608700.084377204904016629.9895544713432
Trimmed Mean ( 18 / 26 )2.513636363636360.079745294127126231.5208112422188
Trimmed Mean ( 19 / 26 )2.495238095238100.073485670694063533.9554374570017
Trimmed Mean ( 20 / 26 )2.48750.07072767383530935.1701090268033
Trimmed Mean ( 21 / 26 )2.484210526315790.068879088382113336.0662515237483
Trimmed Mean ( 22 / 26 )2.480555555555560.067942487869140736.5096368024259
Trimmed Mean ( 23 / 26 )2.476470588235290.066496059354033837.2423661235358
Trimmed Mean ( 24 / 26 )2.468750.065135946544577537.9014988031293
Trimmed Mean ( 25 / 26 )2.460.062990603203605139.0534440835329
Trimmed Mean ( 26 / 26 )2.446428571428570.060527256280410340.4186266116999
Median2.3
Midrange4.75
Midmean - Weighted Average at Xnp2.43953488372093
Midmean - Weighted Average at X(n+1)p2.43953488372093
Midmean - Empirical Distribution Function2.43953488372093
Midmean - Empirical Distribution Function - Averaging2.43953488372093
Midmean - Empirical Distribution Function - Interpolation2.43953488372093
Midmean - Closest Observation2.43953488372093
Midmean - True Basic - Statistics Graphics Toolkit2.43953488372093
Midmean - MS Excel (old versions)2.46363636363636
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.19875 & 0.247535279099231 & 12.9224004418283 \tabularnewline
Geometric Mean & 2.65137546868119 &  &  \tabularnewline
Harmonic Mean & 2.26601250174919 &  &  \tabularnewline
Quadratic Mean & 3.88234787210008 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 3.19875 & 0.247535279099231 & 12.9224004418283 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 3.20375 & 0.246946182255122 & 12.9734745066445 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 3.2 & 0.244444604270501 & 13.0909005316349 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 3.2 & 0.244444604270501 & 13.0909005316349 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 3.2 & 0.244444604270501 & 13.0909005316349 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 3.2 & 0.238786489026855 & 13.4010932236627 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 3.2 & 0.238786489026855 & 13.4010932236627 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 3.17 & 0.227106176027587 & 13.9582289458078 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 3.1475 & 0.217181128105237 & 14.4925115154336 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 3.01 & 0.182602494194564 & 16.4838931323294 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 2.88625 & 0.153706770705651 & 18.7776373594315 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 2.72125 & 0.119342790902955 & 22.8019638170925 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 2.705 & 0.111248666611267 & 24.3148981681911 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 2.6875 & 0.108110571035492 & 24.8588086646744 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 2.6875 & 0.102475298042312 & 26.2258324819931 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 2.6875 & 0.102475298042312 & 26.2258324819931 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 2.6875 & 0.0962488697944493 & 27.9224057980054 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 2.6875 & 0.0962488697944493 & 27.9224057980054 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 2.56875 & 0.076753628331339 & 33.4674732106595 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 2.51875 & 0.0693343976863695 & 36.3275673265878 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 2.51875 & 0.0622645882962074 & 40.4523673716063 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 2.51875 & 0.0622645882962074 & 40.4523673716063 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 2.5475 & 0.0587575742491602 & 43.3561125106592 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 2.5475 & 0.0587575742491602 & 43.3561125106592 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 2.57875 & 0.0551951013121704 & 46.7206316990923 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 2.57875 & 0.0551951013121704 & 46.7206316990923 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 3.15897435897436 & 0.241784325377229 & 13.0652570386677 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 3.11710526315789 & 0.234972101053114 & 13.2658526233005 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 3.07027027027027 & 0.227218013494008 & 13.5124421829840 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 3.02222222222222 & 0.219083864133261 & 13.7948188661850 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 2.97142857142857 & 0.209249302579462 & 14.2004228200483 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 2.91764705882353 & 0.197225500513974 & 14.7934574952026 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 2.86060606060606 & 0.184111028474564 & 15.5373965606915 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 2.8 & 0.167527538603288 & 16.7136700231149 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 2.74032258064516 & 0.149889077221204 & 18.2823367215814 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 2.68 & 0.129749868009904 & 20.6551269847568 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 2.63448275862069 & 0.114696045459944 & 22.9692553745520 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 2.60178571428571 & 0.104057023310229 & 25.0034609055548 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 2.58703703703704 & 0.0998267645629407 & 25.9152647925989 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 2.57307692307692 & 0.0963166043322798 & 26.7147802906355 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 2.56 & 0.0925820099772551 & 27.6511603132069 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 2.54583333333333 & 0.089023381926047 & 28.5973558659925 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 2.53043478260870 & 0.0843772049040166 & 29.9895544713432 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 2.51363636363636 & 0.0797452941271262 & 31.5208112422188 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 2.49523809523810 & 0.0734856706940635 & 33.9554374570017 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 2.4875 & 0.070727673835309 & 35.1701090268033 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 2.48421052631579 & 0.0688790883821133 & 36.0662515237483 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 2.48055555555556 & 0.0679424878691407 & 36.5096368024259 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 2.47647058823529 & 0.0664960593540338 & 37.2423661235358 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 2.46875 & 0.0651359465445775 & 37.9014988031293 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 2.46 & 0.0629906032036051 & 39.0534440835329 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 2.44642857142857 & 0.0605272562804103 & 40.4186266116999 \tabularnewline
Median & 2.3 &  &  \tabularnewline
Midrange & 4.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.43953488372093 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.43953488372093 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.43953488372093 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.43953488372093 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.43953488372093 &  &  \tabularnewline
Midmean - Closest Observation & 2.43953488372093 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.43953488372093 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.46363636363636 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16351&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]3.19875[/C][C]0.247535279099231[/C][C]12.9224004418283[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.65137546868119[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.26601250174919[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.88234787210008[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]3.19875[/C][C]0.247535279099231[/C][C]12.9224004418283[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]3.20375[/C][C]0.246946182255122[/C][C]12.9734745066445[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]3.2[/C][C]0.244444604270501[/C][C]13.0909005316349[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]3.2[/C][C]0.244444604270501[/C][C]13.0909005316349[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]3.2[/C][C]0.244444604270501[/C][C]13.0909005316349[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]3.2[/C][C]0.238786489026855[/C][C]13.4010932236627[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]3.2[/C][C]0.238786489026855[/C][C]13.4010932236627[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]3.17[/C][C]0.227106176027587[/C][C]13.9582289458078[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]3.1475[/C][C]0.217181128105237[/C][C]14.4925115154336[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]3.01[/C][C]0.182602494194564[/C][C]16.4838931323294[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]2.88625[/C][C]0.153706770705651[/C][C]18.7776373594315[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]2.72125[/C][C]0.119342790902955[/C][C]22.8019638170925[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]2.705[/C][C]0.111248666611267[/C][C]24.3148981681911[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]2.6875[/C][C]0.108110571035492[/C][C]24.8588086646744[