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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 27 Oct 2009 15:19:29 -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/2009/Oct/27/t1256678435qxoydaobjnr07vz.htm/, Retrieved Tue, 07 May 2024 08:21:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51254, Retrieved Tue, 07 May 2024 08:21:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS 3 part 2 centr...] [2009-10-27 21:19:29] [b090d569c0a4c77894e0b029f4429f19] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.7
1.8
1.8
1.5
1.5
1.9
2.8
3.1
2.8
2.3
1.7
1.6
1.7
1.8
1.7
1.6
1.4
1.9
2.6
2.8
2.6
1.9
1.5
1.4
1.3
1.2
1
0.8
1.1
1.7
2.9
3.4
3.1
2.4
2
1.9
1.9
2
2.2
2.2
2
1.9
1.7
1.5
1.3
1.6
1.7
1.5
1.1
0.8
0.7
0.7
0.7
0.8
1
1.4
1.4
1.8
1.7
1.6
1.2

Tables (Output of Computation)





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=51254&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=51254&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51254&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

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






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.747540983606560.080660069189303421.6655031562793
Geometric Mean1.63410919713721
Harmonic Mean1.51662799129421
Quadratic Mean1.855872381141
Winsorized Mean ( 1 / 20 )1.742622950819670.079115983766846122.0261806508677
Winsorized Mean ( 2 / 20 )1.742622950819670.079115983766846122.0261806508677
Winsorized Mean ( 3 / 20 )1.737704918032790.075392015000438823.0489252478883
Winsorized Mean ( 4 / 20 )1.731147540983610.073757132973812823.4709169294615
Winsorized Mean ( 5 / 20 )1.731147540983610.073757132973812823.4709169294615
Winsorized Mean ( 6 / 20 )1.750819672131150.069918881602032825.0407276548921
Winsorized Mean ( 7 / 20 )1.727868852459020.064449376395045826.8097063013916
Winsorized Mean ( 8 / 20 )1.740983606557380.062084775866777728.0420373956604
Winsorized Mean ( 9 / 20 )1.711475409836070.055618644938414830.7716128598808
Winsorized Mean ( 10 / 20 )1.711475409836070.049373028668164834.6641771024188
Winsorized Mean ( 11 / 20 )1.693442622950820.045919200387821736.8787480759343
Winsorized Mean ( 12 / 20 )1.713114754098360.042559852412285840.2518960240528
Winsorized Mean ( 13 / 20 )1.670491803278690.035091158593704747.6043502188147
Winsorized Mean ( 14 / 20 )1.693442622950820.031263803723688454.1662376695292
Winsorized Mean ( 15 / 20 )1.693442622950820.031263803723688454.1662376695292
Winsorized Mean ( 16 / 20 )1.66721311475410.027233187672297761.219903259802
Winsorized Mean ( 17 / 20 )1.66721311475410.027233187672297761.219903259802
Winsorized Mean ( 18 / 20 )1.696721311475410.022660142075424874.8769052651053
Winsorized Mean ( 19 / 20 )1.696721311475410.022660142075424874.8769052651053
Winsorized Mean ( 20 / 20 )1.696721311475410.022660142075424874.8769052651053
Trimmed Mean ( 1 / 20 )1.737288135593220.076407437233239322.7371601312843
Trimmed Mean ( 2 / 20 )1.731578947368420.073070754615341223.6972911595589
Trimmed Mean ( 3 / 20 )1.725454545454550.068912582198809125.0383092666112
Trimmed Mean ( 4 / 20 )1.720754716981130.065619659396541626.2231583157505
Trimmed Mean ( 5 / 20 )1.717647058823530.062163975593519627.6309074898130
Trimmed Mean ( 6 / 20 )1.714285714285710.057735026918962629.6922995583236
Trimmed Mean ( 7 / 20 )1.706382978723400.053326378457570931.9988536270298
Trimmed Mean ( 8 / 20 )1.702222222222220.049491238780711334.3944153381274
Trimmed Mean ( 9 / 20 )1.695348837209300.045134656210882637.5620195108638
Trimmed Mean ( 10 / 20 )1.692682926829270.041524345474708240.7636269152094
Trimmed Mean ( 11 / 20 )1.689743589743590.038667912364445743.6988574355329
Trimmed Mean ( 12 / 20 )1.689189189189190.035889341057733547.066598031763
Trimmed Mean ( 13 / 20 )1.685714285714290.033088335333982450.9458777148883
Trimmed Mean ( 14 / 20 )1.687878787878790.031610069765189553.3968700612474
Trimmed Mean ( 15 / 20 )1.687096774193550.030670617610334755.006938419951
Trimmed Mean ( 16 / 20 )1.686206896551720.029245073658254257.6578098676051
Trimmed Mean ( 17 / 20 )1.688888888888890.028411572886486659.4436955545033
Trimmed Mean ( 18 / 20 )1.6920.027030846576951162.595153843341
Trimmed Mean ( 19 / 20 )1.691304347826090.026608747319694663.5619680816113
Trimmed Mean ( 20 / 20 )1.690476190476190.025731916354488265.6956974050375
Median1.7
Midrange2.05
Midmean - Weighted Average at Xnp1.66774193548387
Midmean - Weighted Average at X(n+1)p1.69705882352941
Midmean - Empirical Distribution Function1.69705882352941
Midmean - Empirical Distribution Function - Averaging1.69705882352941
Midmean - Empirical Distribution Function - Interpolation1.69705882352941
Midmean - Closest Observation1.69705882352941
Midmean - True Basic - Statistics Graphics Toolkit1.69705882352941
Midmean - MS Excel (old versions)1.69705882352941
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.74754098360656 & 0.0806600691893034 & 21.6655031562793 \tabularnewline
