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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 09:41:23 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224517336kxuck9ib1yo4zof.htm/, Retrieved Sun, 19 May 2024 14:00:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17509, Retrieved Sun, 19 May 2024 14:00:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Harrell-Davis Quantiles] [Q7 95% confidence...] [2007-10-20 15:02:46] [b731da8b544846036771bbf9bf2f34ce]
- RMPD    [Central Tendency] [Central Tendency ...] [2008-10-20 15:41:23] [e7b118d7688fea522247297d6fc6c452] [Current]
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Dataseries X:
14
18
18
12
16
12
19
13
12
13
11
10
16
12
6
8
6
8
8
9
13
8
11
8
10
15
12
13
12
15
13
13
16
14
12
15
14
19
16
16
11
13
12
11
6
9
6
15
17
13
12
13
10
14
13
10
11
12
7
11
9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17509&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17509&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17509&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean12.14754098360660.41609429467630329.1942022253793
Geometric Mean11.6841659989912
Harmonic Mean11.1804450594414
Quadratic Mean12.5678486493167
Winsorized Mean ( 1 / 20 )12.14754098360660.41609429467630329.1942022253793
Winsorized Mean ( 2 / 20 )12.11475409836070.40764441314881429.7189258765532
Winsorized Mean ( 3 / 20 )12.11475409836070.40764441314881429.7189258765532
Winsorized Mean ( 4 / 20 )12.11475409836070.37700166010834332.1344847523459
Winsorized Mean ( 5 / 20 )12.11475409836070.34284119908497135.3363426877938
Winsorized Mean ( 6 / 20 )12.11475409836070.34284119908497135.3363426877938
Winsorized Mean ( 7 / 20 )12.11475409836070.34284119908497135.3363426877938
Winsorized Mean ( 8 / 20 )12.11475409836070.34284119908497135.3363426877938
Winsorized Mean ( 9 / 20 )12.11475409836070.34284119908497135.3363426877938
Winsorized Mean ( 10 / 20 )12.11475409836070.28158253083208543.0238128145279
Winsorized Mean ( 11 / 20 )12.11475409836070.28158253083208543.0238128145279
Winsorized Mean ( 12 / 20 )12.11475409836070.28158253083208543.0238128145279
Winsorized Mean ( 13 / 20 )12.32786885245900.24486118681047650.3463575139855
Winsorized Mean ( 14 / 20 )12.09836065573770.20606237852420658.7121275721689
Winsorized Mean ( 15 / 20 )12.09836065573770.20606237852420658.7121275721689
Winsorized Mean ( 16 / 20 )12.09836065573770.20606237852420658.7121275721689
Winsorized Mean ( 17 / 20 )12.37704918032790.16223159325605776.292471348615
Winsorized Mean ( 18 / 20 )12.08196721311480.117568912397842102.764982397987
Winsorized Mean ( 19 / 20 )12.08196721311480.117568912397842102.764982397987
Winsorized Mean ( 20 / 20 )12.08196721311480.117568912397842102.764982397987
Trimmed Mean ( 1 / 20 )12.13559322033900.4005093390125430.3004001111670
Trimmed Mean ( 2 / 20 )12.12280701754390.38132319375348631.7914231710251
Trimmed Mean ( 3 / 20 )12.12727272727270.36335005563829733.3762787127381
Trimmed Mean ( 4 / 20 )12.13207547169810.34078980221743235.5998782614908
Trimmed Mean ( 5 / 20 )12.13725490196080.32541931663882037.2972785614685
Trimmed Mean ( 6 / 20 )12.14285714285710.31810450514017638.1725406168211
Trimmed Mean ( 7 / 20 )12.14893617021280.30864617903632639.3620170777585
Trimmed Mean ( 8 / 20 )12.15555555555560.29636783648122341.0150969817728
Trimmed Mean ( 9 / 20 )12.16279069767440.28026690442621843.397170716874
Trimmed Mean ( 10 / 20 )12.17073170731710.25875508484314547.0357199538508
Trimmed Mean ( 11 / 20 )12.17948717948720.24880766916885848.9514138377356
Trimmed Mean ( 12 / 20 )12.18918918918920.23518517985957951.8280496945724
Trimmed Mean ( 13 / 20 )12.20.2161543177353456.4411580014688
Trimmed Mean ( 14 / 20 )12.18181818181820.20157779841894060.4323406514274
Trimmed Mean ( 15 / 20 )12.19354838709680.19354838709677463
Trimmed Mean ( 16 / 20 )12.20689655172410.18153227362254567.243671376615
Trimmed Mean ( 17 / 20 )12.22222222222220.16306653015674374.9523658256172
Trimmed Mean ( 18 / 20 )12.20.15275252316519579.8677478263732
Trimmed Mean ( 19 / 20 )12.21739130434780.15343912208523179.623704426316
Trimmed Mean ( 20 / 20 )12.23809523809520.15282672891315480.0782384411936
Median12
Midrange12.5
Midmean - Weighted Average at Xnp12.1176470588235
Midmean - Weighted Average at X(n+1)p12.1176470588235
Midmean - Empirical Distribution Function12.1176470588235
Midmean - Empirical Distribution Function - Averaging12.1176470588235
Midmean - Empirical Distribution Function - Interpolation12.1176470588235
Midmean - Closest Observation12.1176470588235
Midmean - True Basic - Statistics Graphics Toolkit12.1176470588235
Midmean - MS Excel (old versions)12.1176470588235
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 12.1475409836066 & 0.416094294676303 & 29.1942022253793 \tabularnewline
Geometric Mean & 11.6841659989912 &  &  \tabularnewline