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]2.6875[/C][C]0.102475298042312[/C][C]26.2258324819931[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]2.6875[/C][C]0.102475298042312[/C][C]26.2258324819931[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]2.6875[/C][C]0.0962488697944493[/C][C]27.9224057980054[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]2.6875[/C][C]0.0962488697944493[/C][C]27.9224057980054[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]2.56875[/C][C]0.076753628331339[/C][C]33.4674732106595[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]2.51875[/C][C]0.0693343976863695[/C][C]36.3275673265878[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]2.51875[/C][C]0.0622645882962074[/C][C]40.4523673716063[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]2.51875[/C][C]0.0622645882962074[/C][C]40.4523673716063[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]2.5475[/C][C]0.0587575742491602[/C][C]43.3561125106592[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]2.5475[/C][C]0.0587575742491602[/C][C]43.3561125106592[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]2.57875[/C][C]0.0551951013121704[/C][C]46.7206316990923[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]2.57875[/C][C]0.0551951013121704[/C][C]46.7206316990923[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]3.15897435897436[/C][C]0.241784325377229[/C][C]13.0652570386677[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]3.11710526315789[/C][C]0.234972101053114[/C][C]13.2658526233005[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]3.07027027027027[/C][C]0.227218013494008[/C][C]13.5124421829840[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]3.02222222222222[/C][C]0.219083864133261[/C][C]13.7948188661850[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]2.97142857142857[/C][C]0.209249302579462[/C][C]14.2004228200483[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]2.91764705882353[/C][C]0.197225500513974[/C][C]14.7934574952026[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]2.86060606060606[/C][C]0.184111028474564[/C][C]15.5373965606915[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]2.8[/C][C]0.167527538603288[/C][C]16.7136700231149[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]2.74032258064516[/C][C]0.149889077221204[/C][C]18.2823367215814[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]2.68[/C][C]0.129749868009904[/C][C]20.6551269847568[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]2.63448275862069[/C][C]0.114696045459944[/C][C]22.9692553745520[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]2.60178571428571[/C][C]0.104057023310229[/C][C]25.0034609055548[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]2.58703703703704[/C][C]0.0998267645629407[/C][C]25.9152647925989[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]2.57307692307692[/C][C]0.0963166043322798[/C][C]26.7147802906355[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]2.56[/C][C]0.0925820099772551[/C][C]27.6511603132069[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]2.54583333333333[/C][C]0.089023381926047[/C][C]28.5973558659925[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]2.53043478260870[/C][C]0.0843772049040166[/C][C]29.9895544713432[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]2.51363636363636[/C][C]0.0797452941271262[/C][C]31.5208112422188[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]2.49523809523810[/C][C]0.0734856706940635[/C][C]33.9554374570017[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]2.4875[/C][C]0.070727673835309[/C][C]35.1701090268033[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]2.48421052631579[/C][C]0.0688790883821133[/C][C]36.0662515237483[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]2.48055555555556[/C][C]0.0679424878691407[/C][C]36.5096368024259[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]2.47647058823529[/C][C]0.0664960593540338[/C][C]37.2423661235358[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]2.46875[/C][C]0.0651359465445775[/C][C]37.9014988031293[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]2.46[/C][C]0.0629906032036051[/C][C]39.0534440835329[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]2.44642857142857[/C][C]0.0605272562804103[/C][C]40.4186266116999[/C][/ROW]