Geometric Mean & 1.63410919713721 &  &  \tabularnewline
Harmonic Mean & 1.51662799129421 &  &  \tabularnewline
Quadratic Mean & 1.855872381141 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.74262295081967 & 0.0791159837668461 & 22.0261806508677 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.74262295081967 & 0.0791159837668461 & 22.0261806508677 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.73770491803279 & 0.0753920150004388 & 23.0489252478883 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.73114754098361 & 0.0737571329738128 & 23.4709169294615 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.73114754098361 & 0.0737571329738128 & 23.4709169294615 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.75081967213115 & 0.0699188816020328 & 25.0407276548921 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.72786885245902 & 0.0644493763950458 & 26.8097063013916 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.74098360655738 & 0.0620847758667777 & 28.0420373956604 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.71147540983607 & 0.0556186449384148 & 30.7716128598808 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.71147540983607 & 0.0493730286681648 & 34.6641771024188 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.69344262295082 & 0.0459192003878217 & 36.8787480759343 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.71311475409836 & 0.0425598524122858 & 40.2518960240528 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.67049180327869 & 0.0350911585937047 & 47.6043502188147 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.69344262295082 & 0.0312638037236884 & 54.1662376695292 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.69344262295082 & 0.0312638037236884 & 54.1662376695292 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.6672131147541 & 0.0272331876722977 & 61.219903259802 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.6672131147541 & 0.0272331876722977 & 61.219903259802 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.69672131147541 & 0.0226601420754248 & 74.8769052651053 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.69672131147541 & 0.0226601420754248 & 74.8769052651053 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.69672131147541 & 0.0226601420754248 & 74.8769052651053 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.73728813559322 & 0.0764074372332393 & 22.7371601312843 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.73157894736842 & 0.0730707546153412 & 23.6972911595589 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.72545454545455 & 0.0689125821988091 & 25.0383092666112 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.72075471698113 & 0.0656196593965416 & 26.2231583157505 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.71764705882353 & 0.0621639755935196 & 27.6309074898130 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.71428571428571 & 0.0577350269189626 & 29.6922995583236 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.70638297872340 & 0.0533263784575709 & 31.9988536270298 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.70222222222222 & 0.0494912387807113 & 34.3944153381274 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.69534883720930 & 0.0451346562108826 & 37.5620195108638 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.69268292682927 & 0.0415243454747082 & 40.7636269152094 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.68974358974359 & 0.0386679123644457 & 43.6988574355329 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.68918918918919 & 0.0358893410577335 & 47.066598031763 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.68571428571429 & 0.0330883353339824 & 50.9458777148883 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.68787878787879 & 0.0316100697651895 & 53.3968700612474 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.68709677419355 & 0.0306706176103347 & 55.006938419951 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.68620689655172 & 0.0292450736582542 & 57.6578098676051 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.68888888888889 & 0.0284115728864866 & 59.4436955545033 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.692 & 0.0270308465769511 & 62.595153843341 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.69130434782609 & 0.0266087473196946 & 63.5619680816113 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.69047619047619 & 0.0257319163544882 & 65.6956974050375 \tabularnewline
Median & 1.7 &  &  \tabularnewline
Midrange & 2.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.66774193548387 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.69705882352941 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.69705882352941 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.69705882352941 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.69705882352941 &  &  \tabularnewline