Harmonic Mean & 11.1804450594414 &  &  \tabularnewline
Quadratic Mean & 12.5678486493167 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 12.1475409836066 & 0.416094294676303 & 29.1942022253793 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 12.1147540983607 & 0.407644413148814 & 29.7189258765532 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 12.1147540983607 & 0.407644413148814 & 29.7189258765532 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 12.1147540983607 & 0.377001660108343 & 32.1344847523459 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 12.1147540983607 & 0.342841199084971 & 35.3363426877938 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 12.1147540983607 & 0.342841199084971 & 35.3363426877938 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 12.1147540983607 & 0.342841199084971 & 35.3363426877938 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 12.1147540983607 & 0.342841199084971 & 35.3363426877938 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 12.1147540983607 & 0.342841199084971 & 35.3363426877938 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 12.1147540983607 & 0.281582530832085 & 43.0238128145279 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 12.1147540983607 & 0.281582530832085 & 43.0238128145279 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 12.1147540983607 & 0.281582530832085 & 43.0238128145279 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 12.3278688524590 & 0.244861186810476 & 50.3463575139855 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 12.0983606557377 & 0.206062378524206 & 58.7121275721689 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 12.0983606557377 & 0.206062378524206 & 58.7121275721689 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 12.0983606557377 & 0.206062378524206 & 58.7121275721689 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 12.3770491803279 & 0.162231593256057 & 76.292471348615 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 12.0819672131148 & 0.117568912397842 & 102.764982397987 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 12.0819672131148 & 0.117568912397842 & 102.764982397987 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 12.0819672131148 & 0.117568912397842 & 102.764982397987 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 12.1355932203390 & 0.40050933901254 & 30.3004001111670 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 12.1228070175439 & 0.381323193753486 & 31.7914231710251 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 12.1272727272727 & 0.363350055638297 & 33.3762787127381 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 12.1320754716981 & 0.340789802217432 & 35.5998782614908 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 12.1372549019608 & 0.325419316638820 & 37.2972785614685 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 12.1428571428571 & 0.318104505140176 & 38.1725406168211 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 12.1489361702128 & 0.308646179036326 & 39.3620170777585 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 12.1555555555556 & 0.296367836481223 & 41.0150969817728 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 12.1627906976744 & 0.280266904426218 & 43.397170716874 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 12.1707317073171 & 0.258755084843145 & 47.0357199538508 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 12.1794871794872 & 0.248807669168858 & 48.9514138377356 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 12.1891891891892 & 0.235185179859579 & 51.8280496945724 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 12.2 & 0.21615431773534 & 56.4411580014688 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 12.1818181818182 & 0.201577798418940 & 60.4323406514274 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 12.1935483870968 & 0.193548387096774 & 63 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 12.2068965517241 & 0.181532273622545 & 67.243671376615 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 12.2222222222222 & 0.163066530156743 & 74.9523658256172 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 12.2 & 0.152752523165195 & 79.8677478263732 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 12.2173913043478 & 0.153439122085231 & 79.623704426316 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 12.2380952380952 & 0.152826728913154 & 80.0782384411936 \tabularnewline
Median & 12 &  &  \tabularnewline
Midrange & 12.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 12.1176470588235 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 12.1176470588235 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 12.1176470588235 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 12.1176470588235 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 12.1176470588235 &  &  \tabularnewline