[ROW][C]Median[/C][C]2.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.43953488372093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.43953488372093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.43953488372093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.43953488372093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.43953488372093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.43953488372093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.43953488372093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.46363636363636[/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=16351&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16351&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 Mean3.198750.24753527909923112.9224004418283
Geometric Mean2.65137546868119
Harmonic Mean2.26601250174919
Quadratic Mean3.88234787210008
Winsorized Mean ( 1 / 26 )3.198750.24753527909923112.9224004418283
Winsorized Mean ( 2 / 26 )3.203750.24694618225512212.9734745066445
Winsorized Mean ( 3 / 26 )3.20.24444460427050113.0909005316349
Winsorized Mean ( 4 / 26 )3.20.24444460427050113.0909005316349
Winsorized Mean ( 5 / 26 )3.20.24444460427050113.0909005316349
Winsorized Mean ( 6 / 26 )3.20.23878648902685513.4010932236627
Winsorized Mean ( 7 / 26 )3.20.23878648902685513.4010932236627
Winsorized Mean ( 8 / 26 )3.170.22710617602758713.9582289458078
Winsorized Mean ( 9 / 26 )3.14750.21718112810523714.4925115154336
Winsorized Mean ( 10 / 26 )3.010.18260249419456416.4838931323294
Winsorized Mean ( 11 / 26 )2.886250.15370677070565118.7776373594315
Winsorized Mean ( 12 / 26 )2.721250.11934279090295522.8019638170925
Winsorized Mean ( 13 / 26 )2.7050.11124866661126724.3148981681911
Winsorized Mean ( 14 / 26 )2.68750.10811057103549224.8588086646744
Winsorized Mean ( 15 / 26 )2.68750.10247529804231226.2258324819931
Winsorized Mean ( 16 / 26 )2.68750.10247529804231226.2258324819931
Winsorized Mean ( 17 / 26 )2.68750.096248869794449327.9224057980054
Winsorized Mean ( 18 / 26 )2.68750.096248869794449327.9224057980054
Winsorized Mean ( 19 / 26 )2.568750.07675362833133933.4674732106595
Winsorized Mean ( 20 / 26 )2.518750.069334397686369536.3275673265878
Winsorized Mean ( 21 / 26 )2.518750.062264588296207440.4523673716063
Winsorized Mean ( 22 / 26 )2.518750.062264588296207440.4523673716063
Winsorized Mean ( 23 / 26 )2.54750.058757574249160243.3561125106592
Winsorized Mean ( 24 / 26 )2.54750.058757574249160243.3561125106592
Winsorized Mean ( 25 / 26 )2.578750.055195101312170446.7206316990923
Winsorized Mean ( 26 / 26 )2.578750.055195101312170446.7206316990923
Trimmed Mean ( 1 / 26 )3.158974358974360.24178432537722913.0652570386677
Trimmed Mean ( 2 / 26 )3.117105263157890.23497210105311413.2658526233005
Trimmed Mean ( 3 / 26 )3.070270270270270.22721801349400813.5124421829840
Trimmed Mean ( 4 / 26 )3.022222222222220.21908386413326113.7948188661850
Trimmed Mean ( 5 / 26 )2.971428571428570.20924930257946214.2004228200483
Trimmed Mean ( 6 / 26 )2.917647058823530.19722550051397414.7934574952026
Trimmed Mean ( 7 / 26 )2.860606060606060.18411102847456415.5373965606915
Trimmed Mean ( 8 / 26 )2.80.16752753860328816.7136700231149
Trimmed Mean ( 9 / 26 )2.740322580645160.14988907722120418.2823367215814
Trimmed Mean ( 10 / 26 )2.680.12974986800990420.6551269847568
Trimmed Mean ( 11 / 26 )2.634482758620690.11469604545994422.9692553745520
Trimmed Mean ( 12 / 26 )2.601785714285710.10405702331022925.0034609055548
Trimmed Mean ( 13 / 26 )2.587037037037040.099826764562940725.9152647925989
Trimmed Mean ( 14 / 26 )2.573076923076920.096316604332279826.7147802906355
Trimmed Mean ( 15 / 26 )2.560.092582009977255127.6511603132069
Trimmed Mean ( 16 / 26 )2.545833333333330.08902338192604728.5973558659925
Trimmed Mean ( 17 / 26 )2.530434782608700.084377204904016629.9895544713432
Trimmed Mean ( 18 / 26 )2.513636363636360.079745294127126231.5208112422188
Trimmed Mean ( 19 / 26 )2.495238095238100.073485670694063533.9554374570017
Trimmed Mean ( 20 / 26 )2.48750.07072767383530935.1701090268033
Trimmed Mean ( 21 / 26 )2.484210526315790.068879088382113336.0662515237483
Trimmed Mean ( 22 / 26 )2.480555555555560.067942487869140736.5096368024259
Trimmed Mean ( 23 / 26 )2.476470588235290.066496059354033837.2423661235358
Trimmed Mean ( 24 / 26 )2.468750.065135946544577537.9014988031293
Trimmed Mean ( 25 / 26 )2.460.062990603203605139.0534440835329
Trimmed Mean ( 26 / 26 )2.446428571428570.060527256280410340.4186266116999
Median2.3
Midrange4.75
Midmean - Weighted Average at Xnp2.43953488372093
Midmean - Weighted Average at X(n+1)p2.43953488372093
Midmean - Empirical Distribution Function2.43953488372093
Midmean - Empirical Distribution Function - Averaging2.43953488372093
Midmean - Empirical Distribution Function - Interpolation2.43953488372093
Midmean - Closest Observation2.43953488372093
Midmean - True Basic - Statistics Graphics Toolkit2.43953488372093
Midmean - MS Excel (old versions)2.46363636363636
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')