Midmean - Closest Observation & 1.69705882352941 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.69705882352941 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.69705882352941 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51254&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]1.74754098360656[/C][C]0.0806600691893034[/C][C]21.6655031562793[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.63410919713721[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.51662799129421[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.855872381141[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.74262295081967[/C][C]0.0791159837668461[/C][C]22.0261806508677[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.74262295081967[/C][C]0.0791159837668461[/C][C]22.0261806508677[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.73770491803279[/C][C]0.0753920150004388[/C][C]23.0489252478883[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.73114754098361[/C][C]0.0737571329738128[/C][C]23.4709169294615[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.73114754098361[/C][C]0.0737571329738128[/C][C]23.4709169294615[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.75081967213115[/C][C]0.0699188816020328[/C][C]25.0407276548921[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.72786885245902[/C][C]0.0644493763950458[/C][C]26.8097063013916[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.74098360655738[/C][C]0.0620847758667777[/C][C]28.0420373956604[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.71147540983607[/C][C]0.0556186449384148[/C][C]30.7716128598808[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.71147540983607[/C][C]0.0493730286681648[/C][C]34.6641771024188[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.69344262295082[/C][C]0.0459192003878217[/C][C]36.8787480759343[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.71311475409836[/C][C]0.0425598524122858[/C][C]40.2518960240528[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.67049180327869[/C][C]0.0350911585937047[/C][C]47.6043502188147[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.69344262295082[/C][C]0.0312638037236884[/C][C]54.1662376695292[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.69344262295082[/C][C]0.0312638037236884[/C][C]54.1662376695292[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.6672131147541[/C][C]0.0272331876722977[/C][C]61.219903259802[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.6672131147541[/C][C]0.0272331876722977[/C][C]61.219903259802[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.69672131147541[/C][C]0.0226601420754248[/C][C]74.8769052651053[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.69672131147541[/C][C]0.0226601420754248[/C][C]74.8769052651053[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.69672131147541[/C][C]0.0226601420754248[/C][C]74.8769052651053[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.73728813559322[/C][C]0.0764074372332393[/C][C]22.7371601312843[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.73157894736842[/C][C]0.0730707546153412[/C][C]23.6972911595589[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.72545454545455[/C][C]0.0689125821988091[/C][C]25.0383092666112[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.72075471698113[/C][C]0.0656196593965416[/C][C]26.2231583157505[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.71764705882353[/C][C]0.0621639755935196[/C][C]27.6309074898130[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.71428571428571[/C][C]0.0577350269189626[/C][C]29.6922995583236[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.70638297872340[/C][C]0.0533263784575709[/C][C]31.9988536270298[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.70222222222222[/C][C]0.0494912387807113[/C][C]34.3944153381274[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.69534883720930[/C][C]0.0451346562108826[/C][C]37.5620195108638[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.69268292682927[/C][C]0.0415243454747082[/C][C]40.7636269152094[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.68974358974359[/C][C]0.0386679123644457[/C][C]43.6988574355329[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.68918918918919[/C][C]0.0358893410577335[/C][C]47.066598031763[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.68571428571429[/C][C]0.0330883353339824[/C][C]50.9458777148883[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.68787878787879[/C][C]0.0316100697651895[/C][C]53.3968700612474[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.68709677419355[/C][C]0.0306706176103347[/C][C]55.006938419951[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.68620689655172[/C][C]0.0292450736582542[/C][C]57.6578098676051[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.68888888888889[/C][C]0.0284115728864866[/C][C]59.4436955545033[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.692[/C][C]0.0270308465769511[/C][C]62.595153843341[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.69130434782609[/C][C]0.0266087473196946[/C][C]63.5619680816113[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.69047619047619[/C][C]0.0257319163544882[/C][C]65.6956974050375[/C][/ROW]