Midmean - Closest Observation & 12.1176470588235 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 12.1176470588235 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 12.1176470588235 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17509&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]12.1475409836066[/C][C]0.416094294676303[/C][C]29.1942022253793[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]11.6841659989912[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]11.1804450594414[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]12.5678486493167[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]12.1475409836066[/C][C]0.416094294676303[/C][C]29.1942022253793[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]12.1147540983607[/C][C]0.407644413148814[/C][C]29.7189258765532[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]12.1147540983607[/C][C]0.407644413148814[/C][C]29.7189258765532[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]12.1147540983607[/C][C]0.377001660108343[/C][C]32.1344847523459[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]12.1147540983607[/C][C]0.342841199084971[/C][C]35.3363426877938[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]12.1147540983607[/C][C]0.342841199084971[/C][C]35.3363426877938[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]12.1147540983607[/C][C]0.342841199084971[/C][C]35.3363426877938[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]12.1147540983607[/C][C]0.342841199084971[/C][C]35.3363426877938[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]12.1147540983607[/C][C]0.342841199084971[/C][C]35.3363426877938[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]12.1147540983607[/C][C]0.281582530832085[/C][C]43.0238128145279[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]12.1147540983607[/C][C]0.281582530832085[/C][C]43.0238128145279[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]12.1147540983607[/C][C]0.281582530832085[/C][C]43.0238128145279[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]12.3278688524590[/C][C]0.244861186810476[/C][C]50.3463575139855[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]12.0983606557377[/C][C]0.206062378524206[/C][C]58.7121275721689[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]12.0983606557377[/C][C]0.206062378524206[/C][C]58.7121275721689[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]12.0983606557377[/C][C]0.206062378524206[/C][C]58.7121275721689[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]12.3770491803279[/C][C]0.162231593256057[/C][C]76.292471348615[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]12.0819672131148[/C][C]0.117568912397842[/C][C]102.764982397987[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]12.0819672131148[/C][C]0.117568912397842[/C][C]102.764982397987[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]12.0819672131148[/C][C]0.117568912397842[/C][C]102.764982397987[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]12.1355932203390[/C][C]0.40050933901254[/C][C]30.3004001111670[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]12.1228070175439[/C][C]0.381323193753486[/C][C]31.7914231710251[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]12.1272727272727[/C][C]0.363350055638297[/C][C]33.3762787127381[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]12.1320754716981[/C][C]0.340789802217432[/C][C]35.5998782614908[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]12.1372549019608[/C][C]0.325419316638820[/C][C]37.2972785614685[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]12.1428571428571[/C][C]0.318104505140176[/C][C]38.1725406168211[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]12.1489361702128[/C][C]0.308646179036326[/C][C]39.3620170777585[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]12.1555555555556[/C][C]0.296367836481223[/C][C]41.0150969817728[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]12.1627906976744[/C][C]0.280266904426218[/C][C]43.397170716874[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]12.1707317073171[/C][C]0.258755084843145[/C][C]47.0357199538508[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]12.1794871794872[/C][C]0.248807669168858[/C][C]48.9514138377356[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]12.1891891891892[/C][C]0.235185179859579[/C][C]51.8280496945724[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]12.2[/C][C]0.21615431773534[/C][C]56.4411580014688[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]12.1818181818182[/C][C]0.201577798418940[/C][C]60.4323406514274[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]12.1935483870968[/C][C]0.193548387096774[/C][C]63[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]12.2068965517241[/C][C]0.181532273622545[/C][C]67.243671376615[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]12.2222222222222[/C][C]0.163066530156743[/C][C]74.9523658256172[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]12.2[/C][C]0.152752523165195[/C][C]79.8677478263732[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]12.2173913043478[/C][C]0.153439122085231[/C][C]79.623704426316[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]12.2380952380952[/C][C]0.152826728913154[/C][C]80.0782384411936[/C][/ROW]