[ROW][C]Median[/C][C]1.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.66774193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.69705882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.69705882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.69705882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.69705882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.69705882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.69705882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.69705882352941[/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=51254&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51254&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.747540983606560.080660069189303421.6655031562793
Geometric Mean1.63410919713721
Harmonic Mean1.51662799129421
Quadratic Mean1.855872381141
Winsorized Mean ( 1 / 20 )1.742622950819670.079115983766846122.0261806508677
Winsorized Mean ( 2 / 20 )1.742622950819670.079115983766846122.0261806508677
Winsorized Mean ( 3 / 20 )1.737704918032790.075392015000438823.0489252478883
Winsorized Mean ( 4 / 20 )1.731147540983610.073757132973812823.4709169294615
Winsorized Mean ( 5 / 20 )1.731147540983610.073757132973812823.4709169294615
Winsorized Mean ( 6 / 20 )1.750819672131150.069918881602032825.0407276548921
Winsorized Mean ( 7 / 20 )1.727868852459020.064449376395045826.8097063013916
Winsorized Mean ( 8 / 20 )1.740983606557380.062084775866777728.0420373956604
Winsorized Mean ( 9 / 20 )1.711475409836070.055618644938414830.7716128598808
Winsorized Mean ( 10 / 20 )1.711475409836070.049373028668164834.6641771024188
Winsorized Mean ( 11 / 20 )1.693442622950820.045919200387821736.8787480759343
Winsorized Mean ( 12 / 20 )1.713114754098360.042559852412285840.2518960240528
Winsorized Mean ( 13 / 20 )1.670491803278690.035091158593704747.6043502188147
Winsorized Mean ( 14 / 20 )1.693442622950820.031263803723688454.1662376695292
Winsorized Mean ( 15 / 20 )1.693442622950820.031263803723688454.1662376695292
Winsorized Mean ( 16 / 20 )1.66721311475410.027233187672297761.219903259802
Winsorized Mean ( 17 / 20 )1.66721311475410.027233187672297761.219903259802
Winsorized Mean ( 18 / 20 )1.696721311475410.022660142075424874.8769052651053
Winsorized Mean ( 19 / 20 )1.696721311475410.022660142075424874.8769052651053
Winsorized Mean ( 20 / 20 )1.696721311475410.022660142075424874.8769052651053
Trimmed Mean ( 1 / 20 )1.737288135593220.076407437233239322.7371601312843
Trimmed Mean ( 2 / 20 )1.731578947368420.073070754615341223.6972911595589
Trimmed Mean ( 3 / 20 )1.725454545454550.068912582198809125.0383092666112
Trimmed Mean ( 4 / 20 )1.720754716981130.065619659396541626.2231583157505
Trimmed Mean ( 5 / 20 )1.717647058823530.062163975593519627.6309074898130
Trimmed Mean ( 6 / 20 )1.714285714285710.057735026918962629.6922995583236
Trimmed Mean ( 7 / 20 )1.706382978723400.053326378457570931.9988536270298
Trimmed Mean ( 8 / 20 )1.702222222222220.049491238780711334.3944153381274
Trimmed Mean ( 9 / 20 )1.695348837209300.045134656210882637.5620195108638
Trimmed Mean ( 10 / 20 )1.692682926829270.041524345474708240.7636269152094
Trimmed Mean ( 11 / 20 )1.689743589743590.038667912364445743.6988574355329
Trimmed Mean ( 12 / 20 )1.689189189189190.035889341057733547.066598031763
Trimmed Mean ( 13 / 20 )1.685714285714290.033088335333982450.9458777148883
Trimmed Mean ( 14 / 20 )1.687878787878790.031610069765189553.3968700612474
Trimmed Mean ( 15 / 20 )1.687096774193550.030670617610334755.006938419951
Trimmed Mean ( 16 / 20 )1.686206896551720.029245073658254257.6578098676051
Trimmed Mean ( 17 / 20 )1.688888888888890.028411572886486659.4436955545033
Trimmed Mean ( 18 / 20 )1.6920.027030846576951162.595153843341
Trimmed Mean ( 19 / 20 )1.691304347826090.026608747319694663.5619680816113
Trimmed Mean ( 20 / 20 )1.690476190476190.025731916354488265.6956974050375
Median1.7
Midrange2.05
Midmean - Weighted Average at Xnp1.66774193548387
Midmean - Weighted Average at X(n+1)p1.69705882352941
Midmean - Empirical Distribution Function1.69705882352941
Midmean - Empirical Distribution Function - Averaging1.69705882352941
Midmean - Empirical Distribution Function - Interpolation1.69705882352941
Midmean - Closest Observation1.69705882352941
Midmean - True Basic - Statistics Graphics Toolkit1.69705882352941
Midmean - MS Excel (old versions)1.69705882352941
Number of observations61


Figures (Output of Computation)

Input Parameters & R Code

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')