[ROW][C]Median[/C][C]12[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]12.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]12.1176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]12.1176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]12.1176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]12.1176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]12.1176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]12.1176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]12.1176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]12.1176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17509&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17509&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 Mean12.14754098360660.41609429467630329.1942022253793
Geometric Mean11.6841659989912
Harmonic Mean11.1804450594414
Quadratic Mean12.5678486493167
Winsorized Mean ( 1 / 20 )12.14754098360660.41609429467630329.1942022253793
Winsorized Mean ( 2 / 20 )12.11475409836070.40764441314881429.7189258765532
Winsorized Mean ( 3 / 20 )12.11475409836070.40764441314881429.7189258765532
Winsorized Mean ( 4 / 20 )12.11475409836070.37700166010834332.1344847523459
Winsorized Mean ( 5 / 20 )12.11475409836070.34284119908497135.3363426877938
Winsorized Mean ( 6 / 20 )12.11475409836070.34284119908497135.3363426877938
Winsorized Mean ( 7 / 20 )12.11475409836070.34284119908497135.3363426877938
Winsorized Mean ( 8 / 20 )12.11475409836070.34284119908497135.3363426877938
Winsorized Mean ( 9 / 20 )12.11475409836070.34284119908497135.3363426877938
Winsorized Mean ( 10 / 20 )12.11475409836070.28158253083208543.0238128145279
Winsorized Mean ( 11 / 20 )12.11475409836070.28158253083208543.0238128145279
Winsorized Mean ( 12 / 20 )12.11475409836070.28158253083208543.0238128145279
Winsorized Mean ( 13 / 20 )12.32786885245900.24486118681047650.3463575139855
Winsorized Mean ( 14 / 20 )12.09836065573770.20606237852420658.7121275721689
Winsorized Mean ( 15 / 20 )12.09836065573770.20606237852420658.7121275721689
Winsorized Mean ( 16 / 20 )12.09836065573770.20606237852420658.7121275721689
Winsorized Mean ( 17 / 20 )12.37704918032790.16223159325605776.292471348615
Winsorized Mean ( 18 / 20 )12.08196721311480.117568912397842102.764982397987
Winsorized Mean ( 19 / 20 )12.08196721311480.117568912397842102.764982397987
Winsorized Mean ( 20 / 20 )12.08196721311480.117568912397842102.764982397987
Trimmed Mean ( 1 / 20 )12.13559322033900.4005093390125430.3004001111670
Trimmed Mean ( 2 / 20 )12.12280701754390.38132319375348631.7914231710251
Trimmed Mean ( 3 / 20 )12.12727272727270.36335005563829733.3762787127381
Trimmed Mean ( 4 / 20 )12.13207547169810.34078980221743235.5998782614908
Trimmed Mean ( 5 / 20 )12.13725490196080.32541931663882037.2972785614685
Trimmed Mean ( 6 / 20 )12.14285714285710.31810450514017638.1725406168211
Trimmed Mean ( 7 / 20 )12.14893617021280.30864617903632639.3620170777585
Trimmed Mean ( 8 / 20 )12.15555555555560.29636783648122341.0150969817728
Trimmed Mean ( 9 / 20 )12.16279069767440.28026690442621843.397170716874
Trimmed Mean ( 10 / 20 )12.17073170731710.25875508484314547.0357199538508
Trimmed Mean ( 11 / 20 )12.17948717948720.24880766916885848.9514138377356
Trimmed Mean ( 12 / 20 )12.18918918918920.23518517985957951.8280496945724
Trimmed Mean ( 13 / 20 )12.20.2161543177353456.4411580014688
Trimmed Mean ( 14 / 20 )12.18181818181820.20157779841894060.4323406514274
Trimmed Mean ( 15 / 20 )12.19354838709680.19354838709677463
Trimmed Mean ( 16 / 20 )12.20689655172410.18153227362254567.243671376615
Trimmed Mean ( 17 / 20 )12.22222222222220.16306653015674374.9523658256172
Trimmed Mean ( 18 / 20 )12.20.15275252316519579.8677478263732
Trimmed Mean ( 19 / 20 )12.21739130434780.15343912208523179.623704426316
Trimmed Mean ( 20 / 20 )12.23809523809520.15282672891315480.0782384411936
Median12
Midrange12.5
Midmean - Weighted Average at Xnp12.1176470588235
Midmean - Weighted Average at X(n+1)p12.1176470588235
Midmean - Empirical Distribution Function12.1176470588235
Midmean - Empirical Distribution Function - Averaging12.1176470588235
Midmean - Empirical Distribution Function - Interpolation12.1176470588235
Midmean - Closest Observation12.1176470588235
Midmean - True Basic - Statistics Graphics Toolkit12.1176470588235
Midmean - MS Excel (old versions)12.1176470588235
Number of observations61



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')